TSTP Solution File: SET516-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET516-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 04:30:00 EDT 2022
% Result : Unsatisfiable 1.02s 1.30s
% Output : Refutation 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET516-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 19:00:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.46/1.01 ============================== Prover9 ===============================
% 0.46/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.01 Process 9699 was started by sandbox on n010.cluster.edu,
% 0.46/1.01 Sun Jul 10 19:00:31 2022
% 0.46/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9546_n010.cluster.edu".
% 0.46/1.01 ============================== end of head ===========================
% 0.46/1.01
% 0.46/1.01 ============================== INPUT =================================
% 0.46/1.01
% 0.46/1.01 % Reading from file /tmp/Prover9_9546_n010.cluster.edu
% 0.46/1.01
% 0.46/1.01 set(prolog_style_variables).
% 0.46/1.01 set(auto2).
% 0.46/1.01 % set(auto2) -> set(auto).
% 0.46/1.01 % set(auto) -> set(auto_inference).
% 0.46/1.01 % set(auto) -> set(auto_setup).
% 0.46/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.01 % set(auto) -> set(auto_limits).
% 0.46/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.01 % set(auto) -> set(auto_denials).
% 0.46/1.01 % set(auto) -> set(auto_process).
% 0.46/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.01 % set(auto2) -> assign(stats, some).
% 0.46/1.01 % set(auto2) -> clear(echo_input).
% 0.46/1.01 % set(auto2) -> set(quiet).
% 0.46/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.01 % set(auto2) -> clear(print_given).
% 0.46/1.01 assign(lrs_ticks,-1).
% 0.46/1.01 assign(sos_limit,10000).
% 0.46/1.01 assign(order,kbo).
% 0.46/1.01 set(lex_order_vars).
% 0.46/1.01 clear(print_given).
% 0.46/1.01
% 0.46/1.01 % formulas(sos). % not echoed (113 formulas)
% 0.46/1.01
% 0.46/1.01 ============================== end of input ==========================
% 0.46/1.01
% 0.46/1.01 % From the command line: assign(max_seconds, 300).
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.01
% 0.46/1.01 % Formulas that are not ordinary clauses:
% 0.46/1.01
% 0.46/1.01 ============================== end of process non-clausal formulas ===
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.01
% 0.46/1.01 ============================== PREDICATE ELIMINATION =================
% 0.46/1.01 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.46/1.01 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.46/1.01 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.46/1.01 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.46/1.01 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.46/1.01 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.46/1.01 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.46/1.01 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.46/1.01 Derived: subclass(omega,omega). [resolve(5,a,4,a)].
% 0.46/1.01 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.46/1.01 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.46/1.01 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.46/1.01 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.46/1.01 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.46/1.01 11 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.46/1.01 12 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.46/1.01 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.46/1.01 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.46/1.01 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)].
% 0.46/1.01 15 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.46/1.01 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(15,a,12,a)].
% 0.46/1.01 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(15,a,13,a)].
% 0.46/1.01 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(15,a,14,a)].
% 0.46/1.01 16 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.46/1.01 Derived: -operation(A) | subclass(A,cross_product(universal_class,universal_class)). [resolve(16,b,12,a)].
% 0.46/1.01 Derived: -operation(A) | subclass(compose(A,inverse(A)),identity_relation). [resolve(16,b,13,a)].
% 0.46/1.01 Derived: -operation(A) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(16,b,14,a)].
% 0.46/1.01 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].
% 0.46/1.01 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)].
% 0.46/1.01 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)].
% 0.46/1.01 18 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.46/1.01 Derived: -compatible(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(18,b,12,a)].
% 0.46/1.01 Derived: -compatible(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(18,b,13,a)].
% 0.46/1.01 Derived: -compatible(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(18,b,14,a)].
% 0.46/1.01 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)].
% 0.46/1.01 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].
% 0.46/1.01 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)].
% 0.46/1.01 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)].
% 0.46/1.01 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)].
% 0.46/1.01 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)].
% 0.46/1.01 20 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.46/1.01 Derived: -maps(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(20,b,12,a)].
% 0.46/1.01 Derived: -maps(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(20,b,13,a)].
% 0.46/1.01 Derived: -maps(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(20,b,14,a)].
% 0.46/1.01 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)].
% 0.46/1.01 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)].
% 1.02/1.30 21 -function(A) | -subclass(range_of(A),B) | maps(A,domain_of(A),B) # label(maps4) # label(axiom). [assumption].
% 1.02/1.30 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)].
% 1.02/1.30 Derived: -subclass(range_of(choice),A) | maps(choice,domain_of(choice),A). [resolve(21,a,15,a)].
% 1.02/1.30 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -operation(A). [resolve(21,a,16,b)].
% 1.02/1.30 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -compatible(A,C,D). [resolve(21,a,18,b)].
% 1.02/1.30 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -maps(A,C,D). [resolve(21,a,20,b)].
% 1.02/1.30 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].
% 1.02/1.30 23 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 1.02/1.30 24 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 1.02/1.30 25 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 1.02/1.30 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].
% 1.02/1.30 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)].
% 1.02/1.30 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].
% 1.02/1.30 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)].
% 1.02/1.30
% 1.02/1.30 ============================== end predicate elimination =============
% 1.02/1.30
% 1.02/1.30 Auto_denials: (non-Horn, no changes).
% 1.02/1.30
% 1.02/1.30 Term ordering decisions:
% 1.02/1.30 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. singleton_relation=1. ordered_pair=1. cross_product=1. compose=1. apply=1. intersection=1. image=1. unordered_pair=1. not_subclass_element=1. union=1. symmetric_difference=1. domain_of=1. range_of=1. inverse=1. complement=1. singleton=1. flip=1. compose_class=1. first=1. rotate=1. second=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.
% 1.02/1.30
% 1.02/1.30 ============================== end of process initial clauses ========
% 1.02/1.30
% 1.02/1.30 ============================== CLAUSES FOR SEARCH ====================
% 1.02/1.30
% 1.02/1.30 ============================== end of clauses for search =============
% 1.02/1.30
% 1.02/1.30 ============================== SEARCH ================================
% 1.02/1.30
% 1.02/1.30 % Starting search at 0.03 seconds.
% 1.02/1.30
% 1.02/1.30 ============================== PROOF =================================
% 1.02/1.30 % SZS status Unsatisfiable
% 1.02/1.30 % SZS output start Refutation
% 1.02/1.30
% 1.02/1.30 % Proof 1 at 0.29 (+ 0.00) seconds.
% 1.02/1.30 % Length of proof is 36.
% 1.02/1.30 % Level of proof is 10.
% 1.02/1.30 % Maximum clause weight is 11.000.
% 1.02/1.30 % Given clauses 301.
% 1.02/1.30
% 1.02/1.30 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 1.02/1.30 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 1.02/1.30 28 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 1.02/1.30 31 subclass(A,universal_class) # label(class_elements_are_sets) # label(axiom). [assumption].
% 1.02/1.30 35 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_member) # label(axiom). [assumption].
% 1.02/1.30 37 -member(A,universal_class) | member(A,unordered_pair(B,A)) # label(unordered_pair3) # label(axiom). [assumption].
% 1.02/1.30 38 member(unordered_pair(A,B),universal_class) # label(unordered_pairs_in_universal) # label(axiom). [assumption].
% 1.02/1.30 39 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 1.02/1.30 40 singleton(A) = unordered_pair(A,A). [copy(39),flip(a)].
% 1.02/1.30 58 -member(A,B) | -member(A,C) | member(A,intersection(B,C)) # label(intersection3) # label(axiom). [assumption].
% 1.02/1.30 59 -member(A,complement(B)) | -member(A,B) # label(complement1) # label(axiom). [assumption].
% 1.02/1.30 114 A = null_class | member(regular(A),A) # label(regularity1) # label(axiom). [assumption].
% 1.02/1.30 115 null_class = A | member(regular(A),A). [copy(114),flip(a)].
% 1.02/1.30 116 A = null_class | intersection(A,regular(A)) = null_class # label(regularity2) # label(axiom). [assumption].
% 1.02/1.30 117 null_class = A | intersection(A,regular(A)) = null_class. [copy(116),flip(a)].
% 1.02/1.30 168 singleton(x) = x # label(prove_corollary_to_no_class_belongs_to_itself_1) # label(negated_conjecture). [assumption].
% 1.02/1.30 169 unordered_pair(x,x) = x. [copy(168),rewrite([40(2)])].
% 1.02/1.30 170 member(null_class,omega). [resolve(4,a,2,a)].
% 1.02/1.30 232 -member(A,B) | member(A,intersection(B,B)). [factor(58,a,b)].
% 1.02/1.30 238 -member(A,B) | member(A,universal_class). [resolve(31,a,28,a)].
% 1.02/1.30 286 complement(A) = null_class | -member(regular(complement(A)),A). [resolve(115,b,59,a),flip(a)].
% 1.02/1.30 325 -member(A,x) | x = A. [para(169(a,1),35(a,2)),flip(b),flip(c),merge(c)].
% 1.02/1.30 326 member(x,universal_class). [para(169(a,1),38(a,1))].
% 1.02/1.30 444 member(x,unordered_pair(A,x)). [resolve(326,a,37,a)].
% 1.02/1.30 460 member(null_class,universal_class). [resolve(238,a,170,a)].
% 1.02/1.30 461 member(regular(A),universal_class) | null_class = A. [resolve(238,a,115,b)].
% 1.02/1.30 514 member(x,x). [para(169(a,1),444(a,2))].
% 1.02/1.30 516 member(x,intersection(x,x)). [resolve(514,a,232,a)].
% 1.02/1.30 587 regular(x) = x | x = null_class. [resolve(325,a,115,b),flip(a),flip(b)].
% 1.02/1.30 693 x = null_class | intersection(x,x) = null_class. [para(587(a,1),117(b,1,2)),flip(b),merge(b)].
% 1.02/1.30 2127 x = null_class | member(x,null_class). [para(693(b,1),516(a,2))].
% 1.02/1.30 2346 complement(universal_class) = null_class. [resolve(286,b,461,a),flip(b),merge(b)].
% 1.02/1.30 2347 -member(A,null_class) | -member(A,universal_class). [para(2346(a,1),59(a,2))].
% 1.02/1.30 2353 x = null_class. [resolve(2347,a,2127,b),unit_del(a,326)].
% 1.02/1.30 2956 member(null_class,null_class). [back_rewrite(514),rewrite([2353(1),2353(2)])].
% 1.02/1.30 3182 $F. [resolve(2956,a,2347,a),unit_del(a,460)].
% 1.02/1.30
% 1.02/1.30 % SZS output end Refutation
% 1.02/1.30 ============================== end of proof ==========================
% 1.02/1.30
% 1.02/1.30 ============================== STATISTICS ============================
% 1.02/1.30
% 1.02/1.30 Given=301. Generated=4071. Kept=3071. proofs=1.
% 1.02/1.30 Usable=236. Sos=1685. Demods=28. Limbo=0, Disabled=1296. Hints=0.
% 1.02/1.30 Megabytes=4.58.
% 1.02/1.30 User_CPU=0.29, System_CPU=0.00, Wall_clock=0.
% 1.02/1.30
% 1.02/1.30 ============================== end of statistics =====================
% 1.02/1.30
% 1.02/1.30 ============================== end of search =========================
% 1.02/1.30
% 1.02/1.30 THEOREM PROVED
% 1.02/1.30 % SZS status Unsatisfiable
% 1.02/1.30
% 1.02/1.30 Exiting with 1 proof.
% 1.02/1.30
% 1.02/1.30 Process 9699 exit (max_proofs) Sun Jul 10 19:00:31 2022
% 1.02/1.30 Prover9 interrupted
%------------------------------------------------------------------------------