TSTP Solution File: GRP016-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 : Sat Jul 16 11:16:43 EDT 2022
% Result : Timeout 300.04s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n017.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 Jun 13 10:19:23 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.47/1.07 ============================== Prover9 ===============================
% 0.47/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.07 Process 21139 was started by sandbox on n017.cluster.edu,
% 0.47/1.07 Mon Jun 13 10:19:23 2022
% 0.47/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20986_n017.cluster.edu".
% 0.47/1.07 ============================== end of head ===========================
% 0.47/1.07
% 0.47/1.07 ============================== INPUT =================================
% 0.47/1.07
% 0.47/1.07 % Reading from file /tmp/Prover9_20986_n017.cluster.edu
% 0.47/1.07
% 0.47/1.07 set(prolog_style_variables).
% 0.47/1.07 set(auto2).
% 0.47/1.07 % set(auto2) -> set(auto).
% 0.47/1.07 % set(auto) -> set(auto_inference).
% 0.47/1.07 % set(auto) -> set(auto_setup).
% 0.47/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.07 % set(auto) -> set(auto_limits).
% 0.47/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.07 % set(auto) -> set(auto_denials).
% 0.47/1.07 % set(auto) -> set(auto_process).
% 0.47/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.07 % set(auto2) -> assign(stats, some).
% 0.47/1.07 % set(auto2) -> clear(echo_input).
% 0.47/1.07 % set(auto2) -> set(quiet).
% 0.47/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.07 % set(auto2) -> clear(print_given).
% 0.47/1.07 assign(lrs_ticks,-1).
% 0.47/1.07 assign(sos_limit,10000).
% 0.47/1.07 assign(order,kbo).
% 0.47/1.07 set(lex_order_vars).
% 0.47/1.07 clear(print_given).
% 0.47/1.07
% 0.47/1.07 % formulas(sos). % not echoed (167 formulas)
% 0.47/1.07
% 0.47/1.07 ============================== end of input ==========================
% 0.47/1.07
% 0.47/1.07 % From the command line: assign(max_seconds, 300).
% 0.47/1.07
% 0.47/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.07
% 0.47/1.07 % Formulas that are not ordinary clauses:
% 0.47/1.07
% 0.47/1.07 ============================== end of process non-clausal formulas ===
% 0.47/1.07
% 0.47/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.47/1.07
% 0.47/1.07 ============================== PREDICATE ELIMINATION =================
% 0.47/1.07 1 proper_subset(A,B) | -subset(A,B) | A = B # label(proper_subset3) # label(axiom). [assumption].
% 0.47/1.07 2 -proper_subset(A,B) | subset(A,B) # label(proper_subset1) # label(axiom). [assumption].
% 0.47/1.07 3 -proper_subset(A,B) | A != B # label(proper_subset2) # label(axiom). [assumption].
% 0.47/1.07 4 relation(A) | member(f18(A),A) # label(relation2) # label(axiom). [assumption].
% 0.47/1.07 5 -relation(A) | -member(B,A) | ordered_pair_predicate(B) # label(relation1) # label(axiom). [assumption].
% 0.47/1.07 Derived: member(f18(A),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(4,a,5,a)].
% 0.47/1.07 6 relation(A) | -ordered_pair_predicate(f18(A)) # label(relation3) # label(axiom). [assumption].
% 0.47/1.07 Derived: -ordered_pair_predicate(f18(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(6,a,5,a)].
% 0.47/1.07 7 -function(A) | relation(A) # label(function1) # label(axiom). [assumption].
% 0.47/1.07 Derived: -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.47/1.07 8 function(A) | -relation(A) | -single_valued_set(A) # label(function3) # label(axiom). [assumption].
% 0.47/1.07 Derived: function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.47/1.07 Derived: function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.47/1.07 9 single_valued_set(A) | little_set(f19(A)) # label(single_valued_set2) # label(axiom). [assumption].
% 0.47/1.07 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].
% 0.47/1.07 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)].
% 0.47/1.07 11 single_valued_set(A) | little_set(f20(A)) # label(single_valued_set3) # label(axiom). [assumption].
% 0.47/1.08 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)].
% 0.47/1.08 12 single_valued_set(A) | little_set(f21(A)) # label(single_valued_set4) # label(axiom). [assumption].
% 0.47/1.08 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)].
% 0.47/1.08 13 single_valued_set(A) | member(ordered_pair(f19(A),f20(A)),A) # label(single_valued_set5) # label(axiom). [assumption].
% 0.47/1.08 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)].
% 0.47/1.08 14 single_valued_set(A) | member(ordered_pair(f19(A),f21(A)),A) # label(single_valued_set6) # label(axiom). [assumption].
% 0.47/1.08 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)].
% 0.47/1.08 15 single_valued_set(A) | f20(A) != f21(A) # label(single_valued_set7) # label(axiom). [assumption].
% 0.47/1.08 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)].
% 0.47/1.08 16 -function(A) | single_valued_set(A) # label(function2) # label(axiom). [assumption].
% 0.47/1.08 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)].
% 0.47/1.08 17 function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.47/1.08 Derived: function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.47/1.08 Derived: function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.47/1.08 Derived: function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.47/1.08 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.47/1.08 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.47/1.08 Derived: function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.47/1.08 18 function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.47/1.08 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.47/1.08 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.47/1.08 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.47/1.08 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.47/1.08 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.47/1.08 Derived: function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.47/1.08 19 disjoint(A,B) | member(f23(A,B),A) # label(disjoint2) # label(axiom). [assumption].
% 0.47/1.08 20 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint1) # label(axiom). [assumption].
% 0.47/1.08 Derived: member(f23(A,B),A) | -member(C,A) | -member(C,B). [resolve(19,a,20,a)].
% 0.47/1.08 21 disjoint(A,B) | member(f23(A,B),B) # label(disjoint3) # label(axiom). [assumption].
% 0.47/1.08 Derived: member(f23(A,B),B) | -member(C,A) | -member(C,B). [resolve(21,a,20,a)].
% 0.47/1.08 22 A = empty_set | disjoint(f24(A),A) # label(regularity2) # label(axiom). [assumption].
% 0.47/1.08 Derived: A = empty_set | -member(B,f24(A)) | -member(B,A). [resolve(22,b,20,a)].
% 0.47/1.08 23 one_to_one_function(A) | -function(A) | -function(converse(A)) # label(one_to_one_function3) # label(axiom). [assumption].
% 0.47/1.08 24 -one_to_one_function(A) | function(A) # label(one_to_one_function1) # label(axiom). [assumption].
% 0.47/1.08 25 -one_to_one_function(A) | function(converse(A)) # label(one_to_one_function2) # label(axiom). [assumption].
% 0.47/1.08 26 function(f25) # label(choice1) # label(axiom). [assumption].
% 0.47/1.08 27 -little_set(A) | -function(B) | little_set(image(A,B)) # label(image_and_substitution6) # label(axiom). [assumption].
% 0.47/1.08 Derived: -little_set(A) | little_set(image(A,f25)). [resolve(26,a,27,b)].
% 0.47/1.08 28 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.47/1.08 Derived: -maps(A,B,C) | -little_set(D) | little_set(image(D,A)). [resolve(28,b,27,b)].
% 0.47/1.08 29 maps(A,B,C) | -function(A) | domain_of(A) != B | -subset(range_of(A),C) # label(maps4) # label(axiom). [assumption].
% 0.47/1.08 Derived: maps(f25,A,B) | domain_of(f25) != A | -subset(range_of(f25),B). [resolve(29,b,26,a)].
% 0.47/1.08 Derived: maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C) | -maps(A,D,E). [resolve(29,b,28,b)].
% 0.47/1.08 30 -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.47/1.08 Derived: -member(A,f25) | ordered_pair_predicate(A). [resolve(30,a,26,a)].
% 0.47/1.08 Derived: -member(A,B) | ordered_pair_predicate(A) | -maps(B,C,D). [resolve(30,a,28,b)].
% 0.47/1.08 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)].
% 0.47/1.08 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)].
% 0.47/1.08 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)].
% 0.47/1.08 32 function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.47/1.08 Derived: member(f18(A),A) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(32,a,27,b)].
% 0.47/1.08 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)].
% 0.47/1.08 Derived: member(f18(A),A) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(32,a,30,a)].
% 0.47/1.08 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)].
% 0.47/1.08 33 function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.47/1.08 Derived: member(f18(A),A) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(33,a,27,b)].
% 0.47/1.08 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)].
% 0.47/1.08 Derived: member(f18(A),A) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(33,a,30,a)].
% 0.47/1.08 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)].
% 0.47/1.08 34 function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.47/1.08 Derived: member(f18(A),A) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(34,a,27,b)].
% 0.47/1.08 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)].
% 0.47/1.08 Derived: member(f18(A),A) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(34,a,30,a)].
% 0.47/1.08 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)].
% 0.47/1.08 35 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.47/1.08 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)].
% 0.47/1.08 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)].
% 0.47/1.08 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)].
% 0.47/1.08 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)].
% 0.47/1.08 36 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.47/1.08 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)].
% 0.47/1.09 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)].
% 0.47/1.09 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)].
% 0.47/1.09 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)].
% 0.47/1.09 37 function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.47/1.09 Derived: member(f18(A),A) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(37,a,27,b)].
% 0.47/1.09 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)].
% 0.47/1.09 Derived: member(f18(A),A) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(37,a,30,a)].
% 0.47/1.09 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)].
% 0.47/1.09 38 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.47/1.09 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(38,a,27,b)].
% 0.47/1.09 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)].
% 0.47/1.09 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(38,a,30,a)].
% 0.47/1.09 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)].
% 0.47/1.09 39 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.47/1.09 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(39,a,27,b)].
% 0.47/1.09 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)].
% 0.47/1.09 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(39,a,30,a)].
% 0.47/1.09 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)].
% 0.47/1.09 40 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.47/1.09 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(40,a,27,b)].
% 0.47/1.09 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)].
% 0.47/1.09 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(40,a,30,a)].
% 0.47/1.09 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)].
% 0.47/1.09 41 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.47/1.09 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)].
% 0.47/1.09 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)].
% 0.47/1.09 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)].
% 0.47/1.09 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)].
% 0.47/1.09 42 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.47/1.09 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)].
% 0.47/1.09 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)].
% 0.47/1.09 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)].
% 0.47/1.09 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)].
% 0.47/1.09 43 function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.47/1.09 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(43,a,27,b)].
% 0.79/1.09 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)].
% 0.79/1.09 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(43,a,30,a)].
% 0.79/1.09 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)].
% 0.79/1.09 44 associative(A,B) | member(f34(A,B),A) # label(associative_system2) # label(axiom). [assumption].
% 0.79/1.09 45 -associative(A,B) | -member(C,A) | -member(D,A) | -member(E,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,C,D),E) = apply_to_two_arguments(B,C,apply_to_two_arguments(B,D,E)) # label(associative_system1) # label(axiom). [assumption].
% 0.79/1.09 Derived: member(f34(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,C,D),E) = apply_to_two_arguments(B,C,apply_to_two_arguments(B,D,E)). [resolve(44,a,45,a)].
% 0.79/1.09 46 associative(A,B) | member(f35(A,B),A) # label(associative_system3) # label(axiom). [assumption].
% 0.79/1.09 Derived: member(f35(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,C,D),E) = apply_to_two_arguments(B,C,apply_to_two_arguments(B,D,E)). [resolve(46,a,45,a)].
% 0.79/1.09 47 associative(A,B) | member(f36(A,B),A) # label(associative_system4) # label(axiom). [assumption].
% 0.79/1.09 Derived: member(f36(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,C,D),E) = apply_to_two_arguments(B,C,apply_to_two_arguments(B,D,E)). [resolve(47,a,45,a)].
% 0.79/1.09 48 associative(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) # label(associative_system5) # label(axiom). [assumption].
% 0.79/1.09 Derived: apply_to_two_arguments(A,apply_to_two_arguments(A,f34(B,A),f35(B,A)),f36(B,A)) != apply_to_two_arguments(A,f34(B,A),apply_to_two_arguments(A,f35(B,A),f36(B,A))) | -member(C,B) | -member(D,B) | -member(E,B) | apply_to_two_arguments(A,apply_to_two_arguments(A,C,D),E) = apply_to_two_arguments(A,C,apply_to_two_arguments(A,D,E)). [resolve(48,a,45,a)].
% 0.79/1.09 49 -group(A,B) | associative(A,B) # label(group2) # label(axiom). [assumption].
% 0.79/1.09 Derived: -group(A,B) | -member(C,A) | -member(D,A) | -member(E,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,C,D),E) = apply_to_two_arguments(B,C,apply_to_two_arguments(B,D,E)). [resolve(49,b,45,a)].
% 0.79/1.09 50 group(A,B) | -closed(A,B) | -associative(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) # label(group5) # label(axiom). [assumption].
% 0.79/1.09 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f34(A,B),A). [resolve(50,c,44,a)].
% 0.79/1.09 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f35(A,B),A). [resolve(50,c,46,a)].
% 0.79/1.09 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f36(A,B),A). [resolve(50,c,47,a)].
% 0.79/1.09 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))). [resolve(50,c,48,a)].
% 0.79/1.10 51 identity(A,B,C) | -member(C,A) | member(f37(A,B,C),A) # label(identity4) # label(axiom). [assumption].
% 0.79/1.10 52 -identity(A,B,C) | member(C,A) # label(identity1) # label(axiom). [assumption].
% 0.79/1.10 53 -identity(A,B,C) | -member(D,A) | apply_to_two_arguments(B,C,D) = D # label(identity2) # label(axiom). [assumption].
% 0.79/1.10 54 -identity(A,B,C) | -member(D,A) | apply_to_two_arguments(B,D,C) = D # label(identity3) # label(axiom). [assumption].
% 0.79/1.10 Derived: -member(A,B) | member(f37(B,C,A),B) | -member(D,B) | apply_to_two_arguments(C,A,D) = D. [resolve(51,a,53,a)].
% 0.79/1.10 Derived: -member(A,B) | member(f37(B,C,A),B) | -member(D,B) | apply_to_two_arguments(C,D,A) = D. [resolve(51,a,54,a)].
% 0.79/1.10 55 identity(A,B,C) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) # label(identity5) # label(axiom). [assumption].
% 0.79/1.10 Derived: -member(A,B) | apply_to_two_arguments(C,A,f37(B,C,A)) != f37(B,C,A) | apply_to_two_arguments(C,f37(B,C,A),A) != f37(B,C,A) | -member(D,B) | apply_to_two_arguments(C,A,D) = D. [resolve(55,a,53,a)].
% 0.79/1.10 Derived: -member(A,B) | apply_to_two_arguments(C,A,f37(B,C,A)) != f37(B,C,A) | apply_to_two_arguments(C,f37(B,C,A),A) != f37(B,C,A) | -member(D,B) | apply_to_two_arguments(C,D,A) = D. [resolve(55,a,54,a)].
% 0.79/1.10 56 -group(A,B) | identity(A,B,f39(A,B)) # label(group3) # label(axiom). [assumption].
% 0.79/1.10 Derived: -group(A,B) | member(f39(A,B),A). [resolve(56,b,52,a)].
% 0.79/1.10 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,f39(A,B),C) = C. [resolve(56,b,53,a)].
% 0.79/1.10 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,f39(A,B)) = C. [resolve(56,b,54,a)].
% 0.79/1.10 57 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f34(A,B),A). [resolve(50,c,44,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A). [resolve(57,c,51,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C). [resolve(57,c,55,a)].
% 0.79/1.10 58 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f35(A,B),A). [resolve(50,c,46,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A). [resolve(58,c,51,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C). [resolve(58,c,55,a)].
% 0.79/1.10 59 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f36(A,B),A). [resolve(50,c,47,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A). [resolve(59,c,51,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C). [resolve(59,c,55,a)].
% 0.79/1.10 60 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))). [resolve(50,c,48,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A). [resolve(60,c,51,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C). [resolve(60,c,55,a)].
% 0.79/1.10 61 inverse(A,B,C,D) | -maps(D,A,A) | member(f38(A,B,C,D),A) # label(inverse4) # label(axiom). [assumption].
% 0.79/1.10 62 -inverse(A,B,C,D) | maps(D,A,A) # label(inverse1) # label(axiom). [assumption].
% 0.79/1.10 63 -inverse(A,B,C,D) | -member(E,A) | apply_to_two_arguments(B,apply(D,E),E) = C # label(inverse2) # label(axiom). [assumption].
% 0.79/1.10 64 -inverse(A,B,C,D) | -member(E,A) | apply_to_two_arguments(B,E,apply(D,E)) = C # label(inverse3) # label(axiom). [assumption].
% 0.79/1.10 Derived: -maps(A,B,B) | member(f38(B,C,D,A),B) | -member(E,B) | apply_to_two_arguments(C,apply(A,E),E) = D. [resolve(61,a,63,a)].
% 0.79/1.10 Derived: -maps(A,B,B) | member(f38(B,C,D,A),B) | -member(E,B) | apply_to_two_arguments(C,E,apply(A,E)) = D. [resolve(61,a,64,a)].
% 0.79/1.10 65 inverse(A,B,C,D) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C # label(inverse5) # label(axiom). [assumption].
% 0.79/1.10 Derived: -maps(A,B,B) | apply_to_two_arguments(C,apply(A,f38(B,C,D,A)),f38(B,C,D,A)) != D | apply_to_two_arguments(C,f38(B,C,D,A),apply(A,f38(B,C,D,A))) != D | -member(E,B) | apply_to_two_arguments(C,apply(A,E),E) = D. [resolve(65,a,63,a)].
% 0.79/1.10 Derived: -maps(A,B,B) | apply_to_two_arguments(C,apply(A,f38(B,C,D,A)),f38(B,C,D,A)) != D | apply_to_two_arguments(C,f38(B,C,D,A),apply(A,f38(B,C,D,A))) != D | -member(E,B) | apply_to_two_arguments(C,E,apply(A,E)) = D. [resolve(65,a,64,a)].
% 0.79/1.10 66 -group(A,B) | inverse(A,B,f39(A,B),f40(A,B)) # label(group4) # label(axiom). [assumption].
% 0.79/1.10 Derived: -group(A,B) | maps(f40(A,B),A,A). [resolve(66,b,62,a)].
% 0.79/1.10 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,apply(f40(A,B),C),C) = f39(A,B). [resolve(66,b,63,a)].
% 0.79/1.10 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,apply(f40(A,B),C)) = f39(A,B). [resolve(66,b,64,a)].
% 0.79/1.10 67 group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A). [resolve(57,c,51,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(67,c,61,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(67,c,65,a)].
% 0.79/1.10 68 group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C). [resolve(57,c,55,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(68,c,61,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(68,c,65,a)].
% 0.79/1.10 69 group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A). [resolve(58,c,51,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(69,c,61,a)].
% 0.79/1.10 Derived: group(A,B) | -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(69,c,65,a)].
% 0.79/1.10 70 group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C). [resolve(58,c,55,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(70,c,61,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(70,c,65,a)].
% 0.79/1.11 71 group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A). [resolve(59,c,51,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(71,c,61,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(71,c,65,a)].
% 0.79/1.11 72 group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C). [resolve(59,c,55,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(72,c,61,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(72,c,65,a)].
% 0.79/1.11 73 group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A). [resolve(60,c,51,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(73,c,61,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(73,c,65,a)].
% 0.79/1.11 74 group(A,B) | -closed(A,B) | -inverse(A,B,C,D) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C). [resolve(60,c,55,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(74,c,61,a)].
% 0.79/1.11 Derived: group(A,B) | -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(74,c,65,a)].
% 0.79/1.11 75 group(f69,f70) # label(a_group) # label(negated_conjecture). [assumption].
% 0.79/1.11 76 -group(A,B) | closed(A,B) # label(group1) # label(axiom). [assumption].
% 0.79/1.11 Derived: closed(f69,f70). [resolve(75,a,76,a)].
% 0.79/1.11 77 -group(A,B) | -member(C,A) | -member(D,A) | -member(E,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,C,D),E) = apply_to_two_arguments(B,C,apply_to_two_arguments(B,D,E)). [resolve(49,b,45,a)].
% 0.79/1.11 Derived: -member(A,f69) | -member(B,f69) | -member(C,f69) | apply_to_two_arguments(f70,apply_to_two_arguments(f70,A,B),C) = apply_to_two_arguments(f70,A,apply_to_two_arguments(f70,B,C)). [resolve(77,a,75,a)].
% 0.79/1.11 78 -group(A,B) | member(f39(A,B),A). [resolve(56,b,52,a)].
% 0.79/1.11 Derived: member(f39(f69,f70),f69). [resolve(78,a,75,a)].
% 0.79/1.11 79 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,f39(A,B),C) = C. [resolve(56,b,53,a)].
% 0.79/1.11 Derived: -member(A,f69) | apply_to_two_arguments(f70,f39(f69,f70),A) = A. [resolve(79,a,75,a)].
% 0.79/1.11 80 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,f39(A,B)) = C. [resolve(56,b,54,a)].
% 0.79/1.11 Derived: -member(A,f69) | apply_to_two_arguments(f70,A,f39(f69,f70)) = A. [resolve(80,a,75,a)].
% 0.79/1.11 81 -group(A,B) | maps(f40(A,B),A,A). [resolve(66,b,62,a)].
% 0.79/1.11 Derived: maps(f40(f69,f70),f69,f69). [resolve(81,a,75,a)].
% 0.79/1.11 82 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,apply(f40(A,B),C),C) = f39(A,B). [resolve(66,b,63,a)].
% 0.79/1.11 Derived: -member(A,f69) | apply_to_two_arguments(f70,apply(f40(f69,f70),A),A) = f39(f69,f70). [resolve(82,a,75,a)].
% 0.79/1.11 83 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,apply(f40(A,B),C)) = f39(A,B). [resolve(66,b,64,a)].
% 0.79/1.11 Derived: -member(A,f69) | apply_to_two_arguments(f70,A,apply(f40(f69,f70),A)) = f39(f69,f70). [resolve(83,a,75,a)].
% 0.79/1.11 84 group(A,B) | -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(67,c,61,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(84,a,77,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | member(f39(A,B),A). [resolve(84,a,78,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(84,a,79,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(84,a,80,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | maps(f40(A,B),A,A). [resolve(84,a,81,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(84,a,82,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(84,a,83,a)].
% 0.79/1.11 85 group(A,B) | -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(67,c,65,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(85,a,77,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | member(f39(A,B),A). [resolve(85,a,78,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(85,a,79,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(85,a,80,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | maps(f40(A,B),A,A). [resolve(85,a,81,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(85,a,82,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(85,a,83,a)].
% 0.79/1.11 86 group(A,B) | -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(68,c,61,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(86,a,77,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | member(f39(A,B),A). [resolve(86,a,78,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(86,a,79,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(86,a,80,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | maps(f40(A,B),A,A). [resolve(86,a,81,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(86,a,82,a)].
% 0.79/1.11 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(86,a,83,a)].
% 0.79/1.12 87 group(A,B) | -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(68,c,65,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(87,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | member(f39(A,B),A). [resolve(87,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(87,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(87,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | maps(f40(A,B),A,A). [resolve(87,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(87,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f34(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(87,a,83,a)].
% 0.79/1.12 88 group(A,B) | -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(69,c,61,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(88,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | member(f39(A,B),A). [resolve(88,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(88,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(88,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | maps(f40(A,B),A,A). [resolve(88,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(88,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(88,a,83,a)].
% 0.79/1.12 89 group(A,B) | -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(69,c,65,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(89,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | member(f39(A,B),A). [resolve(89,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(89,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(89,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | maps(f40(A,B),A,A). [resolve(89,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(89,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(89,a,83,a)].
% 0.79/1.12 90 group(A,B) | -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(70,c,61,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(90,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | member(f39(A,B),A). [resolve(90,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(90,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(90,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | maps(f40(A,B),A,A). [resolve(90,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(90,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(90,a,83,a)].
% 0.79/1.12 91 group(A,B) | -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(70,c,65,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(91,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | member(f39(A,B),A). [resolve(91,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(91,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(91,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | maps(f40(A,B),A,A). [resolve(91,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(91,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f35(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(91,a,83,a)].
% 0.79/1.12 92 group(A,B) | -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(71,c,61,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(92,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | member(f39(A,B),A). [resolve(92,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(92,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(92,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | maps(f40(A,B),A,A). [resolve(92,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(92,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(92,a,83,a)].
% 0.79/1.12 93 group(A,B) | -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(71,c,65,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(93,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | member(f39(A,B),A). [resolve(93,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(93,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(93,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | maps(f40(A,B),A,A). [resolve(93,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(93,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(93,a,83,a)].
% 0.79/1.12 94 group(A,B) | -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(72,c,61,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(94,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | member(f39(A,B),A). [resolve(94,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(94,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(94,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | maps(f40(A,B),A,A). [resolve(94,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(94,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(94,a,83,a)].
% 0.79/1.12 95 group(A,B) | -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(72,c,65,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(95,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | member(f39(A,B),A). [resolve(95,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(95,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(95,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | maps(f40(A,B),A,A). [resolve(95,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(95,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | member(f36(A,B),A) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(95,a,83,a)].
% 0.79/1.12 96 group(A,B) | -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(73,c,61,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(96,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | member(f39(A,B),A). [resolve(96,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(96,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(96,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | maps(f40(A,B),A,A). [resolve(96,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(96,a,82,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(96,a,83,a)].
% 0.79/1.12 97 group(A,B) | -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(73,c,65,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(97,a,77,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | member(f39(A,B),A). [resolve(97,a,78,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(97,a,79,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(97,a,80,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | maps(f40(A,B),A,A). [resolve(97,a,81,a)].
% 0.79/1.12 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(97,a,82,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | member(f37(A,B,C),A) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(97,a,83,a)].
% 0.79/1.13 98 group(A,B) | -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A). [resolve(74,c,61,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(98,a,77,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | member(f39(A,B),A). [resolve(98,a,78,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(98,a,79,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(98,a,80,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | maps(f40(A,B),A,A). [resolve(98,a,81,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(98,a,82,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | member(f38(A,B,C,D),A) | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(98,a,83,a)].
% 0.79/1.13 99 group(A,B) | -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C. [resolve(74,c,65,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | -member(F,A) | -member(V6,A) | apply_to_two_arguments(B,apply_to_two_arguments(B,E,F),V6) = apply_to_two_arguments(B,E,apply_to_two_arguments(B,F,V6)). [resolve(99,a,77,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | member(f39(A,B),A). [resolve(99,a,78,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,f39(A,B),E) = E. [resolve(99,a,79,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,f39(A,B)) = E. [resolve(99,a,80,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | maps(f40(A,B),A,A). [resolve(99,a,81,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,apply(f40(A,B),E),E) = f39(A,B). [resolve(99,a,82,a)].
% 0.79/1.13 Derived: -closed(A,B) | apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B)) != apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))) | -member(C,A) | apply_to_two_arguments(B,C,f37(A,B,C)) != f37(A,B,C) | apply_to_two_arguments(B,f37(A,B,C),C) != f37(A,B,C) | -maps(D,A,A) | apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D)) != C | apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D))) != C | -member(E,A) | apply_to_two_arguments(B,E,apply(f40(A,B),E)) = f39(A,B). [resolve(99,a,83,a)].
% 2.24/2.56 100 commutes(A,B) | member(f41(A,B),A) # label(commutes2) # label(axiom). [assumption].
% 2.24/2.56 101 -commutes(A,B) | -member(C,A) | -member(D,A) | apply_to_two_arguments(B,C,D) = apply_to_two_arguments(B,D,C) # label(commutes1) # label(axiom). [assumption].
% 2.24/2.56 Derived: member(f41(A,B),A) | -member(C,A) | -member(D,A) | apply_to_two_arguments(B,C,D) = apply_to_two_arguments(B,D,C). [resolve(100,a,101,a)].
% 2.24/2.56 102 commutes(A,B) | member(f42(A,B),A) # label(commutes3) # label(axiom). [assumption].
% 2.24/2.56 Derived: member(f42(A,B),A) | -member(C,A) | -member(D,A) | apply_to_two_arguments(B,C,D) = apply_to_two_arguments(B,D,C). [resolve(102,a,101,a)].
% 2.24/2.56 103 commutes(A,B) | apply_to_two_arguments(B,f41(A,B),f42(A,B)) != apply_to_two_arguments(B,f42(A,B),f41(A,B)) # label(commutes4) # label(axiom). [assumption].
% 2.24/2.56 Derived: apply_to_two_arguments(A,f41(B,A),f42(B,A)) != apply_to_two_arguments(A,f42(B,A),f41(B,A)) | -member(C,B) | -member(D,B) | apply_to_two_arguments(A,C,D) = apply_to_two_arguments(A,D,C). [resolve(103,a,101,a)].
% 2.24/2.56
% 2.24/2.56 ============================== end predicate elimination =============
% 2.24/2.56
% 2.24/2.56 Auto_denials: (non-Horn, no changes).
% 2.24/2.56
% 2.24/2.56 Term ordering decisions:
% 2.24/2.56 Function symbol KB weights: f69=1. f70=1. f25=1. empty_set=1. infinity=1. estin=1. identity_relation=1. universal_set=1. apply=1. ordered_pair=1. f34=1. f35=1. f36=1. f39=1. f40=1. image=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. f41=1. f42=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. f37=1. f22=1. f28=1. f29=1. f30=1. f31=1. f38=1. f32=1. f33=1.
% 2.24/2.56
% 2.24/2.56 ============================== end of process initial clauses ========
% 2.24/2.56
% 2.24/2.56 ============================== CLAUSES FOR SEARCH ====================
% 2.24/2.56
% 2.24/2.56 ============================== end of clauses for search =============
% 2.24/2.56
% 2.24/2.56 ============================== SEARCH ================================
% 2.24/2.56
% 2.24/2.56 % Starting search at 0.19 seconds.
% 2.24/2.56
% 2.24/2.56 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 790 (0.00 of 0.84 sec).
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=182.000, iters=3413
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=161.000, iters=3338
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=160.000, iters=3333
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=157.000, iters=3532
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=149.000, iters=3470
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=96.000, iters=3461
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=87.000, iters=3345
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=83.000, iters=3351
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=81.000, iters=3459
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=75.000, iters=3346
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=74.000, iters=3382
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=71.000, iters=3365
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=70.000, iters=3431
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=65.000, iters=3336
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=63.000, iters=3395
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=62.000, iters=3351
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=61.000, iters=3343
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=56.000, iters=3335
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=51.000, iters=3378
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=48.000, iters=3339
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=44.000, iters=3346
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=43.000, iters=3346
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=41.000, iters=3345
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=38.000, iters=3336
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=37.000, iters=3543
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=36.000, iters=3363
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=34.000, iters=3491
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=33.000, iters=3407
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=32.000, iters=3541
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=31.000, iters=3541
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=30.000, iters=3355
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=29.000, iters=3365
% 2.24/2.56
% 2.24/2.56 Low Water (keep): wt=28.000, iters=3346
% 2.24/2.56
% 2.24/2.56 Low Water (displace): id=5459, wt=199.000
% 2.24/2.56
% 2.24/2.56 Low Water (displace): id=4905, wt=198.000
% 2.24/2.56
% 2.24/2.56 Low Water (displace): id=5416, wt=196.000
% 2.24/2.56
% 2.24/2.56 Low Water (displace): id=10990, wt=25.000
% 2.24/2.56
% 2.24/2.56 Low Water (displace): id=10991, wt=22.000
% 2.24/2.56
% 2.24/2.56 Low Water (disCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------