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ex0930_participation2_30.p9.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 4691 was started by cchui on stl-ws4.mie.utoronto.ca,
Tue Oct 1 09:41:18 2013
The command was "prover9 -t 120 -f test/p9/dolce_participation.p9 test/p9/dolce_participation2ideal_cem_line_downward_in_foliation.p9 test/p9/dolce_present.p9 test/p9/dolce_time_mereology.p9 test/p9/dolce_taxonomy.p9 test/p9/options.txt test/p9/ex0930_participation2_30.p9".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file test/p9/dolce_participation.p9
formulas(sos).
(all x all y all t (PC(x,y,t) -> ED(x) & PD(y) & T(t))).
(all x all t (PD(x) & PRE(x,t) -> (exists y PC(y,x,t)))).
(all x (ED(x) -> (exists y exists t PC(x,y,t)))).
(all x all y all t (PC(x,y,t) -> PRE(x,t) & PRE(y,t))).
(all x all y all t (PC(x,y,t) <-> (all t1 (P(t1,t) -> PC(x,y,t1))))).
end_of_list.
% Reading from file test/p9/dolce_participation2ideal_cem_line_downward_in_foliation.p9
formulas(sos).
(all x (point2(x) <-> T(x))).
(all x (line2(x) <-> ED(x))).
(all x (plane2(x) <-> PD(x))).
(all x all y (in2(x,y) <-> PRE(x,y) & T(y) & (ED(x) | PD(x) | Q(x)) | PRE(y,x) & T(x) & (ED(y) | PD(y) | Q(y)) | x = y & (ED(y) | PD(y) | Q(y) | T(y)))).
(all x all y all z (tin2(x,y,z) <-> PC(x,y,z))).
(all x all y (part2(x,y) <-> P(x,y) & T(x) & T(y))).
(all x (L_1(x) <-> ED(x))).
(all x (L_2(x) <-> PD(x))).
(all x (L_3(x) <-> Q(x))).
(all x (atomic_part(x) <-> AtP(x) & T(x))).
(all x all y (ppart(x,y) <-> PP(x,y) & T(x) & T(y))).
(all x all y (overlaps(x,y) <-> O(x,y) & T(x) & T(y))).
(all x all y (underlaps(x,y) <-> U(x,y) & T(x) & T(y))).
(all x all y (disjoint(x,y) <-> DJ(x,y) & T(x) & T(y))).
(all x all y all z (sum(x,y,z) <-> SUM(z,x,y) & T(z) & T(x) & T(y))).
end_of_list.
% Reading from file test/p9/dolce_present.p9
formulas(sos).
(all x (ED(x) | PD(x) | Q(x) -> (exists t PRE(x,t)))).
(all x all t all t1 (PRE(x,t) & P(t1,t) -> PRE(x,t1))).
(all x all t (PRE(x,t) -> T(t))).
(all x all t all t1 all t2 (PRE(x,t1) & PRE(x,t2) & SUM(t,t1,t2) -> PRE(x,t))).
end_of_list.
% Reading from file test/p9/dolce_time_mereology.p9
formulas(sos).
(all x all y (P(x,y) -> T(y) & T(y))).
(all x all y (P(x,y) -> (T(x) <-> T(y)))).
(all x all y (T(x) -> P(x,x))).
(all x all y (T(x) & T(y) & P(x,y) & P(y,x) -> x = y)).
(all x all y all z (T(x) & T(y) & P(x,y) & P(y,z) -> P(x,z))).
(all x all y (T(x) & T(y) & -P(x,y) -> (exists z (T(z) & P(z,x) & -O(z,y))))).
(all x all y (T(x) & T(y) & -P(x,y) -> (exists z (P(z,x) & DJ(z,y) & T(z))))).
(all x all y (T(x) & T(y) -> (PP(x,y) <-> P(x,y) & -P(y,x)))).
(all x all y (T(x) & T(y) -> (O(x,y) <-> (exists z (P(z,x) & P(z,y) & T(z)))))).
(all x all y (T(x) & T(y) -> (DJ(x,y) <-> -O(x,y)))).
(all x all y (T(x) & T(y) -> (U(x,y) <-> (exists z (P(x,z) & P(y,z) & T(z)))))).
(all x (AtP(x) <-> T(x) & (all y (T(y) & P(y,x) -> y = x)))).
(all x all y (T(x) & T(y) & U(x,y) -> (exists z (T(z) & (all w (T(w) -> (O(w,z) <-> O(w,x) | O(w,y)))))))).
(all x all y (T(x) & T(y) & O(x,y) -> (exists z (T(z) & (all w (T(w) -> (PP(w,z) <-> PP(w,x) & PP(w,y)))))))).
(all x all y all z (T(x) & T(y) & T(z) -> (SUM(z,x,y) <-> (all w (T(w) -> (O(w,z) <-> O(w,x) | O(w,y))))))).
end_of_list.
% Reading from file test/p9/dolce_taxonomy.p9
formulas(sos).
(all x (ED(x) | PD(x) | Q(x) | AB(x) -> PT(x))).
(all x (PED(x) | NPED(x) | AS(x) -> ED(x))).
(all x (EV(x) | STV(x) -> PD(x))).
(all x (TQ(x) | PQ(x) | AQ(x) -> Q(x))).
(all x (R(x) -> AB(x))).
(all x (M(x) | F(x) | POB(x) -> PED(x))).
(all x (NPOB(x) -> NPED(x))).
(all x (ACH(x) | ACC(x) -> EV(x))).
(all x (ST(x) | PRO(x) -> STV(x))).
(all x (TL(x) -> TQ(x))).
(all x (SL(x) -> PQ(x))).
(all x (TR(x) | PR(x) | AR(x) -> R(x))).
(all x (APO(x) | NAPO(x) -> POB(x))).
(all x (MOB(x) | SOB(x) -> NPOB(x))).
(all x (T(x) -> TR(x))).
(all x (S(x) -> PR(x))).
(all x (ASO(x) | NASO(x) -> SOB(x))).
(all x (SAG(x) | SC(x) -> ASO(x))).
(all x (PT(x) <-> ED(x) | PD(x) | Q(x) | AB(x))).
(all x (ED(x) -> -PD(x) & -Q(x) & -AB(x))).
(all x (PD(x) -> -Q(x) & -AB(x))).
(all x (Q(x) -> -AB(x))).
(all x (ED(x) <-> PED(x) | NPED(x) | AS(x))).
(all x (PED(x) -> -NPED(x) & -AS(x))).
(all x (NPED(x) -> -AS(x))).
(all x (PD(x) <-> EV(x) | STV(x))).
(all x (EV(x) -> -STV(x))).
(all x (Q(x) <-> TQ(x) | PQ(x) | AQ(x))).
(all x (TQ(x) -> -PQ(x) & -AQ(x))).
(all x (PQ(x) -> -AQ(x))).
(all x (PED(x) <-> M(x) | F(x) | POB(x))).
(all x (M(x) -> -F(x) & -POB(x))).
(all x (F(x) -> -POB(x))).
(all x (EV(x) <-> ACH(x) | ACC(x))).
(all x (ACH(x) -> -ACC(x))).
(all x (STV(x) <-> ST(x) | PRO(x))).
(all x (ST(x) -> -PRO(x))).
(all x (R(x) <-> TR(x) | PR(x) | AR(x))).
(all x (TR(x) -> -PR(x) & -AR(x))).
(all x (PR(x) -> -AR(x))).
(all x (POB(x) <-> APO(x) | NAPO(x))).
(all x (APO(x) -> -NAPO(x))).
(all x (NPOB(x) <-> MOB(x) | SOB(x))).
(all x (MOB(x) -> -SOB(x))).
(all x (SOB(x) <-> ASO(x) | NASO(x))).
(all x (ASO(x) -> -NASO(x))).
(all x (ASO(x) <-> SAG(x) | SC(x))).
(all x (SAG(x) -> -SC(x))).
end_of_list.
% Reading from file test/p9/options.txt
clear(auto_denials).
clear(print_initial_clauses).
clear(print_kept).
clear(print_given).
% Reading from file test/p9/ex0930_participation2_30.p9
formulas(goals).
(all x all y (in2(x,y) -> in2(y,x))).
end_of_list.
============================== end of input ==========================
% From the command line: assign(max_seconds, 120).
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x all y all t (PC(x,y,t) -> ED(x) & PD(y) & T(t))) # label(non_clause). [assumption].
2 (all x all t (PD(x) & PRE(x,t) -> (exists y PC(y,x,t)))) # label(non_clause). [assumption].
3 (all x (ED(x) -> (exists y exists t PC(x,y,t)))) # label(non_clause). [assumption].
4 (all x all y all t (PC(x,y,t) -> PRE(x,t) & PRE(y,t))) # label(non_clause). [assumption].
5 (all x all y all t (PC(x,y,t) <-> (all t1 (P(t1,t) -> PC(x,y,t1))))) # label(non_clause). [assumption].
6 (all x (point2(x) <-> T(x))) # label(non_clause). [assumption].
7 (all x (line2(x) <-> ED(x))) # label(non_clause). [assumption].
8 (all x (plane2(x) <-> PD(x))) # label(non_clause). [assumption].
9 (all x all y (in2(x,y) <-> PRE(x,y) & T(y) & (ED(x) | PD(x) | Q(x)) | PRE(y,x) & T(x) & (ED(y) | PD(y) | Q(y)) | x = y & (ED(y) | PD(y) | Q(y) | T(y)))) # label(non_clause). [assumption].
10 (all x all y all z (tin2(x,y,z) <-> PC(x,y,z))) # label(non_clause). [assumption].
11 (all x all y (part2(x,y) <-> P(x,y) & T(x) & T(y))) # label(non_clause). [assumption].
12 (all x (L_1(x) <-> ED(x))) # label(non_clause). [assumption].
13 (all x (L_2(x) <-> PD(x))) # label(non_clause). [assumption].
14 (all x (L_3(x) <-> Q(x))) # label(non_clause). [assumption].
15 (all x (atomic_part(x) <-> AtP(x) & T(x))) # label(non_clause). [assumption].
16 (all x all y (ppart(x,y) <-> PP(x,y) & T(x) & T(y))) # label(non_clause). [assumption].
17 (all x all y (overlaps(x,y) <-> O(x,y) & T(x) & T(y))) # label(non_clause). [assumption].
18 (all x all y (underlaps(x,y) <-> U(x,y) & T(x) & T(y))) # label(non_clause). [assumption].
19 (all x all y (disjoint(x,y) <-> DJ(x,y) & T(x) & T(y))) # label(non_clause). [assumption].
20 (all x all y all z (sum(x,y,z) <-> SUM(z,x,y) & T(z) & T(x) & T(y))) # label(non_clause). [assumption].
21 (all x (ED(x) | PD(x) | Q(x) -> (exists t PRE(x,t)))) # label(non_clause). [assumption].
22 (all x all t all t1 (PRE(x,t) & P(t1,t) -> PRE(x,t1))) # label(non_clause). [assumption].
23 (all x all t (PRE(x,t) -> T(t))) # label(non_clause). [assumption].
24 (all x all t all t1 all t2 (PRE(x,t1) & PRE(x,t2) & SUM(t,t1,t2) -> PRE(x,t))) # label(non_clause). [assumption].
25 (all x all y (P(x,y) -> T(y) & T(y))) # label(non_clause). [assumption].
26 (all x all y (P(x,y) -> (T(x) <-> T(y)))) # label(non_clause). [assumption].
27 (all x all y (T(x) -> P(x,x))) # label(non_clause). [assumption].
28 (all x all y (T(x) & T(y) & P(x,y) & P(y,x) -> x = y)) # label(non_clause). [assumption].
29 (all x all y all z (T(x) & T(y) & P(x,y) & P(y,z) -> P(x,z))) # label(non_clause). [assumption].
30 (all x all y (T(x) & T(y) & -P(x,y) -> (exists z (T(z) & P(z,x) & -O(z,y))))) # label(non_clause). [assumption].
31 (all x all y (T(x) & T(y) & -P(x,y) -> (exists z (P(z,x) & DJ(z,y) & T(z))))) # label(non_clause). [assumption].
32 (all x all y (T(x) & T(y) -> (PP(x,y) <-> P(x,y) & -P(y,x)))) # label(non_clause). [assumption].
33 (all x all y (T(x) & T(y) -> (O(x,y) <-> (exists z (P(z,x) & P(z,y) & T(z)))))) # label(non_clause). [assumption].
34 (all x all y (T(x) & T(y) -> (DJ(x,y) <-> -O(x,y)))) # label(non_clause). [assumption].
35 (all x all y (T(x) & T(y) -> (U(x,y) <-> (exists z (P(x,z) & P(y,z) & T(z)))))) # label(non_clause). [assumption].
36 (all x (AtP(x) <-> T(x) & (all y (T(y) & P(y,x) -> y = x)))) # label(non_clause). [assumption].
37 (all x all y (T(x) & T(y) & U(x,y) -> (exists z (T(z) & (all w (T(w) -> (O(w,z) <-> O(w,x) | O(w,y)))))))) # label(non_clause). [assumption].
38 (all x all y (T(x) & T(y) & O(x,y) -> (exists z (T(z) & (all w (T(w) -> (PP(w,z) <-> PP(w,x) & PP(w,y)))))))) # label(non_clause). [assumption].
39 (all x all y all z (T(x) & T(y) & T(z) -> (SUM(z,x,y) <-> (all w (T(w) -> (O(w,z) <-> O(w,x) | O(w,y))))))) # label(non_clause). [assumption].
40 (all x (ED(x) | PD(x) | Q(x) | AB(x) -> PT(x))) # label(non_clause). [assumption].
41 (all x (PED(x) | NPED(x) | AS(x) -> ED(x))) # label(non_clause). [assumption].
42 (all x (EV(x) | STV(x) -> PD(x))) # label(non_clause). [assumption].
43 (all x (TQ(x) | PQ(x) | AQ(x) -> Q(x))) # label(non_clause). [assumption].
44 (all x (R(x) -> AB(x))) # label(non_clause). [assumption].
45 (all x (M(x) | F(x) | POB(x) -> PED(x))) # label(non_clause). [assumption].
46 (all x (NPOB(x) -> NPED(x))) # label(non_clause). [assumption].
47 (all x (ACH(x) | ACC(x) -> EV(x))) # label(non_clause). [assumption].
48 (all x (ST(x) | PRO(x) -> STV(x))) # label(non_clause). [assumption].
49 (all x (TL(x) -> TQ(x))) # label(non_clause). [assumption].
50 (all x (SL(x) -> PQ(x))) # label(non_clause). [assumption].
51 (all x (TR(x) | PR(x) | AR(x) -> R(x))) # label(non_clause). [assumption].
52 (all x (APO(x) | NAPO(x) -> POB(x))) # label(non_clause). [assumption].
53 (all x (MOB(x) | SOB(x) -> NPOB(x))) # label(non_clause). [assumption].
54 (all x (T(x) -> TR(x))) # label(non_clause). [assumption].
55 (all x (S(x) -> PR(x))) # label(non_clause). [assumption].
56 (all x (ASO(x) | NASO(x) -> SOB(x))) # label(non_clause). [assumption].
57 (all x (SAG(x) | SC(x) -> ASO(x))) # label(non_clause). [assumption].
58 (all x (PT(x) <-> ED(x) | PD(x) | Q(x) | AB(x))) # label(non_clause). [assumption].
59 (all x (ED(x) -> -PD(x) & -Q(x) & -AB(x))) # label(non_clause). [assumption].
60 (all x (PD(x) -> -Q(x) & -AB(x))) # label(non_clause). [assumption].
61 (all x (Q(x) -> -AB(x))) # label(non_clause). [assumption].
62 (all x (ED(x) <-> PED(x) | NPED(x) | AS(x))) # label(non_clause). [assumption].
63 (all x (PED(x) -> -NPED(x) & -AS(x))) # label(non_clause). [assumption].
64 (all x (NPED(x) -> -AS(x))) # label(non_clause). [assumption].
65 (all x (PD(x) <-> EV(x) | STV(x))) # label(non_clause). [assumption].
66 (all x (EV(x) -> -STV(x))) # label(non_clause). [assumption].
67 (all x (Q(x) <-> TQ(x) | PQ(x) | AQ(x))) # label(non_clause). [assumption].
68 (all x (TQ(x) -> -PQ(x) & -AQ(x))) # label(non_clause). [assumption].
69 (all x (PQ(x) -> -AQ(x))) # label(non_clause). [assumption].
70 (all x (PED(x) <-> M(x) | F(x) | POB(x))) # label(non_clause). [assumption].
71 (all x (M(x) -> -F(x) & -POB(x))) # label(non_clause). [assumption].
72 (all x (F(x) -> -POB(x))) # label(non_clause). [assumption].
73 (all x (EV(x) <-> ACH(x) | ACC(x))) # label(non_clause). [assumption].
74 (all x (ACH(x) -> -ACC(x))) # label(non_clause). [assumption].
75 (all x (STV(x) <-> ST(x) | PRO(x))) # label(non_clause). [assumption].
76 (all x (ST(x) -> -PRO(x))) # label(non_clause). [assumption].
77 (all x (R(x) <-> TR(x) | PR(x) | AR(x))) # label(non_clause). [assumption].
78 (all x (TR(x) -> -PR(x) & -AR(x))) # label(non_clause). [assumption].
79 (all x (PR(x) -> -AR(x))) # label(non_clause). [assumption].
80 (all x (POB(x) <-> APO(x) | NAPO(x))) # label(non_clause). [assumption].
81 (all x (APO(x) -> -NAPO(x))) # label(non_clause). [assumption].
82 (all x (NPOB(x) <-> MOB(x) | SOB(x))) # label(non_clause). [assumption].
83 (all x (MOB(x) -> -SOB(x))) # label(non_clause). [assumption].
84 (all x (SOB(x) <-> ASO(x) | NASO(x))) # label(non_clause). [assumption].
85 (all x (ASO(x) -> -NASO(x))) # label(non_clause). [assumption].
86 (all x (ASO(x) <-> SAG(x) | SC(x))) # label(non_clause). [assumption].
87 (all x (SAG(x) -> -SC(x))) # label(non_clause). [assumption].
88 (all x all y (in2(x,y) -> in2(y,x))) # label(non_clause) # label(goal). [goal].
============================== end of process non-clausal formulas ===
============================== PROCESS INITIAL CLAUSES ===============
============================== PREDICATE ELIMINATION =================
Eliminating point2/1
89 point2(x) | -T(x). [clausify(6)].
90 -point2(x) | T(x). [clausify(6)].
Eliminating line2/1
91 line2(x) | -ED(x). [clausify(7)].
92 -line2(x) | ED(x). [clausify(7)].
Eliminating plane2/1
93 plane2(x) | -PD(x). [clausify(8)].
94 -plane2(x) | PD(x). [clausify(8)].
Eliminating tin2/3
95 tin2(x,y,z) | -PC(x,y,z). [clausify(10)].
96 -tin2(x,y,z) | PC(x,y,z). [clausify(10)].
Eliminating part2/2
97 part2(x,y) | -P(x,y) | -T(x) | -T(y). [clausify(11)].
98 -part2(x,y) | P(x,y). [clausify(11)].
99 -part2(x,y) | T(x). [clausify(11)].
100 -part2(x,y) | T(y). [clausify(11)].
Eliminating L_1/1
101 L_1(x) | -ED(x). [clausify(12)].
102 -L_1(x) | ED(x). [clausify(12)].
Eliminating L_2/1
103 L_2(x) | -PD(x). [clausify(13)].
104 -L_2(x) | PD(x). [clausify(13)].
Eliminating L_3/1
105 L_3(x) | -Q(x). [clausify(14)].
106 -L_3(x) | Q(x). [clausify(14)].
Eliminating atomic_part/1
107 atomic_part(x) | -AtP(x) | -T(x). [clausify(15)].
108 -atomic_part(x) | AtP(x). [clausify(15)].
109 -atomic_part(x) | T(x). [clausify(15)].
Eliminating ppart/2
110 ppart(x,y) | -PP(x,y) | -T(x) | -T(y). [clausify(16)].
111 -ppart(x,y) | PP(x,y). [clausify(16)].
112 -ppart(x,y) | T(x). [clausify(16)].
113 -ppart(x,y) | T(y). [clausify(16)].
Eliminating overlaps/2
114 overlaps(x,y) | -O(x,y) | -T(x) | -T(y). [clausify(17)].
115 -overlaps(x,y) | O(x,y). [clausify(17)].
116 -overlaps(x,y) | T(x). [clausify(17)].
117 -overlaps(x,y) | T(y). [clausify(17)].
Eliminating underlaps/2
118 underlaps(x,y) | -U(x,y) | -T(x) | -T(y). [clausify(18)].
119 -underlaps(x,y) | U(x,y). [clausify(18)].
120 -underlaps(x,y) | T(x). [clausify(18)].
121 -underlaps(x,y) | T(y). [clausify(18)].
Eliminating disjoint/2
122 disjoint(x,y) | -DJ(x,y) | -T(x) | -T(y). [clausify(19)].
123 -disjoint(x,y) | DJ(x,y). [clausify(19)].
124 -disjoint(x,y) | T(x). [clausify(19)].
125 -disjoint(x,y) | T(y). [clausify(19)].
Eliminating sum/3
126 sum(x,y,z) | -SUM(z,x,y) | -T(z) | -T(x) | -T(y). [clausify(20)].
127 -sum(x,y,z) | SUM(z,x,y). [clausify(20)].
128 -sum(x,y,z) | T(z). [clausify(20)].
129 -sum(x,y,z) | T(x). [clausify(20)].
130 -sum(x,y,z) | T(y). [clausify(20)].
Eliminating SUM/3
131 -T(x) | -T(y) | -T(z) | SUM(z,x,y) | T(f13(x,y,z)). [clausify(39)].
132 -PRE(x,y) | -PRE(x,z) | -SUM(u,y,z) | PRE(x,u). [clausify(24)].
133 -T(x) | -T(y) | -T(z) | -SUM(z,x,y) | -T(u) | -O(u,z) | O(u,x) | O(u,y). [clausify(39)].
134 -T(x) | -T(y) | -T(z) | -SUM(z,x,y) | -T(u) | O(u,z) | -O(u,x). [clausify(39)].
135 -T(x) | -T(y) | -T(z) | -SUM(z,x,y) | -T(u) | O(u,z) | -O(u,y). [clausify(39)].
Derived: -T(x) | -T(y) | -T(z) | T(f13(x,y,z)) | -PRE(u,x) | -PRE(u,y) | PRE(u,z). [resolve(131,d,132,c)].
Derived: -T(x) | -T(y) | -T(z) | T(f13(x,y,z)) | -T(x) | -T(y) | -T(z) | -T(u) | -O(u,z) | O(u,x) | O(u,y). [resolve(131,d,133,d)].
Derived: -T(x) | -T(y) | -T(z) | T(f13(x,y,z)) | -T(x) | -T(y) | -T(z) | -T(u) | O(u,z) | -O(u,x). [resolve(131,d,134,d)].
Derived: -T(x) | -T(y) | -T(z) | T(f13(x,y,z)) | -T(x) | -T(y) | -T(z) | -T(u) | O(u,z) | -O(u,y). [resolve(131,d,135,d)].
136 -T(x) | -T(y) | -T(z) | SUM(z,x,y) | O(f13(x,y,z),z) | O(f13(x,y,z),x) | O(f13(x,y,z),y). [clausify(39)].
Derived: -T(x) | -T(y) | -T(z) | O(f13(x,y,z),z) | O(f13(x,y,z),x) | O(f13(x,y,z),y) | -PRE(u,x) | -PRE(u,y) | PRE(u,z). [resolve(136,d,132,c)].
Derived: -T(x) | -T(y) | -T(z) | O(f13(x,y,z),z) | O(f13(x,y,z),x) | O(f13(x,y,z),y) | -T(x) | -T(y) | -T(z) | -T(u) | -O(u,z) | O(u,x) | O(u,y). [resolve(136,d,133,d)].
Derived: -T(x) | -T(y) | -T(z) | O(f13(x,y,z),z) | O(f13(x,y,z),x) | O(f13(x,y,z),y) | -T(x) | -T(y) | -T(z) | -T(u) | O(u,z) | -O(u,x). [resolve(136,d,134,d)].
Derived: -T(x) | -T(y) | -T(z) | O(f13(x,y,z),z) | O(f13(x,y,z),x) | O(f13(x,y,z),y) | -T(x) | -T(y) | -T(z) | -T(u) | O(u,z) | -O(u,y). [resolve(136,d,135,d)].
137 -T(x) | -T(y) | -T(z) | SUM(z,x,y) | -O(f13(x,y,z),z) | -O(f13(x,y,z),x). [clausify(39)].
Derived: -T(x) | -T(y) | -T(z) | -O(f13(x,y,z),z) | -O(f13(x,y,z),x) | -PRE(u,x) | -PRE(u,y) | PRE(u,z). [resolve(137,d,132,c)].
Derived: -T(x) | -T(y) | -T(z) | -O(f13(x,y,z),z) | -O(f13(x,y,z),x) | -T(x) | -T(y) | -T(z) | -T(u) | -O(u,z) | O(u,x) | O(u,y). [resolve(137,d,133,d)].
Derived: -T(x) | -T(y) | -T(z) | -O(f13(x,y,z),z) | -O(f13(x,y,z),x) | -T(x) | -T(y) | -T(z) | -T(u) | O(u,z) | -O(u,x). [resolve(137,d,134,d)].
Derived: -T(x) | -T(y) | -T(z) | -O(f13(x,y,z),z) | -O(f13(x,y,z),x) | -T(x) | -T(y) | -T(z) | -T(u) | O(u,z) | -O(u,y). [resolve(137,d,135,d)].
138 -T(x) | -T(y) | -T(z) | SUM(z,x,y) | -O(f13(x,y,z),z) | -O(f13(x,y,z),y). [clausify(39)].
Derived: -T(x) | -T(y) | -T(z) | -O(f13(x,y,z),z) | -O(f13(x,y,z),y) | -PRE(u,x) | -PRE(u,y) | PRE(u,z). [resolve(138,d,132,c)].
Derived: -T(x) | -T(y) | -T(z) | -O(f13(x,y,z),z) | -O(f13(x,y,z),y) | -T(x) | -T(y) | -T(z) | -T(u) | -O(u,z) | O(u,x) | O(u,y). [resolve(138,d,133,d)].
Derived: -T(x) | -T(y) | -T(z) | -O(f13(x,y,z),z) | -O(f13(x,y,z),y) | -T(x) | -T(y) | -T(z) | -T(u) | O(u,z) | -O(u,x). [resolve(138,d,134,d)].
Derived: -T(x) | -T(y) | -T(z) | -O(f13(x,y,z),z) | -O(f13(x,y,z),y) | -T(x) | -T(y) | -T(z) | -T(u) | O(u,z) | -O(u,y). [resolve(138,d,135,d)].
Eliminating DJ/2
139 -T(x) | -T(y) | -DJ(x,y) | -O(x,y). [clausify(34)].
140 -T(x) | -T(y) | P(x,y) | DJ(f7(x,y),y). [clausify(31)].
Derived: -T(f7(x,y)) | -T(y) | -O(f7(x,y),y) | -T(x) | -T(y) | P(x,y). [resolve(139,c,140,d)].
141 -T(x) | -T(y) | DJ(x,y) | O(x,y). [clausify(34)].
Eliminating U/2
142 -T(x) | -T(y) | U(x,y) | -P(x,z) | -P(y,z) | -T(z). [clausify(35)].
143 -T(x) | -T(y) | -U(x,y) | P(x,f9(x,y)). [clausify(35)].
144 -T(x) | -T(y) | -U(x,y) | P(y,f9(x,y)). [clausify(35)].
145 -T(x) | -T(y) | -U(x,y) | T(f9(x,y)). [clausify(35)].
Derived: -T(x) | -T(y) | -P(x,z) | -P(y,z) | -T(z) | -T(x) | -T(y) | P(x,f9(x,y)). [resolve(142,c,143,c)].
Derived: -T(x) | -T(y) | -P(x,z) | -P(y,z) | -T(z) | -T(x) | -T(y) | P(y,f9(x,y)). [resolve(142,c,144,c)].
Derived: -T(x) | -T(y) | -P(x,z) | -P(y,z) | -T(z) | -T(x) | -T(y) | T(f9(x,y)). [resolve(142,c,145,c)].
146 -T(x) | -T(y) | -U(x,y) | T(f11(x,y)). [clausify(37)].
Derived: -T(x) | -T(y) | T(f11(x,y)) | -T(x) | -T(y) | -P(x,z) | -P(y,z) | -T(z). [resolve(146,c,142,c)].
147 -T(x) | -T(y) | -U(x,y) | -T(z) | -O(z,f11(x,y)) | O(z,x) | O(z,y). [clausify(37)].
Derived: -T(x) | -T(y) | -T(z) | -O(z,f11(x,y)) | O(z,x) | O(z,y) | -T(x) | -T(y) | -P(x,u) | -P(y,u) | -T(u). [resolve(147,c,142,c)].
148 -T(x) | -T(y) | -U(x,y) | -T(z) | O(z,f11(x,y)) | -O(z,x). [clausify(37)].
Derived: -T(x) | -T(y) | -T(z) | O(z,f11(x,y)) | -O(z,x) | -T(x) | -T(y) | -P(x,u) | -P(y,u) | -T(u). [resolve(148,c,142,c)].
149 -T(x) | -T(y) | -U(x,y) | -T(z) | O(z,f11(x,y)) | -O(z,y). [clausify(37)].
Derived: -T(x) | -T(y) | -T(z) | O(z,f11(x,y)) | -O(z,y) | -T(x) | -T(y) | -P(x,u) | -P(y,u) | -T(u). [resolve(149,c,142,c)].
Eliminating AtP/1
150 AtP(x) | -T(x) | T(f10(x)). [clausify(36)].
151 -AtP(x) | T(x). [clausify(36)].
152 -AtP(x) | -T(y) | -P(y,x) | y = x. [clausify(36)].
Derived: -T(x) | T(f10(x)) | -T(y) | -P(y,x) | y = x. [resolve(150,a,152,a)].
153 AtP(x) | -T(x) | P(f10(x),x). [clausify(36)].
Derived: -T(x) | P(f10(x),x) | -T(y) | -P(y,x) | y = x. [resolve(153,a,152,a)].
154 AtP(x) | -T(x) | f10(x) != x. [clausify(36)].
Derived: -T(x) | f10(x) != x | -T(y) | -P(y,x) | y = x. [resolve(154,a,152,a)].
Eliminating PT/1
155 -PT(x) | ED(x) | PD(x) | Q(x) | AB(x). [clausify(58)].
156 -ED(x) | PT(x). [clausify(40)].
157 -PD(x) | PT(x). [clausify(40)].
158 -Q(x) | PT(x). [clausify(40)].
159 -AB(x) | PT(x). [clausify(40)].
160 PT(x) | -ED(x). [clausify(58)].
161 PT(x) | -PD(x). [clausify(58)].
162 PT(x) | -Q(x). [clausify(58)].
163 PT(x) | -AB(x). [clausify(58)].
Eliminating PED/1
164 -M(x) | PED(x). [clausify(45)].
165 -PED(x) | ED(x). [clausify(41)].
Derived: -M(x) | ED(x). [resolve(164,b,165,a)].
166 -F(x) | PED(x). [clausify(45)].
Derived: -F(x) | ED(x). [resolve(166,b,165,a)].
167 -POB(x) | PED(x). [clausify(45)].
Derived: -POB(x) | ED(x). [resolve(167,b,165,a)].
168 -ED(x) | PED(x) | NPED(x) | AS(x). [clausify(62)].
169 ED(x) | -PED(x). [clausify(62)].
170 -PED(x) | -NPED(x). [clausify(63)].
Derived: -NPED(x) | -M(x). [resolve(170,a,164,b)].
Derived: -NPED(x) | -F(x). [resolve(170,a,166,b)].
Derived: -NPED(x) | -POB(x). [resolve(170,a,167,b)].
171 -PED(x) | -AS(x). [clausify(63)].
Derived: -AS(x) | -M(x). [resolve(171,a,164,b)].
Derived: -AS(x) | -F(x). [resolve(171,a,166,b)].
Derived: -AS(x) | -POB(x). [resolve(171,a,167,b)].
172 -PED(x) | M(x) | F(x) | POB(x). [clausify(70)].
Derived: M(x) | F(x) | POB(x) | -ED(x) | NPED(x) | AS(x). [resolve(172,a,168,b)].
173 PED(x) | -M(x). [clausify(70)].
174 PED(x) | -F(x). [clausify(70)].
175 PED(x) | -POB(x). [clausify(70)].
Eliminating NPED/1
176 -NPOB(x) | NPED(x). [clausify(46)].
177 -NPED(x) | ED(x). [clausify(41)].
Derived: -NPOB(x) | ED(x). [resolve(176,b,177,a)].
178 ED(x) | -NPED(x). [clausify(62)].
179 -NPED(x) | -AS(x). [clausify(64)].
Derived: -AS(x) | -NPOB(x). [resolve(179,a,176,b)].
180 -NPED(x) | -M(x). [resolve(170,a,164,b)].
Derived: -M(x) | -NPOB(x). [resolve(180,a,176,b)].
181 -NPED(x) | -F(x). [resolve(170,a,166,b)].
Derived: -F(x) | -NPOB(x). [resolve(181,a,176,b)].
182 -NPED(x) | -POB(x). [resolve(170,a,167,b)].
Derived: -POB(x) | -NPOB(x). [resolve(182,a,176,b)].
183 M(x) | F(x) | POB(x) | -ED(x) | NPED(x) | AS(x). [resolve(172,a,168,b)].
Eliminating AS/1
Eliminating EV/1
184 -ACH(x) | EV(x). [clausify(47)].
185 -EV(x) | PD(x). [clausify(42)].
Derived: -ACH(x) | PD(x). [resolve(184,b,185,a)].
186 -ACC(x) | EV(x). [clausify(47)].
Derived: -ACC(x) | PD(x). [resolve(186,b,185,a)].
187 -PD(x) | EV(x) | STV(x). [clausify(65)].
188 PD(x) | -EV(x). [clausify(65)].
189 -EV(x) | -STV(x). [clausify(66)].
Derived: -STV(x) | -ACH(x). [resolve(189,a,184,b)].
Derived: -STV(x) | -ACC(x). [resolve(189,a,186,b)].
190 -EV(x) | ACH(x) | ACC(x). [clausify(73)].
Derived: ACH(x) | ACC(x) | -PD(x) | STV(x). [resolve(190,a,187,b)].
191 EV(x) | -ACH(x). [clausify(73)].
192 EV(x) | -ACC(x). [clausify(73)].
Eliminating STV/1
193 -ST(x) | STV(x). [clausify(48)].
194 -STV(x) | PD(x). [clausify(42)].
Derived: -ST(x) | PD(x). [resolve(193,b,194,a)].
195 -PRO(x) | STV(x). [clausify(48)].
Derived: -PRO(x) | PD(x). [resolve(195,b,194,a)].
196 PD(x) | -STV(x). [clausify(65)].
197 -STV(x) | ST(x) | PRO(x). [clausify(75)].
198 STV(x) | -ST(x). [clausify(75)].
199 STV(x) | -PRO(x). [clausify(75)].
200 -STV(x) | -ACH(x). [resolve(189,a,184,b)].
Derived: -ACH(x) | -ST(x). [resolve(200,a,193,b)].
Derived: -ACH(x) | -PRO(x). [resolve(200,a,195,b)].
201 -STV(x) | -ACC(x). [resolve(189,a,186,b)].
Derived: -ACC(x) | -ST(x). [resolve(201,a,193,b)].
Derived: -ACC(x) | -PRO(x). [resolve(201,a,195,b)].
202 ACH(x) | ACC(x) | -PD(x) | STV(x). [resolve(190,a,187,b)].
Derived: ACH(x) | ACC(x) | -PD(x) | ST(x) | PRO(x). [resolve(202,d,197,a)].
Eliminating TQ/1
203 -TL(x) | TQ(x). [clausify(49)].
204 -TQ(x) | Q(x). [clausify(43)].
Derived: -TL(x) | Q(x). [resolve(203,b,204,a)].
205 -Q(x) | TQ(x) | PQ(x) | AQ(x). [clausify(67)].
206 Q(x) | -TQ(x). [clausify(67)].
207 -TQ(x) | -PQ(x). [clausify(68)].
Derived: -PQ(x) | -TL(x). [resolve(207,a,203,b)].
208 -TQ(x) | -AQ(x). [clausify(68)].
Derived: -AQ(x) | -TL(x). [resolve(208,a,203,b)].
Eliminating PQ/1
209 -SL(x) | PQ(x). [clausify(50)].
210 -PQ(x) | Q(x). [clausify(43)].
Derived: -SL(x) | Q(x). [resolve(209,b,210,a)].
211 Q(x) | -PQ(x). [clausify(67)].
212 -PQ(x) | -AQ(x). [clausify(69)].
Derived: -AQ(x) | -SL(x). [resolve(212,a,209,b)].
213 -PQ(x) | -TL(x). [resolve(207,a,203,b)].
Derived: -TL(x) | -SL(x). [resolve(213,a,209,b)].
Eliminating AQ/1
Eliminating R/1
214 -TR(x) | R(x). [clausify(51)].
215 -R(x) | AB(x). [clausify(44)].
Derived: -TR(x) | AB(x). [resolve(214,b,215,a)].
216 -PR(x) | R(x). [clausify(51)].
Derived: -PR(x) | AB(x). [resolve(216,b,215,a)].
217 -AR(x) | R(x). [clausify(51)].
Derived: -AR(x) | AB(x). [resolve(217,b,215,a)].
218 -R(x) | TR(x) | PR(x) | AR(x). [clausify(77)].
219 R(x) | -TR(x). [clausify(77)].
220 R(x) | -PR(x). [clausify(77)].
221 R(x) | -AR(x). [clausify(77)].
Eliminating APO/1
222 -POB(x) | APO(x) | NAPO(x). [clausify(80)].
223 -APO(x) | POB(x). [clausify(52)].
224 POB(x) | -APO(x). [clausify(80)].
225 -APO(x) | -NAPO(x). [clausify(81)].
Eliminating NAPO/1
Eliminating MOB/1
226 -NPOB(x) | MOB(x) | SOB(x). [clausify(82)].
227 -MOB(x) | NPOB(x). [clausify(53)].
228 NPOB(x) | -MOB(x). [clausify(82)].
229 -MOB(x) | -SOB(x). [clausify(83)].
Eliminating SOB/1
230 -ASO(x) | SOB(x). [clausify(56)].
231 -SOB(x) | NPOB(x). [clausify(53)].
Derived: -ASO(x) | NPOB(x). [resolve(230,b,231,a)].
232 -NASO(x) | SOB(x). [clausify(56)].
Derived: -NASO(x) | NPOB(x). [resolve(232,b,231,a)].
233 NPOB(x) | -SOB(x). [clausify(82)].
234 -SOB(x) | ASO(x) | NASO(x). [clausify(84)].
235 SOB(x) | -ASO(x). [clausify(84)].
236 SOB(x) | -NASO(x). [clausify(84)].
Eliminating TR/1
237 -TR(x) | -PR(x). [clausify(78)].
238 -T(x) | TR(x). [clausify(54)].
Derived: -PR(x) | -T(x). [resolve(237,a,238,b)].
239 -TR(x) | -AR(x). [clausify(78)].
Derived: -AR(x) | -T(x). [resolve(239,a,238,b)].
240 -TR(x) | AB(x). [resolve(214,b,215,a)].
Derived: AB(x) | -T(x). [resolve(240,a,238,b)].
Eliminating S/1
Eliminating SAG/1
241 -ASO(x) | SAG(x) | SC(x). [clausify(86)].
242 -SAG(x) | ASO(x). [clausify(57)].
243 ASO(x) | -SAG(x). [clausify(86)].
244 -SAG(x) | -SC(x). [clausify(87)].
Eliminating SC/1
Eliminating AB/1
245 -PR(x) | AB(x). [resolve(216,b,215,a)].
246 -ED(x) | -AB(x). [clausify(59)].
247 -PD(x) | -AB(x). [clausify(60)].
248 -Q(x) | -AB(x). [clausify(61)].
Derived: -PR(x) | -ED(x). [resolve(245,b,246,b)].
Derived: -PR(x) | -PD(x). [resolve(245,b,247,b)].
Derived: -PR(x) | -Q(x). [resolve(245,b,248,b)].
249 -AR(x) | AB(x). [resolve(217,b,215,a)].
Derived: -AR(x) | -ED(x). [resolve(249,b,246,b)].
Derived: -AR(x) | -PD(x). [resolve(249,b,247,b)].
Derived: -AR(x) | -Q(x). [resolve(249,b,248,b)].
250 AB(x) | -T(x). [resolve(240,a,238,b)].
Derived: -T(x) | -ED(x). [resolve(250,a,246,b)].
Derived: -T(x) | -PD(x). [resolve(250,a,247,b)].
Derived: -T(x) | -Q(x). [resolve(250,a,248,b)].
Eliminating M/1
Eliminating F/1
Eliminating ACH/1
251 ACH(x) | ACC(x) | -PD(x) | ST(x) | PRO(x). [resolve(202,d,197,a)].
252 -ACH(x) | -ACC(x). [clausify(74)].
253 -ACH(x) | PD(x). [resolve(184,b,185,a)].
254 -ACH(x) | -ST(x). [resolve(200,a,193,b)].
255 -ACH(x) | -PRO(x). [resolve(200,a,195,b)].
Eliminating ST/1
Eliminating PR/1
Eliminating ASO/1
Eliminating POB/1
Eliminating NPOB/1
256 -NASO(x) | NPOB(x). [resolve(232,b,231,a)].
257 -NPOB(x) | ED(x). [resolve(176,b,177,a)].
Derived: -NASO(x) | ED(x). [resolve(256,b,257,a)].
Eliminating ACC/1
Eliminating PRO/1
Eliminating TL/1
Eliminating SL/1
Eliminating AR/1
Eliminating NASO/1
============================== end predicate elimination =============
Term ordering decisions:
Predicate symbol precedence: predicate_order([ =, T, ED, PD, Q, O, P, PRE, in2, PP, PC ]).
Function symbol precedence: function_order([ c1, c2, f1, f6, f7, f8, f9, f11, f12, f2, f3, f5, f10, f4, f13 ]).
After inverse_order: (no changes).
Unfolding symbols: (none).
Auto_inference settings:
% set(paramodulation). % (positive equality literals)
% set(binary_resolution). % (non-Horn)
% set(neg_ur_resolution). % (non-Horn, less than 100 clauses)
Auto_process settings:
% set(factor). % (non-Horn)
% set(unit_deletion). % (non-Horn)
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.11 seconds.
============================== PROOF =================================
% Proof 1 at 0.14 (+ 0.01) seconds.
% Length of proof is 37.
% Level of proof is 8.
% Maximum clause weight is 18.000.
% Given clauses 234.
1 (all x all y all t (PC(x,y,t) -> ED(x) & PD(y) & T(t))) # label(non_clause). [assumption].
5 (all x all y all t (PC(x,y,t) <-> (all t1 (P(t1,t) -> PC(x,y,t1))))) # label(non_clause). [assumption].
9 (all x all y (in2(x,y) <-> PRE(x,y) & T(y) & (ED(x) | PD(x) | Q(x)) | PRE(y,x) & T(x) & (ED(y) | PD(y) | Q(y)) | x = y & (ED(y) | PD(y) | Q(y) | T(y)))) # label(non_clause). [assumption].
25 (all x all y (P(x,y) -> T(y) & T(y))) # label(non_clause). [assumption].
44 (all x (R(x) -> AB(x))) # label(non_clause). [assumption].
51 (all x (TR(x) | PR(x) | AR(x) -> R(x))) # label(non_clause). [assumption].
54 (all x (T(x) -> TR(x))) # label(non_clause). [assumption].
59 (all x (ED(x) -> -PD(x) & -Q(x) & -AB(x))) # label(non_clause). [assumption].
60 (all x (PD(x) -> -Q(x) & -AB(x))) # label(non_clause). [assumption].
61 (all x (Q(x) -> -AB(x))) # label(non_clause). [assumption].
88 (all x all y (in2(x,y) -> in2(y,x))) # label(non_clause) # label(goal). [goal].
214 -TR(x) | R(x). [clausify(51)].
215 -R(x) | AB(x). [clausify(44)].
238 -T(x) | TR(x). [clausify(54)].
240 -TR(x) | AB(x). [resolve(214,b,215,a)].
246 -ED(x) | -AB(x). [clausify(59)].
247 -PD(x) | -AB(x). [clausify(60)].
248 -Q(x) | -AB(x). [clausify(61)].
250 AB(x) | -T(x). [resolve(240,a,238,b)].
260 -PC(x,y,z) | T(z). [clausify(1)].
266 PC(x,y,z) | P(f4(x,y,z),z). [clausify(5)].
276 -in2(x,y) | ED(x) | PD(x) | Q(x) | ED(y) | PD(y) | Q(y) | y = x. [clausify(9)].
292 -P(x,y) | T(y). [clausify(25)].
316 in2(c1,c2). [deny(88)].
317 -in2(c2,c1). [deny(88)].
365 -T(x) | -ED(x). [resolve(250,a,246,b)].
366 -T(x) | -PD(x). [resolve(250,a,247,b)].
367 -T(x) | -Q(x). [resolve(250,a,248,b)].
515 P(f4(x,y,z),z) | T(z). [resolve(266,a,260,a)].
519 ED(c1) | PD(c1) | Q(c1) | ED(c2) | PD(c2) | Q(c2) | c2 = c1. [resolve(316,a,276,a)].
539 T(x). [resolve(515,a,292,a),merge(b)].
649 -Q(x). [back_unit_del(367),unit_del(a,539)].
650 -PD(x). [back_unit_del(366),unit_del(a,539)].
651 -ED(x). [back_unit_del(365),unit_del(a,539)].
696 c2 = c1. [back_unit_del(519),unit_del(a,651),unit_del(b,650),unit_del(c,649),unit_del(d,651),unit_del(e,650),unit_del(f,649)].
701 -in2(c1,c1). [back_rewrite(317),rewrite([696(1)])].
702 $F. [back_rewrite(316),rewrite([696(2)]),unit_del(a,701)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=234. Generated=1172. Kept=424. proofs=1.
Usable=8. Sos=56. Demods=1. Limbo=6, Disabled=659. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=747. Back_subsumed=187.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=1 (0 lex), Back_demodulated=2. Back_unit_deleted=165.
Demod_attempts=418. Demod_rewrites=2.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=2892. Nonunit_bsub_feature_tests=4721.
Megabytes=0.93.
User_CPU=0.14, System_CPU=0.01, Wall_clock=1.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 4691 exit (max_proofs) Tue Oct 1 09:41:19 2013