TSTP Solution File: SET236-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET236-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 04:28:27 EDT 2022
% Result : Unsatisfiable 0.74s 1.12s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET236-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jul 11 10:07:55 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.43/1.02 ============================== Prover9 ===============================
% 0.43/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.02 Process 2308 was started by sandbox2 on n023.cluster.edu,
% 0.43/1.02 Mon Jul 11 10:07:55 2022
% 0.43/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2107_n023.cluster.edu".
% 0.43/1.02 ============================== end of head ===========================
% 0.43/1.02
% 0.43/1.02 ============================== INPUT =================================
% 0.43/1.02
% 0.43/1.02 % Reading from file /tmp/Prover9_2107_n023.cluster.edu
% 0.43/1.02
% 0.43/1.02 set(prolog_style_variables).
% 0.43/1.02 set(auto2).
% 0.43/1.02 % set(auto2) -> set(auto).
% 0.43/1.02 % set(auto) -> set(auto_inference).
% 0.43/1.02 % set(auto) -> set(auto_setup).
% 0.43/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.02 % set(auto) -> set(auto_limits).
% 0.43/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.02 % set(auto) -> set(auto_denials).
% 0.43/1.02 % set(auto) -> set(auto_process).
% 0.43/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.02 % set(auto2) -> assign(stats, some).
% 0.43/1.02 % set(auto2) -> clear(echo_input).
% 0.43/1.02 % set(auto2) -> set(quiet).
% 0.43/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.02 % set(auto2) -> clear(print_given).
% 0.43/1.02 assign(lrs_ticks,-1).
% 0.43/1.02 assign(sos_limit,10000).
% 0.43/1.02 assign(order,kbo).
% 0.43/1.02 set(lex_order_vars).
% 0.43/1.02 clear(print_given).
% 0.43/1.02
% 0.43/1.02 % formulas(sos). % not echoed (115 formulas)
% 0.43/1.02
% 0.43/1.02 ============================== end of input ==========================
% 0.43/1.02
% 0.43/1.02 % From the command line: assign(max_seconds, 300).
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.02
% 0.43/1.02 % Formulas that are not ordinary clauses:
% 0.43/1.02
% 0.43/1.02 ============================== end of process non-clausal formulas ===
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.02
% 0.43/1.02 ============================== PREDICATE ELIMINATION =================
% 0.43/1.02 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.43/1.02 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.43/1.02 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.43/1.02 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.43/1.02 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.43/1.02 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.43/1.02 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.43/1.02 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.43/1.02 Derived: subclass(omega,omega). [resolve(5,a,4,a)].
% 0.43/1.02 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.43/1.02 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.43/1.02 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.43/1.02 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.43/1.02 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.43/1.02 11 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.43/1.02 12 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.43/1.02 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.43/1.02 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.43/1.02 Derived: -member(A,universal_class) | member(image(B,A),universal_class) | -subclass(B,cross_product(universal_class,universal_class)) | -subclass(compose(B,inverse(B)),identity_relation). [resolve(14,a,11,c)].
% 0.43/1.02 15 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.43/1.02 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(15,a,12,a)].
% 0.43/1.02 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(15,a,13,a)].
% 0.43/1.02 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(15,a,14,a)].
% 0.43/1.02 16 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.43/1.02 Derived: -operation(A) | subclass(A,cross_product(universal_class,universal_class)). [resolve(16,b,12,a)].
% 0.43/1.02 Derived: -operation(A) | subclass(compose(A,inverse(A)),identity_relation). [resolve(16,b,13,a)].
% 0.43/1.02 Derived: -operation(A) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(16,b,14,a)].
% 0.43/1.02 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].
% 0.43/1.02 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,11,c)].
% 0.43/1.02 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,15,a)].
% 0.43/1.02 18 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.43/1.02 Derived: -compatible(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(18,b,12,a)].
% 0.43/1.02 Derived: -compatible(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(18,b,13,a)].
% 0.43/1.02 Derived: -compatible(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(18,b,14,a)].
% 0.43/1.02 Derived: -compatible(A,B,C) | 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). [resolve(18,b,17,a)].
% 0.43/1.02 19 -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].
% 0.43/1.02 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(19,a,11,c)].
% 0.43/1.02 Derived: domain_of(domain_of(A)) != domain_of(choice) | -subclass(range_of(choice),domain_of(domain_of(B))) | compatible(choice,A,B). [resolve(19,a,15,a)].
% 0.43/1.02 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(19,a,16,b)].
% 0.43/1.02 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(19,a,18,b)].
% 0.43/1.02 20 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.43/1.02 Derived: -maps(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(20,b,12,a)].
% 0.43/1.02 Derived: -maps(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(20,b,13,a)].
% 0.43/1.02 Derived: -maps(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(20,b,14,a)].
% 0.43/1.02 Derived: -maps(A,B,C) | 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). [resolve(20,b,17,a)].
% 0.43/1.02 Derived: -maps(A,B,C) | domain_of(domain_of(D)) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(E))) | compatible(A,D,E). [resolve(20,b,19,a)].
% 0.74/1.12 21 -function(A) | -subclass(range_of(A),B) | maps(A,domain_of(A),B) # label(maps4) # label(axiom). [assumption].
% 0.74/1.12 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation). [resolve(21,a,11,c)].
% 0.74/1.12 Derived: -subclass(range_of(choice),A) | maps(choice,domain_of(choice),A). [resolve(21,a,15,a)].
% 0.74/1.12 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -operation(A). [resolve(21,a,16,b)].
% 0.74/1.12 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -compatible(A,C,D). [resolve(21,a,18,b)].
% 0.74/1.12 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -maps(A,C,D). [resolve(21,a,20,b)].
% 0.74/1.12 22 -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].
% 0.74/1.12 23 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.74/1.12 24 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.74/1.12 25 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.74/1.12 26 -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].
% 0.74/1.12 Derived: -operation(A) | -operation(B) | -compatible(C,A,B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | -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(22,e,26,a)].
% 0.74/1.12 27 -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].
% 0.74/1.12 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(27,e,26,a)].
% 0.74/1.12
% 0.74/1.12 ============================== end predicate elimination =============
% 0.74/1.12
% 0.74/1.12 Auto_denials: (non-Horn, no changes).
% 0.74/1.12
% 0.74/1.12 Term ordering decisions:
% 0.74/1.12 Function symbol KB weights: universal_class=1. choice=1. identity_relation=1. element_relation=1. null_class=1. omega=1. successor_relation=1. application_function=1. composition_function=1. domain_relation=1. subset_relation=1. x=1. y=1. singleton_relation=1. ordered_pair=1. cross_product=1. compose=1. apply=1. intersection=1. image=1. not_subclass_element=1. unordered_pair=1. union=1. symmetric_difference=1. domain_of=1. range_of=1. inverse=1. complement=1. singleton=1. first=1. flip=1. second=1. compose_class=1. rotate=1. successor=1. sum_class=1. diagonalise=1. power_class=1. regular=1. single_valued1=1. single_valued2=1. cantor=1. single_valued3=1. restrict=1. not_homomorphism1=1. not_homomorphism2=1. domain=1. range=1.
% 0.74/1.12
% 0.74/1.12 ============================== end of process initial clauses ========
% 0.74/1.12
% 0.74/1.12 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.12
% 0.74/1.12 ============================== end of clauses for search =============
% 0.74/1.12
% 0.74/1.12 ============================== SEARCH ================================
% 0.74/1.12
% 0.74/1.12 % Starting search at 0.05 seconds.
% 0.74/1.12
% 0.74/1.12 ============================== PROOF =================================
% 0.74/1.12 % SZS status Unsatisfiable
% 0.74/1.12 % SZS output start Refutation
% 0.74/1.12
% 0.74/1.12 % Proof 1 at 0.12 (+ 0.00) seconds.
% 0.74/1.12 % Length of proof is 19.
% 0.74/1.12 % Level of proof is 6.
% 0.74/1.12 % Maximum clause weight is 28.000.
% 0.74/1.12 % Given clauses 177.
% 0.74/1.12
% 0.74/1.12 28 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 0.74/1.12 29 member(not_subclass_element(A,B),A) | subclass(A,B) # label(not_subclass_members1) # label(axiom). [assumption].
% 0.74/1.12 30 -member(not_subclass_element(A,B),B) | subclass(A,B) # label(not_subclass_members2) # label(axiom). [assumption].
% 0.74/1.12 39 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 0.74/1.12 40 singleton(A) = unordered_pair(A,A). [copy(39),flip(a)].
% 0.74/1.12 41 unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B) # label(ordered_pair) # label(axiom). [assumption].
% 0.74/1.12 42 ordered_pair(A,B) = unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))). [copy(41),rewrite([40(1),40(2)]),flip(a)].
% 0.74/1.12 49 -member(A,cross_product(B,C)) | ordered_pair(first(A),second(A)) = A # label(cartesian_product4) # label(axiom). [assumption].
% 0.74/1.12 50 -member(A,cross_product(B,C)) | unordered_pair(unordered_pair(first(A),first(A)),unordered_pair(first(A),unordered_pair(second(A),second(A)))) = A. [copy(49),rewrite([42(5)])].
% 0.74/1.12 168 subclass(x,cross_product(universal_class,universal_class)) # label(prove_cross_product_property11_1) # label(negated_conjecture). [assumption].
% 0.74/1.12 169 member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),y) # label(prove_cross_product_property11_2) # label(negated_conjecture). [assumption].
% 0.74/1.12 170 member(unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),unordered_pair(second(not_subclass_element(x,y)),second(not_subclass_element(x,y))))),y). [copy(169),rewrite([42(9)])].
% 0.74/1.12 171 -subclass(x,y) # label(prove_cross_product_property11_3) # label(negated_conjecture). [assumption].
% 0.74/1.12 328 -member(A,x) | member(A,cross_product(universal_class,universal_class)). [resolve(168,a,28,a)].
% 0.74/1.12 333 member(not_subclass_element(x,y),x). [resolve(171,a,29,b)].
% 0.74/1.12 753 member(not_subclass_element(x,y),cross_product(universal_class,universal_class)). [resolve(328,a,333,a)].
% 0.74/1.12 761 unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),unordered_pair(second(not_subclass_element(x,y)),second(not_subclass_element(x,y))))) = not_subclass_element(x,y). [resolve(753,a,50,a)].
% 0.74/1.12 773 member(not_subclass_element(x,y),y). [back_rewrite(170),rewrite([761(24)])].
% 0.74/1.12 774 $F. [resolve(773,a,30,a),unit_del(a,171)].
% 0.74/1.12
% 0.74/1.12 % SZS output end Refutation
% 0.74/1.12 ============================== end of proof ==========================
% 0.74/1.12
% 0.74/1.12 ============================== STATISTICS ============================
% 0.74/1.12
% 0.74/1.12 Given=177. Generated=953. Kept=663. proofs=1.
% 0.74/1.12 Usable=176. Sos=465. Demods=24. Limbo=0, Disabled=170. Hints=0.
% 0.74/1.12 Megabytes=1.79.
% 0.74/1.12 User_CPU=0.12, System_CPU=0.00, Wall_clock=0.
% 0.74/1.12
% 0.74/1.12 ============================== end of statistics =====================
% 0.74/1.12
% 0.74/1.12 ============================== end of search =========================
% 0.74/1.12
% 0.74/1.12 THEOREM PROVED
% 0.74/1.12 % SZS status Unsatisfiable
% 0.74/1.12
% 0.74/1.12 Exiting with 1 proof.
% 0.74/1.12
% 0.74/1.12 Process 2308 exit (max_proofs) Mon Jul 11 10:07:55 2022
% 0.74/1.12 Prover9 interrupted
%------------------------------------------------------------------------------