TSTP Solution File: SET641+3 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 04:31:05 EDT 2022

% Result   : Theorem 0.76s 1.04s
% Output   : Refutation 0.76s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 08:24:13 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.45/1.02  ============================== Prover9 ===============================
% 0.45/1.02  Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.02  Process 18405 was started by sandbox on n024.cluster.edu,
% 0.45/1.02  Sun Jul 10 08:24:14 2022
% 0.45/1.02  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18252_n024.cluster.edu".
% 0.45/1.02  ============================== end of head ===========================
% 0.45/1.02  
% 0.45/1.02  ============================== INPUT =================================
% 0.45/1.02  
% 0.45/1.02  % Reading from file /tmp/Prover9_18252_n024.cluster.edu
% 0.45/1.02  
% 0.45/1.02  set(prolog_style_variables).
% 0.45/1.02  set(auto2).
% 0.45/1.02      % set(auto2) -> set(auto).
% 0.45/1.02      % set(auto) -> set(auto_inference).
% 0.45/1.02      % set(auto) -> set(auto_setup).
% 0.45/1.02      % set(auto_setup) -> set(predicate_elim).
% 0.45/1.02      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.02      % set(auto) -> set(auto_limits).
% 0.45/1.02      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.02      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.02      % set(auto) -> set(auto_denials).
% 0.45/1.02      % set(auto) -> set(auto_process).
% 0.45/1.02      % set(auto2) -> assign(new_constants, 1).
% 0.45/1.02      % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.02      % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.02      % set(auto2) -> assign(max_hours, 1).
% 0.45/1.02      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.02      % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.02      % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.02      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.02      % set(auto2) -> set(sort_initial_sos).
% 0.45/1.02      % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.02      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.02      % set(auto2) -> assign(max_megs, 400).
% 0.45/1.02      % set(auto2) -> assign(stats, some).
% 0.45/1.02      % set(auto2) -> clear(echo_input).
% 0.45/1.02      % set(auto2) -> set(quiet).
% 0.45/1.02      % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.02      % set(auto2) -> clear(print_given).
% 0.45/1.02  assign(lrs_ticks,-1).
% 0.45/1.02  assign(sos_limit,10000).
% 0.45/1.02  assign(order,kbo).
% 0.45/1.02  set(lex_order_vars).
% 0.45/1.02  clear(print_given).
% 0.45/1.02  
% 0.45/1.02  % formulas(sos).  % not echoed (19 formulas)
% 0.45/1.02  
% 0.45/1.02  ============================== end of input ==========================
% 0.45/1.02  
% 0.45/1.02  % From the command line: assign(max_seconds, 300).
% 0.45/1.02  
% 0.45/1.02  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.02  
% 0.45/1.02  % Formulas that are not ordinary clauses:
% 0.45/1.02  1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))) # label(p1) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p2) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (member(D,cross_product(B,C)) <-> (exists E (ilf_type(E,set_type) & (exists F (ilf_type(F,set_type) & member(E,B) & member(F,C) & D = ordered_pair(E,F)))))))))))) # label(p3) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p4) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p5) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  6 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p6) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  7 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))) # label(p7) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  8 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p8) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  9 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p9) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.02  10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p10) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  11 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p11) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  12 (all B (ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))) # label(p12) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  13 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p13) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  14 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p14) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  15 (all B (ilf_type(B,set_type) -> (relation_like(B) <-> (all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & C = ordered_pair(D,E))))))))))) # label(p15) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  16 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p16) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  17 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> relation_like(D))))))) # label(p17) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  18 (all B ilf_type(B,set_type)) # label(p18) # label(axiom) # label(non_clause).  [assumption].
% 0.45/1.03  19 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (subset(B,cross_product(C,D)) -> ilf_type(B,relation_type(C,D))))))))) # label(prove_relset_1_3) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.45/1.03  
% 0.45/1.03  ============================== end of process non-clausal formulas ===
% 0.45/1.03  
% 0.45/1.03  ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.03  
% 0.45/1.03  ============================== PREDICATE ELIMINATION =================
% 0.45/1.03  20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) # label(p5) # label(axiom).  [clausify(5)].
% 0.45/1.03  21 subset(c1,cross_product(c2,c3)) # label(prove_relset_1_3) # label(negated_conjecture).  [clausify(19)].
% 0.45/1.03  22 -ilf_type(A,set_type) | subset(A,A) # label(p9) # label(axiom).  [clausify(9)].
% 0.45/1.03  23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f4(A,B),set_type) # label(p5) # label(axiom).  [clausify(5)].
% 0.45/1.03  24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f4(A,B),A) # label(p5) # label(axiom).  [clausify(5)].
% 0.45/1.03  25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f4(A,B),B) # label(p5) # label(axiom).  [clausify(5)].
% 0.45/1.03  Derived: -ilf_type(c1,set_type) | -ilf_type(cross_product(c2,c3),set_type) | -ilf_type(A,set_type) | -member(A,c1) | member(A,cross_product(c2,c3)).  [resolve(20,c,21,a)].
% 0.45/1.03  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f4(A,B),set_type).  [resolve(20,c,23,c)].
% 0.45/1.03  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f4(A,B),A).  [resolve(20,c,24,c)].
% 0.45/1.03  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f4(A,B),B).  [resolve(20,c,25,c)].
% 0.45/1.03  26 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) # label(p15) # label(axiom).  [clausify(15)].
% 0.45/1.03  27 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p16) # label(axiom).  [clausify(16)].
% 0.45/1.03  28 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f11(A),set_type) # label(p15) # label(axiom).  [clausify(15)].
% 0.45/1.03  29 -ilf_type(A,set_type) | relation_like(A) | member(f11(A),A) # label(p15) # label(axiom).  [clausify(15)].
% 0.45/1.03  30 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p17) # label(axiom).  [clausify(17)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -empty(A) | -ilf_type(A,set_type).  [resolve(26,b,27,c)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f11(A),set_type).  [resolve(26,b,28,b)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(A,set_type) | member(f11(A),A).  [resolve(26,b,29,b)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(26,b,30,d)].
% 0.76/1.04  31 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) # label(p15) # label(axiom).  [clausify(15)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -empty(A) | -ilf_type(A,set_type).  [resolve(31,b,27,c)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f11(A),set_type).  [resolve(31,b,28,b)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(A,set_type) | member(f11(A),A).  [resolve(31,b,29,b)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(31,b,30,d)].
% 0.76/1.04  32 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(A) # label(p15) # label(axiom).  [clausify(15)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f9(A,D),set_type).  [resolve(32,b,26,b)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f10(A,D),set_type).  [resolve(32,b,31,b)].
% 0.76/1.04  33 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B # label(p15) # label(axiom).  [clausify(15)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -empty(A) | -ilf_type(A,set_type).  [resolve(33,b,27,c)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f11(A),set_type).  [resolve(33,b,28,b)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | member(f11(A),A).  [resolve(33,b,29,b)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(33,b,30,d)].
% 0.76/1.04  Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f9(A,B),f10(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f11(A).  [resolve(33,b,32,b)].
% 0.76/1.04  
% 0.76/1.04  ============================== end predicate elimination =============
% 0.76/1.04  
% 0.76/1.04  Auto_denials:  (non-Horn, no changes).
% 0.76/1.04  
% 0.76/1.04  Term ordering decisions:
% 0.76/1.04  Function symbol KB weights:  set_type=1. c1=1. c2=1. c3=1. cross_product=1. ordered_pair=1. relation_type=1. f1=1. f4=1. f6=1. f9=1. f10=1. subset_type=1. power_set=1. member_type=1. f5=1. f7=1. f8=1. f11=1. f2=1. f3=1.
% 0.76/1.04  
% 0.76/1.04  ============================== end of process initial clauses ========
% 0.76/1.04  
% 0.76/1.04  ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.04  
% 0.76/1.04  ============================== end of clauses for search =============
% 0.76/1.04  
% 0.76/1.04  ============================== SEARCH ================================
% 0.76/1.04  
% 0.76/1.04  % Starting search at 0.02 seconds.
% 0.76/1.04  
% 0.76/1.04  ============================== PROOF =================================
% 0.76/1.04  % SZS status Theorem
% 0.76/1.04  % SZS output start Refutation
% 0.76/1.04  
% 0.76/1.04  % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.76/1.04  % Length of proof is 32.
% 0.76/1.04  % Level of proof is 8.
% 0.76/1.04  % Maximum clause weight is 11.000.
% 0.76/1.04  % Given clauses 40.
% 0.76/1.04  
% 0.76/1.04  1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))) # label(p1) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.04  5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p5) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.04  7 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))) # label(p7) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.04  10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p10) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.04  11 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p11) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.04  12 (all B (ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))) # label(p12) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.04  18 (all B ilf_type(B,set_type)) # label(p18) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.04  19 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (subset(B,cross_product(C,D)) -> ilf_type(B,relation_type(C,D))))))))) # label(prove_relset_1_3) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.76/1.04  20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) # label(p5) # label(axiom).  [clausify(5)].
% 0.76/1.04  21 subset(c1,cross_product(c2,c3)) # label(prove_relset_1_3) # label(negated_conjecture).  [clausify(19)].
% 0.76/1.04  34 ilf_type(A,set_type) # label(p18) # label(axiom).  [clausify(18)].
% 0.76/1.04  35 -ilf_type(c1,relation_type(c2,c3)) # label(prove_relset_1_3) # label(negated_conjecture).  [clausify(19)].
% 0.76/1.04  36 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p11) # label(axiom).  [clausify(11)].
% 0.76/1.04  37 -empty(power_set(A)).  [copy(36),unit_del(a,34)].
% 0.76/1.04  54 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))) # label(p7) # label(axiom).  [clausify(7)].
% 0.76/1.04  55 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))).  [copy(54),unit_del(a,34),unit_del(b,34)].
% 0.76/1.04  57 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f6(A,B),A) # label(p10) # label(axiom).  [clausify(10)].
% 0.76/1.04  58 member(A,power_set(B)) | member(f6(A,B),A).  [copy(57),unit_del(a,34),unit_del(b,34)].
% 0.76/1.04  59 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f6(A,B),B) # label(p10) # label(axiom).  [clausify(10)].
% 0.76/1.04  60 member(A,power_set(B)) | -member(f6(A,B),B).  [copy(59),unit_del(a,34),unit_del(b,34)].
% 0.76/1.04  63 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B) # label(p12) # label(axiom).  [clausify(12)].
% 0.76/1.04  64 empty(A) | ilf_type(B,member_type(A)) | -member(B,A).  [copy(63),unit_del(a,34),unit_del(c,34)].
% 0.76/1.04  65 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)) # label(p1) # label(axiom).  [clausify(1)].
% 0.76/1.04  66 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)).  [copy(65),unit_del(a,34),unit_del(b,34)].
% 0.76/1.04  81 -ilf_type(c1,set_type) | -ilf_type(cross_product(c2,c3),set_type) | -ilf_type(A,set_type) | -member(A,c1) | member(A,cross_product(c2,c3)).  [resolve(20,c,21,a)].
% 0.76/1.04  82 -member(A,c1) | member(A,cross_product(c2,c3)).  [copy(81),unit_del(a,34),unit_del(b,34),unit_del(c,34)].
% 0.76/1.04  116 -ilf_type(c1,subset_type(cross_product(c2,c3))).  [ur(66,b,35,a)].
% 0.76/1.04  148 -ilf_type(c1,member_type(power_set(cross_product(c2,c3)))).  [ur(55,a,116,a)].
% 0.76/1.04  149 -member(c1,power_set(cross_product(c2,c3))).  [ur(64,a,37,a,b,148,a)].
% 0.76/1.04  150 -member(f6(c1,cross_product(c2,c3)),cross_product(c2,c3)).  [ur(60,a,149,a)].
% 0.76/1.04  151 -member(f6(c1,cross_product(c2,c3)),c1).  [ur(82,b,150,a)].
% 0.76/1.04  182 $F.  [resolve(151,a,58,b),unit_del(a,149)].
% 0.76/1.04  
% 0.76/1.04  % SZS output end Refutation
% 0.76/1.04  ============================== end of proof ==========================
% 0.76/1.04  
% 0.76/1.04  ============================== STATISTICS ============================
% 0.76/1.04  
% 0.76/1.04  Given=40. Generated=144. Kept=103. proofs=1.
% 0.76/1.04  Usable=40. Sos=63. Demods=0. Limbo=0, Disabled=64. Hints=0.
% 0.76/1.04  Megabytes=0.23.
% 0.76/1.04  User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.76/1.04  
% 0.76/1.04  ============================== end of statistics =====================
% 0.76/1.04  
% 0.76/1.04  ============================== end of search =========================
% 0.76/1.04  
% 0.76/1.04  THEOREM PROVED
% 0.76/1.04  % SZS status Theorem
% 0.76/1.04  
% 0.76/1.04  Exiting with 1 proof.
% 0.76/1.04  
% 0.76/1.04  Process 18405 exit (max_proofs) Sun Jul 10 08:24:14 2022
% 0.76/1.04  Prover9 interrupted
%------------------------------------------------------------------------------