TSTP Solution File: SET012-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET012-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 04:25:36 EDT 2022
% Result : Unsatisfiable 14.09s 14.43s
% Output : Refutation 14.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET012-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.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 16:38:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.39/0.99 ============================== Prover9 ===============================
% 0.39/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.39/0.99 Process 22844 was started by sandbox on n028.cluster.edu,
% 0.39/0.99 Sun Jul 10 16:38:13 2022
% 0.39/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22492_n028.cluster.edu".
% 0.39/0.99 ============================== end of head ===========================
% 0.39/0.99
% 0.39/0.99 ============================== INPUT =================================
% 0.39/0.99
% 0.39/0.99 % Reading from file /tmp/Prover9_22492_n028.cluster.edu
% 0.39/0.99
% 0.39/0.99 set(prolog_style_variables).
% 0.39/0.99 set(auto2).
% 0.39/0.99 % set(auto2) -> set(auto).
% 0.39/0.99 % set(auto) -> set(auto_inference).
% 0.39/0.99 % set(auto) -> set(auto_setup).
% 0.39/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.39/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.39/0.99 % set(auto) -> set(auto_limits).
% 0.39/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.39/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.39/0.99 % set(auto) -> set(auto_denials).
% 0.39/0.99 % set(auto) -> set(auto_process).
% 0.39/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.39/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.39/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.39/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.39/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.39/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.39/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.39/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.39/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.39/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.39/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.39/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.39/0.99 % set(auto2) -> assign(stats, some).
% 0.39/0.99 % set(auto2) -> clear(echo_input).
% 0.39/0.99 % set(auto2) -> set(quiet).
% 0.39/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.39/0.99 % set(auto2) -> clear(print_given).
% 0.39/0.99 assign(lrs_ticks,-1).
% 0.39/0.99 assign(sos_limit,10000).
% 0.39/0.99 assign(order,kbo).
% 0.39/0.99 set(lex_order_vars).
% 0.39/0.99 clear(print_given).
% 0.39/0.99
% 0.39/0.99 % formulas(sos). % not echoed (144 formulas)
% 0.39/0.99
% 0.39/0.99 ============================== end of input ==========================
% 0.39/0.99
% 0.39/0.99 % From the command line: assign(max_seconds, 300).
% 0.39/0.99
% 0.39/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.39/1.00
% 0.39/1.00 % Formulas that are not ordinary clauses:
% 0.39/1.00
% 0.39/1.00 ============================== end of process non-clausal formulas ===
% 0.39/1.00
% 0.39/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.39/1.00
% 0.39/1.00 ============================== PREDICATE ELIMINATION =================
% 0.39/1.00 1 proper_subset(A,B) | -subset(A,B) | A = B # label(proper_subset3) # label(axiom). [assumption].
% 0.39/1.00 2 -proper_subset(A,B) | subset(A,B) # label(proper_subset1) # label(axiom). [assumption].
% 0.39/1.00 3 -proper_subset(A,B) | A != B # label(proper_subset2) # label(axiom). [assumption].
% 0.39/1.00 4 relation(A) | member(f18(A),A) # label(relation2) # label(axiom). [assumption].
% 0.39/1.00 5 -relation(A) | -member(B,A) | ordered_pair_predicate(B) # label(relation1) # label(axiom). [assumption].
% 0.39/1.00 Derived: member(f18(A),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(4,a,5,a)].
% 0.39/1.00 6 relation(A) | -ordered_pair_predicate(f18(A)) # label(relation3) # label(axiom). [assumption].
% 0.39/1.00 Derived: -ordered_pair_predicate(f18(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(6,a,5,a)].
% 0.39/1.00 7 -function(A) | relation(A) # label(function1) # label(axiom). [assumption].
% 0.39/1.00 Derived: -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.39/1.00 8 function(A) | -relation(A) | -single_valued_set(A) # label(function3) # label(axiom). [assumption].
% 0.39/1.00 Derived: function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.39/1.00 Derived: function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.39/1.00 9 single_valued_set(A) | little_set(f19(A)) # label(single_valued_set2) # label(axiom). [assumption].
% 0.39/1.00 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].
% 0.39/1.00 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)].
% 0.39/1.00 11 single_valued_set(A) | little_set(f20(A)) # label(single_valued_set3) # label(axiom). [assumption].
% 0.71/1.00 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)].
% 0.71/1.00 12 single_valued_set(A) | little_set(f21(A)) # label(single_valued_set4) # label(axiom). [assumption].
% 0.71/1.00 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)].
% 0.71/1.00 13 single_valued_set(A) | member(ordered_pair(f19(A),f20(A)),A) # label(single_valued_set5) # label(axiom). [assumption].
% 0.71/1.00 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)].
% 0.71/1.00 14 single_valued_set(A) | member(ordered_pair(f19(A),f21(A)),A) # label(single_valued_set6) # label(axiom). [assumption].
% 0.71/1.00 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)].
% 0.71/1.00 15 single_valued_set(A) | f20(A) != f21(A) # label(single_valued_set7) # label(axiom). [assumption].
% 0.71/1.00 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)].
% 0.71/1.00 16 -function(A) | single_valued_set(A) # label(function2) # label(axiom). [assumption].
% 0.71/1.00 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)].
% 0.71/1.00 17 function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.71/1.00 Derived: function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.71/1.00 Derived: function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.71/1.00 Derived: function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.71/1.00 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.71/1.00 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.71/1.00 Derived: function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.71/1.00 18 function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.71/1.00 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.71/1.00 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.71/1.00 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.71/1.00 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.71/1.00 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.71/1.00 Derived: function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.71/1.00 19 disjoint(A,B) | member(f23(A,B),A) # label(disjoint2) # label(axiom). [assumption].
% 0.71/1.00 20 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint1) # label(axiom). [assumption].
% 0.71/1.00 Derived: member(f23(A,B),A) | -member(C,A) | -member(C,B). [resolve(19,a,20,a)].
% 0.71/1.00 21 disjoint(A,B) | member(f23(A,B),B) # label(disjoint3) # label(axiom). [assumption].
% 0.71/1.00 Derived: member(f23(A,B),B) | -member(C,A) | -member(C,B). [resolve(21,a,20,a)].
% 0.71/1.00 22 A = empty_set | disjoint(f24(A),A) # label(regularity2) # label(axiom). [assumption].
% 0.71/1.00 Derived: A = empty_set | -member(B,f24(A)) | -member(B,A). [resolve(22,b,20,a)].
% 0.71/1.00 23 one_to_one_function(A) | -function(A) | -function(converse(A)) # label(one_to_one_function3) # label(axiom). [assumption].
% 0.71/1.00 24 -one_to_one_function(A) | function(A) # label(one_to_one_function1) # label(axiom). [assumption].
% 0.71/1.00 25 -one_to_one_function(A) | function(converse(A)) # label(one_to_one_function2) # label(axiom). [assumption].
% 0.71/1.00 26 function(f25) # label(choice1) # label(axiom). [assumption].
% 0.71/1.00 27 -little_set(A) | -function(B) | little_set(image(A,B)) # label(image_and_substitution6) # label(axiom). [assumption].
% 0.71/1.00 Derived: -little_set(A) | little_set(image(A,f25)). [resolve(26,a,27,b)].
% 0.71/1.00 28 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.71/1.00 Derived: -maps(A,B,C) | -little_set(D) | little_set(image(D,A)). [resolve(28,b,27,b)].
% 0.71/1.00 29 maps(A,B,C) | -function(A) | domain_of(A) != B | -subset(range_of(A),C) # label(maps4) # label(axiom). [assumption].
% 0.71/1.00 Derived: maps(f25,A,B) | domain_of(f25) != A | -subset(range_of(f25),B). [resolve(29,b,26,a)].
% 0.71/1.00 Derived: maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C) | -maps(A,D,E). [resolve(29,b,28,b)].
% 0.71/1.00 30 -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.71/1.00 Derived: -member(A,f25) | ordered_pair_predicate(A). [resolve(30,a,26,a)].
% 0.71/1.00 Derived: -member(A,B) | ordered_pair_predicate(A) | -maps(B,C,D). [resolve(30,a,28,b)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 32 function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.71/1.00 Derived: member(f18(A),A) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(32,a,27,b)].
% 0.71/1.00 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)].
% 0.71/1.00 Derived: member(f18(A),A) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(32,a,30,a)].
% 0.71/1.00 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)].
% 0.71/1.00 33 function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.71/1.00 Derived: member(f18(A),A) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(33,a,27,b)].
% 0.71/1.00 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)].
% 0.71/1.00 Derived: member(f18(A),A) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(33,a,30,a)].
% 0.71/1.00 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)].
% 0.71/1.00 34 function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.71/1.00 Derived: member(f18(A),A) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(34,a,27,b)].
% 0.71/1.00 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)].
% 0.71/1.00 Derived: member(f18(A),A) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(34,a,30,a)].
% 0.71/1.00 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)].
% 0.71/1.00 35 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 36 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 37 function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.71/1.00 Derived: member(f18(A),A) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(37,a,27,b)].
% 0.71/1.00 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)].
% 0.71/1.00 Derived: member(f18(A),A) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(37,a,30,a)].
% 0.71/1.00 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)].
% 0.71/1.00 38 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.71/1.00 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(38,a,27,b)].
% 0.71/1.00 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)].
% 0.71/1.00 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(38,a,30,a)].
% 0.71/1.00 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)].
% 0.71/1.00 39 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.71/1.00 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(39,a,27,b)].
% 0.71/1.00 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)].
% 0.71/1.00 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(39,a,30,a)].
% 0.71/1.00 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)].
% 0.71/1.00 40 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.71/1.00 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(40,a,27,b)].
% 0.71/1.00 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)].
% 0.71/1.00 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(40,a,30,a)].
% 0.71/1.00 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)].
% 0.71/1.00 41 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.00 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)].
% 0.71/1.05 42 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.71/1.05 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)].
% 0.71/1.05 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)].
% 0.71/1.05 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)].
% 0.71/1.05 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)].
% 0.71/1.05 43 function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.71/1.05 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(43,a,27,b)].
% 0.71/1.05 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)].
% 0.71/1.05 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(43,a,30,a)].
% 0.71/1.05 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)].
% 0.71/1.05 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].
% 0.71/1.05 45 -homomorphism(A,B,C,D,E) | closed(B,C) # label(homomorphism1) # label(axiom). [assumption].
% 0.71/1.05 46 -homomorphism(A,B,C,D,E) | closed(D,E) # label(homomorphism2) # label(axiom). [assumption].
% 0.71/1.05 47 -homomorphism(A,B,C,D,E) | maps(A,B,D) # label(homomorphism3) # label(axiom). [assumption].
% 0.71/1.05 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].
% 0.71/1.05 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)].
% 0.71/1.05 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].
% 0.71/1.05 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)].
% 0.71/1.05 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].
% 0.71/1.05 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)].
% 0.71/1.05
% 0.71/1.05 ============================== end predicate elimination =============
% 0.71/1.05
% 0.71/1.05 Auto_denials: (non-Horn, no changes).
% 0.71/1.05
% 0.71/1.05 Term ordering decisions:
% 0.71/1.05 Function symbol KB weights: f25=1. empty_set=1. infinity=1. estin=1. identity_relation=1. bs=1. universal_set=1. as=1. cs=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. complement=1. flip_range_of=1. rotate_right=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.
% 14.09/14.43
% 14.09/14.43 ============================== end of process initial clauses ========
% 14.09/14.43
% 14.09/14.43 ============================== CLAUSES FOR SEARCH ====================
% 14.09/14.43
% 14.09/14.43 ============================== end of clauses for search =============
% 14.09/14.43
% 14.09/14.43 ============================== SEARCH ================================
% 14.09/14.43
% 14.09/14.43 % Starting search at 0.07 seconds.
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=51.000, iters=3513
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=49.000, iters=3431
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=44.000, iters=3348
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=41.000, iters=3419
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=37.000, iters=3343
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=34.000, iters=3349
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=33.000, iters=3371
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=31.000, iters=3377
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=30.000, iters=3356
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=29.000, iters=3404
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=28.000, iters=3356
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=27.000, iters=3333
% 14.09/14.43
% 14.09/14.43 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 593 (0.00 of 1.06 sec).
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=26.000, iters=3383
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=25.000, iters=3333
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=24.000, iters=3352
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=23.000, iters=3335
% 14.09/14.43
% 14.09/14.43 Low Water (displace): id=5616, wt=99.000
% 14.09/14.43
% 14.09/14.43 Low Water (displace): id=5615, wt=95.000
% 14.09/14.43
% 14.09/14.43 Low Water (displace): id=10792, wt=16.000
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=22.000, iters=3333
% 14.09/14.43
% 14.09/14.43 Low Water (displace): id=10836, wt=12.000
% 14.09/14.43
% 14.09/14.43 Low Water (displace): id=10929, wt=10.000
% 14.09/14.43
% 14.09/14.43 Low Water (displace): id=10944, wt=9.000
% 14.09/14.43
% 14.09/14.43 Low Water (displace): id=10945, wt=8.000
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=21.000, iters=3354
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=20.000, iters=3340
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=19.000, iters=3405
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=18.000, iters=3341
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=17.000, iters=3355
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=16.000, iters=3336
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=15.000, iters=3337
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=14.000, iters=3338
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=13.000, iters=3341
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=12.000, iters=3340
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=11.000, iters=3335
% 14.09/14.43
% 14.09/14.43 Low Water (keep): wt=10.000, iters=3334
% 14.09/14.43
% 14.09/14.43 ============================== PROOF =================================
% 14.09/14.43 % SZS status Unsatisfiable
% 14.09/14.43 % SZS output start Refutation
% 14.09/14.43
% 14.09/14.43 % Proof 1 at 13.09 (+ 0.37) seconds.
% 14.09/14.43 % Length of proof is 19.
% 14.09/14.43 % Level of proof is 6.
% 14.09/14.43 % Maximum clause weight is 19.000.
% 14.09/14.43 % Given clauses 8875.
% 14.09/14.43
% 14.09/14.43 52 little_set(f1(A,B)) | A = B # label(extensionality1) # label(axiom). [assumption].
% 14.09/14.43 53 member(f1(A,B),A) | member(f1(A,B),B) | A = B # label(extensionality2) # label(axiom). [assumption].
% 14.09/14.43 54 -member(f1(A,B),A) | -member(f1(A,B),B) | A = B # label(extensionality3) # label(axiom). [assumption].
% 14.09/14.43 88 -member(A,complement(B)) | -member(A,B) # label(complement1) # label(axiom). [assumption].
% 14.09/14.43 89 member(A,complement(B)) | -little_set(A) | member(A,B) # label(complement2) # label(axiom). [assumption].
% 14.09/14.43 189 complement(as) = bs # label(complement_of_a_is_b) # label(hypothesis). [assumption].
% 14.09/14.43 190 complement(bs) = cs # label(complement_of_b_is_c) # label(hypothesis). [assumption].
% 14.09/14.43 191 cs = complement(bs). [copy(190),flip(a)].
% 14.09/14.43 192 as != cs # label(prove_a_equals_c) # label(negated_conjecture). [assumption].
% 14.09/14.43 193 complement(bs) != as. [copy(192),rewrite([191(2)]),flip(a)].
% 14.09/14.43 425 -member(f1(complement(A),B),A) | member(f1(complement(A),B),B) | complement(A) = B. [resolve(88,a,53,a)].
% 14.09/14.43 427 member(f1(A,B),complement(C)) | member(f1(A,B),C) | A = B. [resolve(89,b,52,a)].
% 14.09/14.43 643 -member(A,bs) | -member(A,as). [para(189(a,1),88(a,2))].
% 14.09/14.43 9846 member(f1(complement(complement(A)),B),A) | complement(complement(A)) = B | member(f1(complement(complement(A)),B),B). [resolve(427,a,425,a),merge(d)].
% 14.09/14.43 9867 member(f1(complement(complement(A)),A),A) | complement(complement(A)) = A. [factor(9846,a,c)].
% 14.09/14.43 49267 -member(f1(complement(bs),as),bs). [resolve(9867,a,643,b),rewrite([189(2),189(6)]),unit_del(a,193)].
% 14.09/14.43 49269 member(f1(complement(bs),as),as). [para(189(a,1),9867(a,1,1,1)),rewrite([189(8)]),unit_del(b,193)].
% 14.09/14.43 49486 -member(f1(complement(bs),as),complement(bs)). [resolve(49269,a,54,b),unit_del(b,193)].
% 14.09/14.43 49514 $F. [resolve(49486,a,427,a),unit_del(a,49267),unit_del(b,193)].
% 14.09/14.43
% 14.09/14.43 % SZS output end Refutation
% 14.09/14.43 ============================== end of proof ==========================
% 14.09/14.43
% 14.09/14.43 ============================== STATISTICS ============================
% 14.09/14.43
% 14.09/14.43 Given=8875. Generated=734729. Kept=49388. proofs=1.
% 14.09/14.43 Usable=7332. Sos=8141. Demods=29. Limbo=0, Disabled=34145. Hints=0.
% 14.09/14.43 Megabytes=38.55.
% 14.09/14.43 User_CPU=13.09, System_CPU=0.37, Wall_clock=13.
% 14.09/14.43
% 14.09/14.43 ============================== end of statistics =====================
% 14.09/14.43
% 14.09/14.43 ============================== end of search =========================
% 14.09/14.43
% 14.09/14.43 THEOREM PROVED
% 14.09/14.43 % SZS status Unsatisfiable
% 14.09/14.43
% 14.09/14.43 Exiting with 1 proof.
% 14.09/14.43
% 14.09/14.43 Process 22844 exit (max_proofs) Sun Jul 10 16:38:26 2022
% 14.09/14.43 Prover9 interrupted
%------------------------------------------------------------------------------