TSTP Solution File: SET205-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET205-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 04:28:16 EDT 2022
% Result : Unsatisfiable 9.27s 9.59s
% Output : Refutation 9.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET205-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n014.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 04:46:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.77/1.05 ============================== Prover9 ===============================
% 0.77/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.05 Process 3898 was started by sandbox2 on n014.cluster.edu,
% 0.77/1.05 Sun Jul 10 04:46:06 2022
% 0.77/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3578_n014.cluster.edu".
% 0.77/1.05 ============================== end of head ===========================
% 0.77/1.05
% 0.77/1.05 ============================== INPUT =================================
% 0.77/1.05
% 0.77/1.05 % Reading from file /tmp/Prover9_3578_n014.cluster.edu
% 0.77/1.05
% 0.77/1.05 set(prolog_style_variables).
% 0.77/1.05 set(auto2).
% 0.77/1.05 % set(auto2) -> set(auto).
% 0.77/1.05 % set(auto) -> set(auto_inference).
% 0.77/1.05 % set(auto) -> set(auto_setup).
% 0.77/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.05 % set(auto) -> set(auto_limits).
% 0.77/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.05 % set(auto) -> set(auto_denials).
% 0.77/1.05 % set(auto) -> set(auto_process).
% 0.77/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.05 % set(auto2) -> assign(stats, some).
% 0.77/1.05 % set(auto2) -> clear(echo_input).
% 0.77/1.05 % set(auto2) -> set(quiet).
% 0.77/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.05 % set(auto2) -> clear(print_given).
% 0.77/1.05 assign(lrs_ticks,-1).
% 0.77/1.05 assign(sos_limit,10000).
% 0.77/1.05 assign(order,kbo).
% 0.77/1.05 set(lex_order_vars).
% 0.77/1.05 clear(print_given).
% 0.77/1.05
% 0.77/1.05 % formulas(sos). % not echoed (113 formulas)
% 0.77/1.05
% 0.77/1.05 ============================== end of input ==========================
% 0.77/1.05
% 0.77/1.05 % From the command line: assign(max_seconds, 300).
% 0.77/1.05
% 0.77/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.05
% 0.77/1.05 % Formulas that are not ordinary clauses:
% 0.77/1.05
% 0.77/1.05 ============================== end of process non-clausal formulas ===
% 0.77/1.05
% 0.77/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.05
% 0.77/1.05 ============================== PREDICATE ELIMINATION =================
% 0.77/1.05 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.77/1.05 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.77/1.05 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.77/1.05 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.77/1.05 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.77/1.05 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.77/1.05 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.77/1.05 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.77/1.05 Derived: subclass(omega,omega). [resolve(5,a,4,a)].
% 0.77/1.05 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.77/1.05 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.77/1.05 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.77/1.05 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.77/1.05 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.77/1.05 11 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.77/1.05 12 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.77/1.05 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.77/1.05 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.77/1.05 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)].
% 0.77/1.05 15 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.77/1.05 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(15,a,12,a)].
% 0.77/1.05 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(15,a,13,a)].
% 0.77/1.05 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(15,a,14,a)].
% 0.77/1.05 16 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.77/1.05 Derived: -operation(A) | subclass(A,cross_product(universal_class,universal_class)). [resolve(16,b,12,a)].
% 0.77/1.05 Derived: -operation(A) | subclass(compose(A,inverse(A)),identity_relation). [resolve(16,b,13,a)].
% 0.77/1.05 Derived: -operation(A) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(16,b,14,a)].
% 0.77/1.05 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].
% 0.77/1.05 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,11,c)].
% 0.77/1.05 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,15,a)].
% 0.77/1.05 18 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.77/1.05 Derived: -compatible(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(18,b,12,a)].
% 0.77/1.05 Derived: -compatible(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(18,b,13,a)].
% 0.77/1.05 Derived: -compatible(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(18,b,14,a)].
% 0.77/1.05 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)].
% 0.77/1.05 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].
% 0.77/1.05 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(19,a,11,c)].
% 0.77/1.05 Derived: domain_of(domain_of(A)) != domain_of(choice) | -subclass(range_of(choice),domain_of(domain_of(B))) | compatible(choice,A,B). [resolve(19,a,15,a)].
% 0.77/1.05 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(19,a,16,b)].
% 0.77/1.05 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(19,a,18,b)].
% 0.77/1.05 20 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.77/1.05 Derived: -maps(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(20,b,12,a)].
% 0.77/1.05 Derived: -maps(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(20,b,13,a)].
% 0.77/1.05 Derived: -maps(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(20,b,14,a)].
% 0.77/1.05 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)].
% 0.77/1.05 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)].
% 1.48/1.76 21 -function(A) | -subclass(range_of(A),B) | maps(A,domain_of(A),B) # label(maps4) # label(axiom). [assumption].
% 1.48/1.76 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)].
% 1.48/1.76 Derived: -subclass(range_of(choice),A) | maps(choice,domain_of(choice),A). [resolve(21,a,15,a)].
% 1.48/1.76 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -operation(A). [resolve(21,a,16,b)].
% 1.48/1.76 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -compatible(A,C,D). [resolve(21,a,18,b)].
% 1.48/1.76 Derived: -subclass(range_of(A),B) | maps(A,domain_of(A),B) | -maps(A,C,D). [resolve(21,a,20,b)].
% 1.48/1.76 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].
% 1.48/1.76 23 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 1.48/1.76 24 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 1.48/1.76 25 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 1.48/1.76 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].
% 1.48/1.76 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)].
% 1.48/1.76 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].
% 1.48/1.76 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)].
% 1.48/1.76
% 1.48/1.76 ============================== end predicate elimination =============
% 1.48/1.76
% 1.48/1.76 Auto_denials: (non-Horn, no changes).
% 1.48/1.76
% 1.48/1.76 Term ordering decisions:
% 1.48/1.76 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. singleton_relation=1. x=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.
% 1.48/1.76
% 1.48/1.76 ============================== end of process initial clauses ========
% 1.48/1.76
% 1.48/1.76 ============================== CLAUSES FOR SEARCH ====================
% 1.48/1.76
% 1.48/1.76 ============================== end of clauses for search =============
% 1.48/1.76
% 1.48/1.76 ============================== SEARCH ================================
% 1.48/1.76
% 1.48/1.76 % Starting search at 0.05 seconds.
% 1.48/1.76
% 1.48/1.76 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 46 (0.00 of 0.64 sec).
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=50.000, iters=3400
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=49.000, iters=3358
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=44.000, iters=3338
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=39.000, iters=3608
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=25.000, iters=3335
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=24.000, iters=3408
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=23.000, iters=3381
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=22.000, iters=3338
% 1.48/1.76
% 1.48/1.76 Low Water (keep): wt=20.000, iters=3475
% 9.27/9.59
% 9.27/9.59 Low Water (keep): wt=19.000, iters=3343
% 9.27/9.59
% 9.27/9.59 Low Water (keep): wt=18.000, iters=3421
% 9.27/9.59
% 9.27/9.59 Low Water (keep): wt=17.000, iters=3435
% 9.27/9.59
% 9.27/9.59 Low Water (keep): wt=16.000, iters=3345
% 9.27/9.59
% 9.27/9.59 Low Water (displace): id=3588, wt=189.000
% 9.27/9.59
% 9.27/9.59 Low Water (displace): id=2738, wt=175.000
% 9.27/9.59
% 9.27/9.59 Low Water (displace): id=2707, wt=171.000
% 9.27/9.59
% 9.27/9.59 Low Water (displace): id=2704, wt=155.000
% 9.27/9.59
% 9.27/9.59 Low Water (displace): id=12989, wt=15.000
% 9.27/9.59
% 9.27/9.59 Low Water (displace): id=12990, wt=13.000
% 9.27/9.59
% 9.27/9.59 Low Water (displace): id=13614, wt=11.000
% 9.27/9.59
% 9.27/9.59 Low Water (keep): wt=15.000, iters=3341
% 9.27/9.59
% 9.27/9.59 Low Water (displace): id=22149, wt=10.000
% 9.27/9.59
% 9.27/9.59 Low Water (keep): wt=14.000, iters=3337
% 9.27/9.59
% 9.27/9.59 Low Water (keep): wt=13.000, iters=5146
% 9.27/9.59
% 9.27/9.59 ============================== PROOF =================================
% 9.27/9.59 % SZS status Unsatisfiable
% 9.27/9.59 % SZS output start Refutation
% 9.27/9.59
% 9.27/9.59 % Proof 1 at 8.15 (+ 0.41) seconds.
% 9.27/9.59 % Length of proof is 41.
% 9.27/9.59 % Level of proof is 12.
% 9.27/9.59 % Maximum clause weight is 39.000.
% 9.27/9.59 % Given clauses 5521.
% 9.27/9.59
% 9.27/9.59 28 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 9.27/9.59 31 subclass(A,universal_class) # label(class_elements_are_sets) # label(axiom). [assumption].
% 9.27/9.59 39 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 9.27/9.59 40 singleton(A) = unordered_pair(A,A). [copy(39),flip(a)].
% 9.27/9.59 41 unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B) # label(ordered_pair) # label(axiom). [assumption].
% 9.27/9.59 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)].
% 9.27/9.59 45 -member(ordered_pair(A,B),cross_product(C,D)) | member(B,D) # label(cartesian_product2) # label(axiom). [assumption].
% 9.27/9.59 46 -member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(C,D)) | member(B,D). [copy(45),rewrite([42(1)])].
% 9.27/9.59 49 -member(A,cross_product(B,C)) | ordered_pair(first(A),second(A)) = A # label(cartesian_product4) # label(axiom). [assumption].
% 9.27/9.59 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)])].
% 9.27/9.59 57 -member(A,intersection(B,C)) | member(A,C) # label(intersection2) # label(axiom). [assumption].
% 9.27/9.59 58 -member(A,B) | -member(A,C) | member(A,intersection(B,C)) # label(intersection3) # label(axiom). [assumption].
% 9.27/9.59 59 -member(A,complement(B)) | -member(A,B) # label(complement1) # label(axiom). [assumption].
% 9.27/9.59 65 intersection(A,cross_product(B,C)) = restrict(A,B,C) # label(restriction1) # label(axiom). [assumption].
% 9.27/9.59 66 restrict(A,B,C) = intersection(A,cross_product(B,C)). [copy(65),flip(a)].
% 9.27/9.59 67 intersection(cross_product(A,B),C) = restrict(C,A,B) # label(restriction2) # label(axiom). [assumption].
% 9.27/9.59 68 intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)). [copy(67),rewrite([66(3)])].
% 9.27/9.59 69 restrict(A,singleton(B),universal_class) != null_class | -member(B,domain_of(A)) # label(domain1) # label(axiom). [assumption].
% 9.27/9.59 70 intersection(A,cross_product(unordered_pair(B,B),universal_class)) != null_class | -member(B,domain_of(A)). [copy(69),rewrite([40(1),66(3)])].
% 9.27/9.59 114 A = null_class | member(regular(A),A) # label(regularity1) # label(axiom). [assumption].
% 9.27/9.59 115 null_class = A | member(regular(A),A). [copy(114),flip(a)].
% 9.27/9.59 168 cross_product(x,null_class) != null_class # label(prove_cross_product_with_null_class1_1) # label(negated_conjecture). [assumption].
% 9.27/9.59 231 -member(A,B) | member(A,intersection(B,B)). [factor(58,a,b)].
% 9.27/9.59 237 -member(A,B) | member(A,universal_class). [resolve(31,a,28,a)].
% 9.27/9.59 283 domain_of(A) = null_class | intersection(A,cross_product(unordered_pair(regular(domain_of(A)),regular(domain_of(A))),universal_class)) != null_class. [resolve(115,b,70,b),flip(a)].
% 9.27/9.59 285 complement(A) = null_class | -member(regular(complement(A)),A). [resolve(115,b,59,a),flip(a)].
% 9.27/9.59 288 intersection(A,B) = null_class | member(regular(intersection(A,B)),B). [resolve(115,b,57,a),flip(a)].
% 9.27/9.59 290 cross_product(A,B) = null_class | unordered_pair(unordered_pair(first(regular(cross_product(A,B))),first(regular(cross_product(A,B)))),unordered_pair(first(regular(cross_product(A,B))),unordered_pair(second(regular(cross_product(A,B))),second(regular(cross_product(A,B)))))) = regular(cross_product(A,B)). [resolve(115,b,50,a),flip(a)].
% 9.27/9.59 390 member(regular(A),universal_class) | null_class = A. [resolve(237,a,115,b)].
% 9.27/9.59 476 null_class = A | member(regular(A),intersection(universal_class,universal_class)). [resolve(390,a,231,a)].
% 9.27/9.59 1298 complement(intersection(universal_class,universal_class)) = null_class. [resolve(476,b,285,b),flip(a),merge(b)].
% 9.27/9.59 1308 -member(A,null_class) | -member(A,intersection(universal_class,universal_class)). [para(1298(a,1),59(a,2))].
% 9.27/9.59 1361 -member(regular(A),null_class) | null_class = A. [resolve(1308,b,476,b)].
% 9.27/9.59 2536 intersection(A,null_class) = null_class. [resolve(288,b,1361,a),flip(b),merge(b)].
% 9.27/9.59 2587 intersection(null_class,cross_product(A,B)) = null_class. [para(2536(a,1),68(a,1)),flip(a)].
% 9.27/9.59 2588 domain_of(null_class) = null_class. [resolve(2587,a,283,b)].
% 9.27/9.59 2595 -member(A,null_class). [para(2588(a,1),70(b,2)),rewrite([2587(5)]),xx(a)].
% 9.27/9.59 2699 cross_product(A,B) = null_class | -member(regular(cross_product(A,B)),cross_product(C,D)) | member(second(regular(cross_product(A,B))),D). [para(290(b,1),46(a,1))].
% 9.27/9.59 31021 cross_product(A,B) = null_class | member(second(regular(cross_product(A,B))),B). [resolve(2699,b,115,b),flip(c),merge(c)].
% 9.27/9.59 31281 cross_product(A,null_class) = null_class. [resolve(31021,b,2595,a)].
% 9.27/9.59 31282 $F. [resolve(31281,a,168,a)].
% 9.27/9.59
% 9.27/9.59 % SZS output end Refutation
% 9.27/9.59 ============================== end of proof ==========================
% 9.27/9.59
% 9.27/9.59 ============================== STATISTICS ============================
% 9.27/9.59
% 9.27/9.59 Given=5521. Generated=771078. Kept=31172. proofs=1.
% 9.27/9.59 Usable=4949. Sos=9790. Demods=210. Limbo=47, Disabled=16531. Hints=0.
% 9.27/9.59 Megabytes=24.94.
% 9.27/9.59 User_CPU=8.15, System_CPU=0.41, Wall_clock=8.
% 9.27/9.59
% 9.27/9.59 ============================== end of statistics =====================
% 9.27/9.59
% 9.27/9.59 ============================== end of search =========================
% 9.27/9.59
% 9.27/9.59 THEOREM PROVED
% 9.27/9.59 % SZS status Unsatisfiable
% 9.27/9.59
% 9.27/9.59 Exiting with 1 proof.
% 9.27/9.59
% 9.27/9.59 Process 3898 exit (max_proofs) Sun Jul 10 04:46:14 2022
% 9.27/9.59 Prover9 interrupted
%------------------------------------------------------------------------------