TSTP Solution File: SET808+4 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SET808+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n022.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 04:32:13 EDT 2022

% Result   : Timeout 300.01s 300.30s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET808+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 11:30:40 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.41/0.97  ============================== Prover9 ===============================
% 0.41/0.97  Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.97  Process 4999 was started by sandbox2 on n022.cluster.edu,
% 0.41/0.97  Sun Jul 10 11:30:41 2022
% 0.41/0.97  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4845_n022.cluster.edu".
% 0.41/0.97  ============================== end of head ===========================
% 0.41/0.97  
% 0.41/0.97  ============================== INPUT =================================
% 0.41/0.97  
% 0.41/0.97  % Reading from file /tmp/Prover9_4845_n022.cluster.edu
% 0.41/0.97  
% 0.41/0.97  set(prolog_style_variables).
% 0.41/0.97  set(auto2).
% 0.41/0.97      % set(auto2) -> set(auto).
% 0.41/0.97      % set(auto) -> set(auto_inference).
% 0.41/0.97      % set(auto) -> set(auto_setup).
% 0.41/0.97      % set(auto_setup) -> set(predicate_elim).
% 0.41/0.97      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.97      % set(auto) -> set(auto_limits).
% 0.41/0.97      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.97      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.97      % set(auto) -> set(auto_denials).
% 0.41/0.97      % set(auto) -> set(auto_process).
% 0.41/0.97      % set(auto2) -> assign(new_constants, 1).
% 0.41/0.97      % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.97      % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.97      % set(auto2) -> assign(max_hours, 1).
% 0.41/0.97      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.97      % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.97      % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.97      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.97      % set(auto2) -> set(sort_initial_sos).
% 0.41/0.97      % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.97      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.97      % set(auto2) -> assign(max_megs, 400).
% 0.41/0.97      % set(auto2) -> assign(stats, some).
% 0.41/0.97      % set(auto2) -> clear(echo_input).
% 0.41/0.97      % set(auto2) -> set(quiet).
% 0.41/0.97      % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.97      % set(auto2) -> clear(print_given).
% 0.41/0.97  assign(lrs_ticks,-1).
% 0.41/0.97  assign(sos_limit,10000).
% 0.41/0.97  assign(order,kbo).
% 0.41/0.97  set(lex_order_vars).
% 0.41/0.97  clear(print_given).
% 0.41/0.97  
% 0.41/0.97  % formulas(sos).  % not echoed (21 formulas)
% 0.41/0.97  
% 0.41/0.97  ============================== end of input ==========================
% 0.41/0.97  
% 0.41/0.97  % From the command line: assign(max_seconds, 300).
% 0.41/0.97  
% 0.41/0.97  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.98  
% 0.41/0.98  % Formulas that are not ordinary clauses:
% 0.41/0.98  1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  2 (all A all B (equal_set(A,B) <-> subset(A,B) & subset(B,A))) # label(equal_set) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  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].
% 0.41/0.98  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].
% 0.41/0.98  6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  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].
% 0.41/0.98  8 (all X all A (member(X,singleton(A)) <-> X = A)) # label(singleton) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  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].
% 0.41/0.98  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].
% 0.41/0.98  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].
% 0.41/0.98  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].
% 0.41/0.98  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].
% 0.41/0.98  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].
% 0.41/0.98  15 (all X all Y (apply(member_predicate,X,Y) <-> member(X,Y))) # label(rel_member) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  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].
% 0.41/0.98  17 (all X (set(X) -> (all Y (member(Y,X) -> set(Y))))) # label(set_member) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  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].
% 0.41/0.98  19 (all A all X (member(X,suc(A)) <-> member(X,union(A,singleton(A))))) # label(successor) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  20 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(thI3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.98  21 -(all A (member(A,on) -> subset(A,on))) # label(thV1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.41/0.98  
% 0.41/0.98  ============================== end of process non-clausal formulas ===
% 0.41/0.98  
% 0.41/0.98  ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.98  
% 0.41/0.98  ============================== PREDICATE ELIMINATION =================
% 0.41/0.98  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)].
% 0.41/0.98  23 strict_order(A,B) | member(f9(A,B),B) | member(f11(A,B),B) # label(strict_order) # label(axiom).  [clausify(16)].
% 0.41/0.98  24 strict_order(A,B) | member(f9(A,B),B) | member(f12(A,B),B) # label(strict_order) # label(axiom).  [clausify(16)].
% 0.41/0.98  25 strict_order(A,B) | member(f9(A,B),B) | member(f13(A,B),B) # label(strict_order) # label(axiom).  [clausify(16)].
% 0.41/0.98  26 strict_order(A,B) | member(f10(A,B),B) | member(f11(A,B),B) # label(strict_order) # label(axiom).  [clausify(16)].
% 0.41/0.98  27 strict_order(A,B) | member(f10(A,B),B) | member(f12(A,B),B) # label(strict_order) # label(axiom).  [clausify(16)].
% 0.41/0.98  28 strict_order(A,B) | member(f10(A,B),B) | member(f13(A,B),B) # label(strict_order) # label(axiom).  [clausify(16)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  43 -strict_well_order(A,B) | strict_order(A,B) # label(strict_well_order) # label(axiom).  [clausify(13)].
% 0.41/0.98  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)].
% 0.41/0.98  44 strict_well_order(A,B) | -strict_order(A,B) | subset(f6(A,B),B) # label(strict_well_order) # label(axiom).  [clausify(13)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  45 strict_well_order(A,B) | -strict_order(A,B) | -least(C,A,f6(A,B)) # label(strict_well_order) # label(axiom).  [clausify(13)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.98  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 0.41/0.99  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  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)].
% 1.85/2.14  52 equal_set(A,B) | -subset(A,B) | -subset(B,A) # label(equal_set) # label(axiom).  [clausify(2)].
% 1.85/2.14  53 -equal_set(A,B) | subset(A,B) # label(equal_set) # label(axiom).  [clausify(2)].
% 1.85/2.14  54 -equal_set(A,B) | subset(B,A) # label(equal_set) # label(axiom).  [clausify(2)].
% 1.85/2.14  
% 1.85/2.14  ============================== end predicate elimination =============
% 1.85/2.14  
% 1.85/2.14  Auto_denials:  (non-Horn, no changes).
% 1.85/2.14  
% 1.85/2.14  Term ordering decisions:
% 1.85/2.14  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.
% 1.85/2.14  
% 1.85/2.14  ============================== end of process initial clauses ========
% 1.85/2.14  
% 1.85/2.14  ============================== CLAUSES FOR SEARCH ====================
% 1.85/2.14  
% 1.85/2.14  ============================== end of clauses for search =============
% 1.85/2.14  
% 1.85/2.14  ============================== SEARCH ================================
% 1.85/2.14  
% 1.85/2.14  % Starting search at 0.05 seconds.
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=58.000, iters=5846
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=55.000, iters=5549
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=50.000, iters=4631
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=47.000, iters=4199
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=44.000, iters=3866
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=43.000, iters=3668
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=40.000, iters=3394
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=32.000, iters=3927
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=31.000, iters=3807
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=28.000, iters=3390
% 1.85/2.14  
% 1.85/2.14  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 44 (0.00 of 0.75 sec).
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=26.000, iters=3647
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=23.000, iters=3345
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=22.000, iters=3357
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=21.000, iters=3416
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=20.000, iters=3425
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=19.000, iters=3353
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=18.000, iters=3345
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=16.000, iters=3342
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=14.000, iters=3343
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=13.000, iters=3342
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=12.000, iters=3371
% 1.85/2.14  
% 1.85/2.14  Low Water (displace): id=2526, wt=59.000
% 1.85/2.14  
% 1.85/2.14  Low Water (displace): id=2540, wt=57.000
% 1.85/2.14  
% 1.85/2.14  Low Water (displace): id=2536, wt=56.000
% 1.85/2.14  
% 1.85/2.14  Low Water (keep): wt=11.000, iters=3342
% 1.85/2.14  
% 1.85/2.14  Low Water (displace): id=2550, wt=54.000
% 1.85/2.14  
% 1.85/2.14  Low Water (displace): id=2424, wt=53.000
% 1.85/2.14  
% 1.85/2.14  Low Water (displace): id=1126, wt=5Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------