TSTP Solution File: SET814+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET814+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 04:32:15 EDT 2022
% Result : Timeout 300.05s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET814+4 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 14:45:56 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.36/1.07 ============================== Prover9 ===============================
% 0.36/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.36/1.07 Process 32325 was started by sandbox on n016.cluster.edu,
% 0.36/1.07 Sun Jul 10 14:45:57 2022
% 0.36/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32172_n016.cluster.edu".
% 0.36/1.07 ============================== end of head ===========================
% 0.36/1.07
% 0.36/1.07 ============================== INPUT =================================
% 0.36/1.07
% 0.36/1.07 % Reading from file /tmp/Prover9_32172_n016.cluster.edu
% 0.36/1.07
% 0.36/1.07 set(prolog_style_variables).
% 0.36/1.07 set(auto2).
% 0.36/1.07 % set(auto2) -> set(auto).
% 0.36/1.07 % set(auto) -> set(auto_inference).
% 0.36/1.07 % set(auto) -> set(auto_setup).
% 0.36/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.36/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.36/1.07 % set(auto) -> set(auto_limits).
% 0.36/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.36/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.36/1.07 % set(auto) -> set(auto_denials).
% 0.36/1.07 % set(auto) -> set(auto_process).
% 0.36/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.36/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.36/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.36/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.36/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.36/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.36/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.36/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.36/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.36/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.36/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.36/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.36/1.07 % set(auto2) -> assign(stats, some).
% 0.36/1.07 % set(auto2) -> clear(echo_input).
% 0.36/1.07 % set(auto2) -> set(quiet).
% 0.36/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.36/1.07 % set(auto2) -> clear(print_given).
% 0.36/1.07 assign(lrs_ticks,-1).
% 0.36/1.07 assign(sos_limit,10000).
% 0.36/1.07 assign(order,kbo).
% 0.36/1.07 set(lex_order_vars).
% 0.36/1.07 clear(print_given).
% 0.36/1.07
% 0.36/1.07 % formulas(sos). % not echoed (21 formulas)
% 0.36/1.07
% 0.36/1.07 ============================== end of input ==========================
% 0.36/1.07
% 0.36/1.07 % From the command line: assign(max_seconds, 300).
% 0.36/1.07
% 0.36/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.36/1.07
% 0.36/1.07 % Formulas that are not ordinary clauses:
% 0.36/1.07 1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 2 (all A all B (equal_set(A,B) <-> subset(A,B) & subset(B,A))) # label(equal_set) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 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].
% 0.36/1.07 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].
% 0.36/1.07 6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 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].
% 0.36/1.07 8 (all X all A (member(X,singleton(A)) <-> X = A)) # label(singleton) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 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].
% 0.36/1.07 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].
% 0.36/1.07 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].
% 0.36/1.07 12 (all A (member(A,on) <-> set(A) & strict_well_order(member_predicate,A) & (all X (member(X,A) -> subset(X,A))))) # label(ordinal_number) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 13 (all R all E (strict_well_order(R,E) <-> strict_order(R,E) & (all A (subset(A,E) & (exists X member(X,A)) -> (exists Y least(Y,R,A)))))) # label(strict_well_order) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 14 (all R all E all M (least(M,R,E) <-> member(M,E) & (all X (member(X,E) -> M = X | apply(R,M,X))))) # label(least) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 15 (all X all Y (apply(member_predicate,X,Y) <-> member(X,Y))) # label(rel_member) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 16 (all R all E (strict_order(R,E) <-> (all X all Y (member(X,E) & member(Y,E) -> -(apply(R,X,Y) & apply(R,Y,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(strict_order) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 17 (all X (set(X) -> (all Y (member(Y,X) -> set(Y))))) # label(set_member) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 18 (all X all R all A all Y (member(Y,initial_segment(X,R,A)) <-> member(Y,A) & apply(R,Y,X))) # label(initial_segment) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 19 (all A all X (member(X,suc(A)) <-> member(X,union(A,singleton(A))))) # label(successor) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 20 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(thI3) # label(axiom) # label(non_clause). [assumption].
% 0.36/1.07 21 -(all A (member(A,on) -> subset(sum(A),A))) # label(thV14) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.36/1.07
% 0.36/1.07 ============================== end of process non-clausal formulas ===
% 0.36/1.07
% 0.36/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.36/1.07
% 0.36/1.07 ============================== PREDICATE ELIMINATION =================
% 0.36/1.07 22 -strict_order(A,B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | -apply(A,D,C) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 23 strict_order(A,B) | member(f9(A,B),B) | member(f11(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 24 strict_order(A,B) | member(f9(A,B),B) | member(f12(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 25 strict_order(A,B) | member(f9(A,B),B) | member(f13(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 26 strict_order(A,B) | member(f10(A,B),B) | member(f11(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 27 strict_order(A,B) | member(f10(A,B),B) | member(f12(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 28 strict_order(A,B) | member(f10(A,B),B) | member(f13(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 29 strict_order(A,B) | member(f9(A,B),B) | apply(A,f11(A,B),f12(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 30 strict_order(A,B) | member(f9(A,B),B) | apply(A,f12(A,B),f13(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 31 strict_order(A,B) | member(f10(A,B),B) | apply(A,f11(A,B),f12(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 32 strict_order(A,B) | member(f10(A,B),B) | apply(A,f12(A,B),f13(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 33 strict_order(A,B) | apply(A,f9(A,B),f10(A,B)) | member(f11(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 34 strict_order(A,B) | apply(A,f9(A,B),f10(A,B)) | member(f12(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 35 strict_order(A,B) | apply(A,f9(A,B),f10(A,B)) | member(f13(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 36 strict_order(A,B) | apply(A,f10(A,B),f9(A,B)) | member(f11(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 37 strict_order(A,B) | apply(A,f10(A,B),f9(A,B)) | member(f12(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 38 strict_order(A,B) | apply(A,f10(A,B),f9(A,B)) | member(f13(A,B),B) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 39 strict_order(A,B) | apply(A,f9(A,B),f10(A,B)) | apply(A,f11(A,B),f12(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 40 strict_order(A,B) | apply(A,f9(A,B),f10(A,B)) | apply(A,f12(A,B),f13(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 41 strict_order(A,B) | apply(A,f10(A,B),f9(A,B)) | apply(A,f11(A,B),f12(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 42 strict_order(A,B) | apply(A,f10(A,B),f9(A,B)) | apply(A,f12(A,B),f13(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f9(D,B),B) | member(f11(D,B),B). [resolve(22,a,23,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f9(D,B),B) | member(f12(D,B),B). [resolve(22,a,24,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f9(D,B),B) | member(f13(D,B),B). [resolve(22,a,25,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f10(D,B),B) | member(f11(D,B),B). [resolve(22,a,26,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f10(D,B),B) | member(f12(D,B),B). [resolve(22,a,27,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f10(D,B),B) | member(f13(D,B),B). [resolve(22,a,28,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f9(D,B),B) | apply(D,f11(D,B),f12(D,B)). [resolve(22,a,29,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f9(D,B),B) | apply(D,f12(D,B),f13(D,B)). [resolve(22,a,30,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f10(D,B),B) | apply(D,f11(D,B),f12(D,B)). [resolve(22,a,31,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | member(f10(D,B),B) | apply(D,f12(D,B),f13(D,B)). [resolve(22,a,32,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f9(D,B),f10(D,B)) | member(f11(D,B),B). [resolve(22,a,33,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f9(D,B),f10(D,B)) | member(f12(D,B),B). [resolve(22,a,34,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f9(D,B),f10(D,B)) | member(f13(D,B),B). [resolve(22,a,35,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f10(D,B),f9(D,B)) | member(f11(D,B),B). [resolve(22,a,36,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f10(D,B),f9(D,B)) | member(f12(D,B),B). [resolve(22,a,37,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f10(D,B),f9(D,B)) | member(f13(D,B),B). [resolve(22,a,38,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f9(D,B),f10(D,B)) | apply(D,f11(D,B),f12(D,B)). [resolve(22,a,39,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f9(D,B),f10(D,B)) | apply(D,f12(D,B),f13(D,B)). [resolve(22,a,40,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f10(D,B),f9(D,B)) | apply(D,f11(D,B),f12(D,B)). [resolve(22,a,41,a)].
% 0.36/1.07 Derived: -member(A,B) | -member(C,B) | -apply(D,A,C) | -apply(D,C,A) | apply(D,f10(D,B),f9(D,B)) | apply(D,f12(D,B),f13(D,B)). [resolve(22,a,42,a)].
% 0.36/1.07 43 -strict_well_order(A,B) | strict_order(A,B) # label(strict_well_order) # label(axiom). [clausify(13)].
% 0.36/1.07 Derived: -strict_well_order(A,B) | -member(C,B) | -member(D,B) | -apply(A,C,D) | -apply(A,D,C). [resolve(43,b,22,a)].
% 0.36/1.07 44 strict_well_order(A,B) | -strict_order(A,B) | subset(f6(A,B),B) # label(strict_well_order) # label(axiom). [clausify(13)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f9(A,B),B) | member(f11(A,B),B). [resolve(44,b,23,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f9(A,B),B) | member(f12(A,B),B). [resolve(44,b,24,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f9(A,B),B) | member(f13(A,B),B). [resolve(44,b,25,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f10(A,B),B) | member(f11(A,B),B). [resolve(44,b,26,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f10(A,B),B) | member(f12(A,B),B). [resolve(44,b,27,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f10(A,B),B) | member(f13(A,B),B). [resolve(44,b,28,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f9(A,B),B) | apply(A,f11(A,B),f12(A,B)). [resolve(44,b,29,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f9(A,B),B) | apply(A,f12(A,B),f13(A,B)). [resolve(44,b,30,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f10(A,B),B) | apply(A,f11(A,B),f12(A,B)). [resolve(44,b,31,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | member(f10(A,B),B) | apply(A,f12(A,B),f13(A,B)). [resolve(44,b,32,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f9(A,B),f10(A,B)) | member(f11(A,B),B). [resolve(44,b,33,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f9(A,B),f10(A,B)) | member(f12(A,B),B). [resolve(44,b,34,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f9(A,B),f10(A,B)) | member(f13(A,B),B). [resolve(44,b,35,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f10(A,B),f9(A,B)) | member(f11(A,B),B). [resolve(44,b,36,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f10(A,B),f9(A,B)) | member(f12(A,B),B). [resolve(44,b,37,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f10(A,B),f9(A,B)) | member(f13(A,B),B). [resolve(44,b,38,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f9(A,B),f10(A,B)) | apply(A,f11(A,B),f12(A,B)). [resolve(44,b,39,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f9(A,B),f10(A,B)) | apply(A,f12(A,B),f13(A,B)). [resolve(44,b,40,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f10(A,B),f9(A,B)) | apply(A,f11(A,B),f12(A,B)). [resolve(44,b,41,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | subset(f6(A,B),B) | apply(A,f10(A,B),f9(A,B)) | apply(A,f12(A,B),f13(A,B)). [resolve(44,b,42,a)].
% 0.36/1.07 45 strict_well_order(A,B) | -strict_order(A,B) | -least(C,A,f6(A,B)) # label(strict_well_order) # label(axiom). [clausify(13)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f9(A,B),B) | member(f11(A,B),B). [resolve(45,b,23,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f9(A,B),B) | member(f12(A,B),B). [resolve(45,b,24,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f9(A,B),B) | member(f13(A,B),B). [resolve(45,b,25,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f10(A,B),B) | member(f11(A,B),B). [resolve(45,b,26,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f10(A,B),B) | member(f12(A,B),B). [resolve(45,b,27,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f10(A,B),B) | member(f13(A,B),B). [resolve(45,b,28,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f9(A,B),B) | apply(A,f11(A,B),f12(A,B)). [resolve(45,b,29,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f9(A,B),B) | apply(A,f12(A,B),f13(A,B)). [resolve(45,b,30,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f10(A,B),B) | apply(A,f11(A,B),f12(A,B)). [resolve(45,b,31,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | member(f10(A,B),B) | apply(A,f12(A,B),f13(A,B)). [resolve(45,b,32,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | member(f11(A,B),B). [resolve(45,b,33,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | member(f12(A,B),B). [resolve(45,b,34,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | member(f13(A,B),B). [resolve(45,b,35,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | member(f11(A,B),B). [resolve(45,b,36,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | member(f12(A,B),B). [resolve(45,b,37,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | member(f13(A,B),B). [resolve(45,b,38,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | apply(A,f11(A,B),f12(A,B)). [resolve(45,b,39,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | apply(A,f12(A,B),f13(A,B)). [resolve(45,b,40,a)].
% 0.36/1.07 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | apply(A,f11(A,B),f12(A,B)). [resolve(45,b,41,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | -least(C,A,f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | apply(A,f12(A,B),f13(A,B)). [resolve(45,b,42,a)].
% 0.82/1.08 46 strict_well_order(A,B) | -strict_order(A,B) | member(f7(A,B),f6(A,B)) # label(strict_well_order) # label(axiom). [clausify(13)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f9(A,B),B) | member(f11(A,B),B). [resolve(46,b,23,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f9(A,B),B) | member(f12(A,B),B). [resolve(46,b,24,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f9(A,B),B) | member(f13(A,B),B). [resolve(46,b,25,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f10(A,B),B) | member(f11(A,B),B). [resolve(46,b,26,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f10(A,B),B) | member(f12(A,B),B). [resolve(46,b,27,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f10(A,B),B) | member(f13(A,B),B). [resolve(46,b,28,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f9(A,B),B) | apply(A,f11(A,B),f12(A,B)). [resolve(46,b,29,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f9(A,B),B) | apply(A,f12(A,B),f13(A,B)). [resolve(46,b,30,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f10(A,B),B) | apply(A,f11(A,B),f12(A,B)). [resolve(46,b,31,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | member(f10(A,B),B) | apply(A,f12(A,B),f13(A,B)). [resolve(46,b,32,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | member(f11(A,B),B). [resolve(46,b,33,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | member(f12(A,B),B). [resolve(46,b,34,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | member(f13(A,B),B). [resolve(46,b,35,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | member(f11(A,B),B). [resolve(46,b,36,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | member(f12(A,B),B). [resolve(46,b,37,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | member(f13(A,B),B). [resolve(46,b,38,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | apply(A,f11(A,B),f12(A,B)). [resolve(46,b,39,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f9(A,B),f10(A,B)) | apply(A,f12(A,B),f13(A,B)). [resolve(46,b,40,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | apply(A,f11(A,B),f12(A,B)). [resolve(46,b,41,a)].
% 0.82/1.08 Derived: strict_well_order(A,B) | member(f7(A,B),f6(A,B)) | apply(A,f10(A,B),f9(A,B)) | apply(A,f12(A,B),f13(A,B)). [resolve(46,b,42,a)].
% 0.82/1.08 47 strict_order(A,B) | member(f9(A,B),B) | -apply(A,f11(A,B),f13(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.82/1.08 Derived: member(f9(A,B),B) | -apply(A,f11(A,B),f13(A,B)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | -apply(A,D,C). [resolve(47,a,22,a)].
% 0.82/1.08 Derived: member(f9(A,B),B) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | subset(f6(A,B),B). [resolve(47,a,44,b)].
% 0.82/1.08 Derived: member(f9(A,B),B) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | -least(C,A,f6(A,B)). [resolve(47,a,45,b)].
% 0.82/1.08 Derived: member(f9(A,B),B) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | member(f7(A,B),f6(A,B)). [resolve(47,a,46,b)].
% 0.82/1.08 48 strict_order(A,B) | member(f10(A,B),B) | -apply(A,f11(A,B),f13(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.82/1.08 Derived: member(f10(A,B),B) | -apply(A,f11(A,B),f13(A,B)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | -apply(A,D,C). [resolve(48,a,22,a)].
% 0.82/1.08 Derived: member(f10(A,B),B) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | subset(f6(A,B),B). [resolve(48,a,44,b)].
% 0.82/1.08 Derived: member(f10(A,B),B) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | -least(C,A,f6(A,B)). [resolve(48,a,45,b)].
% 0.82/1.08 Derived: member(f10(A,B),B) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | member(f7(A,B),f6(A,B)). [resolve(48,a,46,b)].
% 0.82/1.08 49 strict_order(A,B) | apply(A,f9(A,B),f10(A,B)) | -apply(A,f11(A,B),f13(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.82/1.08 Derived: apply(A,f9(A,B),f10(A,B)) | -apply(A,f11(A,B),f13(A,B)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | -apply(A,D,C). [resolve(49,a,22,a)].
% 0.82/1.08 Derived: apply(A,f9(A,B),f10(A,B)) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | subset(f6(A,B),B). [resolve(49,a,44,b)].
% 0.82/1.08 Derived: apply(A,f9(A,B),f10(A,B)) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | -least(C,A,f6(A,B)). [resolve(49,a,45,b)].
% 0.82/1.08 Derived: apply(A,f9(A,B),f10(A,B)) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | member(f7(A,B),f6(A,B)). [resolve(49,a,46,b)].
% 0.82/1.08 50 strict_order(A,B) | apply(A,f10(A,B),f9(A,B)) | -apply(A,f11(A,B),f13(A,B)) # label(strict_order) # label(axiom). [clausify(16)].
% 0.82/1.08 Derived: apply(A,f10(A,B),f9(A,B)) | -apply(A,f11(A,B),f13(A,B)) | -member(C,B) | -member(D,B) | -apply(A,C,D) | -apply(A,D,C). [resolve(50,a,22,a)].
% 0.82/1.08 Derived: apply(A,f10(A,B),f9(A,B)) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | subset(f6(A,B),B). [resolve(50,a,44,b)].
% 0.82/1.08 Derived: apply(A,f10(A,B),f9(A,B)) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | -least(C,A,f6(A,B)). [resolve(50,a,45,b)].
% 0.82/1.08 Derived: apply(A,f10(A,B),f9(A,B)) | -apply(A,f11(A,B),f13(A,B)) | strict_well_order(A,B) | member(f7(A,B),f6(A,B)). [resolve(50,a,46,b)].
% 0.82/1.08 51 -strict_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(strict_order) # label(axiom). [clausify(16)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f9(E,B),B) | member(f11(E,B),B). [resolve(51,a,23,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f9(E,B),B) | member(f12(E,B),B). [resolve(51,a,24,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f9(E,B),B) | member(f13(E,B),B). [resolve(51,a,25,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f10(E,B),B) | member(f11(E,B),B). [resolve(51,a,26,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f10(E,B),B) | member(f12(E,B),B). [resolve(51,a,27,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f10(E,B),B) | member(f13(E,B),B). [resolve(51,a,28,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f9(E,B),B) | apply(E,f11(E,B),f12(E,B)). [resolve(51,a,29,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f9(E,B),B) | apply(E,f12(E,B),f13(E,B)). [resolve(51,a,30,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f10(E,B),B) | apply(E,f11(E,B),f12(E,B)). [resolve(51,a,31,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f10(E,B),B) | apply(E,f12(E,B),f13(E,B)). [resolve(51,a,32,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f9(E,B),f10(E,B)) | member(f11(E,B),B). [resolve(51,a,33,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f9(E,B),f10(E,B)) | member(f12(E,B),B). [resolve(51,a,34,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f9(E,B),f10(E,B)) | member(f13(E,B),B). [resolve(51,a,35,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f10(E,B),f9(E,B)) | member(f11(E,B),B). [resolve(51,a,36,a)].
% 0.82/1.08 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f10(E,B),f9(E,B)) | member(f12(E,B),B). [resolve(51,a,37,a)].
% 1.91/2.24 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f10(E,B),f9(E,B)) | member(f13(E,B),B). [resolve(51,a,38,a)].
% 1.91/2.24 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f9(E,B),f10(E,B)) | apply(E,f11(E,B),f12(E,B)). [resolve(51,a,39,a)].
% 1.91/2.24 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f9(E,B),f10(E,B)) | apply(E,f12(E,B),f13(E,B)). [resolve(51,a,40,a)].
% 1.91/2.24 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f10(E,B),f9(E,B)) | apply(E,f11(E,B),f12(E,B)). [resolve(51,a,41,a)].
% 1.91/2.24 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f10(E,B),f9(E,B)) | apply(E,f12(E,B),f13(E,B)). [resolve(51,a,42,a)].
% 1.91/2.24 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | -strict_well_order(E,B). [resolve(51,a,43,b)].
% 1.91/2.25 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f9(E,B),B) | -apply(E,f11(E,B),f13(E,B)). [resolve(51,a,47,a)].
% 1.91/2.25 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | member(f10(E,B),B) | -apply(E,f11(E,B),f13(E,B)). [resolve(51,a,48,a)].
% 1.91/2.25 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f9(E,B),f10(E,B)) | -apply(E,f11(E,B),f13(E,B)). [resolve(51,a,49,a)].
% 1.91/2.25 Derived: -member(A,B) | -member(C,B) | -member(D,B) | -apply(E,A,C) | -apply(E,C,D) | apply(E,A,D) | apply(E,f10(E,B),f9(E,B)) | -apply(E,f11(E,B),f13(E,B)). [resolve(51,a,50,a)].
% 1.91/2.25 52 equal_set(A,B) | -subset(A,B) | -subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 1.91/2.25 53 -equal_set(A,B) | subset(A,B) # label(equal_set) # label(axiom). [clausify(2)].
% 1.91/2.25 54 -equal_set(A,B) | subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 1.91/2.25
% 1.91/2.25 ============================== end predicate elimination =============
% 1.91/2.25
% 1.91/2.25 Auto_denials: (non-Horn, no changes).
% 1.91/2.25
% 1.91/2.25 Term ordering decisions:
% 1.91/2.25 Function symbol KB weights: on=1. member_predicate=1. empty_set=1. c1=1. union=1. intersection=1. unordered_pair=1. difference=1. f1=1. f2=1. f3=1. f6=1. f7=1. f9=1. f10=1. f11=1. f12=1. f13=1. singleton=1. product=1. sum=1. power_set=1. suc=1. f4=1. initial_segment=1. f5=1. f8=1.
% 1.91/2.25
% 1.91/2.25 ============================== end of process initial clauses ========
% 1.91/2.25
% 1.91/2.25 ============================== CLAUSES FOR SEARCH ====================
% 1.91/2.25
% 1.91/2.25 ============================== end of clauses for search =============
% 1.91/2.25
% 1.91/2.25 ============================== SEARCH ================================
% 1.91/2.25
% 1.91/2.25 % Starting search at 0.06 seconds.
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=58.000, iters=5844
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=55.000, iters=5547
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=50.000, iters=4629
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=47.000, iters=4197
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=44.000, iters=3864
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=43.000, iters=3666
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=40.000, iters=3391
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=39.000, iters=5025
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=36.000, iters=4747
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=33.000, iters=4260
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=26.000, iters=3378
% 1.91/2.25
% 1.91/2.25 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 44 (0.00 of 0.81 sec).
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=23.000, iters=3359
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=22.000, iters=3364
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=21.000, iters=3470
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=20.000, iters=3424
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=19.000, iters=3337
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=18.000, iters=3333
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=17.000, iters=3438
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=16.000, iters=3343
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=14.000, iters=3339
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=13.000, iters=3339
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=12.000, iters=3400
% 1.91/2.25
% 1.91/2.25 Low Water (displace): id=2526, wt=59.000
% 1.91/2.25
% 1.91/2.25 Low Water (displace): id=2540, wt=57.000
% 1.91/2.25
% 1.91/2.25 Low Water (displace): id=2536, wt=56.000
% 1.91/2.25
% 1.91/2.25 Low Water (keep): wt=11.000, iters=3346
% 1.91/2.25
% 1.91/2.25 Low Water (displace): id=2550, wt=54.000
% 1.91/2.25
% 1.91/2.25 Low Water (displace): id=2424,Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------