TSTP Solution File: NUM009-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 : Mon Jul 18 13:24:36 EDT 2022
% Result : Unsatisfiable 1.42s 1.71s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 12:10:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.77/1.05 ============================== Prover9 ===============================
% 0.77/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.05 Process 4655 was started by sandbox on n019.cluster.edu,
% 0.77/1.05 Thu Jul 7 12:10:24 2022
% 0.77/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4502_n019.cluster.edu".
% 0.77/1.05 ============================== end of head ===========================
% 0.77/1.05
% 0.77/1.05 ============================== INPUT =================================
% 0.77/1.05
% 0.77/1.05 % Reading from file /tmp/Prover9_4502_n019.cluster.edu
% 0.77/1.05
% 0.77/1.05 set(prolog_style_variables).
% 0.77/1.05 set(auto2).
% 0.77/1.05 % set(auto2) -> set(auto).
% 0.77/1.05 % set(auto) -> set(auto_inference).
% 0.77/1.05 % set(auto) -> set(auto_setup).
% 0.77/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.05 % set(auto) -> set(auto_limits).
% 0.77/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.05 % set(auto) -> set(auto_denials).
% 0.77/1.05 % set(auto) -> set(auto_process).
% 0.77/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.05 % set(auto2) -> assign(stats, some).
% 0.77/1.05 % set(auto2) -> clear(echo_input).
% 0.77/1.05 % set(auto2) -> set(quiet).
% 0.77/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.05 % set(auto2) -> clear(print_given).
% 0.77/1.05 assign(lrs_ticks,-1).
% 0.77/1.05 assign(sos_limit,10000).
% 0.77/1.05 assign(order,kbo).
% 0.77/1.05 set(lex_order_vars).
% 0.77/1.05 clear(print_given).
% 0.77/1.05
% 0.77/1.05 % formulas(sos). % not echoed (220 formulas)
% 0.77/1.05
% 0.77/1.05 ============================== end of input ==========================
% 0.77/1.05
% 0.77/1.05 % From the command line: assign(max_seconds, 300).
% 0.77/1.05
% 0.77/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.05
% 0.77/1.05 % Formulas that are not ordinary clauses:
% 0.77/1.05
% 0.77/1.05 ============================== end of process non-clausal formulas ===
% 0.77/1.05
% 0.77/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.05
% 0.77/1.05 ============================== PREDICATE ELIMINATION =================
% 0.77/1.05 1 proper_subset(A,B) | -subset(A,B) | A = B # label(proper_subset3) # label(axiom). [assumption].
% 0.77/1.05 2 -proper_subset(A,B) | subset(A,B) # label(proper_subset1) # label(axiom). [assumption].
% 0.77/1.05 3 -proper_subset(A,B) | A != B # label(proper_subset2) # label(axiom). [assumption].
% 0.77/1.05 4 relation(A) | member(f18(A),A) # label(relation2) # label(axiom). [assumption].
% 0.77/1.05 5 -relation(A) | -member(B,A) | ordered_pair_predicate(B) # label(relation1) # label(axiom). [assumption].
% 0.77/1.05 Derived: member(f18(A),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(4,a,5,a)].
% 0.77/1.05 6 relation(A) | -ordered_pair_predicate(f18(A)) # label(relation3) # label(axiom). [assumption].
% 0.77/1.05 Derived: -ordered_pair_predicate(f18(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(6,a,5,a)].
% 0.77/1.05 7 -function(A) | relation(A) # label(function1) # label(axiom). [assumption].
% 0.77/1.05 Derived: -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(7,b,5,a)].
% 0.77/1.05 8 function(A) | -relation(A) | -single_valued_set(A) # label(function3) # label(axiom). [assumption].
% 0.77/1.05 Derived: function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.77/1.05 Derived: function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.77/1.05 9 single_valued_set(A) | little_set(f19(A)) # label(single_valued_set2) # label(axiom). [assumption].
% 0.77/1.05 10 -single_valued_set(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D # label(single_valued_set1) # label(axiom). [assumption].
% 0.77/1.05 Derived: little_set(f19(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(9,a,10,a)].
% 0.77/1.05 11 single_valued_set(A) | little_set(f20(A)) # label(single_valued_set3) # label(axiom). [assumption].
% 0.77/1.07 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)].
% 0.77/1.07 12 single_valued_set(A) | little_set(f21(A)) # label(single_valued_set4) # label(axiom). [assumption].
% 0.77/1.07 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)].
% 0.77/1.07 13 single_valued_set(A) | member(ordered_pair(f19(A),f20(A)),A) # label(single_valued_set5) # label(axiom). [assumption].
% 0.77/1.07 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)].
% 0.77/1.07 14 single_valued_set(A) | member(ordered_pair(f19(A),f21(A)),A) # label(single_valued_set6) # label(axiom). [assumption].
% 0.77/1.07 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)].
% 0.77/1.07 15 single_valued_set(A) | f20(A) != f21(A) # label(single_valued_set7) # label(axiom). [assumption].
% 0.77/1.07 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)].
% 0.77/1.07 16 -function(A) | single_valued_set(A) # label(function2) # label(axiom). [assumption].
% 0.77/1.07 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)].
% 0.77/1.07 17 function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(8,b,4,a)].
% 0.77/1.07 Derived: function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(17,b,9,a)].
% 0.77/1.07 Derived: function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(17,b,11,a)].
% 0.77/1.07 Derived: function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(17,b,12,a)].
% 0.77/1.07 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(17,b,13,a)].
% 0.77/1.07 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(17,b,14,a)].
% 0.77/1.07 Derived: function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(17,b,15,a)].
% 0.77/1.07 18 function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(8,b,6,a)].
% 0.77/1.07 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(18,b,9,a)].
% 0.77/1.07 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(18,b,11,a)].
% 0.77/1.07 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(18,b,12,a)].
% 0.77/1.07 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(18,b,13,a)].
% 0.77/1.07 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(18,b,14,a)].
% 0.77/1.07 Derived: function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(18,b,15,a)].
% 0.77/1.07 19 disjoint(A,B) | member(f23(A,B),A) # label(disjoint2) # label(axiom). [assumption].
% 0.77/1.07 20 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint1) # label(axiom). [assumption].
% 0.77/1.07 Derived: member(f23(A,B),A) | -member(C,A) | -member(C,B). [resolve(19,a,20,a)].
% 0.77/1.07 21 disjoint(A,B) | member(f23(A,B),B) # label(disjoint3) # label(axiom). [assumption].
% 0.77/1.07 Derived: member(f23(A,B),B) | -member(C,A) | -member(C,B). [resolve(21,a,20,a)].
% 0.77/1.07 22 A = empty_set | disjoint(f24(A),A) # label(regularity2) # label(axiom). [assumption].
% 0.77/1.07 Derived: A = empty_set | -member(B,f24(A)) | -member(B,A). [resolve(22,b,20,a)].
% 0.77/1.07 23 one_to_one_function(A) | -function(A) | -function(converse(A)) # label(one_to_one_function3) # label(axiom). [assumption].
% 0.77/1.07 24 -one_to_one_function(A) | function(A) # label(one_to_one_function1) # label(axiom). [assumption].
% 0.77/1.07 25 -one_to_one_function(A) | function(converse(A)) # label(one_to_one_function2) # label(axiom). [assumption].
% 0.77/1.07 26 -finite(A) | one_to_one_function(f58(A)) # label(finite4) # label(axiom). [assumption].
% 0.77/1.07 Derived: -finite(A) | function(f58(A)). [resolve(26,b,24,a)].
% 0.77/1.08 Derived: -finite(A) | function(converse(f58(A))). [resolve(26,b,25,a)].
% 0.77/1.08 27 finite(A) | -member(B,natural_numbers) | -maps(C,B,A) | range_of(C) != A | -one_to_one_function(C) # label(finite5) # label(axiom). [assumption].
% 0.77/1.08 Derived: finite(A) | -member(B,natural_numbers) | -maps(C,B,A) | range_of(C) != A | -function(C) | -function(converse(C)). [resolve(27,e,23,a)].
% 0.77/1.08 Derived: finite(A) | -member(B,natural_numbers) | -maps(f58(C),B,A) | range_of(f58(C)) != A | -finite(C). [resolve(27,e,26,b)].
% 0.77/1.08 28 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].
% 0.77/1.08 29 -homomorphism(A,B,C,D,E) | closed(B,C) # label(homomorphism1) # label(axiom). [assumption].
% 0.77/1.08 30 -homomorphism(A,B,C,D,E) | closed(D,E) # label(homomorphism2) # label(axiom). [assumption].
% 0.77/1.08 31 -homomorphism(A,B,C,D,E) | maps(A,B,D) # label(homomorphism3) # label(axiom). [assumption].
% 0.77/1.08 32 -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].
% 0.77/1.08 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(28,a,32,a)].
% 0.77/1.08 33 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].
% 0.77/1.08 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(33,a,32,a)].
% 0.77/1.08 34 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].
% 0.77/1.08 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(34,a,32,a)].
% 0.77/1.08 35 associative(A,B) | member(f34(A,B),A) # label(associative_system2) # label(axiom). [assumption].
% 0.77/1.08 36 -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].
% 0.77/1.08 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(35,a,36,a)].
% 0.77/1.08 37 associative(A,B) | member(f35(A,B),A) # label(associative_system3) # label(axiom). [assumption].
% 0.77/1.08 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(37,a,36,a)].
% 0.77/1.08 38 associative(A,B) | member(f36(A,B),A) # label(associative_system4) # label(axiom). [assumption].
% 0.77/1.08 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(38,a,36,a)].
% 0.77/1.08 39 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].
% 0.77/1.08 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(39,a,36,a)].
% 0.82/1.08 40 -group(A,B) | associative(A,B) # label(group2) # label(axiom). [assumption].
% 0.82/1.08 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(40,b,36,a)].
% 0.82/1.08 41 group(A,B) | -closed(A,B) | -associative(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) # label(group5) # label(axiom). [assumption].
% 0.82/1.08 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f34(A,B),A). [resolve(41,c,35,a)].
% 0.82/1.08 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f35(A,B),A). [resolve(41,c,37,a)].
% 0.82/1.08 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f36(A,B),A). [resolve(41,c,38,a)].
% 0.82/1.08 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(41,c,39,a)].
% 0.82/1.08 42 identity(A,B,C) | -member(C,A) | member(f37(A,B,C),A) # label(identity4) # label(axiom). [assumption].
% 0.82/1.08 43 -identity(A,B,C) | member(C,A) # label(identity1) # label(axiom). [assumption].
% 0.82/1.08 44 -identity(A,B,C) | -member(D,A) | apply_to_two_arguments(B,C,D) = D # label(identity2) # label(axiom). [assumption].
% 0.82/1.08 45 -identity(A,B,C) | -member(D,A) | apply_to_two_arguments(B,D,C) = D # label(identity3) # label(axiom). [assumption].
% 0.82/1.08 Derived: -member(A,B) | member(f37(B,C,A),B) | -member(D,B) | apply_to_two_arguments(C,A,D) = D. [resolve(42,a,44,a)].
% 0.82/1.08 Derived: -member(A,B) | member(f37(B,C,A),B) | -member(D,B) | apply_to_two_arguments(C,D,A) = D. [resolve(42,a,45,a)].
% 0.82/1.08 46 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].
% 0.82/1.08 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(46,a,44,a)].
% 0.82/1.08 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(46,a,45,a)].
% 0.82/1.08 47 -group(A,B) | identity(A,B,f39(A,B)) # label(group3) # label(axiom). [assumption].
% 0.82/1.08 Derived: -group(A,B) | member(f39(A,B),A). [resolve(47,b,43,a)].
% 0.82/1.08 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,f39(A,B),C) = C. [resolve(47,b,44,a)].
% 0.82/1.08 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,f39(A,B)) = C. [resolve(47,b,45,a)].
% 0.82/1.08 48 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f34(A,B),A). [resolve(41,c,35,a)].
% 0.82/1.08 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(48,c,42,a)].
% 0.82/1.08 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(48,c,46,a)].
% 0.82/1.08 49 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f35(A,B),A). [resolve(41,c,37,a)].
% 0.82/1.08 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(49,c,42,a)].
% 0.82/1.08 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(49,c,46,a)].
% 0.82/1.08 50 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f36(A,B),A). [resolve(41,c,38,a)].
% 0.82/1.08 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(50,c,42,a)].
% 0.82/1.08 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(50,c,46,a)].
% 0.82/1.09 51 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(41,c,39,a)].
% 0.82/1.09 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(51,c,42,a)].
% 0.82/1.09 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(51,c,46,a)].
% 0.82/1.09 52 inverse(A,B,C,D) | -maps(D,A,A) | member(f38(A,B,C,D),A) # label(inverse4) # label(axiom). [assumption].
% 0.82/1.09 53 -inverse(A,B,C,D) | maps(D,A,A) # label(inverse1) # label(axiom). [assumption].
% 0.82/1.09 54 -inverse(A,B,C,D) | -member(E,A) | apply_to_two_arguments(B,apply(D,E),E) = C # label(inverse2) # label(axiom). [assumption].
% 0.82/1.09 55 -inverse(A,B,C,D) | -member(E,A) | apply_to_two_arguments(B,E,apply(D,E)) = C # label(inverse3) # label(axiom). [assumption].
% 0.82/1.09 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(52,a,54,a)].
% 0.82/1.09 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(52,a,55,a)].
% 0.82/1.09 56 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].
% 0.82/1.09 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(56,a,54,a)].
% 0.82/1.09 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(56,a,55,a)].
% 0.82/1.09 57 -group(A,B) | inverse(A,B,f39(A,B),f40(A,B)) # label(group4) # label(axiom). [assumption].
% 0.82/1.09 Derived: -group(A,B) | maps(f40(A,B),A,A). [resolve(57,b,53,a)].
% 0.82/1.09 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,apply(f40(A,B),C),C) = f39(A,B). [resolve(57,b,54,a)].
% 0.82/1.09 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,apply(f40(A,B),C)) = f39(A,B). [resolve(57,b,55,a)].
% 0.82/1.09 58 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(48,c,42,a)].
% 0.82/1.09 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(58,c,52,a)].
% 0.82/1.09 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(58,c,56,a)].
% 0.82/1.09 59 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(48,c,46,a)].
% 0.82/1.09 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(59,c,52,a)].
% 0.82/1.09 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(59,c,56,a)].
% 0.82/1.09 60 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(49,c,42,a)].
% 0.82/1.09 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(60,c,52,a)].
% 0.82/1.09 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(60,c,56,a)].
% 0.82/1.09 61 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(49,c,46,a)].
% 0.82/1.09 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(61,c,52,a)].
% 0.82/1.09 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(61,c,56,a)].
% 0.82/1.09 62 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(50,c,42,a)].
% 0.82/1.09 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(62,c,52,a)].
% 0.82/1.09 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(62,c,56,a)].
% 0.82/1.09 63 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(50,c,46,a)].
% 0.82/1.09 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(63,c,52,a)].
% 0.82/1.09 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(63,c,56,a)].
% 0.82/1.09 64 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(51,c,42,a)].
% 0.82/1.09 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(64,c,52,a)].
% 0.82/1.09 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(64,c,56,a)].
% 0.82/1.09 65 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(51,c,46,a)].
% 0.82/1.10 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(65,c,52,a)].
% 0.82/1.10 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(65,c,56,a)].
% 0.82/1.10 66 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(58,c,52,a)].
% 0.82/1.10 67 -group(A,B) | closed(A,B) # label(group1) # label(axiom). [assumption].
% 0.82/1.10 68 -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(40,b,36,a)].
% 0.82/1.10 69 -group(A,B) | member(f39(A,B),A). [resolve(47,b,43,a)].
% 0.82/1.10 70 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,f39(A,B),C) = C. [resolve(47,b,44,a)].
% 0.82/1.10 71 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,f39(A,B)) = C. [resolve(47,b,45,a)].
% 0.82/1.10 72 -group(A,B) | maps(f40(A,B),A,A). [resolve(57,b,53,a)].
% 0.82/1.10 73 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,apply(f40(A,B),C),C) = f39(A,B). [resolve(57,b,54,a)].
% 0.82/1.10 74 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,apply(f40(A,B),C)) = f39(A,B). [resolve(57,b,55,a)].
% 0.82/1.10 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(66,a,68,a)].
% 0.82/1.10 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(66,a,69,a)].
% 0.82/1.10 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(66,a,70,a)].
% 0.82/1.10 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(66,a,71,a)].
% 0.82/1.10 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(66,a,72,a)].
% 0.82/1.10 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(66,a,73,a)].
% 0.82/1.10 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(66,a,74,a)].
% 0.82/1.10 75 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(58,c,56,a)].
% 0.82/1.10 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(75,a,68,a)].
% 0.82/1.10 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(75,a,69,a)].
% 0.82/1.10 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(75,a,70,a)].
% 0.82/1.10 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(75,a,71,a)].
% 0.82/1.10 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(75,a,72,a)].
% 0.82/1.10 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(75,a,73,a)].
% 0.82/1.10 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(75,a,74,a)].
% 0.82/1.10 76 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(59,c,52,a)].
% 0.82/1.10 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(76,a,68,a)].
% 0.82/1.10 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(76,a,69,a)].
% 0.82/1.10 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(76,a,70,a)].
% 0.82/1.10 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(76,a,71,a)].
% 0.82/1.10 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(76,a,72,a)].
% 0.82/1.10 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(76,a,73,a)].
% 0.82/1.10 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(76,a,74,a)].
% 0.82/1.10 77 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(59,c,56,a)].
% 0.82/1.10 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(77,a,68,a)].
% 0.82/1.10 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(77,a,69,a)].
% 0.82/1.10 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(77,a,70,a)].
% 0.82/1.10 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(77,a,71,a)].
% 0.82/1.10 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(77,a,72,a)].
% 0.82/1.10 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(77,a,73,a)].
% 0.82/1.10 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(77,a,74,a)].
% 0.82/1.10 78 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(60,c,52,a)].
% 0.82/1.10 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(78,a,68,a)].
% 0.82/1.10 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(78,a,69,a)].
% 0.82/1.10 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(78,a,70,a)].
% 0.82/1.10 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(78,a,71,a)].
% 0.82/1.10 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(78,a,72,a)].
% 0.82/1.10 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(78,a,73,a)].
% 0.82/1.10 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(78,a,74,a)].
% 0.82/1.10 79 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(60,c,56,a)].
% 0.82/1.10 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(79,a,68,a)].
% 0.82/1.10 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(79,a,69,a)].
% 0.82/1.10 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(79,a,70,a)].
% 0.82/1.10 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(79,a,71,a)].
% 0.82/1.10 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(79,a,72,a)].
% 0.82/1.10 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(79,a,73,a)].
% 0.82/1.10 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(79,a,74,a)].
% 0.82/1.10 80 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(61,c,52,a)].
% 0.82/1.10 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(80,a,68,a)].
% 0.82/1.10 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(80,a,69,a)].
% 0.82/1.10 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(80,a,70,a)].
% 0.82/1.10 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(80,a,71,a)].
% 0.82/1.10 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(80,a,72,a)].
% 0.82/1.10 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(80,a,73,a)].
% 0.82/1.10 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(80,a,74,a)].
% 0.82/1.10 81 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(61,c,56,a)].
% 0.82/1.10 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(81,a,68,a)].
% 0.82/1.10 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(81,a,69,a)].
% 0.82/1.10 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(81,a,70,a)].
% 0.82/1.10 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(81,a,71,a)].
% 0.82/1.10 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(81,a,72,a)].
% 0.82/1.10 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(81,a,73,a)].
% 0.82/1.11 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(81,a,74,a)].
% 0.82/1.11 82 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(62,c,52,a)].
% 0.82/1.11 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(82,a,68,a)].
% 0.82/1.11 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(82,a,69,a)].
% 0.82/1.11 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(82,a,70,a)].
% 0.82/1.11 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(82,a,71,a)].
% 0.82/1.11 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(82,a,72,a)].
% 0.82/1.11 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(82,a,73,a)].
% 0.82/1.11 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(82,a,74,a)].
% 0.82/1.11 83 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(62,c,56,a)].
% 0.82/1.11 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(83,a,68,a)].
% 0.82/1.11 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(83,a,69,a)].
% 0.82/1.11 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(83,a,70,a)].
% 0.82/1.11 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(83,a,71,a)].
% 0.82/1.11 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(83,a,72,a)].
% 0.82/1.11 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(83,a,73,a)].
% 0.82/1.11 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(83,a,74,a)].
% 0.82/1.11 84 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(63,c,52,a)].
% 0.82/1.11 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(84,a,68,a)].
% 0.82/1.11 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(84,a,69,a)].
% 0.82/1.11 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(84,a,70,a)].
% 0.82/1.11 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(84,a,71,a)].
% 0.82/1.11 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(84,a,72,a)].
% 0.82/1.11 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(84,a,73,a)].
% 0.82/1.11 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(84,a,74,a)].
% 0.82/1.11 85 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(63,c,56,a)].
% 0.82/1.11 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(85,a,68,a)].
% 0.82/1.11 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(85,a,69,a)].
% 0.82/1.11 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(85,a,70,a)].
% 0.82/1.11 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(85,a,71,a)].
% 0.82/1.11 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(85,a,72,a)].
% 0.82/1.11 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(85,a,73,a)].
% 0.82/1.11 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(85,a,74,a)].
% 0.82/1.11 86 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(64,c,52,a)].
% 0.82/1.11 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(86,a,68,a)].
% 0.82/1.11 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(86,a,69,a)].
% 0.82/1.11 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(86,a,70,a)].
% 0.82/1.11 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(86,a,71,a)].
% 0.82/1.11 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(86,a,72,a)].
% 0.82/1.11 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(86,a,73,a)].
% 0.82/1.11 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(86,a,74,a)].
% 0.82/1.11 87 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(64,c,56,a)].
% 0.82/1.11 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(87,a,68,a)].
% 0.82/1.11 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(87,a,69,a)].
% 0.82/1.11 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(87,a,70,a)].
% 0.82/1.11 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(87,a,71,a)].
% 0.82/1.11 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(87,a,72,a)].
% 0.82/1.11 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(87,a,73,a)].
% 0.82/1.11 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(87,a,74,a)].
% 0.82/1.11 88 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(65,c,52,a)].
% 0.82/1.11 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(88,a,68,a)].
% 0.82/1.11 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(88,a,69,a)].
% 0.82/1.11 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(88,a,70,a)].
% 0.82/1.11 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(88,a,71,a)].
% 0.82/1.11 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(88,a,72,a)].
% 0.82/1.11 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(88,a,73,a)].
% 0.82/1.11 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(88,a,74,a)].
% 0.82/1.11 89 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(65,c,56,a)].
% 0.82/1.11 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(89,a,68,a)].
% 0.82/1.11 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(89,a,69,a)].
% 0.82/1.11 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(89,a,70,a)].
% 0.82/1.11 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(89,a,71,a)].
% 0.82/1.11 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(89,a,72,a)].
% 0.82/1.11 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(89,a,73,a)].
% 0.82/1.11 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(89,a,74,a)].
% 1.42/1.71 90 commutes(A,B) | member(f41(A,B),A) # label(commutes2) # label(axiom). [assumption].
% 1.42/1.71 91 -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].
% 1.42/1.71 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(90,a,91,a)].
% 1.42/1.71 92 commutes(A,B) | member(f42(A,B),A) # label(commutes3) # label(axiom). [assumption].
% 1.42/1.71 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(92,a,91,a)].
% 1.42/1.71 93 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].
% 1.42/1.71 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(93,a,91,a)].
% 1.42/1.71
% 1.42/1.71 ============================== end predicate elimination =============
% 1.42/1.71
% 1.42/1.71 Auto_denials: (non-Horn, no changes).
% 1.42/1.71
% 1.42/1.71 Term ordering decisions:
% 1.42/1.71 Function symbol KB weights: natural_numbers=1. empty_set=1. plus=1. times=1. prime_numbers=1. even_numbers=1. infinity=1. estin=1. identity_relation=1. twin_prime_numbers=1. f25=1. universal_set=1. apply=1. ordered_pair=1. f34=1. f35=1. f36=1. f39=1. f40=1. f45=1. f50=1. non_ordered_pair=1. f52=1. compose=1. cross_product=1. f46=1. f47=1. f48=1. f51=1. f53=1. image=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. f43=1. f5=1. f6=1. union=1. restrict=1. successor=1. first=1. second=1. f18=1. f19=1. f20=1. f21=1. range_of=1. domain_of=1. f58=1. flip_range_of=1. rotate_right=1. converse=1. f44=1. f49=1. f54=1. complement=1. sigma=1. f55=1. f59=1. powerset=1. singleton_set=1. f2=1. f24=1. f26=1. f3=1. f56=1. f57=1. apply_to_two_arguments=1. f37=1. f22=1. f28=1. f29=1. f30=1. f31=1. f38=1. f32=1. f33=1.
% 1.42/1.71
% 1.42/1.71 ============================== end of process initial clauses ========
% 1.42/1.71
% 1.42/1.71 ============================== CLAUSES FOR SEARCH ====================
% 1.42/1.71
% 1.42/1.71 ============================== end of clauses for search =============
% 1.42/1.71
% 1.42/1.71 ============================== SEARCH ================================
% 1.42/1.71
% 1.42/1.71 % Starting search at 0.23 seconds.
% 1.42/1.71
% 1.42/1.71 ============================== PROOF =================================
% 1.42/1.71 % SZS status Unsatisfiable
% 1.42/1.71 % SZS output start Refutation
% 1.42/1.71
% 1.42/1.71 % Proof 1 at 0.68 (+ 0.01) seconds.
% 1.42/1.71 % Length of proof is 8.
% 1.42/1.71 % Level of proof is 3.
% 1.42/1.71 % Maximum clause weight is 9.000.
% 1.42/1.71 % Given clauses 489.
% 1.42/1.71
% 1.42/1.71 94 -member(A,B) | little_set(A) # label(a2) # label(axiom). [assumption].
% 1.42/1.71 172 member(empty_set,infinity) # label(infinity2) # label(axiom). [assumption].
% 1.42/1.71 240 member(A,natural_numbers) | -little_set(A) | member(empty_set,f44(A)) # label(natural_numbers4) # label(axiom). [assumption].
% 1.42/1.71 243 member(A,natural_numbers) | -member(A,f44(A)) # label(natural_numbers6) # label(axiom). [assumption].
% 1.42/1.71 319 -member(empty_set,natural_numbers) # label(prove_zero_is_a_natural) # label(negated_conjecture). [assumption].
% 1.42/1.71 892 little_set(empty_set). [resolve(172,a,94,a)].
% 1.42/1.71 2593 member(empty_set,f44(empty_set)). [resolve(892,a,240,b),unit_del(a,319)].
% 1.42/1.71 3216 $F. [resolve(2593,a,243,b),unit_del(a,319)].
% 1.42/1.71
% 1.42/1.71 % SZS output end Refutation
% 1.42/1.71 ============================== end of proof ==========================
% 1.42/1.71
% 1.42/1.71 ============================== STATISTICS ============================
% 1.42/1.71
% 1.42/1.71 Given=489. Generated=3780. Kept=2922. proofs=1.
% 1.42/1.71 Usable=489. Sos=2364. Demods=6. Limbo=64, Disabled=421. Hints=0.
% 1.42/1.71 Megabytes=11.81.
% 1.42/1.71 User_CPU=0.68, System_CPU=0.01, Wall_clock=0.
% 1.42/1.71
% 1.42/1.71 ============================== end of statistics =====================
% 1.42/1.71
% 1.42/1.71 ============================== end of search =========================
% 1.42/1.71
% 1.42/1.71 THEOREM PROVED
% 1.42/1.71 % SZS status Unsatisfiable
% 1.42/1.71
% 1.42/1.71 Exiting with 1 proof.
% 1.42/1.71
% 1.42/1.71 Process 4655 exit (max_proofs) Thu Jul 7 12:10:24 2022
% 1.42/1.71 Prover9 interrupted
%------------------------------------------------------------------------------