0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.35 % Computer : n013.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % DateTime : Thu Jul 2 13:35:18 EDT 2020 0.13/0.35 % CPUTime : 0.47/1.05 ============================== Prover9 =============================== 0.47/1.05 Prover9 (32) version 2009-11A, November 2009. 0.47/1.05 Process 12587 was started by sandbox2 on n013.cluster.edu, 0.47/1.05 Thu Jul 2 13:35:19 2020 0.47/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_12416_n013.cluster.edu". 0.47/1.05 ============================== end of head =========================== 0.47/1.05 0.47/1.05 ============================== INPUT ================================= 0.47/1.05 0.47/1.05 % Reading from file /tmp/Prover9_12416_n013.cluster.edu 0.47/1.05 0.47/1.05 set(prolog_style_variables). 0.47/1.05 set(auto2). 0.47/1.05 % set(auto2) -> set(auto). 0.47/1.05 % set(auto) -> set(auto_inference). 0.47/1.05 % set(auto) -> set(auto_setup). 0.47/1.05 % set(auto_setup) -> set(predicate_elim). 0.47/1.05 % set(auto_setup) -> assign(eq_defs, unfold). 0.47/1.05 % set(auto) -> set(auto_limits). 0.47/1.05 % set(auto_limits) -> assign(max_weight, "100.000"). 0.47/1.05 % set(auto_limits) -> assign(sos_limit, 20000). 0.47/1.05 % set(auto) -> set(auto_denials). 0.47/1.05 % set(auto) -> set(auto_process). 0.47/1.05 % set(auto2) -> assign(new_constants, 1). 0.47/1.05 % set(auto2) -> assign(fold_denial_max, 3). 0.47/1.05 % set(auto2) -> assign(max_weight, "200.000"). 0.47/1.05 % set(auto2) -> assign(max_hours, 1). 0.47/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.47/1.05 % set(auto2) -> assign(max_seconds, 0). 0.47/1.05 % set(auto2) -> assign(max_minutes, 5). 0.47/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.47/1.05 % set(auto2) -> set(sort_initial_sos). 0.47/1.05 % set(auto2) -> assign(sos_limit, -1). 0.47/1.05 % set(auto2) -> assign(lrs_ticks, 3000). 0.47/1.05 % set(auto2) -> assign(max_megs, 400). 0.47/1.05 % set(auto2) -> assign(stats, some). 0.47/1.05 % set(auto2) -> clear(echo_input). 0.47/1.05 % set(auto2) -> set(quiet). 0.47/1.05 % set(auto2) -> clear(print_initial_clauses). 0.47/1.05 % set(auto2) -> clear(print_given). 0.47/1.05 assign(lrs_ticks,-1). 0.47/1.05 assign(sos_limit,10000). 0.47/1.05 assign(order,kbo). 0.47/1.05 set(lex_order_vars). 0.47/1.05 clear(print_given). 0.47/1.05 0.47/1.05 % formulas(sos). % not echoed (18 formulas) 0.47/1.05 0.47/1.05 ============================== end of input ========================== 0.47/1.05 0.47/1.05 % From the command line: assign(max_seconds, 960). 0.47/1.05 0.47/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.47/1.05 0.47/1.05 % Formulas that are not ordinary clauses: 0.47/1.05 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]. 0.47/1.05 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]. 0.47/1.05 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]. 0.47/1.05 4 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption]. 0.47/1.05 5 (all X all A (member(X,singleton(A)) <-> A = X)) # label(singleton) # label(axiom) # label(non_clause). [assumption]. 0.47/1.05 6 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption]. 0.47/1.05 7 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption]. 0.47/1.05 8 (all A all B (subset(A,B) & subset(B,A) <-> equal_set(A,B))) # label(equal_set) # label(axiom) # label(non_clause). [assumption]. 0.47/1.05 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]. 0.47/1.05 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]. 0.47/1.05 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]. 0.47/1.05 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]. 0.47/1.05 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]. 0.47/1.05 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]. 0.47/1.05 15 (all A all B (-(exists X (member(X,B) & member(X,A))) <-> disjoint(A,B))) # label(disjoint) # label(axiom) # label(non_clause). [assumption]. 0.47/1.05 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]. 0.47/1.05 17 (all X all Y (equal_set(X,Y) <-> apply(equal_set_predicate,X,Y))) # label(rel_equal_set) # label(hypothesis) # label(non_clause). [assumption]. 0.47/1.05 18 -(all E equivalence(equal_set_predicate,power_set(E))) # label(thIII13) # label(negated_conjecture) # label(non_clause). [assumption]. 0.47/1.05 0.47/1.05 ============================== end of process non-clausal formulas === 0.47/1.05 0.47/1.05 ============================== PROCESS INITIAL CLAUSES =============== 0.47/1.05 0.47/1.05 ============================== PREDICATE ELIMINATION ================= 0.47/1.05 19 subset(A,B) | -equal_set(A,B) # label(equal_set) # label(axiom). [clausify(8)]. 0.47/1.05 20 -subset(A,B) | -subset(B,A) | equal_set(A,B) # label(equal_set) # label(axiom). [clausify(8)]. 0.47/1.05 21 subset(A,B) | -equal_set(B,A) # label(equal_set) # label(axiom). [clausify(8)]. 0.47/1.05 22 -equal_set(A,B) | apply(equal_set_predicate,A,B) # label(rel_equal_set) # label(hypothesis). [clausify(17)]. 0.47/1.05 Derived: apply(equal_set_predicate,A,B) | -subset(A,B) | -subset(B,A). [resolve(22,a,20,c)]. 0.47/1.05 23 equal_set(A,B) | -apply(equal_set_predicate,A,B) # label(rel_equal_set) # label(hypothesis). [clausify(17)]. 0.47/1.05 Derived: -apply(equal_set_predicate,A,B) | subset(A,B). [resolve(23,a,19,b)]. 0.47/1.05 Derived: -apply(equal_set_predicate,A,B) | subset(B,A). [resolve(23,a,21,b)]. 0.47/1.05 24 pre_order(A,B) | member(f4(A,B),B) | member(f5(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.47/1.05 25 -pre_order(A,B) | -member(C,B) | apply(A,C,C) # label(pre_order) # label(axiom). [clausify(12)]. 0.47/1.05 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)]. 0.47/1.05 Derived: member(f4(A,B),B) | member(f5(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(24,a,25,a)]. 0.47/1.05 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)]. 0.47/1.05 27 pre_order(A,B) | member(f4(A,B),B) | member(f6(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.47/1.05 Derived: member(f4(A,B),B) | member(f6(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(27,a,25,a)]. 0.47/1.05 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)]. 0.47/1.05 28 pre_order(A,B) | member(f4(A,B),B) | member(f7(A,B),B) # label(pre_order) # label(axiom). [clausify(12)]. 0.47/1.05 Derived: member(f4(A,B),B) | member(f7(A,B),B) | -member(C,B) | apply(A,C,C). [resolve(28,a,25,a)]. 0.47/1.05 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)]. 0.47/1.05 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)]. 0.47/1.05 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)]. 0.47/1.05 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)]. 0.47/1.05 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)]. 0.47/1.05 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)]. 0.47/1.05 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 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)]. 0.47/1.06 38 partition(A,B) | member(f9(A,B),A) | member(f10(A,B),B) | member(f11(A,B),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 39 -partition(A,B) | -member(C,A) | subset(C,B) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 40 -partition(A,B) | -member(C,B) | member(f8(A,B,C),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 41 -partition(A,B) | -member(C,B) | member(C,f8(A,B,C)) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 42 -partition(A,B) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f11(A,B),A) | -member(C,A) | subset(C,B). [resolve(38,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f11(A,B),A) | -member(C,B) | member(f8(A,B,C),A). [resolve(38,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f11(A,B),A) | -member(C,B) | member(C,f8(A,B,C)). [resolve(38,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f11(A,B),A) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(38,a,42,a)]. 0.47/1.06 43 partition(A,B) | member(f9(A,B),A) | member(f10(A,B),B) | member(f12(A,B),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f12(A,B),A) | -member(C,A) | subset(C,B). [resolve(43,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f12(A,B),A) | -member(C,B) | member(f8(A,B,C),A). [resolve(43,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f12(A,B),A) | -member(C,B) | member(C,f8(A,B,C)). [resolve(43,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f12(A,B),A) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(43,a,42,a)]. 0.47/1.06 44 partition(A,B) | member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) | -member(C,A) | subset(C,B). [resolve(44,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) | -member(C,B) | member(f8(A,B,C),A). [resolve(44,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) | -member(C,B) | member(C,f8(A,B,C)). [resolve(44,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(44,a,42,a)]. 0.47/1.06 45 partition(A,B) | member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) | -member(C,A) | subset(C,B). [resolve(45,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) | -member(C,B) | member(f8(A,B,C),A). [resolve(45,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) | -member(C,B) | member(C,f8(A,B,C)). [resolve(45,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(45,a,42,a)]. 0.47/1.06 46 partition(A,B) | member(f9(A,B),A) | member(f10(A,B),B) | f12(A,B) != f11(A,B) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | f12(A,B) != f11(A,B) | -member(C,A) | subset(C,B). [resolve(46,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | f12(A,B) != f11(A,B) | -member(C,B) | member(f8(A,B,C),A). [resolve(46,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | f12(A,B) != f11(A,B) | -member(C,B) | member(C,f8(A,B,C)). [resolve(46,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | member(f10(A,B),B) | f12(A,B) != f11(A,B) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(46,a,42,a)]. 0.47/1.06 47 partition(A,B) | member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) | -member(D,A) | subset(D,B). [resolve(47,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) | -member(D,B) | member(f8(A,B,D),A). [resolve(47,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) | -member(D,B) | member(D,f8(A,B,D)). [resolve(47,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(47,a,42,a)]. 0.47/1.06 48 partition(A,B) | member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) | -member(D,A) | subset(D,B). [resolve(48,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) | -member(D,B) | member(f8(A,B,D),A). [resolve(48,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) | -member(D,B) | member(D,f8(A,B,D)). [resolve(48,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(48,a,42,a)]. 0.47/1.06 49 partition(A,B) | member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) | -member(D,A) | subset(D,B). [resolve(49,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) | -member(D,B) | member(f8(A,B,D),A). [resolve(49,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) | -member(D,B) | member(D,f8(A,B,D)). [resolve(49,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(49,a,42,a)]. 0.47/1.06 50 partition(A,B) | member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) | -member(D,A) | subset(D,B). [resolve(50,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) | -member(D,B) | member(f8(A,B,D),A). [resolve(50,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) | -member(D,B) | member(D,f8(A,B,D)). [resolve(50,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(50,a,42,a)]. 0.47/1.06 51 partition(A,B) | member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) | -member(D,A) | subset(D,B). [resolve(51,a,39,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) | -member(D,B) | member(f8(A,B,D),A). [resolve(51,a,40,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) | -member(D,B) | member(D,f8(A,B,D)). [resolve(51,a,41,a)]. 0.47/1.06 Derived: member(f9(A,B),A) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(51,a,42,a)]. 0.47/1.06 52 partition(A,B) | -subset(f9(A,B),B) | member(f10(A,B),B) | member(f11(A,B),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f11(A,B),A) | -member(C,A) | subset(C,B). [resolve(52,a,39,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f11(A,B),A) | -member(C,B) | member(f8(A,B,C),A). [resolve(52,a,40,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f11(A,B),A) | -member(C,B) | member(C,f8(A,B,C)). [resolve(52,a,41,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f11(A,B),A) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(52,a,42,a)]. 0.47/1.06 53 partition(A,B) | -subset(f9(A,B),B) | member(f10(A,B),B) | member(f12(A,B),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f12(A,B),A) | -member(C,A) | subset(C,B). [resolve(53,a,39,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f12(A,B),A) | -member(C,B) | member(f8(A,B,C),A). [resolve(53,a,40,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f12(A,B),A) | -member(C,B) | member(C,f8(A,B,C)). [resolve(53,a,41,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f12(A,B),A) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(53,a,42,a)]. 0.47/1.06 54 partition(A,B) | -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) | -member(C,A) | subset(C,B). [resolve(54,a,39,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) | -member(C,B) | member(f8(A,B,C),A). [resolve(54,a,40,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) | -member(C,B) | member(C,f8(A,B,C)). [resolve(54,a,41,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f11(A,B)) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(54,a,42,a)]. 0.47/1.06 55 partition(A,B) | -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) | -member(C,A) | subset(C,B). [resolve(55,a,39,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) | -member(C,B) | member(f8(A,B,C),A). [resolve(55,a,40,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) | -member(C,B) | member(C,f8(A,B,C)). [resolve(55,a,41,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | member(f13(A,B),f12(A,B)) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(55,a,42,a)]. 0.47/1.06 56 partition(A,B) | -subset(f9(A,B),B) | member(f10(A,B),B) | f12(A,B) != f11(A,B) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | f12(A,B) != f11(A,B) | -member(C,A) | subset(C,B). [resolve(56,a,39,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | f12(A,B) != f11(A,B) | -member(C,B) | member(f8(A,B,C),A). [resolve(56,a,40,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | f12(A,B) != f11(A,B) | -member(C,B) | member(C,f8(A,B,C)). [resolve(56,a,41,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | member(f10(A,B),B) | f12(A,B) != f11(A,B) | -member(C,A) | -member(D,A) | -member(E,C) | -member(E,D) | D = C. [resolve(56,a,42,a)]. 0.47/1.06 57 partition(A,B) | -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) | -member(D,A) | subset(D,B). [resolve(57,a,39,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) | -member(D,B) | member(f8(A,B,D),A). [resolve(57,a,40,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) | -member(D,B) | member(D,f8(A,B,D)). [resolve(57,a,41,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f11(A,B),A) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(57,a,42,a)]. 0.47/1.06 58 partition(A,B) | -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) | -member(D,A) | subset(D,B). [resolve(58,a,39,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) | -member(D,B) | member(f8(A,B,D),A). [resolve(58,a,40,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) | -member(D,B) | member(D,f8(A,B,D)). [resolve(58,a,41,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f12(A,B),A) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(58,a,42,a)]. 0.47/1.06 59 partition(A,B) | -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) # label(partition) # label(axiom). [clausify(13)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) | -member(D,A) | subset(D,B). [resolve(59,a,39,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) | -member(D,B) | member(f8(A,B,D),A). [resolve(59,a,40,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) | -member(D,B) | member(D,f8(A,B,D)). [resolve(59,a,41,a)]. 0.47/1.06 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f11(A,B)) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(59,a,42,a)]. 2.26/2.58 60 partition(A,B) | -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) # label(partition) # label(axiom). [clausify(13)]. 2.26/2.58 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) | -member(D,A) | subset(D,B). [resolve(60,a,39,a)]. 2.26/2.58 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) | -member(D,B) | member(f8(A,B,D),A). [resolve(60,a,40,a)]. 2.26/2.58 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) | -member(D,B) | member(D,f8(A,B,D)). [resolve(60,a,41,a)]. 2.26/2.58 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | member(f13(A,B),f12(A,B)) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(60,a,42,a)]. 2.26/2.58 61 partition(A,B) | -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) # label(partition) # label(axiom). [clausify(13)]. 2.26/2.58 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) | -member(D,A) | subset(D,B). [resolve(61,a,39,a)]. 2.26/2.58 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) | -member(D,B) | member(f8(A,B,D),A). [resolve(61,a,40,a)]. 2.26/2.58 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) | -member(D,B) | member(D,f8(A,B,D)). [resolve(61,a,41,a)]. 2.26/2.58 Derived: -subset(f9(A,B),B) | -member(C,A) | -member(f10(A,B),C) | f12(A,B) != f11(A,B) | -member(D,A) | -member(E,A) | -member(F,D) | -member(F,E) | E = D. [resolve(61,a,42,a)]. 2.26/2.58 62 -member(A,B) | -member(A,C) | -disjoint(C,B) # label(disjoint) # label(axiom). [clausify(15)]. 2.26/2.58 63 member(f14(A,B),B) | disjoint(A,B) # label(disjoint) # label(axiom). [clausify(15)]. 2.26/2.58 64 member(f14(A,B),A) | disjoint(A,B) # label(disjoint) # label(axiom). [clausify(15)]. 2.26/2.58 Derived: -member(A,B) | -member(A,C) | member(f14(C,B),B). [resolve(62,c,63,b)]. 2.26/2.58 Derived: -member(A,B) | -member(A,C) | member(f14(C,B),C). [resolve(62,c,64,b)]. 2.26/2.58 2.26/2.58 ============================== end predicate elimination ============= 2.26/2.58 2.26/2.58 Auto_denials: (non-Horn, no changes). 2.26/2.58 2.26/2.58 Term ordering decisions: 2.26/2.58 Function symbol KB weights: equal_set_predicate=1. empty_set=1. c1=1. intersection=1. union=1. unordered_pair=1. difference=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. product=1. sum=1. power_set=1. singleton=1. equivalence_class=1. f8=1. 2.26/2.58 2.26/2.58 ============================== end of process initial clauses ======== 2.26/2.58 2.26/2.58 ============================== CLAUSES FOR SEARCH ==================== 2.26/2.58 2.26/2.58 ============================== end of clauses for search ============= 2.26/2.58 2.26/2.58 ============================== SEARCH ================================ 2.26/2.58 2.26/2.58 % Starting search at 0.06 seconds. 2.26/2.58 2.26/2.58 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.21 sec). 2.26/2.58 2.26/2.58 Low Water (keep): wt=75.000, iters=3335 2.26/2.58 2.26/2.58 Low Water (keep): wt=72.000, iters=3333 2.26/2.58 2.26/2.58 Low Water (keep): wt=68.000, iters=3335 2.26/2.58 2.26/2.58 Low Water (keep): wt=66.000, iters=3333 2.26/2.58 2.26/2.58 Low Water (keep): wt=65.000, iters=3345 2.26/2.58 2.26/2.58 Low Water (keep): wt=63.000, iters=3340 2.26/2.58 2.26/2.58 Low Water (keep): wt=59.000, iters=3372 2.26/2.58 2.26/2.58 Low Water (keep): wt=54.000, iters=3410 2.26/2.58 2.26/2.58 Low Water (keep): wt=53.000, iters=3354 2.26/2.58 2.26/2.58 Low Water (keep): wt=51.000, iters=3380 2.26/2.58 2.26/2.58 Low Water (keep): wt=46.000, iters=3353 2.26/2.58 2.26/2.58 Low Water (keep): wt=45.000, iters=3333 2.26/2.58 2.26/2.58 Low Water (keep): wt=43.000, iters=3351 2.26/2.58 2.26/2.58 Low Water (keep): wt=42.000, iters=3401 2.26/2.58 2.26/2.58 Low Water (keep): wt=41.000, iters=3338 2.26/2.58 2.26/2.58 Low Water (keep): wt=40.000, iters=3333 2.26/2.58 2.26/2.58 Low Water (keep): wt=39.000, iters=3363 2.26/2.58 2.26/2.58 Low Water (keep): wt=38.000, iters=3338 2.26/2.58 2.26/2.58 Low Water (keep): wt=37.000, iters=3351 2.26/2.58 2.26/2.58 Low Water (keep): wt=36.000, iters=3337 2.26/2.58 2.26/2.58 Low Water (keep): wt=35.000, iters=3372 2.26/2.58 2.26/2.58 Low Water (keep): wt=32.000, iters=4447 2.26/2.58 2.26/2.58 Low Water (keep): wt=30.000, iters=3429 2.26/2.58 2.26/2.58 Low Water (keep): wt=29.000, iters=3682 2.26/2.58 2.26/2.58 Low Water (displace): id=2753, wt=77.000 2.26/2.58 2.26/2.58 Low Water (displace): id=2779, wt=75.000 2.26/2.58 2.26/2.58 Low Alarm clock 119.76/120.05 Prover9 interrupted 119.76/120.05 EOF