0.10/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.35 % Computer : n008.cluster.edu 0.10/0.35 % Model : x86_64 x86_64 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.35 % Memory : 8042.1875MB 0.10/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.35 % CPULimit : 960 0.10/0.35 % DateTime : Thu Jul 2 12:53:44 EDT 2020 0.10/0.35 % CPUTime : 0.40/1.11 ============================== Prover9 =============================== 0.40/1.11 Prover9 (32) version 2009-11A, November 2009. 0.40/1.11 Process 1391 was started by sandbox2 on n008.cluster.edu, 0.40/1.11 Thu Jul 2 12:53:44 2020 0.40/1.11 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_1207_n008.cluster.edu". 0.40/1.11 ============================== end of head =========================== 0.40/1.11 0.40/1.11 ============================== INPUT ================================= 0.40/1.11 0.40/1.11 % Reading from file /tmp/Prover9_1207_n008.cluster.edu 0.40/1.11 0.40/1.11 set(prolog_style_variables). 0.40/1.11 set(auto2). 0.40/1.11 % set(auto2) -> set(auto). 0.40/1.11 % set(auto) -> set(auto_inference). 0.40/1.11 % set(auto) -> set(auto_setup). 0.40/1.11 % set(auto_setup) -> set(predicate_elim). 0.40/1.11 % set(auto_setup) -> assign(eq_defs, unfold). 0.40/1.11 % set(auto) -> set(auto_limits). 0.40/1.11 % set(auto_limits) -> assign(max_weight, "100.000"). 0.40/1.11 % set(auto_limits) -> assign(sos_limit, 20000). 0.40/1.11 % set(auto) -> set(auto_denials). 0.40/1.11 % set(auto) -> set(auto_process). 0.40/1.11 % set(auto2) -> assign(new_constants, 1). 0.40/1.11 % set(auto2) -> assign(fold_denial_max, 3). 0.40/1.11 % set(auto2) -> assign(max_weight, "200.000"). 0.40/1.11 % set(auto2) -> assign(max_hours, 1). 0.40/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.40/1.11 % set(auto2) -> assign(max_seconds, 0). 0.40/1.11 % set(auto2) -> assign(max_minutes, 5). 0.40/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.40/1.11 % set(auto2) -> set(sort_initial_sos). 0.40/1.11 % set(auto2) -> assign(sos_limit, -1). 0.40/1.11 % set(auto2) -> assign(lrs_ticks, 3000). 0.40/1.11 % set(auto2) -> assign(max_megs, 400). 0.40/1.11 % set(auto2) -> assign(stats, some). 0.40/1.11 % set(auto2) -> clear(echo_input). 0.40/1.11 % set(auto2) -> set(quiet). 0.40/1.11 % set(auto2) -> clear(print_initial_clauses). 0.40/1.11 % set(auto2) -> clear(print_given). 0.40/1.11 assign(lrs_ticks,-1). 0.40/1.11 assign(sos_limit,10000). 0.40/1.11 assign(order,kbo). 0.40/1.11 set(lex_order_vars). 0.40/1.11 clear(print_given). 0.40/1.11 0.40/1.11 % formulas(sos). % not echoed (20 formulas) 0.40/1.11 0.40/1.11 ============================== end of input ========================== 0.40/1.11 0.40/1.11 % From the command line: assign(max_seconds, 960). 0.40/1.11 0.40/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.40/1.11 0.40/1.11 % Formulas that are not ordinary clauses: 0.40/1.11 1 (all X all A all B (member(X,A) & member(X,B) <-> member(X,intersection(A,B)))) # label(intersection) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 2 (all X all A ((all Y (member(Y,A) -> member(X,Y))) <-> member(X,product(A)))) # label(product) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 3 (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]. 0.40/1.11 4 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 5 (all X all A (member(X,singleton(A)) <-> A = X)) # label(singleton) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 6 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 7 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 8 (all A all B (subset(A,B) & subset(B,A) <-> equal_set(A,B))) # label(equal_set) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 9 (all X all A all B (member(X,B) | member(X,A) <-> member(X,union(A,B)))) # label(union) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 10 (all X all A all B (B = X | X = A <-> member(X,unordered_pair(A,B)))) # label(unordered_pair) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 11 (all X all A (member(X,sum(A)) <-> (exists Y (member(Y,A) & member(X,Y))))) # label(sum) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 12 (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]. 0.40/1.11 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]. 0.40/1.11 14 (all R all E all A all X (apply(R,A,X) & member(X,E) <-> member(X,equivalence_class(A,E,R)))) # label(equivalence_class) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 15 (all A all B (-(exists X (member(X,B) & member(X,A))) <-> disjoint(A,B))) # label(disjoint) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 16 (all A all R (equivalence(R,A) <-> (all X all Y (member(X,A) & member(Y,A) -> (apply(R,X,Y) -> apply(R,Y,X)))) & (all X (member(X,A) -> apply(R,X,X))) & (all X all Y all Z (member(X,A) & member(Z,A) & member(Y,A) -> (apply(R,X,Y) & apply(R,Y,Z) -> apply(R,X,Z)))))) # label(equivalence) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 17 (all A all B ((all C (member(C,B) <-> (exists D (member(D,A) & member(C,D))))) <-> B = unaryUnion(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 18 (all X (non_overlapping(X) <-> (exists U partition(X,U)))) # label(non_overlapping) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 19 (all A all B all C insertIntoMember(A,B,C) = union(union(B,singleton(A)),difference(C,singleton(B)))) # label(insertIntoMember) # label(axiom) # label(non_clause). [assumption]. 0.40/1.11 20 -(all E (E != empty_set -> partition(singleton(E),E))) # label(set_partitions_itself) # label(negated_conjecture) # label(non_clause). [assumption]. 0.40/1.11 0.40/1.11 ============================== end of process non-clausal formulas === 0.40/1.11 0.40/1.11 ============================== PROCESS INITIAL CLAUSES =============== 0.40/1.11 0.40/1.11 ============================== PREDICATE ELIMINATION ================= 0.40/1.11 21 subset(A,B) | -equal_set(A,B) # label(equal_set) # label(axiom). [clausify(8)]. 0.40/1.11 22 -subset(A,B) | -subset(B,A) | equal_set(A,B) # label(equal_set) # label(axiom). [clausify(8)]. 0.40/1.11 23 subset(A,B) | -equal_set(B,A) # label(equal_set) # label(axiom). [clausify(8)]. 0.40/1.11 24 pre_order(A,B) | member(f4(A,B),B) | member(f5(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.11 25 -pre_order(A,B) | -member(C,B) | apply(A,C,C) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.11 26 -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(12)]. 0.40/1.11 Derived: member(f4(A,B),B) | member(f5(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(24,a,25,a)]. 0.40/1.11 Derived: member(f4(A,B),B) | member(f5(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(24,a,26,a)]. 0.40/1.11 27 pre_order(A,B) | member(f4(A,B),B) | member(f6(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.11 Derived: member(f4(A,B),B) | member(f6(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(27,a,25,a)]. 0.40/1.11 Derived: member(f4(A,B),B) | member(f6(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(27,a,26,a)]. 0.40/1.11 28 pre_order(A,B) | member(f4(A,B),B) | member(f7(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.11 Derived: member(f4(A,B),B) | member(f7(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(28,a,25,a)]. 0.40/1.11 Derived: member(f4(A,B),B) | member(f7(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(28,a,26,a)]. 0.40/1.11 29 pre_order(A,B) | member(f4(A,B),B) | apply(A,f5(A,B),f6(A,B)) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.11 Derived: member(f4(A,B),B) | apply(A,f5(A,B),f6(A,B)) | -member(C,B) | apply(A,C,C). [resolve(29,a,25,a)]. 0.40/1.11 Derived: member(f4(A,B),B) | apply(A,f5(A,B),f6(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(29,a,26,a)]. 0.40/1.11 30 pre_order(A,B) | member(f4(A,B),B) | apply(A,f6(A,B),f7(A,B)) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.11 Derived: member(f4(A,B),B) | apply(A,f6(A,B),f7(A,B)) | -member(C,B) | apply(A,C,C). [resolve(30,a,25,a)]. 0.40/1.11 Derived: member(f4(A,B),B) | apply(A,f6(A,B),f7(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(30,a,26,a)]. 0.40/1.11 31 pre_order(A,B) | member(f4(A,B),B) | -apply(A,f5(A,B),f7(A,B)) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.12 Derived: member(f4(A,B),B) | -apply(A,f5(A,B),f7(A,B)) | -member(C,B) | apply(A,C,C). [resolve(31,a,25,a)]. 0.40/1.12 Derived: member(f4(A,B),B) | -apply(A,f5(A,B),f7(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(31,a,26,a)]. 0.40/1.12 32 pre_order(A,B) | -apply(A,f4(A,B),f4(A,B)) | member(f5(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | member(f5(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(32,a,25,a)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | member(f5(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(32,a,26,a)]. 0.40/1.12 33 pre_order(A,B) | -apply(A,f4(A,B),f4(A,B)) | member(f6(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | member(f6(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(33,a,25,a)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | member(f6(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(33,a,26,a)]. 0.40/1.12 34 pre_order(A,B) | -apply(A,f4(A,B),f4(A,B)) | member(f7(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | member(f7(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(34,a,25,a)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | member(f7(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(34,a,26,a)]. 0.40/1.12 35 pre_order(A,B) | -apply(A,f4(A,B),f4(A,B)) | apply(A,f5(A,B),f6(A,B)) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | apply(A,f5(A,B),f6(A,B)) | -member(C,B) | apply(A,C,C). [resolve(35,a,25,a)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | apply(A,f5(A,B),f6(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(35,a,26,a)]. 0.40/1.12 36 pre_order(A,B) | -apply(A,f4(A,B),f4(A,B)) | apply(A,f6(A,B),f7(A,B)) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | apply(A,f6(A,B),f7(A,B)) | -member(C,B) | apply(A,C,C). [resolve(36,a,25,a)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | apply(A,f6(A,B),f7(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(36,a,26,a)]. 0.40/1.12 37 pre_order(A,B) | -apply(A,f4(A,B),f4(A,B)) | -apply(A,f5(A,B),f7(A,B)) # label(pre_order) # label(axiom). [clausify(12)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | -apply(A,f5(A,B),f7(A,B)) | -member(C,B) | apply(A,C,C). [resolve(37,a,25,a)]. 0.40/1.12 Derived: -apply(A,f4(A,B),f4(A,B)) | -apply(A,f5(A,B),f7(A,B)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,D) | -apply(A,D,E) | apply(A,C,E). [resolve(37,a,26,a)]. 0.40/1.12 38 -member(A,B) | -member(A,C) | -disjoint(C,B) # label(disjoint) # label(axiom). [clausify(15)]. 0.40/1.12 39 member(f14(A,B),B) | disjoint(A,B) # label(disjoint) # label(axiom). [clausify(15)]. 0.40/1.12 40 member(f14(A,B),A) | disjoint(A,B) # label(disjoint) # label(axiom). [clausify(15)]. 0.40/1.12 Derived: -member(A,B) | -member(A,C) | member(f14(C,B),B). [resolve(38,c,39,b)]. 0.40/1.12 Derived: -member(A,B) | -member(A,C) | member(f14(C,B),C). [resolve(38,c,40,b)]. 0.40/1.12 41 equivalence(A,B) | member(f15(B,A),B) | member(f17(B,A),B) | member(f18(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 42 -equivalence(A,B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 43 -equivalence(A,B) | -member(C,B) | apply(A,C,C) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 44 -equivalence(A,B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f18(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(41,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f18(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(41,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f18(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(41,a,44,a)]. 0.40/1.12 45 equivalence(A,B) | member(f15(B,A),B) | member(f17(B,A),B) | member(f20(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f20(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(45,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f20(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(45,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f20(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(45,a,44,a)]. 0.40/1.12 46 equivalence(A,B) | member(f15(B,A),B) | member(f17(B,A),B) | member(f19(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f19(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(46,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f19(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(46,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | member(f19(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(46,a,44,a)]. 0.40/1.12 47 equivalence(A,B) | member(f15(B,A),B) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(47,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | apply(B,C,C). [resolve(47,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(47,a,44,a)]. 0.40/1.12 48 equivalence(A,B) | member(f15(B,A),B) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(48,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | apply(B,C,C). [resolve(48,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(48,a,44,a)]. 0.40/1.12 49 equivalence(A,B) | member(f15(B,A),B) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(49,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | apply(B,C,C). [resolve(49,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | member(f17(A,B),A) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(49,a,44,a)]. 0.40/1.12 50 equivalence(A,B) | member(f15(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f18(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(50,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f18(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(50,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f18(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(50,a,44,a)]. 0.40/1.12 51 equivalence(A,B) | member(f15(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f20(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(51,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f20(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(51,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f20(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(51,a,44,a)]. 0.40/1.12 52 equivalence(A,B) | member(f15(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f19(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(52,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f19(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(52,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f19(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(52,a,44,a)]. 0.40/1.12 53 equivalence(A,B) | member(f15(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(53,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | apply(B,C,C). [resolve(53,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(53,a,44,a)]. 0.40/1.12 54 equivalence(A,B) | member(f15(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(54,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | apply(B,C,C). [resolve(54,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(54,a,44,a)]. 0.40/1.12 55 equivalence(A,B) | member(f15(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(55,a,42,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | apply(B,C,C). [resolve(55,a,43,a)]. 0.40/1.12 Derived: member(f15(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(55,a,44,a)]. 0.40/1.12 56 equivalence(A,B) | member(f16(B,A),B) | member(f17(B,A),B) | member(f18(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f18(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(56,a,42,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f18(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(56,a,43,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f18(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(56,a,44,a)]. 0.40/1.12 57 equivalence(A,B) | member(f16(B,A),B) | member(f17(B,A),B) | member(f20(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f20(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(57,a,42,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f20(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(57,a,43,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f20(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(57,a,44,a)]. 0.40/1.12 58 equivalence(A,B) | member(f16(B,A),B) | member(f17(B,A),B) | member(f19(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f19(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(58,a,42,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f19(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(58,a,43,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | member(f19(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(58,a,44,a)]. 0.40/1.12 59 equivalence(A,B) | member(f16(B,A),B) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(59,a,42,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | apply(B,C,C). [resolve(59,a,43,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(59,a,44,a)]. 0.40/1.12 60 equivalence(A,B) | member(f16(B,A),B) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(60,a,42,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | apply(B,C,C). [resolve(60,a,43,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(60,a,44,a)]. 0.40/1.12 61 equivalence(A,B) | member(f16(B,A),B) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(61,a,42,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | apply(B,C,C). [resolve(61,a,43,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | member(f17(A,B),A) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(61,a,44,a)]. 0.40/1.12 62 equivalence(A,B) | member(f16(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f18(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(62,a,42,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f18(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(62,a,43,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f18(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(62,a,44,a)]. 0.40/1.12 63 equivalence(A,B) | member(f16(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.12 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f20(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(63,a,42,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f20(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(63,a,43,a)]. 0.40/1.12 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f20(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(63,a,44,a)]. 0.40/1.12 64 equivalence(A,B) | member(f16(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f19(A,B),A) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(64,a,42,a)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f19(A,B),A) | -member(C,A) | apply(B,C,C). [resolve(64,a,43,a)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | member(f19(A,B),A) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(64,a,44,a)]. 0.40/1.13 65 equivalence(A,B) | member(f16(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(65,a,42,a)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | apply(B,C,C). [resolve(65,a,43,a)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f18(A,B),f19(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(65,a,44,a)]. 0.40/1.13 66 equivalence(A,B) | member(f16(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(66,a,42,a)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | apply(B,C,C). [resolve(66,a,43,a)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | apply(B,f19(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(66,a,44,a)]. 0.40/1.13 67 equivalence(A,B) | member(f16(B,A),B) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -apply(B,C,D) | apply(B,D,C). [resolve(67,a,42,a)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | apply(B,C,C). [resolve(67,a,43,a)]. 0.40/1.13 Derived: member(f16(A,B),A) | -apply(B,f17(A,B),f17(A,B)) | -apply(B,f18(A,B),f20(A,B)) | -member(C,A) | -member(D,A) | -member(E,A) | -apply(B,C,E) | -apply(B,E,D) | apply(B,C,D). [resolve(67,a,44,a)]. 0.40/1.13 68 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f18(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f18(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(68,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f18(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(68,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f18(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(68,a,44,a)]. 0.40/1.13 69 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f20(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f20(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(69,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f20(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(69,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f20(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(69,a,44,a)]. 0.40/1.13 70 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f19(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f19(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(70,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f19(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(70,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | member(f19(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(70,a,44,a)]. 0.40/1.13 71 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(71,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | apply(A,C,C). [resolve(71,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(71,a,44,a)]. 0.40/1.13 72 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(72,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | apply(A,C,C). [resolve(72,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(72,a,44,a)]. 0.40/1.13 73 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(73,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | apply(A,C,C). [resolve(73,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(73,a,44,a)]. 0.40/1.13 74 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(74,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(74,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(74,a,44,a)]. 0.40/1.13 75 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(75,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(75,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(75,a,44,a)]. 0.40/1.13 76 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(76,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(76,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(76,a,44,a)]. 0.40/1.13 77 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(77,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | apply(A,C,C). [resolve(77,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(77,a,44,a)]. 0.40/1.13 78 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(78,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | apply(A,C,C). [resolve(78,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(78,a,44,a)]. 0.40/1.13 79 equivalence(A,B) | apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(79,a,42,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | apply(A,C,C). [resolve(79,a,43,a)]. 0.40/1.13 Derived: apply(A,f15(B,A),f16(B,A)) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(79,a,44,a)]. 0.40/1.13 80 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f18(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f18(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(80,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f18(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(80,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f18(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(80,a,44,a)]. 0.40/1.13 81 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f20(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f20(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(81,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f20(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(81,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f20(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(81,a,44,a)]. 0.40/1.13 82 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f19(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f19(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(82,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f19(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(82,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | member(f19(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(82,a,44,a)]. 0.40/1.13 83 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(83,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | apply(A,C,C). [resolve(83,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(83,a,44,a)]. 0.40/1.13 84 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(84,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | apply(A,C,C). [resolve(84,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(84,a,44,a)]. 0.40/1.13 85 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(85,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | apply(A,C,C). [resolve(85,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | member(f17(B,A),B) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(85,a,44,a)]. 0.40/1.13 86 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(86,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(86,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f18(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(86,a,44,a)]. 0.40/1.13 87 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(87,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(87,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f20(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(87,a,44,a)]. 0.40/1.13 88 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) # label(equivalence) # label(axiom). [clausify(16)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(88,a,42,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) | -member(C,B) | apply(A,C,C). [resolve(88,a,43,a)]. 0.40/1.13 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | member(f19(B,A),B) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(88,a,44,a)]. 2.70/3.06 89 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(89,a,42,a)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | apply(A,C,C). [resolve(89,a,43,a)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f18(B,A),f19(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(89,a,44,a)]. 2.70/3.06 90 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(90,a,42,a)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | apply(A,C,C). [resolve(90,a,43,a)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | apply(A,f19(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(90,a,44,a)]. 2.70/3.06 91 equivalence(A,B) | -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) # label(equivalence) # label(axiom). [clausify(16)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | apply(A,D,C). [resolve(91,a,42,a)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | apply(A,C,C). [resolve(91,a,43,a)]. 2.70/3.06 Derived: -apply(A,f16(B,A),f15(B,A)) | -apply(A,f17(B,A),f17(B,A)) | -apply(A,f18(B,A),f20(B,A)) | -member(C,B) | -member(D,B) | -member(E,B) | -apply(A,C,E) | -apply(A,E,D) | apply(A,C,D). [resolve(91,a,44,a)]. 2.70/3.06 92 non_overlapping(A) | -partition(A,B) # label(non_overlapping) # label(axiom). [clausify(18)]. 2.70/3.06 93 -non_overlapping(A) | partition(A,f24(A)) # label(non_overlapping) # label(axiom). [clausify(18)]. 2.70/3.06 Derived: -partition(A,B) | partition(A,f24(A)). [resolve(92,a,93,a)]. 2.70/3.06 2.70/3.06 ============================== end predicate elimination ============= 2.70/3.06 2.70/3.06 Auto_denials: (non-Horn, no changes). 2.70/3.06 2.70/3.06 Term ordering decisions: 2.70/3.06 Function symbol KB weights: empty_set=1. c1=1. union=1. difference=1. intersection=1. unordered_pair=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=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. f21=1. f22=1. unaryUnion=1. singleton=1. product=1. sum=1. power_set=1. f24=1. equivalence_class=1. insertIntoMember=1. f8=1. f23=1. 2.70/3.06 2.70/3.06 ============================== end of process initial clauses ======== 2.70/3.06 2.70/3.06 ============================== CLAUSES FOR SEARCH ==================== 2.70/3.06 2.70/3.06 ============================== end of clauses for search ============= 2.70/3.06 2.70/3.06 ============================== SEARCH ================================ 2.70/3.06 2.70/3.06 % Starting search at 0.10 seconds. 2.70/3.06 2.70/3.06 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 0.76 sec). 2.70/3.06 2.70/3.06 Low Water (keep): wt=63.000, iters=3395 2.70/3.06 2.70/3.06 Low Water (keep): wt=54.000, iters=3340 2.70/3.06 2.70/3.06 Low Water (keep): wt=51.000, iters=3347 2.70/3.06 2.70/3.06 Low Water (keep): wt=48.000, iters=3347 2.70/3.06 2.70/3.06 Low Water (keep): wt=46.000, iters=3343 2.70/3.06 2.70/3.06 Low Water (keep): wt=30.000, iters=4258 2.70/3.06 2.70/3.06 Low Water (keep): wt=29.000, iters=4069 2.70/3.06 2.70/3.06 Low Water (keep): wt=26.000, iters=3758 2.70/3.06 2.70/3.06 Low Water (keep): wt=25.000, iters=3657 2.70/3.06 2.70/3.06 Low Water (keep): wt=22.000, iters=3382 2.70/3.06 2.70/3.06 Low Water (keep): wt=17.000, iters=3353 2.70/3.06 2.70/3.06 Low Water (keep): wt=16.000, iters=3388 2.70/3.06 2.70/3.06 Low Water (displace): id=5721, wt=80.000 2.70/3.06 2.70/3.06 Low Water (displace): id=5000, wt=78.000 2.70/3.06 2.70/3.06 Low Water (displace): id=5028, wt=75.Alarm clock 119.65/120.09 Prover9 interrupted 119.65/120.09 EOF