TSTP Solution File: ALG009-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG009-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Thu Jul 14 17:53:35 EDT 2022
% Result : Timeout 300.06s 300.53s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG009-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 04:12:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.76/1.02 ============================== Prover9 ===============================
% 0.76/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.02 Process 26652 was started by sandbox on n019.cluster.edu,
% 0.76/1.02 Wed Jun 8 04:12:41 2022
% 0.76/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26499_n019.cluster.edu".
% 0.76/1.02 ============================== end of head ===========================
% 0.76/1.02
% 0.76/1.02 ============================== INPUT =================================
% 0.76/1.02
% 0.76/1.02 % Reading from file /tmp/Prover9_26499_n019.cluster.edu
% 0.76/1.02
% 0.76/1.02 set(prolog_style_variables).
% 0.76/1.02 set(auto2).
% 0.76/1.02 % set(auto2) -> set(auto).
% 0.76/1.02 % set(auto) -> set(auto_inference).
% 0.76/1.02 % set(auto) -> set(auto_setup).
% 0.76/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.02 % set(auto) -> set(auto_limits).
% 0.76/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.02 % set(auto) -> set(auto_denials).
% 0.76/1.02 % set(auto) -> set(auto_process).
% 0.76/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.02 % set(auto2) -> assign(stats, some).
% 0.76/1.02 % set(auto2) -> clear(echo_input).
% 0.76/1.02 % set(auto2) -> set(quiet).
% 0.76/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.02 % set(auto2) -> clear(print_given).
% 0.76/1.02 assign(lrs_ticks,-1).
% 0.76/1.02 assign(sos_limit,10000).
% 0.76/1.02 assign(order,kbo).
% 0.76/1.02 set(lex_order_vars).
% 0.76/1.02 clear(print_given).
% 0.76/1.02
% 0.76/1.02 % formulas(sos). % not echoed (165 formulas)
% 0.76/1.02
% 0.76/1.02 ============================== end of input ==========================
% 0.76/1.02
% 0.76/1.02 % From the command line: assign(max_seconds, 300).
% 0.76/1.02
% 0.76/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.02
% 0.76/1.02 % Formulas that are not ordinary clauses:
% 0.76/1.02
% 0.76/1.02 ============================== end of process non-clausal formulas ===
% 0.76/1.02
% 0.76/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.02
% 0.76/1.02 ============================== PREDICATE ELIMINATION =================
% 0.76/1.02 1 associative(A,B) | member(f34(A,B),A) # label(associative_system2) # label(axiom). [assumption].
% 0.76/1.02 2 -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].
% 0.76/1.02 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(1,a,2,a)].
% 0.76/1.02 3 associative(A,B) | member(f35(A,B),A) # label(associative_system3) # label(axiom). [assumption].
% 0.76/1.02 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(3,a,2,a)].
% 0.76/1.02 4 associative(A,B) | member(f36(A,B),A) # label(associative_system4) # label(axiom). [assumption].
% 0.76/1.02 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(4,a,2,a)].
% 0.76/1.02 5 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].
% 0.76/1.02 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(5,a,2,a)].
% 0.76/1.03 6 -group(A,B) | associative(A,B) # label(group2) # label(axiom). [assumption].
% 0.76/1.03 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(6,b,2,a)].
% 0.76/1.03 7 group(A,B) | -closed(A,B) | -associative(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) # label(group5) # label(axiom). [assumption].
% 0.76/1.03 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f34(A,B),A). [resolve(7,c,1,a)].
% 0.76/1.03 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f35(A,B),A). [resolve(7,c,3,a)].
% 0.76/1.03 Derived: group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f36(A,B),A). [resolve(7,c,4,a)].
% 0.76/1.03 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(7,c,5,a)].
% 0.76/1.03 8 identity(A,B,C) | -member(C,A) | member(f37(A,B,C),A) # label(identity4) # label(axiom). [assumption].
% 0.76/1.03 9 -identity(A,B,C) | member(C,A) # label(identity1) # label(axiom). [assumption].
% 0.76/1.03 10 -identity(A,B,C) | -member(D,A) | apply_to_two_arguments(B,C,D) = D # label(identity2) # label(axiom). [assumption].
% 0.76/1.03 11 -identity(A,B,C) | -member(D,A) | apply_to_two_arguments(B,D,C) = D # label(identity3) # label(axiom). [assumption].
% 0.76/1.03 Derived: -member(A,B) | member(f37(B,C,A),B) | -member(D,B) | apply_to_two_arguments(C,A,D) = D. [resolve(8,a,10,a)].
% 0.76/1.03 Derived: -member(A,B) | member(f37(B,C,A),B) | -member(D,B) | apply_to_two_arguments(C,D,A) = D. [resolve(8,a,11,a)].
% 0.76/1.03 12 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].
% 0.76/1.03 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(12,a,10,a)].
% 0.76/1.03 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(12,a,11,a)].
% 0.76/1.03 13 -group(A,B) | identity(A,B,f39(A,B)) # label(group3) # label(axiom). [assumption].
% 0.76/1.03 Derived: -group(A,B) | member(f39(A,B),A). [resolve(13,b,9,a)].
% 0.76/1.03 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,f39(A,B),C) = C. [resolve(13,b,10,a)].
% 0.76/1.03 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,f39(A,B)) = C. [resolve(13,b,11,a)].
% 0.76/1.03 14 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f34(A,B),A). [resolve(7,c,1,a)].
% 0.76/1.03 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(14,c,8,a)].
% 0.76/1.03 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(14,c,12,a)].
% 0.76/1.03 15 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f35(A,B),A). [resolve(7,c,3,a)].
% 0.76/1.03 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(15,c,8,a)].
% 0.76/1.03 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(15,c,12,a)].
% 0.76/1.03 16 group(A,B) | -closed(A,B) | -identity(A,B,C) | -inverse(A,B,C,D) | member(f36(A,B),A). [resolve(7,c,4,a)].
% 0.76/1.03 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(16,c,8,a)].
% 0.76/1.03 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(16,c,12,a)].
% 0.76/1.03 17 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(7,c,5,a)].
% 0.76/1.03 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(17,c,8,a)].
% 0.76/1.03 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(17,c,12,a)].
% 0.76/1.03 18 inverse(A,B,C,D) | -maps(D,A,A) | member(f38(A,B,C,D),A) # label(inverse4) # label(axiom). [assumption].
% 0.76/1.03 19 -inverse(A,B,C,D) | maps(D,A,A) # label(inverse1) # label(axiom). [assumption].
% 0.76/1.03 20 -inverse(A,B,C,D) | -member(E,A) | apply_to_two_arguments(B,apply(D,E),E) = C # label(inverse2) # label(axiom). [assumption].
% 0.76/1.03 21 -inverse(A,B,C,D) | -member(E,A) | apply_to_two_arguments(B,E,apply(D,E)) = C # label(inverse3) # label(axiom). [assumption].
% 0.76/1.03 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(18,a,20,a)].
% 0.76/1.03 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(18,a,21,a)].
% 0.76/1.03 22 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].
% 0.76/1.03 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(22,a,20,a)].
% 0.76/1.03 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(22,a,21,a)].
% 0.76/1.03 23 -group(A,B) | inverse(A,B,f39(A,B),f40(A,B)) # label(group4) # label(axiom). [assumption].
% 0.76/1.03 Derived: -group(A,B) | maps(f40(A,B),A,A). [resolve(23,b,19,a)].
% 0.76/1.03 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,apply(f40(A,B),C),C) = f39(A,B). [resolve(23,b,20,a)].
% 0.76/1.03 Derived: -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,apply(f40(A,B),C)) = f39(A,B). [resolve(23,b,21,a)].
% 0.76/1.03 24 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(14,c,8,a)].
% 0.76/1.03 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(24,c,18,a)].
% 0.76/1.03 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(24,c,22,a)].
% 0.76/1.03 25 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(14,c,12,a)].
% 0.76/1.03 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(25,c,18,a)].
% 0.76/1.03 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(25,c,22,a)].
% 0.76/1.03 26 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(15,c,8,a)].
% 0.76/1.03 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(26,c,18,a)].
% 0.76/1.03 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(26,c,22,a)].
% 0.76/1.03 27 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(15,c,12,a)].
% 0.76/1.03 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(27,c,18,a)].
% 0.76/1.03 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(27,c,22,a)].
% 0.76/1.03 28 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(16,c,8,a)].
% 0.76/1.03 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(28,c,18,a)].
% 0.76/1.03 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(28,c,22,a)].
% 0.76/1.03 29 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(16,c,12,a)].
% 0.76/1.03 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(29,c,18,a)].
% 0.76/1.03 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(29,c,22,a)].
% 0.76/1.03 30 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(17,c,8,a)].
% 0.76/1.03 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(30,c,18,a)].
% 0.76/1.03 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(30,c,22,a)].
% 0.76/1.03 31 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(17,c,12,a)].
% 0.76/1.04 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(31,c,18,a)].
% 0.76/1.04 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(31,c,22,a)].
% 0.76/1.04 32 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(24,c,18,a)].
% 0.76/1.04 33 -group(A,B) | closed(A,B) # label(group1) # label(axiom). [assumption].
% 0.76/1.04 34 -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(6,b,2,a)].
% 0.76/1.04 35 -group(A,B) | member(f39(A,B),A). [resolve(13,b,9,a)].
% 0.76/1.04 36 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,f39(A,B),C) = C. [resolve(13,b,10,a)].
% 0.76/1.04 37 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,f39(A,B)) = C. [resolve(13,b,11,a)].
% 0.76/1.04 38 -group(A,B) | maps(f40(A,B),A,A). [resolve(23,b,19,a)].
% 0.76/1.04 39 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,apply(f40(A,B),C),C) = f39(A,B). [resolve(23,b,20,a)].
% 0.76/1.04 40 -group(A,B) | -member(C,A) | apply_to_two_arguments(B,C,apply(f40(A,B),C)) = f39(A,B). [resolve(23,b,21,a)].
% 0.76/1.04 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(32,a,34,a)].
% 0.76/1.04 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(32,a,35,a)].
% 0.76/1.04 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(32,a,36,a)].
% 0.76/1.04 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(32,a,37,a)].
% 0.76/1.04 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(32,a,38,a)].
% 0.76/1.04 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(32,a,39,a)].
% 0.76/1.04 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(32,a,40,a)].
% 0.76/1.04 41 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(24,c,22,a)].
% 0.76/1.04 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(41,a,34,a)].
% 0.76/1.04 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(41,a,35,a)].
% 0.76/1.04 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(41,a,36,a)].
% 0.76/1.04 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(41,a,37,a)].
% 0.76/1.04 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(41,a,38,a)].
% 0.76/1.04 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(41,a,39,a)].
% 0.76/1.04 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(41,a,40,a)].
% 0.76/1.04 42 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(25,c,18,a)].
% 0.76/1.04 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(42,a,34,a)].
% 0.76/1.04 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(42,a,35,a)].
% 0.76/1.04 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(42,a,36,a)].
% 0.76/1.04 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(42,a,37,a)].
% 0.76/1.04 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(42,a,38,a)].
% 0.76/1.04 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(42,a,39,a)].
% 0.76/1.04 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(42,a,40,a)].
% 0.76/1.04 43 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(25,c,22,a)].
% 0.76/1.04 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(43,a,34,a)].
% 0.76/1.04 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(43,a,35,a)].
% 0.76/1.04 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(43,a,36,a)].
% 0.76/1.04 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(43,a,37,a)].
% 0.76/1.04 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(43,a,38,a)].
% 0.76/1.04 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(43,a,39,a)].
% 0.76/1.04 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(43,a,40,a)].
% 0.76/1.04 44 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(26,c,18,a)].
% 0.76/1.04 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(44,a,34,a)].
% 0.76/1.04 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(44,a,35,a)].
% 0.76/1.04 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(44,a,36,a)].
% 0.76/1.04 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(44,a,37,a)].
% 0.76/1.04 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(44,a,38,a)].
% 0.76/1.04 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(44,a,39,a)].
% 0.76/1.04 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(44,a,40,a)].
% 0.76/1.04 45 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(26,c,22,a)].
% 0.76/1.04 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(45,a,34,a)].
% 0.76/1.04 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(45,a,35,a)].
% 0.76/1.04 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(45,a,36,a)].
% 0.76/1.04 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(45,a,37,a)].
% 0.76/1.04 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(45,a,38,a)].
% 0.76/1.04 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(45,a,39,a)].
% 0.76/1.04 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(45,a,40,a)].
% 0.76/1.04 46 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(27,c,18,a)].
% 0.76/1.04 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(46,a,34,a)].
% 0.76/1.04 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(46,a,35,a)].
% 0.76/1.04 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(46,a,36,a)].
% 0.76/1.04 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(46,a,37,a)].
% 0.76/1.04 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(46,a,38,a)].
% 0.76/1.04 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(46,a,39,a)].
% 0.76/1.04 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(46,a,40,a)].
% 0.76/1.04 47 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(27,c,22,a)].
% 0.76/1.04 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(47,a,34,a)].
% 0.76/1.04 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(47,a,35,a)].
% 0.76/1.04 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(47,a,36,a)].
% 0.76/1.04 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(47,a,37,a)].
% 0.76/1.04 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(47,a,38,a)].
% 0.76/1.04 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(47,a,39,a)].
% 0.76/1.04 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(47,a,40,a)].
% 0.76/1.04 48 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(28,c,18,a)].
% 0.76/1.04 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(48,a,34,a)].
% 0.76/1.04 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(48,a,35,a)].
% 0.76/1.04 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(48,a,36,a)].
% 0.76/1.04 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(48,a,37,a)].
% 0.76/1.04 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(48,a,38,a)].
% 0.76/1.04 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(48,a,39,a)].
% 0.76/1.05 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(48,a,40,a)].
% 0.76/1.05 49 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(28,c,22,a)].
% 0.76/1.05 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(49,a,34,a)].
% 0.76/1.05 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(49,a,35,a)].
% 0.76/1.05 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(49,a,36,a)].
% 0.76/1.05 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(49,a,37,a)].
% 0.76/1.05 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(49,a,38,a)].
% 0.76/1.05 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(49,a,39,a)].
% 0.76/1.05 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(49,a,40,a)].
% 0.76/1.05 50 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(29,c,18,a)].
% 0.76/1.05 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(50,a,34,a)].
% 0.76/1.05 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(50,a,35,a)].
% 0.76/1.05 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(50,a,36,a)].
% 0.76/1.05 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(50,a,37,a)].
% 0.76/1.05 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(50,a,38,a)].
% 0.76/1.05 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(50,a,39,a)].
% 0.76/1.05 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(50,a,40,a)].
% 0.76/1.05 51 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(29,c,22,a)].
% 0.76/1.05 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(51,a,34,a)].
% 0.76/1.05 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(51,a,35,a)].
% 0.76/1.05 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(51,a,36,a)].
% 0.76/1.05 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(51,a,37,a)].
% 0.76/1.05 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(51,a,38,a)].
% 0.76/1.05 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(51,a,39,a)].
% 0.76/1.05 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(51,a,40,a)].
% 0.76/1.05 52 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(30,c,18,a)].
% 0.76/1.05 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(52,a,34,a)].
% 0.76/1.05 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(52,a,35,a)].
% 0.76/1.05 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(52,a,36,a)].
% 0.76/1.05 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(52,a,37,a)].
% 0.76/1.05 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(52,a,38,a)].
% 0.76/1.05 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(52,a,39,a)].
% 0.76/1.05 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(52,a,40,a)].
% 0.76/1.05 53 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(30,c,22,a)].
% 0.76/1.05 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(53,a,34,a)].
% 0.76/1.05 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(53,a,35,a)].
% 0.76/1.05 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(53,a,36,a)].
% 0.76/1.05 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(53,a,37,a)].
% 0.76/1.05 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(53,a,38,a)].
% 0.76/1.05 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(53,a,39,a)].
% 0.76/1.05 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(53,a,40,a)].
% 0.76/1.05 54 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(31,c,18,a)].
% 0.76/1.05 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(54,a,34,a)].
% 0.76/1.05 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(54,a,35,a)].
% 0.76/1.05 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(54,a,36,a)].
% 0.76/1.05 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(54,a,37,a)].
% 0.76/1.05 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(54,a,38,a)].
% 0.76/1.05 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(54,a,39,a)].
% 0.76/1.05 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(54,a,40,a)].
% 0.76/1.05 55 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(31,c,22,a)].
% 0.76/1.05 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(55,a,34,a)].
% 0.76/1.05 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(55,a,35,a)].
% 0.76/1.05 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(55,a,36,a)].
% 0.76/1.05 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(55,a,37,a)].
% 0.76/1.05 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(55,a,38,a)].
% 0.76/1.05 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(55,a,39,a)].
% 0.76/1.05 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(55,a,40,a)].
% 0.76/1.10 56 commutes(A,B) | member(f41(A,B),A) # label(commutes2) # label(axiom). [assumption].
% 0.76/1.10 57 -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].
% 0.76/1.10 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(56,a,57,a)].
% 0.76/1.10 58 commutes(A,B) | member(f42(A,B),A) # label(commutes3) # label(axiom). [assumption].
% 0.76/1.10 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(58,a,57,a)].
% 0.76/1.10 59 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].
% 0.76/1.10 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(59,a,57,a)].
% 0.76/1.10 60 proper_subset(A,B) | -subset(A,B) | A = B # label(proper_subset3) # label(axiom). [assumption].
% 0.76/1.10 61 -proper_subset(A,B) | subset(A,B) # label(proper_subset1) # label(axiom). [assumption].
% 0.76/1.10 62 -proper_subset(A,B) | A != B # label(proper_subset2) # label(axiom). [assumption].
% 0.76/1.10 63 relation(A) | member(f18(A),A) # label(relation2) # label(axiom). [assumption].
% 0.76/1.10 64 -relation(A) | -member(B,A) | ordered_pair_predicate(B) # label(relation1) # label(axiom). [assumption].
% 0.76/1.10 Derived: member(f18(A),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(63,a,64,a)].
% 0.76/1.10 65 relation(A) | -ordered_pair_predicate(f18(A)) # label(relation3) # label(axiom). [assumption].
% 0.76/1.10 Derived: -ordered_pair_predicate(f18(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(65,a,64,a)].
% 0.76/1.10 66 -function(A) | relation(A) # label(function1) # label(axiom). [assumption].
% 0.76/1.10 Derived: -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(66,b,64,a)].
% 0.76/1.10 67 function(A) | -relation(A) | -single_valued_set(A) # label(function3) # label(axiom). [assumption].
% 0.76/1.10 Derived: function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(67,b,63,a)].
% 0.76/1.10 Derived: function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(67,b,65,a)].
% 0.76/1.10 68 single_valued_set(A) | little_set(f19(A)) # label(single_valued_set2) # label(axiom). [assumption].
% 0.76/1.10 69 -single_valued_set(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D # label(single_valued_set1) # label(axiom). [assumption].
% 0.76/1.10 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(68,a,69,a)].
% 0.76/1.10 70 single_valued_set(A) | little_set(f20(A)) # label(single_valued_set3) # label(axiom). [assumption].
% 0.76/1.10 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(70,a,69,a)].
% 0.76/1.10 71 single_valued_set(A) | little_set(f21(A)) # label(single_valued_set4) # label(axiom). [assumption].
% 0.76/1.10 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(71,a,69,a)].
% 0.76/1.10 72 single_valued_set(A) | member(ordered_pair(f19(A),f20(A)),A) # label(single_valued_set5) # label(axiom). [assumption].
% 0.76/1.10 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(72,a,69,a)].
% 0.76/1.10 73 single_valued_set(A) | member(ordered_pair(f19(A),f21(A)),A) # label(single_valued_set6) # label(axiom). [assumption].
% 0.76/1.10 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(73,a,69,a)].
% 0.76/1.10 74 single_valued_set(A) | f20(A) != f21(A) # label(single_valued_set7) # label(axiom). [assumption].
% 0.76/1.13 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(74,a,69,a)].
% 0.76/1.13 75 -function(A) | single_valued_set(A) # label(function2) # label(axiom). [assumption].
% 0.76/1.13 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(75,b,69,a)].
% 0.76/1.13 76 function(A) | -single_valued_set(A) | member(f18(A),A). [resolve(67,b,63,a)].
% 0.76/1.13 Derived: function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(76,b,68,a)].
% 0.76/1.13 Derived: function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(76,b,70,a)].
% 0.76/1.13 Derived: function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(76,b,71,a)].
% 0.76/1.13 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(76,b,72,a)].
% 0.76/1.13 Derived: function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(76,b,73,a)].
% 0.76/1.13 Derived: function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(76,b,74,a)].
% 0.76/1.13 77 function(A) | -single_valued_set(A) | -ordered_pair_predicate(f18(A)). [resolve(67,b,65,a)].
% 0.76/1.13 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(77,b,68,a)].
% 0.76/1.13 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(77,b,70,a)].
% 0.76/1.13 Derived: function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(77,b,71,a)].
% 0.76/1.13 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(77,b,72,a)].
% 0.76/1.13 Derived: function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(77,b,73,a)].
% 0.76/1.13 Derived: function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(77,b,74,a)].
% 0.76/1.13 78 disjoint(A,B) | member(f23(A,B),A) # label(disjoint2) # label(axiom). [assumption].
% 0.76/1.13 79 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint1) # label(axiom). [assumption].
% 0.76/1.13 Derived: member(f23(A,B),A) | -member(C,A) | -member(C,B). [resolve(78,a,79,a)].
% 0.76/1.13 80 disjoint(A,B) | member(f23(A,B),B) # label(disjoint3) # label(axiom). [assumption].
% 0.76/1.13 Derived: member(f23(A,B),B) | -member(C,A) | -member(C,B). [resolve(80,a,79,a)].
% 0.76/1.13 81 A = empty_set | disjoint(f24(A),A) # label(regularity2) # label(axiom). [assumption].
% 0.76/1.13 Derived: A = empty_set | -member(B,f24(A)) | -member(B,A). [resolve(81,b,79,a)].
% 0.76/1.13 82 one_to_one_function(A) | -function(A) | -function(converse(A)) # label(one_to_one_function3) # label(axiom). [assumption].
% 0.76/1.13 83 -one_to_one_function(A) | function(A) # label(one_to_one_function1) # label(axiom). [assumption].
% 0.76/1.13 84 -one_to_one_function(A) | function(converse(A)) # label(one_to_one_function2) # label(axiom). [assumption].
% 0.76/1.13 85 function(f25) # label(choice1) # label(axiom). [assumption].
% 0.76/1.13 86 -little_set(A) | -function(B) | little_set(image(A,B)) # label(image_and_substitution6) # label(axiom). [assumption].
% 0.76/1.13 Derived: -little_set(A) | little_set(image(A,f25)). [resolve(85,a,86,b)].
% 0.76/1.13 87 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.76/1.13 Derived: -maps(A,B,C) | -little_set(D) | little_set(image(D,A)). [resolve(87,b,86,b)].
% 0.76/1.13 88 maps(A,B,C) | -function(A) | domain_of(A) != B | -subset(range_of(A),C) # label(maps4) # label(axiom). [assumption].
% 0.76/1.13 Derived: maps(f25,A,B) | domain_of(f25) != A | -subset(range_of(f25),B). [resolve(88,b,85,a)].
% 0.76/1.13 Derived: maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C) | -maps(A,D,E). [resolve(88,b,87,b)].
% 0.76/1.13 89 -function(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(66,b,64,a)].
% 0.76/1.13 Derived: -member(A,f25) | ordered_pair_predicate(A). [resolve(89,a,85,a)].
% 0.76/1.13 Derived: -member(A,B) | ordered_pair_predicate(A) | -maps(B,C,D). [resolve(89,a,87,b)].
% 0.76/1.13 90 -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(75,b,69,a)].
% 0.76/1.13 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(90,a,85,a)].
% 0.76/1.13 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(90,a,87,b)].
% 0.76/1.13 91 function(A) | member(f18(A),A) | little_set(f19(A)). [resolve(76,b,68,a)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(91,a,86,b)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f19(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(91,a,88,b)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(91,a,89,a)].
% 0.76/1.13 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(91,a,90,a)].
% 0.76/1.13 92 function(A) | member(f18(A),A) | little_set(f20(A)). [resolve(76,b,70,a)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(92,a,86,b)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f20(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(92,a,88,b)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(92,a,89,a)].
% 0.76/1.13 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(92,a,90,a)].
% 0.76/1.13 93 function(A) | member(f18(A),A) | little_set(f21(A)). [resolve(76,b,71,a)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(93,a,86,b)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f21(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(93,a,88,b)].
% 0.76/1.13 Derived: member(f18(A),A) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(93,a,89,a)].
% 0.76/1.13 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(93,a,90,a)].
% 0.76/1.13 94 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(76,b,72,a)].
% 0.76/1.13 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(94,a,86,b)].
% 0.76/1.13 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(94,a,88,b)].
% 0.76/1.13 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f20(A)),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(94,a,89,a)].
% 0.76/1.13 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(94,a,90,a)].
% 0.76/1.13 95 function(A) | member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(76,b,73,a)].
% 0.76/1.13 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(95,a,86,b)].
% 0.76/1.13 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(95,a,88,b)].
% 0.76/1.13 Derived: member(f18(A),A) | member(ordered_pair(f19(A),f21(A)),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(95,a,89,a)].
% 0.76/1.13 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(95,a,90,a)].
% 0.76/1.13 96 function(A) | member(f18(A),A) | f20(A) != f21(A). [resolve(76,b,74,a)].
% 0.76/1.13 Derived: member(f18(A),A) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(96,a,86,b)].
% 0.76/1.13 Derived: member(f18(A),A) | f20(A) != f21(A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(96,a,88,b)].
% 0.76/1.13 Derived: member(f18(A),A) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(96,a,89,a)].
% 0.76/1.13 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(96,a,90,a)].
% 0.76/1.13 97 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f19(A)). [resolve(77,b,68,a)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(97,a,86,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(97,a,88,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f19(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(97,a,89,a)].
% 0.76/1.13 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(97,a,90,a)].
% 0.76/1.13 98 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f20(A)). [resolve(77,b,70,a)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(98,a,86,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(98,a,88,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f20(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(98,a,89,a)].
% 0.76/1.13 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(98,a,90,a)].
% 0.76/1.13 99 function(A) | -ordered_pair_predicate(f18(A)) | little_set(f21(A)). [resolve(77,b,71,a)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(99,a,86,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(99,a,88,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | little_set(f21(A)) | -member(B,A) | ordered_pair_predicate(B). [resolve(99,a,89,a)].
% 0.76/1.13 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(99,a,90,a)].
% 0.76/1.13 100 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A). [resolve(77,b,72,a)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(100,a,86,b)].
% 0.76/1.13 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(100,a,88,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f20(A)),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(100,a,89,a)].
% 0.76/1.13 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(100,a,90,a)].
% 0.76/1.13 101 function(A) | -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A). [resolve(77,b,73,a)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(101,a,86,b)].
% 0.76/1.13 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(101,a,88,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | member(ordered_pair(f19(A),f21(A)),A) | -member(B,A) | ordered_pair_predicate(B). [resolve(101,a,89,a)].
% 0.76/1.13 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(101,a,90,a)].
% 0.76/1.13 102 function(A) | -ordered_pair_predicate(f18(A)) | f20(A) != f21(A). [resolve(77,b,74,a)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(102,a,86,b)].
% 0.76/1.13 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(102,a,88,b)].
% 1.83/2.11 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -member(B,A) | ordered_pair_predicate(B). [resolve(102,a,89,a)].
% 1.83/2.11 Derived: -ordered_pair_predicate(f18(A)) | f20(A) != f21(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(102,a,90,a)].
% 1.83/2.11 103 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].
% 1.83/2.11 104 -homomorphism(A,B,C,D,E) | closed(B,C) # label(homomorphism1) # label(axiom). [assumption].
% 1.83/2.11 105 -homomorphism(A,B,C,D,E) | closed(D,E) # label(homomorphism2) # label(axiom). [assumption].
% 1.83/2.11 106 -homomorphism(A,B,C,D,E) | maps(A,B,D) # label(homomorphism3) # label(axiom). [assumption].
% 1.83/2.11 107 -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].
% 1.83/2.11 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | member(f32(E,A,B,C,D),A) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(103,a,107,a)].
% 1.83/2.11 108 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].
% 1.83/2.11 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | member(f33(E,A,B,C,D),A) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(108,a,107,a)].
% 1.83/2.11 109 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].
% 1.83/2.11 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | apply(E,apply_to_two_arguments(B,f32(E,A,B,C,D),f33(E,A,B,C,D))) != apply_to_two_arguments(D,apply(E,f32(E,A,B,C,D)),apply(E,f33(E,A,B,C,D))) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(109,a,107,a)].
% 1.83/2.11
% 1.83/2.11 ============================== end predicate elimination =============
% 1.83/2.11
% 1.83/2.11 Auto_denials: (non-Horn, no changes).
% 1.83/2.11
% 1.83/2.11 Term ordering decisions:
% 1.83/2.11 Function symbol KB weights: 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.
% 1.83/2.11
% 1.83/2.11 ============================== end of process initial clauses ========
% 1.83/2.11
% 1.83/2.11 ============================== CLAUSES FOR SEARCH ====================
% 1.83/2.11
% 1.83/2.11 ============================== end of clauses for search =============
% 1.83/2.11
% 1.83/2.11 ============================== SEARCH ================================
% 1.83/2.11
% 1.83/2.11 % Starting search at 0.21 seconds.
% 1.83/2.11
% 1.83/2.11 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 839 (0.00 of 0.79 sec).
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=195.000, iters=3413
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=193.000, iters=3411
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=189.000, iters=3400
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=116.000, iters=3541
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=96.000, iters=3442
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=95.000, iters=3416
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=93.000, iters=3368
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=83.000, iters=3336
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=80.000, iters=3373
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=79.000, iters=3349
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=77.000, iters=3358
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=76.000, iters=3418
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=74.000, iters=3342
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=71.000, iters=3394
% 1.83/2.11
% 1.83/2.11 Low Water (keep): wt=70.000, iters=3341
% 300.06/300.53 Cputime limit exceeded (core dumped)
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