TSTP Solution File: SET076-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET076-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 04:26:51 EDT 2022
% Result : Unsatisfiable 2.28s 2.54s
% Output : Refutation 2.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET076-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 21:57:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.02 ============================== Prover9 ===============================
% 0.44/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02 Process 31744 was started by sandbox2 on n008.cluster.edu,
% 0.44/1.02 Sun Jul 10 21:57:39 2022
% 0.44/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31590_n008.cluster.edu".
% 0.44/1.02 ============================== end of head ===========================
% 0.44/1.02
% 0.44/1.02 ============================== INPUT =================================
% 0.44/1.02
% 0.44/1.02 % Reading from file /tmp/Prover9_31590_n008.cluster.edu
% 0.44/1.02
% 0.44/1.02 set(prolog_style_variables).
% 0.44/1.02 set(auto2).
% 0.44/1.02 % set(auto2) -> set(auto).
% 0.44/1.02 % set(auto) -> set(auto_inference).
% 0.44/1.02 % set(auto) -> set(auto_setup).
% 0.44/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02 % set(auto) -> set(auto_limits).
% 0.44/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02 % set(auto) -> set(auto_denials).
% 0.44/1.02 % set(auto) -> set(auto_process).
% 0.44/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02 % set(auto2) -> assign(stats, some).
% 0.44/1.02 % set(auto2) -> clear(echo_input).
% 0.44/1.02 % set(auto2) -> set(quiet).
% 0.44/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02 % set(auto2) -> clear(print_given).
% 0.44/1.02 assign(lrs_ticks,-1).
% 0.44/1.02 assign(sos_limit,10000).
% 0.44/1.02 assign(order,kbo).
% 0.44/1.02 set(lex_order_vars).
% 0.44/1.02 clear(print_given).
% 0.44/1.02
% 0.44/1.02 % formulas(sos). % not echoed (94 formulas)
% 0.44/1.02
% 0.44/1.02 ============================== end of input ==========================
% 0.44/1.02
% 0.44/1.02 % From the command line: assign(max_seconds, 300).
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02
% 0.44/1.02 % Formulas that are not ordinary clauses:
% 0.44/1.02
% 0.44/1.02 ============================== end of process non-clausal formulas ===
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.02
% 0.44/1.02 ============================== PREDICATE ELIMINATION =================
% 0.44/1.02 1 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.44/1.02 2 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.44/1.02 Derived: member(null_class,omega). [resolve(1,a,2,a)].
% 0.44/1.02 3 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.44/1.02 Derived: subclass(omega,omega). [resolve(3,a,2,a)].
% 0.44/1.02 4 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.44/1.02 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,2,a)].
% 0.44/1.02 5 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.44/1.02 Derived: -member(null_class,A) | -subclass(image(successor_relation,A),A) | subclass(omega,A). [resolve(5,c,3,a)].
% 0.44/1.02 6 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.44/1.02 7 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.44/1.02 8 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.44/1.02 9 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.44/1.02 10 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.44/1.02 11 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.44/1.02 12 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.44/1.02 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(9,a,10,a)].
% 0.44/1.02 Derived: subclass(A,cross_product(universal_class,universal_class)) | -operation(A). [resolve(9,a,11,b)].
% 0.44/1.02 Derived: subclass(A,cross_product(universal_class,universal_class)) | -compatible(A,B,C). [resolve(9,a,12,b)].
% 0.44/1.02 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.44/1.02 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(13,a,10,a)].
% 0.44/1.02 Derived: subclass(compose(A,inverse(A)),identity_relation) | -operation(A). [resolve(13,a,11,b)].
% 0.44/1.02 Derived: subclass(compose(A,inverse(A)),identity_relation) | -compatible(A,B,C). [resolve(13,a,12,b)].
% 0.44/1.02 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.44/1.02 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(14,a,10,a)].
% 0.44/1.02 Derived: -member(A,universal_class) | member(image(B,A),universal_class) | -operation(B). [resolve(14,a,11,b)].
% 0.44/1.02 Derived: -member(A,universal_class) | member(image(B,A),universal_class) | -compatible(B,C,D). [resolve(14,a,12,b)].
% 0.44/1.02 15 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.44/1.02 Derived: -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(15,c,14,a)].
% 0.44/1.02 16 -function(A) | domain_of(domain_of(B)) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(C))) | compatible(A,B,C) # label(compatible4) # label(axiom). [assumption].
% 0.44/1.02 Derived: domain_of(domain_of(A)) != domain_of(choice) | -subclass(range_of(choice),domain_of(domain_of(B))) | compatible(choice,A,B). [resolve(16,a,10,a)].
% 0.44/1.02 Derived: domain_of(domain_of(A)) != domain_of(B) | -subclass(range_of(B),domain_of(domain_of(C))) | compatible(B,A,C) | -operation(B). [resolve(16,a,11,b)].
% 0.44/1.02 Derived: domain_of(domain_of(A)) != domain_of(B) | -subclass(range_of(B),domain_of(domain_of(C))) | compatible(B,A,C) | -compatible(B,D,E). [resolve(16,a,12,b)].
% 0.44/1.02 Derived: domain_of(domain_of(A)) != domain_of(B) | -subclass(range_of(B),domain_of(domain_of(C))) | compatible(B,A,C) | -subclass(B,cross_product(universal_class,universal_class)) | -subclass(compose(B,inverse(B)),identity_relation). [resolve(16,a,15,c)].
% 0.44/1.02 17 -function(A) | cross_product(domain_of(domain_of(A)),domain_of(domain_of(A))) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(A))) | operation(A) # label(operation4) # label(axiom). [assumption].
% 0.44/1.02 Derived: cross_product(domain_of(domain_of(choice)),domain_of(domain_of(choice))) != domain_of(choice) | -subclass(range_of(choice),domain_of(domain_of(choice))) | operation(choice). [resolve(17,a,10,a)].
% 0.44/1.02 Derived: cross_product(domain_of(domain_of(A)),domain_of(domain_of(A))) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(A))) | operation(A) | -compatible(A,B,C). [resolve(17,a,12,b)].
% 0.44/1.02 Derived: cross_product(domain_of(domain_of(A)),domain_of(domain_of(A))) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(A))) | operation(A) | -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation). [resolve(17,a,15,c)].
% 0.44/1.02 18 -operation(A) | -operation(B) | -compatible(C,A,B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | homomorphism(C,A,B) # label(homomorphism5) # label(axiom). [assumption].
% 0.44/1.02 19 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.44/1.02 20 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.44/1.02 21 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.44/1.02 22 -homomorphism(A,B,C) | -member(ordered_pair(D,E),domain_of(B)) | apply(C,ordered_pair(apply(A,D),apply(A,E))) = apply(A,apply(B,ordered_pair(D,E))) # label(homomorphism4) # label(axiom). [assumption].
% 0.44/1.02 Derived: -member(ordered_pair(A,B),domain_of(C)) | apply(D,ordered_pair(apply(E,A),apply(E,B))) = apply(E,apply(C,ordered_pair(A,B))) | -operation(C) | -operation(D) | -compatible(E,C,D) | member(ordered_pair(not_homomorphism1(E,C,D),not_homomorphism2(E,C,D)),domain_of(C)). [resolve(22,a,18,e)].
% 2.28/2.54 23 -operation(A) | -operation(B) | -compatible(C,A,B) | apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B)))) != apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)))) | homomorphism(C,A,B) # label(homomorphism6) # label(axiom). [assumption].
% 2.28/2.54 Derived: -operation(A) | -operation(B) | -compatible(C,A,B) | apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B)))) != apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)))) | -member(ordered_pair(D,E),domain_of(A)) | apply(B,ordered_pair(apply(C,D),apply(C,E))) = apply(C,apply(A,ordered_pair(D,E))). [resolve(23,e,22,a)].
% 2.28/2.54 24 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 2.28/2.54 25 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 2.28/2.54
% 2.28/2.54 ============================== end predicate elimination =============
% 2.28/2.54
% 2.28/2.54 Auto_denials: (non-Horn, no changes).
% 2.28/2.54
% 2.28/2.54 Term ordering decisions:
% 2.28/2.54 Function symbol KB weights: universal_class=1. choice=1. null_class=1. element_relation=1. identity_relation=1. omega=1. successor_relation=1. subset_relation=1. z=1. x=1. y=1. ordered_pair=1. cross_product=1. apply=1. intersection=1. image=1. compose=1. unordered_pair=1. not_subclass_element=1. union=1. symmetric_difference=1. domain_of=1. complement=1. inverse=1. range_of=1. singleton=1. flip=1. rotate=1. successor=1. sum_class=1. diagonalise=1. first=1. power_class=1. regular=1. second=1. cantor=1. restrict=1. not_homomorphism1=1. not_homomorphism2=1. domain=1. range=1.
% 2.28/2.54
% 2.28/2.54 ============================== end of process initial clauses ========
% 2.28/2.54
% 2.28/2.54 ============================== CLAUSES FOR SEARCH ====================
% 2.28/2.54
% 2.28/2.54 ============================== end of clauses for search =============
% 2.28/2.54
% 2.28/2.54 ============================== SEARCH ================================
% 2.28/2.54
% 2.28/2.54 % Starting search at 0.04 seconds.
% 2.28/2.54
% 2.28/2.54 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 117 (0.00 of 0.48 sec).
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=32.000, iters=3371
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=31.000, iters=3368
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=28.000, iters=3499
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=27.000, iters=3440
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=25.000, iters=3558
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=23.000, iters=3345
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=22.000, iters=3480
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=21.000, iters=3420
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=20.000, iters=3346
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=19.000, iters=3335
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=12.000, iters=3357
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=11.000, iters=3377
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=10.000, iters=3334
% 2.28/2.54
% 2.28/2.54 Low Water (keep): wt=9.000, iters=3334
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=4153, wt=171.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=4150, wt=155.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=1687, wt=143.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=3976, wt=122.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=4174, wt=114.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=2925, wt=111.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=11597, wt=16.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=11599, wt=15.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=11736, wt=14.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=11738, wt=11.000
% 2.28/2.54
% 2.28/2.54 Low Water (displace): id=12420, wt=7.000
% 2.28/2.54
% 2.28/2.54 ============================== PROOF =================================
% 2.28/2.54 % SZS status Unsatisfiable
% 2.28/2.54 % SZS output start Refutation
% 2.28/2.54
% 2.28/2.54 % Proof 1 at 1.49 (+ 0.05) seconds.
% 2.28/2.54 % Length of proof is 26.
% 2.28/2.54 % Level of proof is 8.
% 2.28/2.54 % Maximum clause weight is 14.000.
% 2.28/2.54 % Given clauses 1890.
% 2.28/2.54
% 2.28/2.54 26 subclass(A,universal_class) # label(class_elements_are_sets) # label(axiom). [assumption].
% 2.28/2.54 28 member(x,z) # label(prove_unordered_pair_is_subset_1) # label(negated_conjecture). [assumption].
% 2.28/2.54 29 member(y,z) # label(prove_unordered_pair_is_subset_2) # label(negated_conjecture). [assumption].
% 2.28/2.54 43 member(not_subclass_element(A,B),A) | subclass(A,B) # label(not_subclass_members1) # label(axiom). [assumption].
% 2.28/2.54 78 -subclass(unordered_pair(x,y),z) # label(prove_unordered_pair_is_subset_3) # label(negated_conjecture). [assumption].
% 2.28/2.54 88 -member(not_subclass_element(A,B),B) | subclass(A,B) # label(not_subclass_members2) # label(axiom). [assumption].
% 2.28/2.54 93 -member(A,intersection(B,C)) | member(A,B) # label(intersection1) # label(axiom). [assumption].
% 2.28/2.54 97 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 2.28/2.54 109 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_member) # label(axiom). [assumption].
% 2.28/2.54 110 -member(A,B) | -member(A,C) | member(A,intersection(B,C)) # label(intersection3) # label(axiom). [assumption].
% 2.28/2.54 185 -member(A,B) | member(A,intersection(B,B)). [factor(110,a,b)].
% 2.28/2.54 195 member(not_subclass_element(unordered_pair(x,y),z),unordered_pair(x,y)). [resolve(78,a,43,b)].
% 2.28/2.54 223 -member(not_subclass_element(unordered_pair(x,y),z),z). [ur(88,b,78,a)].
% 2.28/2.54 242 -member(A,B) | member(A,universal_class). [resolve(97,a,26,a)].
% 2.28/2.54 259 -member(x,A) | member(x,intersection(z,A)). [resolve(110,a,28,a)].
% 2.28/2.54 321 member(x,intersection(z,z)). [resolve(185,a,28,a)].
% 2.28/2.54 420 member(x,universal_class). [resolve(242,a,321,a)].
% 2.28/2.54 450 -member(x,A) | member(x,intersection(universal_class,A)). [resolve(420,a,110,a)].
% 2.28/2.54 563 not_subclass_element(unordered_pair(x,y),z) = x | not_subclass_element(unordered_pair(x,y),z) = y. [resolve(195,a,109,a)].
% 2.28/2.54 1283 -member(not_subclass_element(unordered_pair(x,y),z),intersection(z,A)). [ur(93,b,223,a)].
% 2.28/2.54 4307 member(x,intersection(universal_class,intersection(z,z))). [resolve(450,a,321,a)].
% 2.28/2.54 4635 member(x,intersection(z,intersection(universal_class,intersection(z,z)))). [resolve(4307,a,259,a)].
% 2.28/2.54 13060 member(x,intersection(z,intersection(z,intersection(universal_class,intersection(z,z))))). [resolve(4635,a,259,a)].
% 2.28/2.54 17658 not_subclass_element(unordered_pair(x,y),z) = x. [para(563(b,1),88(a,1)),unit_del(b,29),unit_del(c,78)].
% 2.28/2.54 17659 -member(x,intersection(z,A)). [back_rewrite(1283),rewrite([17658(5)])].
% 2.28/2.54 17660 $F. [resolve(17659,a,13060,a)].
% 2.28/2.54
% 2.28/2.54 % SZS output end Refutation
% 2.28/2.54 ============================== end of proof ==========================
% 2.28/2.54
% 2.28/2.54 ============================== STATISTICS ============================
% 2.28/2.54
% 2.28/2.54 Given=1890. Generated=92670. Kept=17575. proofs=1.
% 2.28/2.54 Usable=1858. Sos=9978. Demods=27. Limbo=1, Disabled=5854. Hints=0.
% 2.28/2.54 Megabytes=13.91.
% 2.28/2.54 User_CPU=1.49, System_CPU=0.05, Wall_clock=1.
% 2.28/2.54
% 2.28/2.54 ============================== end of statistics =====================
% 2.28/2.54
% 2.28/2.54 ============================== end of search =========================
% 2.28/2.54
% 2.28/2.54 THEOREM PROVED
% 2.28/2.54 % SZS status Unsatisfiable
% 2.28/2.54
% 2.28/2.54 Exiting with 1 proof.
% 2.28/2.54
% 2.28/2.54 Process 31744 exit (max_proofs) Sun Jul 10 21:57:40 2022
% 2.28/2.54 Prover9 interrupted
%------------------------------------------------------------------------------