TSTP Solution File: SET024-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 04:25:58 EDT 2022
% Result : Unsatisfiable 3.21s 3.54s
% Output : Refutation 3.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.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 : Sun Jul 10 20:30:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/1.05 ============================== Prover9 ===============================
% 0.43/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.05 Process 12858 was started by sandbox2 on n025.cluster.edu,
% 0.43/1.05 Sun Jul 10 20:30:47 2022
% 0.43/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12705_n025.cluster.edu".
% 0.43/1.05 ============================== end of head ===========================
% 0.43/1.05
% 0.43/1.05 ============================== INPUT =================================
% 0.43/1.05
% 0.43/1.05 % Reading from file /tmp/Prover9_12705_n025.cluster.edu
% 0.43/1.05
% 0.43/1.05 set(prolog_style_variables).
% 0.43/1.05 set(auto2).
% 0.43/1.05 % set(auto2) -> set(auto).
% 0.43/1.05 % set(auto) -> set(auto_inference).
% 0.43/1.05 % set(auto) -> set(auto_setup).
% 0.43/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.05 % set(auto) -> set(auto_limits).
% 0.43/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.05 % set(auto) -> set(auto_denials).
% 0.43/1.05 % set(auto) -> set(auto_process).
% 0.43/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.05 % set(auto2) -> assign(stats, some).
% 0.43/1.05 % set(auto2) -> clear(echo_input).
% 0.43/1.05 % set(auto2) -> set(quiet).
% 0.43/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.05 % set(auto2) -> clear(print_given).
% 0.43/1.05 assign(lrs_ticks,-1).
% 0.43/1.05 assign(sos_limit,10000).
% 0.43/1.05 assign(order,kbo).
% 0.43/1.05 set(lex_order_vars).
% 0.43/1.05 clear(print_given).
% 0.43/1.05
% 0.43/1.05 % formulas(sos). % not echoed (151 formulas)
% 0.43/1.05
% 0.43/1.05 ============================== end of input ==========================
% 0.43/1.05
% 0.43/1.05 % From the command line: assign(max_seconds, 300).
% 0.43/1.05
% 0.43/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.05
% 0.43/1.05 % Formulas that are not ordinary clauses:
% 0.43/1.05
% 0.43/1.05 ============================== end of process non-clausal formulas ===
% 0.43/1.05
% 0.43/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.05
% 0.43/1.05 ============================== PREDICATE ELIMINATION =================
% 0.43/1.05 1 proper_subset(A,B) | -subset(A,B) | A = B # label(proper_subset3) # label(axiom). [assumption].
% 0.43/1.05 2 -proper_subset(A,B) | subset(A,B) # label(proper_subset1) # label(axiom). [assumption].
% 0.43/1.05 3 -proper_subset(A,B) | A != B # label(proper_subset2) # label(axiom). [assumption].
% 0.43/1.05 4 relation(A) | member(f18(A),A) # label(relation2) # label(axiom). [assumption].
% 0.43/1.05 5 -relation(A) | -member(B,A) | ordered_pair_predicate(B) # label(relation1) # label(axiom). [assumption].
% 0.43/1.05 Derived: member(f18(A),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(4,a,5,a)].
% 0.43/1.05 6 relation(A) | -ordered_pair_predicate(f18(A)) # label(relation3) # label(axiom). [assumption].
% 0.43/1.05 Derived: -ordered_pair_predicate(f18(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(6,a,5,a)].
% 0.43/1.05 7 -function(A) | relation(A) # label(function1) # label(axiom). [assumption].
% 0.43/1.05 Derived: -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.43/1.05 8 function(A) | -relation(A) | -single_valued_set(A) # label(function3) # label(axiom). [assumption].
% 0.43/1.05 Derived: function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.43/1.05 Derived: function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.43/1.05 9 single_valued_set(A) | little_set(f19(A)) # label(single_valued_set2) # label(axiom). [assumption].
% 0.43/1.05 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].
% 0.43/1.05 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)].
% 0.43/1.05 11 single_valued_set(A) | little_set(f20(A)) # label(single_valued_set3) # label(axiom). [assumption].
% 0.43/1.06 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)].
% 0.43/1.06 12 single_valued_set(A) | little_set(f21(A)) # label(single_valued_set4) # label(axiom). [assumption].
% 0.43/1.06 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)].
% 0.43/1.06 13 single_valued_set(A) | member(ordered_pair(f19(A),f20(A)),A) # label(single_valued_set5) # label(axiom). [assumption].
% 0.43/1.06 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)].
% 0.43/1.06 14 single_valued_set(A) | member(ordered_pair(f19(A),f21(A)),A) # label(single_valued_set6) # label(axiom). [assumption].
% 0.43/1.06 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)].
% 0.43/1.06 15 single_valued_set(A) | f20(A) != f21(A) # label(single_valued_set7) # label(axiom). [assumption].
% 0.43/1.06 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)].
% 0.43/1.06 16 -function(A) | single_valued_set(A) # label(function2) # label(axiom). [assumption].
% 0.43/1.06 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)].
% 0.43/1.06 17 function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.43/1.06 Derived: function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.43/1.06 Derived: function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.43/1.06 Derived: function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.43/1.06 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.43/1.06 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.43/1.06 Derived: function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.43/1.06 18 function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.43/1.06 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.43/1.06 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.43/1.06 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.43/1.06 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.43/1.06 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.43/1.06 Derived: function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.43/1.06 19 disjoint(A,B) | member(f23(A,B),A) # label(disjoint2) # label(axiom). [assumption].
% 0.43/1.06 20 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint1) # label(axiom). [assumption].
% 0.43/1.06 Derived: member(f23(A,B),A) | -member(C,A) | -member(C,B). [resolve(19,a,20,a)].
% 0.43/1.06 21 disjoint(A,B) | member(f23(A,B),B) # label(disjoint3) # label(axiom). [assumption].
% 0.43/1.06 Derived: member(f23(A,B),B) | -member(C,A) | -member(C,B). [resolve(21,a,20,a)].
% 0.43/1.06 22 A = empty_set | disjoint(f24(A),A) # label(regularity2) # label(axiom). [assumption].
% 0.43/1.06 Derived: A = empty_set | -member(B,f24(A)) | -member(B,A). [resolve(22,b,20,a)].
% 0.43/1.06 23 one_to_one_function(A) | -function(A) | -function(converse(A)) # label(one_to_one_function3) # label(axiom). [assumption].
% 0.43/1.06 24 -one_to_one_function(A) | function(A) # label(one_to_one_function1) # label(axiom). [assumption].
% 0.43/1.06 25 -one_to_one_function(A) | function(converse(A)) # label(one_to_one_function2) # label(axiom). [assumption].
% 0.43/1.06 26 function(f25) # label(choice1) # label(axiom). [assumption].
% 0.43/1.06 27 -little_set(A) | -function(B) | little_set(image(A,B)) # label(image_and_substitution6) # label(axiom). [assumption].
% 0.43/1.06 Derived: -little_set(A) | little_set(image(A,f25)). [resolve(26,a,27,b)].
% 0.43/1.06 28 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.43/1.06 Derived: -maps(A,B,C) | -little_set(D) | little_set(image(D,A)). [resolve(28,b,27,b)].
% 0.43/1.06 29 maps(A,B,C) | -function(A) | domain_of(A) != B | -subset(range_of(A),C) # label(maps4) # label(axiom). [assumption].
% 0.43/1.06 Derived: maps(f25,A,B) | domain_of(f25) != A | -subset(range_of(f25),B). [resolve(29,b,26,a)].
% 0.43/1.06 Derived: maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C) | -maps(A,D,E). [resolve(29,b,28,b)].
% 0.43/1.06 30 -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.43/1.06 Derived: -member(A,f25) | ordered_pair_predicate(A). [resolve(30,a,26,a)].
% 0.43/1.06 Derived: -member(A,B) | ordered_pair_predicate(A) | -maps(B,C,D). [resolve(30,a,28,b)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 32 function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.43/1.06 Derived: member(f18(A),A) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(32,a,27,b)].
% 0.43/1.06 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)].
% 0.43/1.06 Derived: member(f18(A),A) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(32,a,30,a)].
% 0.43/1.06 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)].
% 0.43/1.06 33 function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.43/1.06 Derived: member(f18(A),A) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(33,a,27,b)].
% 0.43/1.06 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)].
% 0.43/1.06 Derived: member(f18(A),A) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(33,a,30,a)].
% 0.43/1.06 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)].
% 0.43/1.06 34 function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.43/1.06 Derived: member(f18(A),A) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(34,a,27,b)].
% 0.43/1.06 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)].
% 0.43/1.06 Derived: member(f18(A),A) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(34,a,30,a)].
% 0.43/1.06 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)].
% 0.43/1.06 35 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 36 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 37 function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.43/1.06 Derived: member(f18(A),A) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(37,a,27,b)].
% 0.43/1.06 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)].
% 0.43/1.06 Derived: member(f18(A),A) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(37,a,30,a)].
% 0.43/1.06 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)].
% 0.43/1.06 38 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.43/1.06 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(38,a,27,b)].
% 0.43/1.06 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)].
% 0.43/1.06 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(38,a,30,a)].
% 0.43/1.06 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)].
% 0.43/1.06 39 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.43/1.06 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(39,a,27,b)].
% 0.43/1.06 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)].
% 0.43/1.06 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(39,a,30,a)].
% 0.43/1.06 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)].
% 0.43/1.06 40 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.43/1.06 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(40,a,27,b)].
% 0.43/1.06 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)].
% 0.43/1.06 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(40,a,30,a)].
% 0.43/1.06 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)].
% 0.43/1.06 41 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.43/1.06 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)].
% 0.81/1.11 42 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.81/1.11 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)].
% 0.81/1.11 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)].
% 0.81/1.11 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)].
% 0.81/1.11 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)].
% 0.81/1.11 43 function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.81/1.11 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(43,a,27,b)].
% 0.81/1.11 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)].
% 0.81/1.11 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(43,a,30,a)].
% 0.81/1.11 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)].
% 0.81/1.11 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].
% 0.81/1.11 45 -homomorphism(A,B,C,D,E) | closed(B,C) # label(homomorphism1) # label(axiom). [assumption].
% 0.81/1.11 46 -homomorphism(A,B,C,D,E) | closed(D,E) # label(homomorphism2) # label(axiom). [assumption].
% 0.81/1.11 47 -homomorphism(A,B,C,D,E) | maps(A,B,D) # label(homomorphism3) # label(axiom). [assumption].
% 0.81/1.11 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].
% 0.81/1.11 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)].
% 0.81/1.11 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].
% 0.81/1.11 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)].
% 0.81/1.11 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].
% 0.81/1.11 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)].
% 0.81/1.11
% 0.81/1.11 ============================== end predicate elimination =============
% 0.81/1.11
% 0.81/1.11 Auto_denials: (non-Horn, no changes).
% 0.81/1.11
% 0.81/1.11 Term ordering decisions:
% 0.81/1.11 Function symbol KB weights: f25=1. empty_set=1. infinity=1. estin=1. identity_relation=1. universal_set=1. a=1. ordered_pair=1. image=1. apply=1. non_ordered_pair=1. compose=1. cross_product=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. first=1. second=1. domain_of=1. range_of=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.
% 3.21/3.54
% 3.21/3.54 ============================== end of process initial clauses ========
% 3.21/3.54
% 3.21/3.54 ============================== CLAUSES FOR SEARCH ====================
% 3.21/3.54
% 3.21/3.54 ============================== end of clauses for search =============
% 3.21/3.54
% 3.21/3.54 ============================== SEARCH ================================
% 3.21/3.54
% 3.21/3.54 % Starting search at 0.08 seconds.
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=44.000, iters=3350
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=42.000, iters=3385
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=40.000, iters=3426
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=37.000, iters=3345
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=34.000, iters=3341
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=33.000, iters=3400
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=32.000, iters=3353
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=31.000, iters=3364
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=30.000, iters=3354
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=29.000, iters=3346
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=28.000, iters=3359
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=27.000, iters=3373
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=26.000, iters=3347
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=25.000, iters=3355
% 3.21/3.54
% 3.21/3.54 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 62 (0.00 of 1.23 sec).
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=24.000, iters=3364
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=23.000, iters=3353
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=22.000, iters=3395
% 3.21/3.54
% 3.21/3.54 Low Water (displace): id=4142, wt=99.000
% 3.21/3.54
% 3.21/3.54 Low Water (displace): id=4141, wt=95.000
% 3.21/3.54
% 3.21/3.54 Low Water (displace): id=1230, wt=91.000
% 3.21/3.54
% 3.21/3.54 Low Water (displace): id=10876, wt=16.000
% 3.21/3.54
% 3.21/3.54 Low Water (displace): id=10904, wt=15.000
% 3.21/3.54
% 3.21/3.54 Low Water (displace): id=10988, wt=13.000
% 3.21/3.54
% 3.21/3.54 Low Water (displace): id=11006, wt=8.000
% 3.21/3.54
% 3.21/3.54 Low Water (displace): id=11014, wt=7.000
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=21.000, iters=3333
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=20.000, iters=3333
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=19.000, iters=3350
% 3.21/3.54
% 3.21/3.54 Low Water (keep): wt=18.000, iters=3335
% 3.21/3.54
% 3.21/3.54 ============================== PROOF =================================
% 3.21/3.54 % SZS status Unsatisfiable
% 3.21/3.54 % SZS output start Refutation
% 3.21/3.54
% 3.21/3.54 % Proof 1 at 2.46 (+ 0.05) seconds.
% 3.21/3.54 % Length of proof is 8.
% 3.21/3.54 % Level of proof is 3.
% 3.21/3.54 % Maximum clause weight is 10.000.
% 3.21/3.54 % Given clauses 1229.
% 3.21/3.54
% 3.21/3.54 57 member(A,non_ordered_pair(B,C)) | -little_set(A) | A != C # label(non_ordered_pair3) # label(axiom). [assumption].
% 3.21/3.54 59 singleton_set(A) = non_ordered_pair(A,A) # label(singleton_set) # label(axiom). [assumption].
% 3.21/3.54 201 little_set(a) # label(a_little_set) # label(hypothesis). [assumption].
% 3.21/3.54 202 -member(a,singleton_set(a)) # label(prove_membership_of_singleton_set) # label(negated_conjecture). [assumption].
% 3.21/3.54 203 -member(a,non_ordered_pair(a,a)). [copy(202),rewrite([59(3)])].
% 3.21/3.54 740 member(a,non_ordered_pair(A,B)) | a != B. [resolve(201,a,57,b)].
% 3.21/3.54 20949 member(a,non_ordered_pair(A,a)). [xx_res(740,b)].
% 3.21/3.54 20950 $F. [resolve(20949,a,203,a)].
% 3.21/3.54
% 3.21/3.54 % SZS output end Refutation
% 3.21/3.54 ============================== end of proof ==========================
% 3.21/3.54
% 3.21/3.54 ============================== STATISTICS ============================
% 3.21/3.54
% 3.21/3.54 Given=1229. Generated=67599. Kept=20821. proofs=1.
% 3.21/3.54 Usable=1148. Sos=9999. Demods=162. Limbo=1, Disabled=9909. Hints=0.
% 3.21/3.54 Megabytes=25.32.
% 3.21/3.54 User_CPU=2.46, System_CPU=0.05, Wall_clock=3.
% 3.21/3.54
% 3.21/3.54 ============================== end of statistics =====================
% 3.21/3.54
% 3.21/3.54 ============================== end of search =========================
% 3.21/3.54
% 3.21/3.54 THEOREM PROVED
% 3.21/3.54 % SZS status Unsatisfiable
% 3.21/3.54
% 3.21/3.54 Exiting with 1 proof.
% 3.21/3.54
% 3.21/3.54 Process 12858 exit (max_proofs) Sun Jul 10 20:30:50 2022
% 3.21/3.54 Prover9 interrupted
%------------------------------------------------------------------------------