TSTP Solution File: SET025-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET025-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 04:26:00 EDT 2022
% Result : Unsatisfiable 0.76s 1.05s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET025-4 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.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 : Mon Jul 11 00:21:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.76/1.03 ============================== Prover9 ===============================
% 0.76/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.03 Process 17878 was started by sandbox2 on n024.cluster.edu,
% 0.76/1.03 Mon Jul 11 00:21:59 2022
% 0.76/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17501_n024.cluster.edu".
% 0.76/1.03 ============================== end of head ===========================
% 0.76/1.03
% 0.76/1.03 ============================== INPUT =================================
% 0.76/1.03
% 0.76/1.03 % Reading from file /tmp/Prover9_17501_n024.cluster.edu
% 0.76/1.03
% 0.76/1.03 set(prolog_style_variables).
% 0.76/1.03 set(auto2).
% 0.76/1.03 % set(auto2) -> set(auto).
% 0.76/1.03 % set(auto) -> set(auto_inference).
% 0.76/1.03 % set(auto) -> set(auto_setup).
% 0.76/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.03 % set(auto) -> set(auto_limits).
% 0.76/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.03 % set(auto) -> set(auto_denials).
% 0.76/1.03 % set(auto) -> set(auto_process).
% 0.76/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.03 % set(auto2) -> assign(stats, some).
% 0.76/1.03 % set(auto2) -> clear(echo_input).
% 0.76/1.03 % set(auto2) -> set(quiet).
% 0.76/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.03 % set(auto2) -> clear(print_given).
% 0.76/1.03 assign(lrs_ticks,-1).
% 0.76/1.03 assign(sos_limit,10000).
% 0.76/1.03 assign(order,kbo).
% 0.76/1.03 set(lex_order_vars).
% 0.76/1.03 clear(print_given).
% 0.76/1.03
% 0.76/1.03 % formulas(sos). % not echoed (142 formulas)
% 0.76/1.03
% 0.76/1.03 ============================== end of input ==========================
% 0.76/1.03
% 0.76/1.03 % From the command line: assign(max_seconds, 300).
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.03
% 0.76/1.03 % Formulas that are not ordinary clauses:
% 0.76/1.03
% 0.76/1.03 ============================== end of process non-clausal formulas ===
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.03
% 0.76/1.03 ============================== PREDICATE ELIMINATION =================
% 0.76/1.03 1 proper_subset(A,B) | -subset(A,B) | A = B # label(proper_subset3) # label(axiom). [assumption].
% 0.76/1.03 2 -proper_subset(A,B) | subset(A,B) # label(proper_subset1) # label(axiom). [assumption].
% 0.76/1.03 3 -proper_subset(A,B) | A != B # label(proper_subset2) # label(axiom). [assumption].
% 0.76/1.03 4 relation(A) | member(f18(A),A) # label(relation2) # label(axiom). [assumption].
% 0.76/1.03 5 -relation(A) | -member(B,A) | ordered_pair_predicate(B) # label(relation1) # label(axiom). [assumption].
% 0.76/1.03 Derived: member(f18(A),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(4,a,5,a)].
% 0.76/1.03 6 relation(A) | -ordered_pair_predicate(f18(A)) # label(relation3) # label(axiom). [assumption].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(6,a,5,a)].
% 0.76/1.03 7 -function(A) | relation(A) # label(function1) # label(axiom). [assumption].
% 0.76/1.03 Derived: -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.76/1.03 8 function(A) | -relation(A) | -single_valued_set(A) # label(function3) # label(axiom). [assumption].
% 0.76/1.03 Derived: function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.76/1.03 Derived: function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.76/1.03 9 single_valued_set(A) | little_set(f19(A)) # label(single_valued_set2) # label(axiom). [assumption].
% 0.76/1.03 10 -single_valued_set(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D # label(single_valued_set1) # label(axiom). [assumption].
% 0.76/1.03 Derived: little_set(f19(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(9,a,10,a)].
% 0.76/1.03 11 single_valued_set(A) | little_set(f20(A)) # label(single_valued_set3) # label(axiom). [assumption].
% 0.76/1.03 Derived: little_set(f20(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(11,a,10,a)].
% 0.76/1.03 12 single_valued_set(A) | little_set(f21(A)) # label(single_valued_set4) # label(axiom). [assumption].
% 0.76/1.03 Derived: little_set(f21(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(12,a,10,a)].
% 0.76/1.03 13 single_valued_set(A) | member(ordered_pair(f19(A),f20(A)),A) # label(single_valued_set5) # label(axiom). [assumption].
% 0.76/1.03 Derived: member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(13,a,10,a)].
% 0.76/1.03 14 single_valued_set(A) | member(ordered_pair(f19(A),f21(A)),A) # label(single_valued_set6) # label(axiom). [assumption].
% 0.76/1.03 Derived: member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(14,a,10,a)].
% 0.76/1.03 15 single_valued_set(A) | f20(A) != f21(A) # label(single_valued_set7) # label(axiom). [assumption].
% 0.76/1.03 Derived: f20(A) != f21(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(15,a,10,a)].
% 0.76/1.03 16 -function(A) | single_valued_set(A) # label(function2) # label(axiom). [assumption].
% 0.76/1.03 Derived: -function(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(16,b,10,a)].
% 0.76/1.03 17 function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.76/1.03 Derived: function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.76/1.03 Derived: function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.76/1.03 Derived: function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.76/1.03 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.76/1.03 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.76/1.03 Derived: function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.76/1.03 18 function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.76/1.03 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.76/1.03 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.76/1.03 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.76/1.03 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.76/1.03 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.76/1.03 Derived: function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.76/1.03 19 disjoint(A,B) | member(f23(A,B),A) # label(disjoint2) # label(axiom). [assumption].
% 0.76/1.03 20 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint1) # label(axiom). [assumption].
% 0.76/1.03 Derived: member(f23(A,B),A) | -member(C,A) | -member(C,B). [resolve(19,a,20,a)].
% 0.76/1.03 21 disjoint(A,B) | member(f23(A,B),B) # label(disjoint3) # label(axiom). [assumption].
% 0.76/1.03 Derived: member(f23(A,B),B) | -member(C,A) | -member(C,B). [resolve(21,a,20,a)].
% 0.76/1.03 22 A = empty_set | disjoint(f24(A),A) # label(regularity2) # label(axiom). [assumption].
% 0.76/1.03 Derived: A = empty_set | -member(B,f24(A)) | -member(B,A). [resolve(22,b,20,a)].
% 0.76/1.03 23 one_to_one_function(A) | -function(A) | -function(converse(A)) # label(one_to_one_function3) # label(axiom). [assumption].
% 0.76/1.03 24 -one_to_one_function(A) | function(A) # label(one_to_one_function1) # label(axiom). [assumption].
% 0.76/1.03 25 -one_to_one_function(A) | function(converse(A)) # label(one_to_one_function2) # label(axiom). [assumption].
% 0.76/1.03 26 function(f25) # label(choice1) # label(axiom). [assumption].
% 0.76/1.03 27 -little_set(A) | -function(B) | little_set(image(A,B)) # label(image_and_substitution6) # label(axiom). [assumption].
% 0.76/1.03 Derived: -little_set(A) | little_set(image(A,f25)). [resolve(26,a,27,b)].
% 0.76/1.03 28 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.76/1.03 Derived: -maps(A,B,C) | -little_set(D) | little_set(image(D,A)). [resolve(28,b,27,b)].
% 0.76/1.03 29 maps(A,B,C) | -function(A) | domain_of(A) != B | -subset(range_of(A),C) # label(maps4) # label(axiom). [assumption].
% 0.76/1.03 Derived: maps(f25,A,B) | domain_of(f25) != A | -subset(range_of(f25),B). [resolve(29,b,26,a)].
% 0.76/1.03 Derived: maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C) | -maps(A,D,E). [resolve(29,b,28,b)].
% 0.76/1.03 30 -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.76/1.03 Derived: -member(A,f25) | ordered_pair_predicate(A). [resolve(30,a,26,a)].
% 0.76/1.03 Derived: -member(A,B) | ordered_pair_predicate(A) | -maps(B,C,D). [resolve(30,a,28,b)].
% 0.76/1.03 31 -function(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(16,b,10,a)].
% 0.76/1.03 Derived: -little_set(A) | -little_set(B) | -little_set(C) | -member(ordered_pair(A,B),f25) | -member(ordered_pair(A,C),f25) | B = C. [resolve(31,a,26,a)].
% 0.76/1.03 Derived: -little_set(A) | -little_set(B) | -little_set(C) | -member(ordered_pair(A,B),D) | -member(ordered_pair(A,C),D) | B = C | -maps(D,E,F). [resolve(31,a,28,b)].
% 0.76/1.03 32 function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(32,a,27,b)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f19(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(32,a,29,b)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(32,a,30,a)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f19(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(32,a,31,a)].
% 0.76/1.03 33 function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(33,a,27,b)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f20(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(33,a,29,b)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(33,a,30,a)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f20(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(33,a,31,a)].
% 0.76/1.03 34 function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(34,a,27,b)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f21(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(34,a,29,b)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(34,a,30,a)].
% 0.76/1.03 Derived: member(f18(A),A) | little_set(f21(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(34,a,31,a)].
% 0.76/1.03 35 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.76/1.03 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(35,a,27,b)].
% 0.76/1.03 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(35,a,29,b)].
% 0.76/1.03 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(35,a,30,a)].
% 0.76/1.03 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(35,a,31,a)].
% 0.76/1.03 36 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.76/1.03 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(36,a,27,b)].
% 0.76/1.03 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(36,a,29,b)].
% 0.76/1.03 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(36,a,30,a)].
% 0.76/1.03 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(36,a,31,a)].
% 0.76/1.03 37 function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.76/1.03 Derived: member(f18(A),A) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(37,a,27,b)].
% 0.76/1.03 Derived: member(f18(A),A) | f20(A) != f21(A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(37,a,29,b)].
% 0.76/1.03 Derived: member(f18(A),A) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(37,a,30,a)].
% 0.76/1.03 Derived: member(f18(A),A) | f20(A) != f21(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(37,a,31,a)].
% 0.76/1.03 38 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(38,a,27,b)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(38,a,29,b)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(38,a,30,a)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(38,a,31,a)].
% 0.76/1.03 39 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(39,a,27,b)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(39,a,29,b)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(39,a,30,a)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(39,a,31,a)].
% 0.76/1.03 40 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(40,a,27,b)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(40,a,29,b)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(40,a,30,a)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(40,a,31,a)].
% 0.76/1.03 41 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(41,a,27,b)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(41,a,29,b)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(41,a,30,a)].
% 0.76/1.03 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(41,a,31,a)].
% 0.76/1.05 42 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.76/1.05 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(42,a,27,b)].
% 0.76/1.05 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(42,a,29,b)].
% 0.76/1.05 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(42,a,30,a)].
% 0.76/1.05 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(42,a,31,a)].
% 0.76/1.05 43 function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.76/1.05 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(43,a,27,b)].
% 0.76/1.05 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(43,a,29,b)].
% 0.76/1.05 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(43,a,30,a)].
% 0.76/1.05 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(43,a,31,a)].
% 0.76/1.05 44 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | member(f32(A,B,C,D,E),B) # label(homomorphism5) # label(axiom). [assumption].
% 0.76/1.05 45 -homomorphism(A,B,C,D,E) | closed(B,C) # label(homomorphism1) # label(axiom). [assumption].
% 0.76/1.05 46 -homomorphism(A,B,C,D,E) | closed(D,E) # label(homomorphism2) # label(axiom). [assumption].
% 0.76/1.05 47 -homomorphism(A,B,C,D,E) | maps(A,B,D) # label(homomorphism3) # label(axiom). [assumption].
% 0.76/1.05 48 -homomorphism(A,B,C,D,E) | -member(F,B) | -member(V6,B) | apply(A,apply_to_two_arguments(C,F,V6)) = apply_to_two_arguments(E,apply(A,F),apply(A,V6)) # label(homomorphism4) # label(axiom). [assumption].
% 0.76/1.05 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | member(f32(E,A,B,C,D),A) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(44,a,48,a)].
% 0.76/1.05 49 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | member(f33(A,B,C,D,E),B) # label(homomorphism6) # label(axiom). [assumption].
% 0.76/1.05 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | member(f33(E,A,B,C,D),A) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(49,a,48,a)].
% 0.76/1.05 50 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | apply(A,apply_to_two_arguments(C,f32(A,B,C,D,E),f33(A,B,C,D,E))) != apply_to_two_arguments(E,apply(A,f32(A,B,C,D,E)),apply(A,f33(A,B,C,D,E))) # label(homomorphism7) # label(axiom). [assumption].
% 0.76/1.05 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | apply(E,apply_to_two_arguments(B,f32(E,A,B,C,D),f33(E,A,B,C,D))) != apply_to_two_arguments(D,apply(E,f32(E,A,B,C,D)),apply(E,f33(E,A,B,C,D))) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(50,a,48,a)].
% 0.76/1.05
% 0.76/1.05 ============================== end predicate elimination =============
% 0.76/1.05
% 0.76/1.05 Auto_denials: (non-Horn, no changes).
% 0.76/1.05
% 0.76/1.05 Term ordering decisions:
% 0.76/1.05 Function symbol KB weights: f25=1. empty_set=1. infinity=1. estin=1. identity_relation=1. universal_set=1. a=1. b=1. ordered_pair=1. image=1. apply=1. compose=1. cross_product=1. non_ordered_pair=1. f1=1. intersection=1. f10=1. f11=1. f12=1. f13=1. f14=1. f27=1. f4=1. f7=1. f8=1. f9=1. f16=1. f17=1. f23=1. f5=1. f6=1. union=1. restrict=1. f18=1. f19=1. f20=1. f21=1. domain_of=1. first=1. range_of=1. second=1. flip_range_of=1. rotate_right=1. complement=1. sigma=1. converse=1. powerset=1. singleton_set=1. f2=1. f24=1. f26=1. f3=1. successor=1. apply_to_two_arguments=1. f22=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1.
% 0.76/1.05
% 0.76/1.05 ============================== PROOF =================================
% 0.76/1.05 % SZS status Unsatisfiable
% 0.76/1.05 % SZS output start Refutation
% 0.76/1.05
% 0.76/1.05 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.76/1.05 % Length of proof is 6.
% 0.76/1.05 % Level of proof is 2.
% 0.76/1.05 % Maximum clause weight is 11.000.
% 0.76/1.05 % Given clauses 0.
% 0.76/1.05
% 0.76/1.05 58 little_set(non_ordered_pair(A,B)) # label(non_ordered_pair4) # label(axiom). [assumption].
% 0.76/1.05 59 singleton_set(A) = non_ordered_pair(A,A) # label(singleton_set) # label(axiom). [assumption].
% 0.76/1.05 60 ordered_pair(A,B) = non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)) # label(ordered_pair) # label(axiom). [assumption].
% 0.76/1.05 61 ordered_pair(A,B) = non_ordered_pair(non_ordered_pair(A,A),non_ordered_pair(A,B)). [copy(60),rewrite([59(2)])].
% 0.76/1.05 189 -little_set(ordered_pair(a,b)) # label(prove_ordered_pairs_are_small) # label(negated_conjecture). [assumption].
% 0.76/1.05 190 $F. [copy(189),rewrite([61(3)]),unit_del(a,58)].
% 0.76/1.05
% 0.76/1.05 % SZS output end Refutation
% 0.76/1.05 ============================== end of proof ==========================
% 0.76/1.05
% 0.76/1.05 ============================== STATISTICS ============================
% 0.76/1.05
% 0.76/1.05 Given=0. Generated=108. Kept=107. proofs=1.
% 0.76/1.05 Usable=0. Sos=0. Demods=6. Limbo=107, Disabled=158. Hints=0.
% 0.76/1.05 Megabytes=0.40.
% 0.76/1.05 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.76/1.05
% 0.76/1.05 ============================== end of statistics =====================
% 0.76/1.05
% 0.76/1.05 ============================== end of search =========================
% 0.76/1.05
% 0.76/1.05 THEOREM PROVED
% 0.76/1.05 % SZS status Unsatisfiable
% 0.76/1.05
% 0.76/1.05 Exiting with 1 proof.
% 0.76/1.05
% 0.76/1.05 Process 17878 exit (max_proofs) Mon Jul 11 00:21:59 2022
% 0.76/1.05 Prover9 interrupted
%------------------------------------------------------------------------------