TSTP Solution File: SET041-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET041-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 04:26:16 EDT 2022
% Result : Unsatisfiable 5.49s 5.74s
% Output : Refutation 5.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET041-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 10 12:28:18 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.83/1.08 ============================== Prover9 ===============================
% 0.83/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.08 Process 27451 was started by sandbox2 on n017.cluster.edu,
% 0.83/1.08 Sun Jul 10 12:28:18 2022
% 0.83/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27297_n017.cluster.edu".
% 0.83/1.08 ============================== end of head ===========================
% 0.83/1.08
% 0.83/1.08 ============================== INPUT =================================
% 0.83/1.08
% 0.83/1.08 % Reading from file /tmp/Prover9_27297_n017.cluster.edu
% 0.83/1.08
% 0.83/1.08 set(prolog_style_variables).
% 0.83/1.08 set(auto2).
% 0.83/1.08 % set(auto2) -> set(auto).
% 0.83/1.08 % set(auto) -> set(auto_inference).
% 0.83/1.08 % set(auto) -> set(auto_setup).
% 0.83/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.08 % set(auto) -> set(auto_limits).
% 0.83/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.08 % set(auto) -> set(auto_denials).
% 0.83/1.08 % set(auto) -> set(auto_process).
% 0.83/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.08 % set(auto2) -> assign(stats, some).
% 0.83/1.08 % set(auto2) -> clear(echo_input).
% 0.83/1.08 % set(auto2) -> set(quiet).
% 0.83/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.08 % set(auto2) -> clear(print_given).
% 0.83/1.08 assign(lrs_ticks,-1).
% 0.83/1.08 assign(sos_limit,10000).
% 0.83/1.08 assign(order,kbo).
% 0.83/1.08 set(lex_order_vars).
% 0.83/1.08 clear(print_given).
% 0.83/1.08
% 0.83/1.08 % formulas(sos). % not echoed (169 formulas)
% 0.83/1.08
% 0.83/1.08 ============================== end of input ==========================
% 0.83/1.08
% 0.83/1.08 % From the command line: assign(max_seconds, 300).
% 0.83/1.08
% 0.83/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.08
% 0.83/1.08 % Formulas that are not ordinary clauses:
% 0.83/1.08
% 0.83/1.08 ============================== end of process non-clausal formulas ===
% 0.83/1.08
% 0.83/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.08
% 0.83/1.08 ============================== PREDICATE ELIMINATION =================
% 0.83/1.08 1 proper_subset(A,B) | -subset(A,B) | A = B # label(proper_subset3) # label(axiom). [assumption].
% 0.83/1.08 2 -proper_subset(A,B) | subset(A,B) # label(proper_subset1) # label(axiom). [assumption].
% 0.83/1.08 3 -proper_subset(A,B) | A != B # label(proper_subset2) # label(axiom). [assumption].
% 0.83/1.08 4 relation(A) | member(f18(A),A) # label(relation2) # label(axiom). [assumption].
% 0.83/1.08 5 -relation(A) | -member(B,A) | ordered_pair_predicate(B) # label(relation1) # label(axiom). [assumption].
% 0.83/1.08 Derived: member(f18(A),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(4,a,5,a)].
% 0.83/1.08 6 relation(A) | -ordered_pair_predicate(f18(A)) # label(relation3) # label(axiom). [assumption].
% 0.83/1.08 Derived: -ordered_pair_predicate(f18(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(6,a,5,a)].
% 0.83/1.08 7 -function(A) | relation(A) # label(function1) # label(axiom). [assumption].
% 0.83/1.08 Derived: -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.83/1.08 8 function(A) | -relation(A) | -single_valued_set(A) # label(function3) # label(axiom). [assumption].
% 0.83/1.08 Derived: function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.83/1.08 Derived: function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.83/1.08 9 relation(compose(A,B)) # label(composition_is_a_relation) # label(axiom). [assumption].
% 0.83/1.08 Derived: -member(A,compose(B,C)) | ordered_pair_predicate(A). [resolve(9,a,5,a)].
% 0.83/1.08 Derived: function(compose(A,B)) | -single_valued_set(compose(A,B)). [resolve(9,a,8,b)].
% 0.83/1.08 10 disjoint(A,B) | member(f23(A,B),A) # label(disjoint2) # label(axiom). [assumption].
% 0.83/1.08 11 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint1) # label(axiom). [assumption].
% 0.83/1.08 Derived: member(f23(A,B),A) | -member(C,A) | -member(C,B). [resolve(10,a,11,a)].
% 1.87/2.13 12 disjoint(A,B) | member(f23(A,B),B) # label(disjoint3) # label(axiom). [assumption].
% 1.87/2.13 Derived: member(f23(A,B),B) | -member(C,A) | -member(C,B). [resolve(12,a,11,a)].
% 1.87/2.13 13 A = empty_set | disjoint(f24(A),A) # label(regularity2) # label(axiom). [assumption].
% 1.87/2.13 Derived: A = empty_set | -member(B,f24(A)) | -member(B,A). [resolve(13,b,11,a)].
% 1.87/2.13 14 one_to_one_function(A) | -function(A) | -function(converse(A)) # label(one_to_one_function3) # label(axiom). [assumption].
% 1.87/2.13 15 -one_to_one_function(A) | function(A) # label(one_to_one_function1) # label(axiom). [assumption].
% 1.87/2.13 16 -one_to_one_function(A) | function(converse(A)) # label(one_to_one_function2) # label(axiom). [assumption].
% 1.87/2.13 17 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | member(f32(A,B,C,D,E),B) # label(homomorphism5) # label(axiom). [assumption].
% 1.87/2.13 18 -homomorphism(A,B,C,D,E) | closed(B,C) # label(homomorphism1) # label(axiom). [assumption].
% 1.87/2.13 19 -homomorphism(A,B,C,D,E) | closed(D,E) # label(homomorphism2) # label(axiom). [assumption].
% 1.87/2.13 20 -homomorphism(A,B,C,D,E) | maps(A,B,D) # label(homomorphism3) # label(axiom). [assumption].
% 1.87/2.13 21 -homomorphism(A,B,C,D,E) | -member(F,B) | -member(V6,B) | apply(A,apply_to_two_arguments(C,F,V6)) = apply_to_two_arguments(E,apply(A,F),apply(A,V6)) # label(homomorphism4) # label(axiom). [assumption].
% 1.87/2.13 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | member(f32(E,A,B,C,D),A) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(17,a,21,a)].
% 1.87/2.13 22 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | member(f33(A,B,C,D,E),B) # label(homomorphism6) # label(axiom). [assumption].
% 1.87/2.13 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | member(f33(E,A,B,C,D),A) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(22,a,21,a)].
% 1.87/2.13 23 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | apply(A,apply_to_two_arguments(C,f32(A,B,C,D,E),f33(A,B,C,D,E))) != apply_to_two_arguments(E,apply(A,f32(A,B,C,D,E)),apply(A,f33(A,B,C,D,E))) # label(homomorphism7) # label(axiom). [assumption].
% 1.87/2.13 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | apply(E,apply_to_two_arguments(B,f32(E,A,B,C,D),f33(E,A,B,C,D))) != apply_to_two_arguments(D,apply(E,f32(E,A,B,C,D)),apply(E,f33(E,A,B,C,D))) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(23,a,21,a)].
% 1.87/2.13
% 1.87/2.13 ============================== end predicate elimination =============
% 1.87/2.13
% 1.87/2.13 Auto_denials: (non-Horn, no changes).
% 1.87/2.13
% 1.87/2.13 Term ordering decisions:
% 1.87/2.13 Function symbol KB weights: empty_set=1. infinity=1. estin=1. identity_relation=1. a_function=1. f25=1. universal_set=1. a=1. another_function=1. ordered_pair=1. apply=1. compose=1. non_ordered_pair=1. image=1. cross_product=1. f1=1. intersection=1. f10=1. f11=1. f12=1. f13=1. f14=1. f27=1. f4=1. f7=1. f8=1. f9=1. f16=1. f17=1. f23=1. f5=1. f6=1. union=1. restrict=1. first=1. second=1. domain_of=1. range_of=1. flip_range_of=1. rotate_right=1. singleton_set=1. sigma=1. complement=1. f18=1. converse=1. f19=1. f20=1. f21=1. powerset=1. f2=1. f24=1. f26=1. f3=1. successor=1. apply_to_two_arguments=1. f22=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1.
% 1.87/2.13
% 1.87/2.13 ============================== end of process initial clauses ========
% 1.87/2.13
% 1.87/2.13 ============================== CLAUSES FOR SEARCH ====================
% 1.87/2.13
% 1.87/2.13 ============================== end of clauses for search =============
% 1.87/2.13
% 1.87/2.13 ============================== SEARCH ================================
% 1.87/2.13
% 1.87/2.13 % Starting search at 0.07 seconds.
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=56.000, iters=3371
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=44.000, iters=3348
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=41.000, iters=3338
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=40.000, iters=3343
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=38.000, iters=3341
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=37.000, iters=3354
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=36.000, iters=3417
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=34.000, iters=3376
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=33.000, iters=3373
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=32.000, iters=3347
% 1.87/2.13
% 1.87/2.13 Low Water (keep): wt=31.000, iters=3366
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=30.000, iters=3360
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=29.000, iters=3346
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=28.000, iters=3405
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=27.000, iters=3396
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=26.000, iters=3361
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=25.000, iters=3394
% 5.49/5.74
% 5.49/5.74 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 53 (0.00 of 1.35 sec).
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=24.000, iters=3334
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=23.000, iters=3378
% 5.49/5.74
% 5.49/5.74 Low Water (displace): id=10851, wt=18.000
% 5.49/5.74
% 5.49/5.74 Low Water (displace): id=10852, wt=10.000
% 5.49/5.74
% 5.49/5.74 Low Water (displace): id=10860, wt=8.000
% 5.49/5.74
% 5.49/5.74 Low Water (displace): id=10868, wt=7.000
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=22.000, iters=3407
% 5.49/5.74
% 5.49/5.74 Low Water (displace): id=14465, wt=6.000
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=21.000, iters=3333
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=20.000, iters=3333
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=19.000, iters=3365
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=18.000, iters=3335
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=17.000, iters=3333
% 5.49/5.74
% 5.49/5.74 Low Water (keep): wt=16.000, iters=3335
% 5.49/5.74
% 5.49/5.74 ============================== PROOF =================================
% 5.49/5.74 % SZS status Unsatisfiable
% 5.49/5.74 % SZS output start Refutation
% 5.49/5.74
% 5.49/5.74 % Proof 1 at 4.57 (+ 0.12) seconds.
% 5.49/5.74 % Length of proof is 11.
% 5.49/5.74 % Level of proof is 3.
% 5.49/5.74 % Maximum clause weight is 17.000.
% 5.49/5.74 % Given clauses 2352.
% 5.49/5.74
% 5.49/5.74 183 -subset(A,B) | -subset(B,A) | A = B # label(two_sets_equal) # label(axiom). [assumption].
% 5.49/5.74 210 -function(A) | -member(B,domain_of(A)) | subset(apply(C,apply(A,B)),apply(compose(C,A),B)) # label(apply_for_composition1) # label(axiom). [assumption].
% 5.49/5.74 211 -function(A) | subset(apply(compose(B,A),C),apply(B,apply(A,C))) # label(apply_for_composition2) # label(axiom). [assumption].
% 5.49/5.74 212 function(a_function) # label(a_function) # label(hypothesis). [assumption].
% 5.49/5.74 213 member(a,domain_of(a_function)) # label(member_of_domain) # label(hypothesis). [assumption].
% 5.49/5.74 214 apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a) # label(prove_apply_for_composition3) # label(negated_conjecture). [assumption].
% 5.49/5.74 215 apply(compose(another_function,a_function),a) != apply(another_function,apply(a_function,a)). [copy(214),flip(a)].
% 5.49/5.74 871 subset(apply(compose(A,a_function),B),apply(A,apply(a_function,B))). [resolve(212,a,211,a)].
% 5.49/5.74 877 subset(apply(A,apply(a_function,a)),apply(compose(A,a_function),a)). [resolve(213,a,210,b),unit_del(a,212)].
% 5.49/5.74 33144 apply(compose(A,a_function),a) = apply(A,apply(a_function,a)). [resolve(877,a,183,b),unit_del(a,871)].
% 5.49/5.74 33145 $F. [resolve(33144,a,215,a)].
% 5.49/5.74
% 5.49/5.74 % SZS output end Refutation
% 5.49/5.74 ============================== end of proof ==========================
% 5.49/5.74
% 5.49/5.74 ============================== STATISTICS ============================
% 5.49/5.74
% 5.49/5.74 Given=2352. Generated=181690. Kept=33070. proofs=1.
% 5.49/5.74 Usable=2144. Sos=9999. Demods=157. Limbo=4, Disabled=21104. Hints=0.
% 5.49/5.74 Megabytes=32.57.
% 5.49/5.74 User_CPU=4.57, System_CPU=0.12, Wall_clock=5.
% 5.49/5.74
% 5.49/5.74 ============================== end of statistics =====================
% 5.49/5.74
% 5.49/5.74 ============================== end of search =========================
% 5.49/5.74
% 5.49/5.74 THEOREM PROVED
% 5.49/5.74 % SZS status Unsatisfiable
% 5.49/5.74
% 5.49/5.74 Exiting with 1 proof.
% 5.49/5.74
% 5.49/5.74 Process 27451 exit (max_proofs) Sun Jul 10 12:28:23 2022
% 5.49/5.74 Prover9 interrupted
%------------------------------------------------------------------------------