TSTP Solution File: SET766+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 04:31:56 EDT 2022
% Result : Theorem 7.77s 8.03s
% Output : Refutation 7.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 07:50:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 12852 was started by sandbox2 on n010.cluster.edu,
% 0.43/0.99 Sun Jul 10 07:50:31 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12698_n010.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_12698_n010.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (17 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 2 (all A all B (equal_set(A,B) <-> subset(A,B) & subset(B,A))) # label(equal_set) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 4 (all X all A all B (member(X,intersection(A,B)) <-> member(X,A) & member(X,B))) # label(intersection) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 5 (all X all A all B (member(X,union(A,B)) <-> member(X,A) | member(X,B))) # label(union) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all B all A all E (member(B,difference(E,A)) <-> member(B,E) & -member(B,A))) # label(difference) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 8 (all X all A (member(X,singleton(A)) <-> X = A)) # label(singleton) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 9 (all X all A all B (member(X,unordered_pair(A,B)) <-> X = A | X = B)) # label(unordered_pair) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 10 (all X all A (member(X,sum(A)) <-> (exists Y (member(Y,A) & member(X,Y))))) # label(sum) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 11 (all X all A (member(X,product(A)) <-> (all Y (member(Y,A) -> member(X,Y))))) # label(product) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 12 (all A all B (disjoint(A,B) <-> -(exists X (member(X,A) & member(X,B))))) # label(disjoint) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 13 (all A all E (partition(A,E) <-> (all X (member(X,A) -> subset(X,E))) & (all X (member(X,E) -> (exists Y (member(Y,A) & member(X,Y))))) & (all X all Y (member(X,A) & member(Y,A) -> ((exists Z (member(Z,X) & member(Z,Y))) -> X = Y))))) # label(partition) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 14 (all A all R (equivalence(R,A) <-> (all X (member(X,A) -> apply(R,X,X))) & (all X all Y (member(X,A) & member(Y,A) -> (apply(R,X,Y) -> apply(R,Y,X)))) & (all X all Y all Z (member(X,A) & member(Y,A) & member(Z,A) -> (apply(R,X,Y) & apply(R,Y,Z) -> apply(R,X,Z)))))) # label(equivalence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 15 (all R all E all A all X (member(X,equivalence_class(A,E,R)) <-> member(X,E) & apply(R,A,X))) # label(equivalence_class) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 16 (all R all E (pre_order(R,E) <-> (all X (member(X,E) -> apply(R,X,X))) & (all X all Y all Z (member(X,E) & member(Y,E) & member(Z,E) -> (apply(R,X,Y) & apply(R,Y,Z) -> apply(R,X,Z)))))) # label(pre_order) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 17 -(all E all R all A (equivalence(R,E) & member(A,E) -> member(A,equivalence_class(A,E,R)))) # label(thIII02) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.99
% 0.43/0.99 ============================== end of process non-clausal formulas ===
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.99
% 0.43/0.99 ============================== PREDICATE ELIMINATION =================
% 0.43/0.99 18 equal_set(A,B) | -subset(A,B) | -subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 0.43/0.99 19 -equal_set(A,B) | subset(A,B) # label(equal_set) # label(axiom). [clausify(2)].
% 0.43/0.99 20 -equal_set(A,B) | subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 0.43/0.99 21 disjoint(A,B) | member(f4(A,B),A) # label(disjoint) # label(axiom). [clausify(12)].
% 0.43/0.99 22 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint) # label(axiom). [clausify(12)].
% 0.43/0.99 Derived: member(f4(A,B),A) | -member(C,A) | -member(C,B). [resolve(21,a,22,a)].
% 0.43/0.99 23 disjoint(A,B) | member(f4(A,B),B) # label(disjoint) # label(axiom). [clausify(12)].
% 0.43/0.99 Derived: member(f4(A,B),B) | -member(C,A) | -member(C,B). [resolve(23,a,22,a)].
% 0.43/0.99 24 partition(A,B) | member(f6(A,B),A) | member(f7(A,B),B) | member(f8(A,B),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/0.99 25 -partition(A,B) | -member(C,A) | subset(C,B) # label(partition) # label(axiom). [clausify(13)].
% 0.43/0.99 26 -partition(A,B) | -member(C,B) | member(f5(A,B,C),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/0.99 27 -partition(A,B) | -member(C,B) | member(C,f5(A,B,C)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/0.99 28 -partition(A,B) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C # label(partition) # label(axiom). [clausify(13)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f8(A,B),A) | -member(C,A) | subset(C,B). [resolve(24,a,25,a)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f8(A,B),A) | -member(C,B) | member(f5(A,B,C),A). [resolve(24,a,26,a)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f8(A,B),A) | -member(C,B) | member(C,f5(A,B,C)). [resolve(24,a,27,a)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f8(A,B),A) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(24,a,28,a)].
% 0.43/0.99 29 partition(A,B) | member(f6(A,B),A) | member(f7(A,B),B) | member(f9(A,B),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f9(A,B),A) | -member(C,A) | subset(C,B). [resolve(29,a,25,a)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f9(A,B),A) | -member(C,B) | member(f5(A,B,C),A). [resolve(29,a,26,a)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f9(A,B),A) | -member(C,B) | member(C,f5(A,B,C)). [resolve(29,a,27,a)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f9(A,B),A) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(29,a,28,a)].
% 0.43/0.99 30 partition(A,B) | member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) | -member(C,A) | subset(C,B). [resolve(30,a,25,a)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) | -member(C,B) | member(f5(A,B,C),A). [resolve(30,a,26,a)].
% 0.43/0.99 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) | -member(C,B) | member(C,f5(A,B,C)). [resolve(30,a,27,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(30,a,28,a)].
% 0.43/1.00 31 partition(A,B) | member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) | -member(C,A) | subset(C,B). [resolve(31,a,25,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) | -member(C,B) | member(f5(A,B,C),A). [resolve(31,a,26,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) | -member(C,B) | member(C,f5(A,B,C)). [resolve(31,a,27,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(31,a,28,a)].
% 0.43/1.00 32 partition(A,B) | member(f6(A,B),A) | member(f7(A,B),B) | f9(A,B) != f8(A,B) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | f9(A,B) != f8(A,B) | -member(C,A) | subset(C,B). [resolve(32,a,25,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | f9(A,B) != f8(A,B) | -member(C,B) | member(f5(A,B,C),A). [resolve(32,a,26,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | f9(A,B) != f8(A,B) | -member(C,B) | member(C,f5(A,B,C)). [resolve(32,a,27,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | member(f7(A,B),B) | f9(A,B) != f8(A,B) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(32,a,28,a)].
% 0.43/1.00 33 partition(A,B) | member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) | -member(D,A) | subset(D,B). [resolve(33,a,25,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) | -member(D,B) | member(f5(A,B,D),A). [resolve(33,a,26,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) | -member(D,B) | member(D,f5(A,B,D)). [resolve(33,a,27,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(33,a,28,a)].
% 0.43/1.00 34 partition(A,B) | member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) | -member(D,A) | subset(D,B). [resolve(34,a,25,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) | -member(D,B) | member(f5(A,B,D),A). [resolve(34,a,26,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) | -member(D,B) | member(D,f5(A,B,D)). [resolve(34,a,27,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(34,a,28,a)].
% 0.43/1.00 35 partition(A,B) | member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) | -member(D,A) | subset(D,B). [resolve(35,a,25,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) | -member(D,B) | member(f5(A,B,D),A). [resolve(35,a,26,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) | -member(D,B) | member(D,f5(A,B,D)). [resolve(35,a,27,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(35,a,28,a)].
% 0.43/1.00 36 partition(A,B) | member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) | -member(D,A) | subset(D,B). [resolve(36,a,25,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) | -member(D,B) | member(f5(A,B,D),A). [resolve(36,a,26,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) | -member(D,B) | member(D,f5(A,B,D)). [resolve(36,a,27,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(36,a,28,a)].
% 0.43/1.00 37 partition(A,B) | member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) | -member(D,A) | subset(D,B). [resolve(37,a,25,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) | -member(D,B) | member(f5(A,B,D),A). [resolve(37,a,26,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) | -member(D,B) | member(D,f5(A,B,D)). [resolve(37,a,27,a)].
% 0.43/1.00 Derived: member(f6(A,B),A) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(37,a,28,a)].
% 0.43/1.00 38 partition(A,B) | -subset(f6(A,B),B) | member(f7(A,B),B) | member(f8(A,B),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f8(A,B),A) | -member(C,A) | subset(C,B). [resolve(38,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f8(A,B),A) | -member(C,B) | member(f5(A,B,C),A). [resolve(38,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f8(A,B),A) | -member(C,B) | member(C,f5(A,B,C)). [resolve(38,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f8(A,B),A) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(38,a,28,a)].
% 0.43/1.00 39 partition(A,B) | -subset(f6(A,B),B) | member(f7(A,B),B) | member(f9(A,B),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f9(A,B),A) | -member(C,A) | subset(C,B). [resolve(39,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f9(A,B),A) | -member(C,B) | member(f5(A,B,C),A). [resolve(39,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f9(A,B),A) | -member(C,B) | member(C,f5(A,B,C)). [resolve(39,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f9(A,B),A) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(39,a,28,a)].
% 0.43/1.00 40 partition(A,B) | -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) | -member(C,A) | subset(C,B). [resolve(40,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) | -member(C,B) | member(f5(A,B,C),A). [resolve(40,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) | -member(C,B) | member(C,f5(A,B,C)). [resolve(40,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f8(A,B)) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(40,a,28,a)].
% 0.43/1.00 41 partition(A,B) | -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) | -member(C,A) | subset(C,B). [resolve(41,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) | -member(C,B) | member(f5(A,B,C),A). [resolve(41,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) | -member(C,B) | member(C,f5(A,B,C)). [resolve(41,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | member(f10(A,B),f9(A,B)) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(41,a,28,a)].
% 0.43/1.00 42 partition(A,B) | -subset(f6(A,B),B) | member(f7(A,B),B) | f9(A,B) != f8(A,B) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | f9(A,B) != f8(A,B) | -member(C,A) | subset(C,B). [resolve(42,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | f9(A,B) != f8(A,B) | -member(C,B) | member(f5(A,B,C),A). [resolve(42,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | f9(A,B) != f8(A,B) | -member(C,B) | member(C,f5(A,B,C)). [resolve(42,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | member(f7(A,B),B) | f9(A,B) != f8(A,B) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(42,a,28,a)].
% 0.43/1.00 43 partition(A,B) | -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) | -member(D,A) | subset(D,B). [resolve(43,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) | -member(D,B) | member(f5(A,B,D),A). [resolve(43,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) | -member(D,B) | member(D,f5(A,B,D)). [resolve(43,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f8(A,B),A) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(43,a,28,a)].
% 0.43/1.00 44 partition(A,B) | -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) | -member(D,A) | subset(D,B). [resolve(44,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) | -member(D,B) | member(f5(A,B,D),A). [resolve(44,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) | -member(D,B) | member(D,f5(A,B,D)). [resolve(44,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f9(A,B),A) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(44,a,28,a)].
% 0.43/1.00 45 partition(A,B) | -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) | -member(D,A) | subset(D,B). [resolve(45,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) | -member(D,B) | member(f5(A,B,D),A). [resolve(45,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) | -member(D,B) | member(D,f5(A,B,D)). [resolve(45,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f8(A,B)) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(45,a,28,a)].
% 0.43/1.00 46 partition(A,B) | -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) | -member(D,A) | subset(D,B). [resolve(46,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) | -member(D,B) | member(f5(A,B,D),A). [resolve(46,a,26,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) | -member(D,B) | member(D,f5(A,B,D)). [resolve(46,a,27,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | member(f10(A,B),f9(A,B)) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(46,a,28,a)].
% 0.43/1.00 47 partition(A,B) | -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) # label(partition) # label(axiom). [clausify(13)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) | -member(D,A) | subset(D,B). [resolve(47,a,25,a)].
% 0.43/1.00 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) | -member(D,B) | member(f5(A,B,D),A). [resolve(47,a,26,a)].
% 0.43/1.01 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) | -member(D,B) | member(D,f5(A,B,D)). [resolve(47,a,27,a)].
% 0.43/1.01 Derived: -subset(f6(A,B),B) | -member(C,A) | -member(f7(A,B),C) | f9(A,B) != f8(A,B) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(47,a,28,a)].
% 0.43/1.01 48 equivalence(A,B) | member(f11(B,A),B) | member(f12(B,A),B) | member(f14(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 49 -equivalence(A,B) | -member(C,B) | apply(A,C,C) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 50 -equivalence(A,B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 51 -equivalence(A,B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f14(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(48,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f14(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(48,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f14(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(48,a,51,a)].
% 0.43/1.01 52 equivalence(A,B) | member(f11(B,A),B) | member(f12(B,A),B) | member(f15(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f15(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(52,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f15(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(52,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f15(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(52,a,51,a)].
% 0.43/1.01 53 equivalence(A,B) | member(f11(B,A),B) | member(f12(B,A),B) | member(f16(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f16(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(53,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f16(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(53,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | member(f16(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(53,a,51,a)].
% 0.43/1.01 54 equivalence(A,B) | member(f11(B,A),B) | member(f12(B,A),B) | apply(A,f14(B,A),f15(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | apply(B,C,C). [resolve(54,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(54,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(54,a,51,a)].
% 0.43/1.01 55 equivalence(A,B) | member(f11(B,A),B) | member(f12(B,A),B) | apply(A,f15(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | apply(B,C,C). [resolve(55,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(55,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(55,a,51,a)].
% 0.43/1.01 56 equivalence(A,B) | member(f11(B,A),B) | member(f12(B,A),B) | -apply(A,f14(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | apply(B,C,C). [resolve(56,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(56,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f12(A,B),A) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(56,a,51,a)].
% 0.43/1.01 57 equivalence(A,B) | member(f11(B,A),B) | member(f13(B,A),B) | member(f14(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f14(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(57,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f14(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(57,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f14(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(57,a,51,a)].
% 0.43/1.01 58 equivalence(A,B) | member(f11(B,A),B) | member(f13(B,A),B) | member(f15(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f15(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(58,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f15(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(58,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f15(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(58,a,51,a)].
% 0.43/1.01 59 equivalence(A,B) | member(f11(B,A),B) | member(f13(B,A),B) | member(f16(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f16(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(59,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f16(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(59,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | member(f16(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(59,a,51,a)].
% 0.43/1.01 60 equivalence(A,B) | member(f11(B,A),B) | member(f13(B,A),B) | apply(A,f14(B,A),f15(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | apply(B,C,C). [resolve(60,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(60,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(60,a,51,a)].
% 0.43/1.01 61 equivalence(A,B) | member(f11(B,A),B) | member(f13(B,A),B) | apply(A,f15(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | apply(B,C,C). [resolve(61,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(61,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(61,a,51,a)].
% 0.43/1.01 62 equivalence(A,B) | member(f11(B,A),B) | member(f13(B,A),B) | -apply(A,f14(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | apply(B,C,C). [resolve(62,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(62,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | member(f13(A,B),A) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(62,a,51,a)].
% 0.43/1.01 63 equivalence(A,B) | member(f11(B,A),B) | apply(A,f12(B,A),f13(B,A)) | member(f14(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f14(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(63,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f14(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(63,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f14(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(63,a,51,a)].
% 0.43/1.01 64 equivalence(A,B) | member(f11(B,A),B) | apply(A,f12(B,A),f13(B,A)) | member(f15(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f15(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(64,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f15(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(64,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f15(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(64,a,51,a)].
% 0.43/1.01 65 equivalence(A,B) | member(f11(B,A),B) | apply(A,f12(B,A),f13(B,A)) | member(f16(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f16(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(65,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f16(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(65,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | member(f16(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(65,a,51,a)].
% 0.43/1.01 66 equivalence(A,B) | member(f11(B,A),B) | apply(A,f12(B,A),f13(B,A)) | apply(A,f14(B,A),f15(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | apply(B,C,C). [resolve(66,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(66,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(66,a,51,a)].
% 0.43/1.01 67 equivalence(A,B) | member(f11(B,A),B) | apply(A,f12(B,A),f13(B,A)) | apply(A,f15(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | apply(B,C,C). [resolve(67,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(67,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(67,a,51,a)].
% 0.43/1.01 68 equivalence(A,B) | member(f11(B,A),B) | apply(A,f12(B,A),f13(B,A)) | -apply(A,f14(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | apply(B,C,C). [resolve(68,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(68,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | apply(B,f12(A,B),f13(A,B)) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(68,a,51,a)].
% 0.43/1.01 69 equivalence(A,B) | member(f11(B,A),B) | -apply(A,f13(B,A),f12(B,A)) | member(f14(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f14(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(69,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f14(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(69,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f14(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(69,a,51,a)].
% 0.43/1.01 70 equivalence(A,B) | member(f11(B,A),B) | -apply(A,f13(B,A),f12(B,A)) | member(f15(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f15(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(70,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f15(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(70,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f15(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(70,a,51,a)].
% 0.43/1.01 71 equivalence(A,B) | member(f11(B,A),B) | -apply(A,f13(B,A),f12(B,A)) | member(f16(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f16(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(71,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f16(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(71,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | member(f16(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(71,a,51,a)].
% 0.43/1.01 72 equivalence(A,B) | member(f11(B,A),B) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f14(B,A),f15(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | apply(B,C,C). [resolve(72,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(72,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | apply(B,f14(A,B),f15(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(72,a,51,a)].
% 0.43/1.01 73 equivalence(A,B) | member(f11(B,A),B) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f15(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | apply(B,C,C). [resolve(73,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(73,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | apply(B,f15(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(73,a,51,a)].
% 0.43/1.01 74 equivalence(A,B) | member(f11(B,A),B) | -apply(A,f13(B,A),f12(B,A)) | -apply(A,f14(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | apply(B,C,C). [resolve(74,a,49,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(74,a,50,a)].
% 0.43/1.01 Derived: member(f11(A,B),A) | -apply(B,f13(A,B),f12(A,B)) | -apply(B,f14(A,B),f16(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,D) | -apply(B,D,E) | apply(B,C,E). [resolve(74,a,51,a)].
% 0.43/1.01 75 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f14(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f14(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(75,a,49,a)].
% 0.43/1.01 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f14(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(75,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f14(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(75,a,51,a)].
% 0.43/1.02 76 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f15(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f15(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(76,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f15(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(76,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f15(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(76,a,51,a)].
% 0.43/1.02 77 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f16(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f16(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(77,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f16(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(77,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | member(f16(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(77,a,51,a)].
% 0.43/1.02 78 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | apply(A,f14(B,A),f15(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | apply(A,C,C). [resolve(78,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(78,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(78,a,51,a)].
% 0.43/1.02 79 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | apply(A,f15(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | apply(A,C,C). [resolve(79,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(79,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(79,a,51,a)].
% 0.43/1.02 80 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | -apply(A,f14(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | apply(A,C,C). [resolve(80,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(80,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f12(B,A),B) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(80,a,51,a)].
% 0.43/1.02 81 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f14(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f14(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(81,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f14(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(81,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f14(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(81,a,51,a)].
% 0.43/1.02 82 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f15(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f15(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(82,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f15(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(82,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f15(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(82,a,51,a)].
% 0.43/1.02 83 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f16(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f16(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(83,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f16(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(83,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | member(f16(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(83,a,51,a)].
% 0.43/1.02 84 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | apply(A,f14(B,A),f15(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | apply(A,C,C). [resolve(84,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(84,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(84,a,51,a)].
% 0.43/1.02 85 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | apply(A,f15(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | apply(A,C,C). [resolve(85,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(85,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(85,a,51,a)].
% 0.43/1.02 86 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | -apply(A,f14(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | apply(A,C,C). [resolve(86,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(86,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | member(f13(B,A),B) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(86,a,51,a)].
% 0.43/1.02 87 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f14(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f14(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(87,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f14(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(87,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f14(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(87,a,51,a)].
% 0.43/1.02 88 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f15(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f15(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(88,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f15(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(88,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f15(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(88,a,51,a)].
% 0.43/1.02 89 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f16(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f16(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(89,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f16(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(89,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | member(f16(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(89,a,51,a)].
% 0.43/1.02 90 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | apply(A,f14(B,A),f15(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | apply(A,C,C). [resolve(90,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(90,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(90,a,51,a)].
% 0.43/1.02 91 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | apply(A,f15(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | apply(A,C,C). [resolve(91,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(91,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(91,a,51,a)].
% 0.43/1.02 92 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | -apply(A,f14(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | apply(A,C,C). [resolve(92,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(92,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | apply(A,f12(B,A),f13(B,A)) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(92,a,51,a)].
% 0.43/1.02 93 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f14(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f14(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(93,a,49,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f14(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(93,a,50,a)].
% 0.43/1.02 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f14(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(93,a,51,a)].
% 0.73/1.04 94 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f15(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f15(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(94,a,49,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f15(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(94,a,50,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f15(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(94,a,51,a)].
% 0.73/1.04 95 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f16(B,A),B) # label(equivalence) # label(axiom). [clausify(14)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f16(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(95,a,49,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f16(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(95,a,50,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | member(f16(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(95,a,51,a)].
% 0.73/1.04 96 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f14(B,A),f15(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | apply(A,C,C). [resolve(96,a,49,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(96,a,50,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f14(B,A),f15(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(96,a,51,a)].
% 0.73/1.04 97 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f15(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | apply(A,C,C). [resolve(97,a,49,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(97,a,50,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | apply(A,f15(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(97,a,51,a)].
% 0.73/1.04 98 equivalence(A,B) | -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | -apply(A,f14(B,A),f16(B,A)) # label(equivalence) # label(axiom). [clausify(14)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | apply(A,C,C). [resolve(98,a,49,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(98,a,50,a)].
% 0.73/1.04 Derived: -apply(A,f11(B,A),f11(B,A)) | -apply(A,f13(B,A),f12(B,A)) | -apply(A,f14(B,A),f16(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(98,a,51,a)].
% 0.73/1.04 99 equivalence(c2,c1) # label(thIII02) # label(negated_conjecture). [clausify(17)].
% 0.73/1.04 Derived: -member(A,c1) | apply(c2,A,A). [resolve(99,a,49,a)].
% 0.73/1.04 Derived: -member(A,c1) | -member(B,c1) | -apply(c2,A,B) | apply(c2,B,A). [resolve(99,a,50,a)].
% 0.73/1.04 Derived: -member(A,c1) | -member(B,c1) | -member(C,c1) | -apply(c2,A,B) | -apply(c2,B,C) | apply(c2,A,C). [resolve(99,a,51,a)].
% 0.73/1.04 100 pre_order(A,B) | member(f17(A,B),B) | member(f18(A,B),B) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 101 -pre_order(A,B) | -member(C,B) | apply(A,C,C) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 102 -pre_order(A,B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: member(f17(A,B),B) | member(f18(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(100,a,101,a)].
% 0.73/1.04 Derived: member(f17(A,B),B) | member(f18(A,B),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(100,a,102,a)].
% 0.73/1.04 103 pre_order(A,B) | member(f17(A,B),B) | member(f19(A,B),B) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: member(f17(A,B),B) | member(f19(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(103,a,101,a)].
% 0.73/1.04 Derived: member(f17(A,B),B) | member(f19(A,B),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(103,a,102,a)].
% 0.73/1.04 104 pre_order(A,B) | member(f17(A,B),B) | member(f20(A,B),B) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: member(f17(A,B),B) | member(f20(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(104,a,101,a)].
% 0.73/1.04 Derived: member(f17(A,B),B) | member(f20(A,B),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(104,a,102,a)].
% 0.73/1.04 105 pre_order(A,B) | member(f17(A,B),B) | apply(A,f18(A,B),f19(A,B)) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: member(f17(A,B),B) | apply(A,f18(A,B),f19(A,B)) | -member(C,B) | apply(A,C,C). [resolve(105,a,101,a)].
% 0.73/1.04 Derived: member(f17(A,B),B) | apply(A,f18(A,B),f19(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(105,a,102,a)].
% 0.73/1.04 106 pre_order(A,B) | member(f17(A,B),B) | apply(A,f19(A,B),f20(A,B)) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: member(f17(A,B),B) | apply(A,f19(A,B),f20(A,B)) | -member(C,B) | apply(A,C,C). [resolve(106,a,101,a)].
% 0.73/1.04 Derived: member(f17(A,B),B) | apply(A,f19(A,B),f20(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(106,a,102,a)].
% 0.73/1.04 107 pre_order(A,B) | member(f17(A,B),B) | -apply(A,f18(A,B),f20(A,B)) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: member(f17(A,B),B) | -apply(A,f18(A,B),f20(A,B)) | -member(C,B) | apply(A,C,C). [resolve(107,a,101,a)].
% 0.73/1.04 Derived: member(f17(A,B),B) | -apply(A,f18(A,B),f20(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(107,a,102,a)].
% 0.73/1.04 108 pre_order(A,B) | -apply(A,f17(A,B),f17(A,B)) | member(f18(A,B),B) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: -apply(A,f17(A,B),f17(A,B)) | member(f18(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(108,a,101,a)].
% 0.73/1.04 Derived: -apply(A,f17(A,B),f17(A,B)) | member(f18(A,B),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(108,a,102,a)].
% 0.73/1.04 109 pre_order(A,B) | -apply(A,f17(A,B),f17(A,B)) | member(f19(A,B),B) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: -apply(A,f17(A,B),f17(A,B)) | member(f19(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(109,a,101,a)].
% 0.73/1.04 Derived: -apply(A,f17(A,B),f17(A,B)) | member(f19(A,B),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(109,a,102,a)].
% 0.73/1.04 110 pre_order(A,B) | -apply(A,f17(A,B),f17(A,B)) | member(f20(A,B),B) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: -apply(A,f17(A,B),f17(A,B)) | member(f20(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(110,a,101,a)].
% 0.73/1.04 Derived: -apply(A,f17(A,B),f17(A,B)) | member(f20(A,B),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(110,a,102,a)].
% 0.73/1.04 111 pre_order(A,B) | -apply(A,f17(A,B),f17(A,B)) | apply(A,f18(A,B),f19(A,B)) # label(pre_order) # label(axiom). [clausify(16)].
% 0.73/1.04 Derived: -apply(A,f17(A,B),f17(A,B)) | apply(A,f18(A,B),f19(A,B)) | -member(C,B) | apply(A,C,C). [resolve(111,a,101,a)].
% 0.73/1.04 Derived: -apply(A,f17(A,B),f17(A,B)) | apply(A,f18(A,B),f19(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(111,a,102,a)].
% 7.77/8.03 112 pre_order(A,B) | -apply(A,f17(A,B),f17(A,B)) | apply(A,f19(A,B),f20(A,B)) # label(pre_order) # label(axiom). [clausify(16)].
% 7.77/8.03 Derived: -apply(A,f17(A,B),f17(A,B)) | apply(A,f19(A,B),f20(A,B)) | -member(C,B) | apply(A,C,C). [resolve(112,a,101,a)].
% 7.77/8.03 Derived: -apply(A,f17(A,B),f17(A,B)) | apply(A,f19(A,B),f20(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(112,a,102,a)].
% 7.77/8.03 113 pre_order(A,B) | -apply(A,f17(A,B),f17(A,B)) | -apply(A,f18(A,B),f20(A,B)) # label(pre_order) # label(axiom). [clausify(16)].
% 7.77/8.03 Derived: -apply(A,f17(A,B),f17(A,B)) | -apply(A,f18(A,B),f20(A,B)) | -member(C,B) | apply(A,C,C). [resolve(113,a,101,a)].
% 7.77/8.03 Derived: -apply(A,f17(A,B),f17(A,B)) | -apply(A,f18(A,B),f20(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(113,a,102,a)].
% 7.77/8.03
% 7.77/8.03 ============================== end predicate elimination =============
% 7.77/8.03
% 7.77/8.03 Auto_denials: (non-Horn, no changes).
% 7.77/8.03
% 7.77/8.03 Term ordering decisions:
% 7.77/8.03 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. intersection=1. union=1. unordered_pair=1. difference=1. f1=1. f2=1. f3=1. f4=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. product=1. sum=1. power_set=1. singleton=1. equivalence_class=1. f5=1.
% 7.77/8.03
% 7.77/8.03 ============================== end of process initial clauses ========
% 7.77/8.03
% 7.77/8.03 ============================== CLAUSES FOR SEARCH ====================
% 7.77/8.03
% 7.77/8.03 ============================== end of clauses for search =============
% 7.77/8.03
% 7.77/8.03 ============================== SEARCH ================================
% 7.77/8.03
% 7.77/8.03 % Starting search at 0.16 seconds.
% 7.77/8.03
% 7.77/8.03 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.32 sec).
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=41.000, iters=4083
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=39.000, iters=3811
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=38.000, iters=3651
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=37.000, iters=3578
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=36.000, iters=3397
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=35.000, iters=3343
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=34.000, iters=3340
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=33.000, iters=3352
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=32.000, iters=4987
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=30.000, iters=3930
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5760, wt=84.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5788, wt=82.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5721, wt=81.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5729, wt=79.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5946, wt=76.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5970, wt=74.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5949, wt=67.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5975, wt=65.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5947, wt=64.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5990, wt=63.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5972, wt=62.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5092, wt=61.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5994, wt=59.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=6005, wt=58.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=6043, wt=57.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=6020, wt=56.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=6018, wt=55.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=5989, wt=54.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=6065, wt=53.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=6041, wt=52.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=6067, wt=51.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=11205, wt=24.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=11214, wt=13.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=11230, wt=12.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=11409, wt=11.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=11627, wt=9.000
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=11628, wt=8.000
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=29.000, iters=3360
% 7.77/8.03
% 7.77/8.03 Low Water (displace): id=15741, wt=7.000
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=28.000, iters=3344
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=27.000, iters=5400
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=25.000, iters=4377
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=24.000, iters=3992
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=22.000, iters=3537
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=19.000, iters=3520
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=17.000, iters=3422
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=15.000, iters=3550
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=14.000, iters=3432
% 7.77/8.03
% 7.77/8.03 Low Water (keep): wt=13.000, iters=3439
% 7.77/8.03
% 7.77/8.03 ============================== PROOF =================================
% 7.77/8.03 % SZS status Theorem
% 7.77/8.03 % SZS output start Refutation
% 7.77/8.03
% 7.77/8.03 % Proof 1 at 6.81 (+ 0.24) seconds.
% 7.77/8.03 % Length of proof is 12.
% 7.77/8.03 % Level of proof is 5.
% 7.77/8.03 % Maximum clause weight is 13.000.
% 7.77/8.03 % Given clauses 1940.
% 7.77/8.03
% 7.77/8.03 14 (all A all R (equivalence(R,A) <-> (all X (member(X,A) -> apply(R,X,X))) & (all X all Y (member(X,A) & member(Y,A) -> (apply(R,X,Y) -> apply(R,Y,X)))) & (all X all Y all Z (member(X,A) & member(Y,A) & member(Z,A) -> (apply(R,X,Y) & apply(R,Y,Z) -> apply(R,X,Z)))))) # label(equivalence) # label(axiom) # label(non_clause). [assumption].
% 7.77/8.03 15 (all R all E all A all X (member(X,equivalence_class(A,E,R)) <-> member(X,E) & apply(R,A,X))) # label(equivalence_class) # label(axiom) # label(non_clause). [assumption].
% 7.77/8.03 17 -(all E all R all A (equivalence(R,E) & member(A,E) -> member(A,equivalence_class(A,E,R)))) # label(thIII02) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.77/8.03 49 -equivalence(A,B) | -member(C,B) | apply(A,C,C) # label(equivalence) # label(axiom). [clausify(14)].
% 7.77/8.03 99 equivalence(c2,c1) # label(thIII02) # label(negated_conjecture). [clausify(17)].
% 7.77/8.03 142 member(A,equivalence_class(B,C,D)) | -member(A,C) | -apply(D,B,A) # label(equivalence_class) # label(axiom). [clausify(15)].
% 7.77/8.03 143 member(c3,c1) # label(thIII02) # label(negated_conjecture). [clausify(17)].
% 7.77/8.03 144 -member(c3,equivalence_class(c3,c1,c2)) # label(thIII02) # label(negated_conjecture). [clausify(17)].
% 7.77/8.03 371 -member(A,c1) | apply(c2,A,A). [resolve(99,a,49,a)].
% 7.77/8.03 1515 apply(c2,c3,c3). [resolve(371,a,143,a)].
% 7.77/8.03 1916 member(c3,equivalence_class(c3,A,c2)) | -member(c3,A). [resolve(1515,a,142,c)].
% 7.77/8.03 38963 $F. [resolve(1916,b,143,a),unit_del(a,144)].
% 7.77/8.03
% 7.77/8.03 % SZS output end Refutation
% 7.77/8.03 ============================== end of proof ==========================
% 7.77/8.03
% 7.77/8.03 ============================== STATISTICS ============================
% 7.77/8.03
% 7.77/8.03 Given=1940. Generated=419847. Kept=38849. proofs=1.
% 7.77/8.03 Usable=1931. Sos=9998. Demods=6. Limbo=493, Disabled=26807. Hints=0.
% 7.77/8.03 Megabytes=30.27.
% 7.77/8.03 User_CPU=6.81, System_CPU=0.24, Wall_clock=7.
% 7.77/8.03
% 7.77/8.03 ============================== end of statistics =====================
% 7.77/8.03
% 7.77/8.03 ============================== end of search =========================
% 7.77/8.03
% 7.77/8.03 THEOREM PROVED
% 7.77/8.03 % SZS status Theorem
% 7.77/8.03
% 7.77/8.03 Exiting with 1 proof.
% 7.77/8.03
% 7.77/8.03 Process 12852 exit (max_proofs) Sun Jul 10 07:50:38 2022
% 7.77/8.03 Prover9 interrupted
%------------------------------------------------------------------------------