TSTP Solution File: SET120-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET120-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 04:27:32 EDT 2022
% Result : Unsatisfiable 31.68s 31.98s
% Output : Refutation 31.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET120-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 07:49:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.06 ============================== Prover9 ===============================
% 0.46/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.06 Process 2028 was started by sandbox2 on n007.cluster.edu,
% 0.46/1.06 Mon Jul 11 07:49:33 2022
% 0.46/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1873_n007.cluster.edu".
% 0.46/1.06 ============================== end of head ===========================
% 0.46/1.06
% 0.46/1.06 ============================== INPUT =================================
% 0.46/1.06
% 0.46/1.06 % Reading from file /tmp/Prover9_1873_n007.cluster.edu
% 0.46/1.06
% 0.46/1.06 set(prolog_style_variables).
% 0.46/1.06 set(auto2).
% 0.46/1.06 % set(auto2) -> set(auto).
% 0.46/1.06 % set(auto) -> set(auto_inference).
% 0.46/1.06 % set(auto) -> set(auto_setup).
% 0.46/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.06 % set(auto) -> set(auto_limits).
% 0.46/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.06 % set(auto) -> set(auto_denials).
% 0.46/1.06 % set(auto) -> set(auto_process).
% 0.46/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.06 % set(auto2) -> assign(stats, some).
% 0.46/1.06 % set(auto2) -> clear(echo_input).
% 0.46/1.06 % set(auto2) -> set(quiet).
% 0.46/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.06 % set(auto2) -> clear(print_given).
% 0.46/1.06 assign(lrs_ticks,-1).
% 0.46/1.06 assign(sos_limit,10000).
% 0.46/1.06 assign(order,kbo).
% 0.46/1.06 set(lex_order_vars).
% 0.46/1.06 clear(print_given).
% 0.46/1.06
% 0.46/1.06 % formulas(sos). % not echoed (167 formulas)
% 0.46/1.06
% 0.46/1.06 ============================== end of input ==========================
% 0.46/1.06
% 0.46/1.06 % From the command line: assign(max_seconds, 300).
% 0.46/1.06
% 0.46/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.06
% 0.46/1.06 % Formulas that are not ordinary clauses:
% 0.46/1.06
% 0.46/1.06 ============================== end of process non-clausal formulas ===
% 0.46/1.06
% 0.46/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.06
% 0.46/1.06 ============================== PREDICATE ELIMINATION =================
% 0.46/1.06 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.46/1.06 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.46/1.06 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.46/1.06 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.46/1.06 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.46/1.06 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.46/1.06 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.46/1.06 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.46/1.06 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.46/1.06 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.46/1.06 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.46/1.06 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.46/1.06 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.46/1.06 11 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.46/1.06 12 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.46/1.06 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.46/1.06 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.46/1.06 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)].
% 0.46/1.06 15 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.46/1.06 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(15,a,12,a)].
% 0.46/1.06 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(15,a,13,a)].
% 0.46/1.06 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(15,a,14,a)].
% 0.46/1.06 16 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.46/1.06 Derived: -operation(A) | subclass(A,cross_product(universal_class,universal_class)). [resolve(16,b,12,a)].
% 0.46/1.06 Derived: -operation(A) | subclass(compose(A,inverse(A)),identity_relation). [resolve(16,b,13,a)].
% 0.46/1.06 Derived: -operation(A) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(16,b,14,a)].
% 0.46/1.06 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].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 18 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.46/1.06 Derived: -compatible(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(18,b,12,a)].
% 0.46/1.06 Derived: -compatible(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(18,b,13,a)].
% 0.46/1.06 Derived: -compatible(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(18,b,14,a)].
% 0.46/1.06 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)].
% 0.46/1.06 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].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 20 -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].
% 0.46/1.06 21 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.46/1.06 22 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.46/1.06 23 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.46/1.06 24 -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].
% 0.46/1.06 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(20,e,24,a)].
% 19.23/19.52 25 -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].
% 19.23/19.52 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(25,e,24,a)].
% 19.23/19.52
% 19.23/19.52 ============================== end predicate elimination =============
% 19.23/19.52
% 19.23/19.52 Auto_denials: (non-Horn, no changes).
% 19.23/19.52
% 19.23/19.52 Term ordering decisions:
% 19.23/19.52 Function symbol KB weights: universal_class=1. null_class=1. choice=1. element_relation=1. identity_relation=1. omega=1. successor_relation=1. subset_relation=1. x=1. y=1. ordered_pair=1. cross_product=1. unordered_pair=1. not_subclass_element=1. intersection=1. apply=1. image=1. compose=1. union=1. symmetric_difference=1. domain_of=1. singleton=1. complement=1. first=1. second=1. member_of=1. inverse=1. range_of=1. flip=1. rotate=1. successor=1. sum_class=1. diagonalise=1. member_of1=1. power_class=1. regular=1. cantor=1. restrict=1. not_homomorphism1=1. not_homomorphism2=1. domain=1. range=1.
% 19.23/19.52
% 19.23/19.52 ============================== end of process initial clauses ========
% 19.23/19.52
% 19.23/19.52 ============================== CLAUSES FOR SEARCH ====================
% 19.23/19.52
% 19.23/19.52 ============================== end of clauses for search =============
% 19.23/19.52
% 19.23/19.52 ============================== SEARCH ================================
% 19.23/19.52
% 19.23/19.52 % Starting search at 0.04 seconds.
% 19.23/19.52
% 19.23/19.52 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 64 (0.00 of 0.46 sec).
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=34.000, iters=3470
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=31.000, iters=3369
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=30.000, iters=3341
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=29.000, iters=3352
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=28.000, iters=3343
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=27.000, iters=3364
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=24.000, iters=3504
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=22.000, iters=3408
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=21.000, iters=3453
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=20.000, iters=3442
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=19.000, iters=3400
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=18.000, iters=3363
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=17.000, iters=3337
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=16.000, iters=3372
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=15.000, iters=3336
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=14.000, iters=3340
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=13.000, iters=3339
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=12.000, iters=3344
% 19.23/19.52
% 19.23/19.52 Low Water (keep): wt=11.000, iters=3334
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=3529, wt=188.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=2519, wt=126.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=2520, wt=117.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=3531, wt=112.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=4149, wt=90.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=3646, wt=86.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=3640, wt=84.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=3642, wt=83.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=4184, wt=82.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=2443, wt=79.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=7932, wt=70.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=7228, wt=69.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=14489, wt=65.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=14544, wt=63.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=15916, wt=62.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=15586, wt=61.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=16006, wt=60.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=15518, wt=59.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=16013, wt=58.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=16298, wt=57.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=16312, wt=56.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=16300, wt=55.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=16330, wt=54.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=20457, wt=53.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=21267, wt=52.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=21496, wt=51.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=21982, wt=50.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=22046, wt=49.000
% 19.23/19.52
% 19.23/19.52 Low Water (displace): id=22650, wt=48.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=23305, wt=47.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24101, wt=46.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24969, wt=45.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24963, wt=44.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24854, wt=43.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24961, wt=42.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24804, wt=41.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24805, wt=40.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24745, wt=39.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24727, wt=38.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24704, wt=37.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=24693, wt=36.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=27895, wt=35.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=27207, wt=34.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=26550, wt=33.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=28149, wt=32.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=28163, wt=31.000
% 31.68/31.98
% 31.68/31.98 Low Water (displace): id=28162, wt=30.000
% 31.68/31.98
% 31.68/31.98 ============================== PROOF =================================
% 31.68/31.98 % SZS status Unsatisfiable
% 31.68/31.98 % SZS output start Refutation
% 31.68/31.98
% 31.68/31.98 % Proof 1 at 30.28 (+ 0.67) seconds.
% 31.68/31.98 % Length of proof is 47.
% 31.68/31.98 % Level of proof is 10.
% 31.68/31.98 % Maximum clause weight is 17.000.
% 31.72/31.98 % Given clauses 11286.
% 31.72/31.98
% 31.72/31.98 26 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 31.72/31.98 29 subclass(A,universal_class) # label(class_elements_are_sets) # label(axiom). [assumption].
% 31.72/31.98 33 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_member) # label(axiom). [assumption].
% 31.72/31.98 37 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 31.72/31.98 38 unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B) # label(ordered_pair) # label(axiom). [assumption].
% 31.72/31.98 48 -member(A,B) | -member(A,C) | member(A,intersection(B,C)) # label(intersection3) # label(axiom). [assumption].
% 31.72/31.98 98 A = null_class | member(regular(A),A) # label(regularity1) # label(axiom). [assumption].
% 31.72/31.98 99 null_class = A | member(regular(A),A). [copy(98),flip(a)].
% 31.72/31.98 100 A = null_class | intersection(A,regular(A)) = null_class # label(regularity2) # label(axiom). [assumption].
% 31.72/31.98 101 null_class = A | intersection(A,regular(A)) = null_class. [copy(100),flip(a)].
% 31.72/31.98 122 -member(ordered_pair(A,B),cross_product(C,D)) | member(A,universal_class) # label(corollary_1_to_cartesian_product) # label(axiom). [assumption].
% 31.72/31.98 131 -member(A,null_class) # label(existence_of_null_class) # label(axiom). [assumption].
% 31.72/31.98 137 member(null_class,universal_class) # label(null_class_is_a_set) # label(axiom). [assumption].
% 31.72/31.98 138 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_of_unordered_pair) # label(axiom). [assumption].
% 31.72/31.98 141 member(A,universal_class) | unordered_pair(B,A) = singleton(B) # label(unordered_pair_equals_singleton1) # label(axiom). [assumption].
% 31.72/31.98 142 member(A,universal_class) | unordered_pair(A,B) = singleton(B). [copy(141),rewrite([138(3)])].
% 31.72/31.98 154 -member(A,universal_class) | singleton(A) != null_class # label(corollary_to_set_in_its_singleton) # label(axiom). [assumption].
% 31.72/31.98 157 member(A,universal_class) | singleton(A) = null_class # label(singleton_is_null_class) # label(axiom). [assumption].
% 31.72/31.98 163 -member(A,universal_class) | singleton(member_of(singleton(A))) = singleton(A) # label(member_exists2) # label(axiom). [assumption].
% 31.72/31.98 164 member(member_of(A),universal_class) | member_of(A) = A # label(member_exists3) # label(axiom). [assumption].
% 31.72/31.98 165 singleton(member_of(A)) = A | member_of(A) = A # label(member_exists4) # label(axiom). [assumption].
% 31.72/31.98 195 member(ordered_pair(first(A),second(A)),cross_product(universal_class,universal_class)) | second(A) = A # label(existence_of_1st_and_2nd_3) # label(axiom). [assumption].
% 31.72/31.98 197 ordered_pair(first(A),second(A)) = A | second(A) = A # label(existence_of_1st_and_2nd_5) # label(axiom). [assumption].
% 31.72/31.98 202 -member(x,universal_class) # label(prove_corollary_2_to_OP_determines_components1_1) # label(negated_conjecture). [assumption].
% 31.72/31.98 203 second(ordered_pair(x,y)) != ordered_pair(x,y) # label(prove_corollary_2_to_OP_determines_components1_2) # label(negated_conjecture). [assumption].
% 31.72/31.98 252 -member(A,B) | member(A,universal_class). [resolve(29,a,26,a)].
% 31.72/31.98 301 null_class = A | -member(regular(A),B) | member(regular(A),intersection(A,B)). [resolve(99,b,48,a)].
% 31.72/31.98 308 unordered_pair(A,B) = null_class | regular(unordered_pair(A,B)) = A | regular(unordered_pair(A,B)) = B. [resolve(99,b,33,a),flip(a)].
% 31.72/31.98 309 singleton(A) = null_class | regular(singleton(A)) = A. [factor(308,b,c),rewrite([37(1),37(4)])].
% 31.72/31.98 474 singleton(null_class) != null_class. [resolve(154,a,137,a)].
% 31.72/31.98 540 singleton(member_of(singleton(A))) = singleton(A) | unordered_pair(A,B) = singleton(B). [resolve(163,a,142,a)].
% 31.72/31.98 551 member_of(A) = A | singleton(member_of(A)) != null_class. [resolve(164,a,154,a)].
% 31.72/31.98 874 second(A) = A | member(A,cross_product(universal_class,universal_class)). [para(197(a,1),195(a,1)),merge(c)].
% 31.72/31.98 882 singleton(x) = null_class. [resolve(202,a,157,a)].
% 31.72/31.98 1055 unordered_pair(null_class,unordered_pair(x,singleton(A))) = ordered_pair(x,A). [para(882(a,1),38(a,1,1))].
% 31.72/31.98 1083 member(regular(A),universal_class) | null_class = A. [resolve(252,a,99,b)].
% 31.72/31.98 4007 null_class = A | member(regular(A),intersection(A,universal_class)). [resolve(301,b,1083,a),merge(c)].
% 31.72/31.98 4906 singleton(A) = null_class | intersection(singleton(A),A) = null_class. [para(309(b,1),101(b,1,2)),flip(b),merge(b)].
% 31.72/31.98 6734 member_of(null_class) = null_class. [resolve(551,b,165,a),merge(b)].
% 31.72/31.98 12294 unordered_pair(null_class,singleton(singleton(A))) = ordered_pair(x,A). [para(540(b,1),1055(a,1,2)),rewrite([882(2),6734(2),882(4)]),unit_del(a,474)].
% 31.72/31.98 14794 singleton(universal_class) = null_class. [para(4906(b,1),4007(b,2)),flip(b),merge(b),unit_del(b,131)].
% 31.72/31.98 14824 unordered_pair(null_class,unordered_pair(universal_class,singleton(A))) = ordered_pair(universal_class,A). [para(14794(a,1),38(a,1,1))].
% 31.72/31.98 31236 ordered_pair(x,A) = ordered_pair(universal_class,A). [para(540(b,1),14824(a,1,2)),rewrite([14794(2),6734(2),14794(4),12294(8)]),unit_del(a,474)].
% 31.72/31.98 31866 second(ordered_pair(universal_class,y)) != ordered_pair(universal_class,y). [back_rewrite(203),rewrite([31236(3),31236(7)])].
% 31.72/31.98 31876 -member(ordered_pair(universal_class,A),cross_product(B,C)). [para(31236(a,1),122(a,1)),unit_del(b,202)].
% 31.72/31.98 31900 second(ordered_pair(universal_class,A)) = ordered_pair(universal_class,A). [resolve(31876,a,874,b)].
% 31.72/31.98 31901 $F. [resolve(31900,a,31866,a)].
% 31.72/31.98
% 31.72/31.98 % SZS output end Refutation
% 31.72/31.98 ============================== end of proof ==========================
% 31.72/31.98
% 31.72/31.98 ============================== STATISTICS ============================
% 31.72/31.98
% 31.72/31.98 Given=11286. Generated=1194854. Kept=31814. proofs=1.
% 31.72/31.98 Usable=9108. Sos=9476. Demods=342. Limbo=0, Disabled=13418. Hints=0.
% 31.72/31.98 Megabytes=42.28.
% 31.72/31.98 User_CPU=30.28, System_CPU=0.67, Wall_clock=31.
% 31.72/31.98
% 31.72/31.98 ============================== end of statistics =====================
% 31.72/31.98
% 31.72/31.98 ============================== end of search =========================
% 31.72/31.98
% 31.72/31.98 THEOREM PROVED
% 31.72/31.98 % SZS status Unsatisfiable
% 31.72/31.98
% 31.72/31.98 Exiting with 1 proof.
% 31.72/31.98
% 31.72/31.98 Process 2028 exit (max_proofs) Mon Jul 11 07:50:04 2022
% 31.72/31.98 Prover9 interrupted
%------------------------------------------------------------------------------