TSTP Solution File: NUM172-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM172-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : Mon Jul 18 13:25:38 EDT 2022
% Result : Unsatisfiable 10.41s 10.69s
% Output : Refutation 10.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM172-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 01:21:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.01 ============================== Prover9 ===============================
% 0.42/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.01 Process 24068 was started by sandbox on n029.cluster.edu,
% 0.42/1.01 Thu Jul 7 01:21:14 2022
% 0.42/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23912_n029.cluster.edu".
% 0.42/1.01 ============================== end of head ===========================
% 0.42/1.01
% 0.42/1.01 ============================== INPUT =================================
% 0.42/1.01
% 0.42/1.01 % Reading from file /tmp/Prover9_23912_n029.cluster.edu
% 0.42/1.01
% 0.42/1.01 set(prolog_style_variables).
% 0.42/1.01 set(auto2).
% 0.42/1.01 % set(auto2) -> set(auto).
% 0.42/1.01 % set(auto) -> set(auto_inference).
% 0.42/1.01 % set(auto) -> set(auto_setup).
% 0.42/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.01 % set(auto) -> set(auto_limits).
% 0.42/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.01 % set(auto) -> set(auto_denials).
% 0.42/1.01 % set(auto) -> set(auto_process).
% 0.42/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.01 % set(auto2) -> assign(stats, some).
% 0.42/1.01 % set(auto2) -> clear(echo_input).
% 0.42/1.01 % set(auto2) -> set(quiet).
% 0.42/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.01 % set(auto2) -> clear(print_given).
% 0.42/1.01 assign(lrs_ticks,-1).
% 0.42/1.01 assign(sos_limit,10000).
% 0.42/1.01 assign(order,kbo).
% 0.42/1.01 set(lex_order_vars).
% 0.42/1.01 clear(print_given).
% 0.42/1.01
% 0.42/1.01 % formulas(sos). % not echoed (160 formulas)
% 0.42/1.01
% 0.42/1.01 ============================== end of input ==========================
% 0.42/1.01
% 0.42/1.01 % From the command line: assign(max_seconds, 300).
% 0.42/1.01
% 0.42/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.01
% 0.42/1.01 % Formulas that are not ordinary clauses:
% 0.42/1.01
% 0.42/1.01 ============================== end of process non-clausal formulas ===
% 0.42/1.01
% 0.42/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/1.01
% 0.42/1.01 ============================== PREDICATE ELIMINATION =================
% 0.42/1.01 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.42/1.01 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.42/1.01 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.42/1.01 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.42/1.01 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.42/1.01 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.42/1.01 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.42/1.01 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.42/1.01 Derived: subclass(omega,omega). [resolve(5,a,4,a)].
% 0.42/1.01 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.42/1.01 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.42/1.01 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.42/1.01 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.42/1.01 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.42/1.01 11 -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].
% 0.42/1.01 12 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.42/1.01 13 -compatible(A,B,C) | domain_of(domain_of(B)) = domain_of(A) # label(compatible2) # label(axiom). [assumption].
% 0.42/1.02 14 -compatible(A,B,C) | subclass(range_of(A),domain_of(domain_of(C))) # label(compatible3) # label(axiom). [assumption].
% 0.42/1.02 15 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.42/1.02 Derived: -homomorphism(A,B,C) | function(A). [resolve(15,b,12,a)].
% 0.42/1.02 Derived: -homomorphism(A,B,C) | domain_of(domain_of(B)) = domain_of(A). [resolve(15,b,13,a)].
% 0.42/1.02 Derived: -homomorphism(A,B,C) | subclass(range_of(A),domain_of(domain_of(C))). [resolve(15,b,14,a)].
% 0.42/1.02 16 -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].
% 0.42/1.02 Derived: -operation(A) | -operation(B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | homomorphism(C,A,B) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))). [resolve(16,c,11,d)].
% 0.42/1.02 17 -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].
% 0.42/1.02 Derived: -operation(A) | -operation(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) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))). [resolve(17,c,11,d)].
% 0.42/1.02 18 -operation(A) | -operation(B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | homomorphism(C,A,B) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))). [resolve(16,c,11,d)].
% 0.42/1.02 19 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.42/1.02 20 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.42/1.02 21 -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].
% 0.42/1.02 22 -homomorphism(A,B,C) | function(A). [resolve(15,b,12,a)].
% 0.42/1.02 23 -homomorphism(A,B,C) | domain_of(domain_of(B)) = domain_of(A). [resolve(15,b,13,a)].
% 0.42/1.02 24 -homomorphism(A,B,C) | subclass(range_of(A),domain_of(domain_of(C))). [resolve(15,b,14,a)].
% 0.42/1.02 Derived: -operation(A) | -operation(B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(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(18,d,21,a)].
% 0.42/1.02 25 -operation(A) | -operation(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) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))). [resolve(17,c,11,d)].
% 0.42/1.02 Derived: -operation(A) | -operation(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)))) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(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(25,d,21,a)].
% 0.42/1.02 26 -function(A) | -subclass(range_of(A),B) | maps(A,domain_of(A),B) # label(maps4) # label(axiom). [assumption].
% 0.42/1.02 27 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.42/1.02 28 -maps(A,B,C) | domain_of(A) = B # label(maps2) # label(axiom). [assumption].
% 0.42/1.02 29 -maps(A,B,C) | subclass(range_of(A),C) # label(maps3) # label(axiom). [assumption].
% 0.74/1.05 Derived: -function(A) | -subclass(range_of(A),B) | domain_of(A) = domain_of(A). [resolve(26,c,28,a)].
% 0.74/1.05 30 -subclass(restrict(A,B,B),complement(identity_relation)) | irreflexive(A,B) # label(irreflexive2) # label(axiom). [assumption].
% 0.74/1.05 31 -irreflexive(A,B) | subclass(restrict(A,B,B),complement(identity_relation)) # label(irreflexive1) # label(axiom). [assumption].
% 0.74/1.05 32 -subclass(cross_product(A,A),union(identity_relation,symmetrization_of(B))) | connected(B,A) # label(connected2) # label(axiom). [assumption].
% 0.74/1.05 33 -connected(A,B) | subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))) # label(connected1) # label(axiom). [assumption].
% 0.74/1.05 34 -well_ordering(A,B) | connected(A,B) # label(well_ordering1) # label(axiom). [assumption].
% 0.74/1.05 Derived: -well_ordering(A,B) | subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))). [resolve(34,b,33,a)].
% 0.74/1.05 35 -connected(A,B) | not_well_ordering(A,B) != null_class | well_ordering(A,B) # label(well_ordering6) # label(axiom). [assumption].
% 0.74/1.05 Derived: not_well_ordering(A,B) != null_class | well_ordering(A,B) | -subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))). [resolve(35,a,32,b)].
% 0.74/1.05 36 -connected(A,B) | subclass(not_well_ordering(A,B),B) | well_ordering(A,B) # label(well_ordering7) # label(axiom). [assumption].
% 0.74/1.05 Derived: subclass(not_well_ordering(A,B),B) | well_ordering(A,B) | -subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))). [resolve(36,a,32,b)].
% 0.74/1.05 37 -member(A,not_well_ordering(B,C)) | segment(B,not_well_ordering(B,C),A) != null_class | -connected(B,C) | well_ordering(B,C) # label(well_ordering8) # label(axiom). [assumption].
% 0.74/1.05 Derived: -member(A,not_well_ordering(B,C)) | segment(B,not_well_ordering(B,C),A) != null_class | well_ordering(B,C) | -subclass(cross_product(C,C),union(identity_relation,symmetrization_of(B))). [resolve(37,c,32,b)].
% 0.74/1.05 38 -subclass(compose(restrict(A,B,B),restrict(A,B,B)),restrict(A,B,B)) | transitive(A,B) # label(transitive2) # label(axiom). [assumption].
% 0.74/1.05 39 -transitive(A,B) | subclass(compose(restrict(A,B,B),restrict(A,B,B)),restrict(A,B,B)) # label(transitive1) # label(axiom). [assumption].
% 0.74/1.05 40 restrict(intersection(A,inverse(A)),B,B) != null_class | asymmetric(A,B) # label(asymmetric2) # label(axiom). [assumption].
% 0.74/1.05 41 -asymmetric(A,B) | restrict(intersection(A,inverse(A)),B,B) = null_class # label(asymmetric1) # label(axiom). [assumption].
% 0.74/1.05 42 -subclass(A,B) | -subclass(domain_of(restrict(C,B,A)),A) | section(C,A,B) # label(section3) # label(axiom). [assumption].
% 0.74/1.05 43 -section(A,B,C) | subclass(B,C) # label(section1) # label(axiom). [assumption].
% 0.74/1.05 44 -section(A,B,C) | subclass(domain_of(restrict(A,C,B)),B) # label(section2) # label(axiom). [assumption].
% 0.74/1.05
% 0.74/1.05 ============================== end predicate elimination =============
% 0.74/1.05
% 0.74/1.05 Auto_denials: (non-Horn, no changes).
% 0.74/1.05
% 0.74/1.05 Term ordering decisions:
% 0.74/1.05 Function symbol KB weights: universal_class=1. null_class=1. element_relation=1. identity_relation=1. omega=1. ordinal_numbers=1. successor_relation=1. union_of_range_map=1. application_function=1. composition_function=1. domain_relation=1. rest_relation=1. subset_relation=1. x=1. choice=1. kind_1_ordinals=1. add_relation=1. limit_ordinals=1. singleton_relation=1. ordered_pair=1. cross_product=1. apply=1. intersection=1. compose=1. image=1. union=1. unordered_pair=1. not_subclass_element=1. not_well_ordering=1. least=1. ordinal_add=1. ordinal_multiply=1. symmetric_difference=1. domain_of=1. complement=1. singleton=1. inverse=1. range_of=1. rest_of=1. sum_class=1. recursion_equation_functions=1. symmetrization_of=1. flip=1. successor=1. compose_class=1. first=1. rotate=1. second=1. diagonalise=1. integer_of=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. segment=1. domain=1. recursion=1. range=1.
% 0.74/1.05
% 0.74/1.05 ============================== end of process initial clauses ========
% 0.74/1.05
% 0.74/1.05 ============================== CLAUSES FOR SEARCH ====================
% 10.41/10.69
% 10.41/10.69 ============================== end of clauses for search =============
% 10.41/10.69
% 10.41/10.69 ============================== SEARCH ================================
% 10.41/10.69
% 10.41/10.69 % Starting search at 0.06 seconds.
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=72.000, iters=4448
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=55.000, iters=4396
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=34.000, iters=4243
% 10.41/10.69
% 10.41/10.69 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 135 (0.00 of 0.66 sec).
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=29.000, iters=3442
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=28.000, iters=3418
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=26.000, iters=3370
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=25.000, iters=3338
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=24.000, iters=3341
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=23.000, iters=3501
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=22.000, iters=3339
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=21.000, iters=3371
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=20.000, iters=3361
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=19.000, iters=3341
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=2735, wt=175.000
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=2699, wt=171.000
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=5499, wt=157.000
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=2696, wt=155.000
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=2603, wt=152.000
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=5483, wt=150.000
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=967, wt=149.000
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=10937, wt=13.000
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=11012, wt=11.000
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=18.000, iters=3360
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=13364, wt=10.000
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=17.000, iters=3336
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=16.000, iters=3349
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=15.000, iters=3355
% 10.41/10.69
% 10.41/10.69 Low Water (displace): id=20004, wt=9.000
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=14.000, iters=3333
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=13.000, iters=5475
% 10.41/10.69
% 10.41/10.69 Low Water (keep): wt=12.000, iters=3333
% 10.41/10.69
% 10.41/10.69 ============================== PROOF =================================
% 10.41/10.69 % SZS status Unsatisfiable
% 10.41/10.69 % SZS output start Refutation
% 10.41/10.69
% 10.41/10.69 % Proof 1 at 9.27 (+ 0.43) seconds.
% 10.41/10.69 % Length of proof is 55.
% 10.41/10.69 % Level of proof is 12.
% 10.41/10.69 % Maximum clause weight is 17.000.
% 10.41/10.69 % Given clauses 5548.
% 10.41/10.69
% 10.41/10.69 45 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 10.41/10.69 48 subclass(A,universal_class) # label(class_elements_are_sets) # label(axiom). [assumption].
% 10.41/10.69 52 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_member) # label(axiom). [assumption].
% 10.41/10.69 53 -member(A,universal_class) | member(A,unordered_pair(A,B)) # label(unordered_pair2) # label(axiom). [assumption].
% 10.41/10.69 54 -member(A,universal_class) | member(A,unordered_pair(B,A)) # label(unordered_pair3) # label(axiom). [assumption].
% 10.41/10.69 56 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 10.41/10.69 57 singleton(A) = unordered_pair(A,A). [copy(56),flip(a)].
% 10.41/10.69 74 -member(A,intersection(B,C)) | member(A,C) # label(intersection2) # label(axiom). [assumption].
% 10.41/10.69 75 -member(A,B) | -member(A,C) | member(A,intersection(B,C)) # label(intersection3) # label(axiom). [assumption].
% 10.41/10.69 76 -member(A,complement(B)) | -member(A,B) # label(complement1) # label(axiom). [assumption].
% 10.41/10.69 77 -member(A,universal_class) | member(A,complement(B)) | member(A,B) # label(complement2) # label(axiom). [assumption].
% 10.41/10.69 78 complement(intersection(complement(A),complement(B))) = union(A,B) # label(union) # label(axiom). [assumption].
% 10.41/10.69 79 union(A,B) = complement(intersection(complement(A),complement(B))). [copy(78),flip(a)].
% 10.41/10.69 82 intersection(A,cross_product(B,C)) = restrict(A,B,C) # label(restriction1) # label(axiom). [assumption].
% 10.41/10.69 83 restrict(A,B,C) = intersection(A,cross_product(B,C)). [copy(82),flip(a)].
% 10.41/10.69 84 intersection(cross_product(A,B),C) = restrict(C,A,B) # label(restriction2) # label(axiom). [assumption].
% 10.41/10.69 85 intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)). [copy(84),rewrite([83(3)])].
% 10.41/10.69 86 restrict(A,singleton(B),universal_class) != null_class | -member(B,domain_of(A)) # label(domain1) # label(axiom). [assumption].
% 10.41/10.69 87 intersection(A,cross_product(unordered_pair(B,B),universal_class)) != null_class | -member(B,domain_of(A)). [copy(86),rewrite([57(1),83(3)])].
% 10.41/10.69 110 union(A,singleton(A)) = successor(A) # label(successor) # label(axiom). [assumption].
% 10.41/10.69 111 successor(A) = complement(intersection(complement(A),complement(unordered_pair(A,A)))). [copy(110),rewrite([57(1),79(2)]),flip(a)].
% 10.41/10.69 138 A = null_class | member(regular(A),A) # label(regularity1) # label(axiom). [assumption].
% 10.41/10.69 139 null_class = A | member(regular(A),A). [copy(138),flip(a)].
% 10.41/10.69 140 A = null_class | intersection(A,regular(A)) = null_class # label(regularity2) # label(axiom). [assumption].
% 10.41/10.69 141 null_class = A | intersection(A,regular(A)) = null_class. [copy(140),flip(a)].
% 10.41/10.69 239 member(x,universal_class) # label(prove_successor_is_different_1) # label(negated_conjecture). [assumption].
% 10.41/10.69 240 successor(x) = x # label(prove_successor_is_different_2) # label(negated_conjecture). [assumption].
% 10.41/10.69 241 complement(intersection(complement(x),complement(unordered_pair(x,x)))) = x. [copy(240),rewrite([111(2)])].
% 10.41/10.69 263 -member(A,B) | member(A,intersection(B,B)). [factor(75,a,b)].
% 10.41/10.69 270 -member(A,B) | member(A,universal_class). [resolve(48,a,45,a)].
% 10.41/10.69 320 domain_of(A) = null_class | intersection(A,cross_product(unordered_pair(regular(domain_of(A)),regular(domain_of(A))),universal_class)) != null_class. [resolve(139,b,87,b),flip(a)].
% 10.41/10.69 322 complement(A) = null_class | -member(regular(complement(A)),A). [resolve(139,b,76,a),flip(a)].
% 10.41/10.69 325 intersection(A,B) = null_class | member(regular(intersection(A,B)),B). [resolve(139,b,74,a),flip(a)].
% 10.41/10.69 332 unordered_pair(A,B) = null_class | regular(unordered_pair(A,B)) = A | regular(unordered_pair(A,B)) = B. [resolve(139,b,52,a),flip(a)].
% 10.41/10.69 333 unordered_pair(A,A) = null_class | regular(unordered_pair(A,A)) = A. [factor(332,b,c)].
% 10.41/10.69 402 member(x,complement(A)) | member(x,A). [resolve(239,a,77,a)].
% 10.41/10.69 407 member(x,unordered_pair(A,x)). [resolve(239,a,54,a)].
% 10.41/10.69 408 member(x,unordered_pair(x,A)). [resolve(239,a,53,a)].
% 10.41/10.69 462 member(regular(A),universal_class) | null_class = A. [resolve(270,a,139,b)].
% 10.41/10.69 492 -member(x,A) | member(x,intersection(unordered_pair(x,B),A)). [resolve(408,a,75,a)].
% 10.41/10.69 593 member(x,x) | member(x,intersection(complement(x),complement(unordered_pair(x,x)))). [para(241(a,1),402(a,2))].
% 10.41/10.69 631 null_class = A | member(regular(A),intersection(universal_class,universal_class)). [resolve(462,a,263,a)].
% 10.41/10.69 2052 complement(intersection(universal_class,universal_class)) = null_class. [resolve(631,b,322,b),flip(a),merge(b)].
% 10.41/10.69 2064 -member(A,null_class) | -member(A,intersection(universal_class,universal_class)). [para(2052(a,1),76(a,2))].
% 10.41/10.69 2082 -member(regular(A),null_class) | null_class = A. [resolve(2064,b,631,b)].
% 10.41/10.69 2526 intersection(A,null_class) = null_class. [resolve(325,b,2082,a),flip(b),merge(b)].
% 10.41/10.69 2592 intersection(null_class,cross_product(A,B)) = null_class. [para(2526(a,1),85(a,1)),flip(a)].
% 10.41/10.69 2593 domain_of(null_class) = null_class. [resolve(2592,a,320,b)].
% 10.41/10.69 2600 -member(A,null_class). [para(2593(a,1),87(b,2)),rewrite([2592(5)]),xx(a)].
% 10.41/10.69 3316 unordered_pair(A,A) = null_class | intersection(unordered_pair(A,A),A) = null_class. [para(333(b,1),141(b,1,2)),flip(b),merge(b)].
% 10.41/10.69 15505 member(x,x) | member(x,complement(unordered_pair(x,x))). [resolve(593,b,74,a)].
% 10.41/10.69 15517 member(x,x). [resolve(15505,b,76,a),unit_del(b,407)].
% 10.41/10.69 15531 member(x,intersection(unordered_pair(x,A),x)). [resolve(15517,a,492,a)].
% 10.41/10.69 38334 unordered_pair(x,x) = null_class. [para(3316(b,1),15531(a,2)),unit_del(b,2600)].
% 10.41/10.69 38669 $F. [para(38334(a,1),407(a,2)),unit_del(a,2600)].
% 10.41/10.69
% 10.41/10.69 % SZS output end Refutation
% 10.41/10.69 ============================== end of proof ==========================
% 10.41/10.69
% 10.41/10.69 ============================== STATISTICS ============================
% 10.41/10.69
% 10.41/10.69 Given=5548. Generated=768954. Kept=38539. proofs=1.
% 10.41/10.69 Usable=5238. Sos=8496. Demods=190. Limbo=3, Disabled=24978. Hints=0.
% 10.41/10.69 Megabytes=31.95.
% 10.41/10.69 User_CPU=9.27, System_CPU=0.43, Wall_clock=10.
% 10.41/10.69
% 10.41/10.69 ============================== end of statistics =====================
% 10.41/10.69
% 10.41/10.69 ============================== end of search =========================
% 10.41/10.69
% 10.41/10.69 THEOREM PROVED
% 10.41/10.69 % SZS status Unsatisfiable
% 10.41/10.69
% 10.41/10.69 Exiting with 1 proof.
% 10.41/10.69
% 10.41/10.69 Process 24068 exit (max_proofs) Thu Jul 7 01:21:24 2022
% 10.41/10.69 Prover9 interrupted
%------------------------------------------------------------------------------