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dragon_exercise.out
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dragon_exercise.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 64804 was started by qwang on grid01,
Fri May 31 17:38:26 2019
The command was "prover9 -f dragon_exercise.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file dragon_exercise.in
formulas(sos).
C(f1(x),x) | H(x).
-F(f1(x)) | H(x).
-G(x) | F(x).
-G(y) | -C(x,y) | G(x).
-H(c1).
G(c1).
end_of_list.
formulas(goals).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
============================== end of process non-clausal formulas ===
============================== PROCESS INITIAL CLAUSES ===============
% Clauses before input processing:
formulas(usable).
end_of_list.
formulas(sos).
C(f1(x),x) | H(x). [assumption].
-F(f1(x)) | H(x). [assumption].
-G(x) | F(x). [assumption].
-G(x) | -C(y,x) | G(y). [assumption].
-H(c1). [assumption].
G(c1). [assumption].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating C/2
1 -G(x) | -C(y,x) | G(y). [assumption].
2 C(f1(x),x) | H(x). [assumption].
Derived: -G(x) | G(f1(x)) | H(x). [resolve(1,b,2,a)].
Eliminating F/1
3 -G(x) | F(x). [assumption].
4 -F(f1(x)) | H(x). [assumption].
Derived: -G(f1(x)) | H(x). [resolve(3,b,4,a)].
Eliminating H/1
5 -G(x) | G(f1(x)) | H(x). [resolve(1,b,2,a)].
6 -H(c1). [assumption].
Derived: -G(c1) | G(f1(c1)). [resolve(5,c,6,a)].
7 -G(f1(x)) | H(x). [resolve(3,b,4,a)].
Derived: -G(f1(c1)). [resolve(7,b,6,a)].
============================== end predicate elimination =============
Auto_denials: (no changes).
Term ordering decisions:
Predicate symbol precedence: predicate_order([ G ]).
Function symbol precedence: function_order([ c1, f1 ]).
After inverse_order: (no changes).
Unfolding symbols: (none).
Auto_inference settings:
% set(neg_binary_resolution). % (HNE depth_diff=-1)
% clear(ordered_res). % (HNE depth_diff=-1)
% set(ur_resolution). % (HNE depth_diff=-1)
% set(ur_resolution) -> set(pos_ur_resolution).
% set(ur_resolution) -> set(neg_ur_resolution).
Auto_process settings: (no changes).
kept: 8 G(c1). [assumption].
kept: 9 -G(c1) | G(f1(c1)). [resolve(5,c,6,a)].
kept: 10 -G(f1(c1)). [resolve(7,b,6,a)].
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
% Clauses after input processing:
formulas(usable).
end_of_list.
formulas(sos).
8 G(c1). [assumption].
9 -G(c1) | G(f1(c1)). [resolve(5,c,6,a)].
10 -G(f1(c1)). [resolve(7,b,6,a)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.00 seconds.
given #1 (I,wt=2): 8 G(c1). [assumption].
given #2 (I,wt=5): 9 -G(c1) | G(f1(c1)). [resolve(5,c,6,a)].
-------- Proof 1 --------
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 12.
% Level of proof is 4.
% Maximum clause weight is 5.000.
% Given clauses 2.
1 -G(x) | -C(y,x) | G(y). [assumption].
2 C(f1(x),x) | H(x). [assumption].
3 -G(x) | F(x). [assumption].
4 -F(f1(x)) | H(x). [assumption].
5 -G(x) | G(f1(x)) | H(x). [resolve(1,b,2,a)].
6 -H(c1). [assumption].
7 -G(f1(x)) | H(x). [resolve(3,b,4,a)].
8 G(c1). [assumption].
9 -G(c1) | G(f1(c1)). [resolve(5,c,6,a)].
10 -G(f1(c1)). [resolve(7,b,6,a)].
11 G(f1(c1)). [ur(9,a,8,a)].
12 $F. [resolve(11,a,10,a)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=2. Generated=4. Kept=4. proofs=1.
Usable=2. Sos=1. Demods=0. Limbo=0, Disabled=10. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=0. Back_subsumed=0.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
Demod_attempts=0. Demod_rewrites=0.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=2.
Megabytes=0.03.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
THEOREM PROVED
Exiting with 1 proof.
------ process 64804 exit (max_proofs) ------
Process 64804 exit (max_proofs) Fri May 31 17:38:26 2019