TSTP Solution File: SET137-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET137-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 04:27:39 EDT 2022
% Result : Unsatisfiable 1.26s 1.53s
% Output : Refutation 1.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET137-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n021.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 01:01:07 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.47/1.05 ============================== Prover9 ===============================
% 0.47/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.05 Process 1155 was started by sandbox on n021.cluster.edu,
% 0.47/1.05 Sun Jul 10 01:01:07 2022
% 0.47/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_974_n021.cluster.edu".
% 0.47/1.05 ============================== end of head ===========================
% 0.47/1.05
% 0.47/1.05 ============================== INPUT =================================
% 0.47/1.05
% 0.47/1.05 % Reading from file /tmp/Prover9_974_n021.cluster.edu
% 0.47/1.05
% 0.47/1.05 set(prolog_style_variables).
% 0.47/1.05 set(auto2).
% 0.47/1.05 % set(auto2) -> set(auto).
% 0.47/1.05 % set(auto) -> set(auto_inference).
% 0.47/1.05 % set(auto) -> set(auto_setup).
% 0.47/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.05 % set(auto) -> set(auto_limits).
% 0.47/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.05 % set(auto) -> set(auto_denials).
% 0.47/1.05 % set(auto) -> set(auto_process).
% 0.47/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.05 % set(auto2) -> assign(stats, some).
% 0.47/1.05 % set(auto2) -> clear(echo_input).
% 0.47/1.05 % set(auto2) -> set(quiet).
% 0.47/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.05 % set(auto2) -> clear(print_given).
% 0.47/1.05 assign(lrs_ticks,-1).
% 0.47/1.05 assign(sos_limit,10000).
% 0.47/1.05 assign(order,kbo).
% 0.47/1.05 set(lex_order_vars).
% 0.47/1.05 clear(print_given).
% 0.47/1.05
% 0.47/1.05 % formulas(sos). % not echoed (96 formulas)
% 0.47/1.05
% 0.47/1.05 ============================== end of input ==========================
% 0.47/1.05
% 0.47/1.05 % From the command line: assign(max_seconds, 300).
% 0.47/1.05
% 0.47/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.05
% 0.47/1.05 % Formulas that are not ordinary clauses:
% 0.47/1.05
% 0.47/1.05 ============================== end of process non-clausal formulas ===
% 0.47/1.05
% 0.47/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.47/1.05
% 0.47/1.05 ============================== PREDICATE ELIMINATION =================
% 0.47/1.05 1 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.47/1.05 2 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.47/1.05 Derived: member(null_class,omega). [resolve(1,a,2,a)].
% 0.47/1.05 3 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.47/1.05 Derived: subclass(omega,omega). [resolve(3,a,2,a)].
% 0.47/1.05 4 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.47/1.05 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,2,a)].
% 0.47/1.05 5 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.47/1.05 Derived: -member(null_class,A) | -subclass(image(successor_relation,A),A) | subclass(omega,A). [resolve(5,c,3,a)].
% 0.47/1.05 6 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.47/1.05 7 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.47/1.05 8 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.47/1.05 9 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.47/1.05 10 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.47/1.05 11 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.47/1.05 12 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.47/1.05 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(9,a,10,a)].
% 0.47/1.05 Derived: subclass(A,cross_product(universal_class,universal_class)) | -operation(A). [resolve(9,a,11,b)].
% 0.47/1.05 Derived: subclass(A,cross_product(universal_class,universal_class)) | -compatible(A,B,C). [resolve(9,a,12,b)].
% 0.47/1.05 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.47/1.05 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(13,a,10,a)].
% 0.47/1.05 Derived: subclass(compose(A,inverse(A)),identity_relation) | -operation(A). [resolve(13,a,11,b)].
% 0.47/1.05 Derived: subclass(compose(A,inverse(A)),identity_relation) | -compatible(A,B,C). [resolve(13,a,12,b)].
% 0.47/1.05 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.47/1.05 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(14,a,10,a)].
% 0.47/1.05 Derived: -member(A,universal_class) | member(image(B,A),universal_class) | -operation(B). [resolve(14,a,11,b)].
% 0.47/1.05 Derived: -member(A,universal_class) | member(image(B,A),universal_class) | -compatible(B,C,D). [resolve(14,a,12,b)].
% 0.47/1.05 15 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.47/1.05 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)].
% 0.47/1.05 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].
% 0.47/1.05 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)].
% 0.47/1.05 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)].
% 0.47/1.05 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)].
% 0.47/1.05 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)].
% 0.47/1.05 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].
% 0.47/1.05 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)].
% 0.47/1.05 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)].
% 0.47/1.05 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)].
% 0.47/1.05 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].
% 0.47/1.05 19 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.47/1.05 20 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.47/1.05 21 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.47/1.05 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].
% 0.47/1.05 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)].
% 1.26/1.53 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].
% 1.26/1.53 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)].
% 1.26/1.53 24 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 1.26/1.53 25 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 1.26/1.53
% 1.26/1.53 ============================== end predicate elimination =============
% 1.26/1.53
% 1.26/1.53 Auto_denials: (non-Horn, no changes).
% 1.26/1.53
% 1.26/1.53 Term ordering decisions:
% 1.26/1.53 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. x=1. u=1. v=1. w=1. ordered_pair=1. cross_product=1. apply=1. intersection=1. image=1. compose=1. unordered_pair=1. not_subclass_element=1. set_builder=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.
% 1.26/1.53
% 1.26/1.53 ============================== end of process initial clauses ========
% 1.26/1.53
% 1.26/1.53 ============================== CLAUSES FOR SEARCH ====================
% 1.26/1.53
% 1.26/1.53 ============================== end of clauses for search =============
% 1.26/1.53
% 1.26/1.53 ============================== SEARCH ================================
% 1.26/1.53
% 1.26/1.53 % Starting search at 0.04 seconds.
% 1.26/1.53
% 1.26/1.53 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 111 (0.00 of 0.48 sec).
% 1.26/1.53
% 1.26/1.53 ============================== PROOF =================================
% 1.26/1.53 % SZS status Unsatisfiable
% 1.26/1.53 % SZS output start Refutation
% 1.26/1.53
% 1.26/1.53 % Proof 1 at 0.48 (+ 0.01) seconds.
% 1.26/1.53 % Length of proof is 34.
% 1.26/1.53 % Level of proof is 7.
% 1.26/1.53 % Maximum clause weight is 24.000.
% 1.26/1.53 % Given clauses 500.
% 1.26/1.53
% 1.26/1.53 26 subclass(A,universal_class) # label(class_elements_are_sets) # label(axiom). [assumption].
% 1.26/1.53 28 member(u,x) # label(prove_member_of_triple_kludge1_1) # label(negated_conjecture). [assumption].
% 1.26/1.53 34 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 1.26/1.53 35 singleton(A) = unordered_pair(A,A). [copy(34),flip(a)].
% 1.26/1.53 42 A = null_class | member(regular(A),A) # label(regularity1) # label(axiom). [assumption].
% 1.26/1.53 43 null_class = A | member(regular(A),A). [copy(42),flip(a)].
% 1.26/1.53 55 union(singleton(A),B) = set_builder(A,B) # label(definition_of_set_builder) # label(axiom). [assumption].
% 1.26/1.53 56 set_builder(A,B) = union(unordered_pair(A,A),B). [copy(55),rewrite([35(1)]),flip(a)].
% 1.26/1.53 63 set_builder(u,set_builder(v,set_builder(w,null_class))) = null_class # label(prove_member_of_triple_kludge1_4) # label(negated_conjecture). [assumption].
% 1.26/1.53 64 union(unordered_pair(u,u),union(unordered_pair(v,v),union(unordered_pair(w,w),null_class))) = null_class. [copy(63),rewrite([56(5),56(8),56(11)])].
% 1.26/1.53 65 complement(intersection(complement(A),complement(B))) = union(A,B) # label(union) # label(axiom). [assumption].
% 1.26/1.53 66 union(A,B) = complement(intersection(complement(A),complement(B))). [copy(65),flip(a)].
% 1.26/1.53 83 -member(A,complement(B)) | -member(A,B) # label(complement1) # label(axiom). [assumption].
% 1.26/1.53 94 -member(A,universal_class) | member(A,unordered_pair(B,A)) # label(unordered_pair3) # label(axiom). [assumption].
% 1.26/1.53 97 -member(A,intersection(B,C)) | member(A,B) # label(intersection1) # label(axiom). [assumption].
% 1.26/1.53 101 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 1.26/1.53 109 -member(A,universal_class) | member(A,complement(B)) | member(A,B) # label(complement2) # label(axiom). [assumption].
% 1.26/1.53 114 -member(A,B) | -member(A,C) | member(A,intersection(B,C)) # label(intersection3) # label(axiom). [assumption].
% 1.26/1.53 184 complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) = null_class. [back_rewrite(64),rewrite([66(11),66(15),66(19)])].
% 1.26/1.53 191 -member(A,B) | member(A,intersection(B,B)). [factor(114,a,b)].
% 1.26/1.53 201 -member(regular(complement(A)),A) | complement(A) = null_class. [resolve(83,a,43,b),flip(b)].
% 1.26/1.53 246 -member(A,B) | member(A,universal_class). [resolve(101,a,26,a)].
% 1.26/1.53 331 member(u,intersection(x,x)). [resolve(191,a,28,a)].
% 1.26/1.53 456 member(u,universal_class). [resolve(246,a,331,a)].
% 1.26/1.53 460 member(regular(A),universal_class) | null_class = A. [resolve(246,a,43,b)].
% 1.26/1.53 471 member(u,complement(A)) | member(u,A). [resolve(456,a,109,a)].
% 1.26/1.53 472 member(u,unordered_pair(A,u)). [resolve(456,a,94,a)].
% 1.26/1.53 477 -member(u,complement(universal_class)). [ur(83,b,456,a)].
% 1.26/1.53 569 -member(u,complement(unordered_pair(A,u))). [ur(83,b,472,a)].
% 1.26/1.53 1066 complement(universal_class) = null_class. [resolve(460,a,201,a),flip(a),merge(b)].
% 1.26/1.53 1232 -member(u,null_class). [back_rewrite(477),rewrite([1066(3)])].
% 1.26/1.53 1297 member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))). [para(184(a,1),471(a,2)),unit_del(a,1232)].
% 1.26/1.53 5562 -member(u,intersection(complement(unordered_pair(A,u)),B)). [ur(97,b,569,a)].
% 1.26/1.53 5563 $F. [resolve(5562,a,1297,a)].
% 1.26/1.53
% 1.26/1.53 % SZS output end Refutation
% 1.26/1.53 ============================== end of proof ==========================
% 1.26/1.53
% 1.26/1.53 ============================== STATISTICS ============================
% 1.26/1.53
% 1.26/1.53 Given=500. Generated=7472. Kept=5476. proofs=1.
% 1.26/1.53 Usable=478. Sos=4722. Demods=23. Limbo=26, Disabled=368. Hints=0.
% 1.26/1.53 Megabytes=6.41.
% 1.26/1.53 User_CPU=0.48, System_CPU=0.01, Wall_clock=1.
% 1.26/1.53
% 1.26/1.53 ============================== end of statistics =====================
% 1.26/1.53
% 1.26/1.53 ============================== end of search =========================
% 1.26/1.53
% 1.26/1.53 THEOREM PROVED
% 1.26/1.53 % SZS status Unsatisfiable
% 1.26/1.53
% 1.26/1.53 Exiting with 1 proof.
% 1.26/1.53
% 1.26/1.53 Process 1155 exit (max_proofs) Sun Jul 10 01:01:08 2022
% 1.26/1.53 Prover9 interrupted
%------------------------------------------------------------------------------