TSTP Solution File: SET662+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 04:31:14 EDT 2022
% Result : Theorem 0.41s 1.00s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 03:53:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.41/0.99 ============================== Prover9 ===============================
% 0.41/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.99 Process 30885 was started by sandbox on n027.cluster.edu,
% 0.41/0.99 Sun Jul 10 03:53:18 2022
% 0.41/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30730_n027.cluster.edu".
% 0.41/0.99 ============================== end of head ===========================
% 0.41/0.99
% 0.41/0.99 ============================== INPUT =================================
% 0.41/0.99
% 0.41/0.99 % Reading from file /tmp/Prover9_30730_n027.cluster.edu
% 0.41/0.99
% 0.41/0.99 set(prolog_style_variables).
% 0.41/0.99 set(auto2).
% 0.41/0.99 % set(auto2) -> set(auto).
% 0.41/0.99 % set(auto) -> set(auto_inference).
% 0.41/0.99 % set(auto) -> set(auto_setup).
% 0.41/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.99 % set(auto) -> set(auto_limits).
% 0.41/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.99 % set(auto) -> set(auto_denials).
% 0.41/0.99 % set(auto) -> set(auto_process).
% 0.41/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.99 % set(auto2) -> assign(stats, some).
% 0.41/0.99 % set(auto2) -> clear(echo_input).
% 0.41/0.99 % set(auto2) -> set(quiet).
% 0.41/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.99 % set(auto2) -> clear(print_given).
% 0.41/0.99 assign(lrs_ticks,-1).
% 0.41/0.99 assign(sos_limit,10000).
% 0.41/0.99 assign(order,kbo).
% 0.41/0.99 set(lex_order_vars).
% 0.41/0.99 clear(print_given).
% 0.41/0.99
% 0.41/0.99 % formulas(sos). % not echoed (22 formulas)
% 0.41/0.99
% 0.41/0.99 ============================== end of input ==========================
% 0.41/0.99
% 0.41/0.99 % From the command line: assign(max_seconds, 300).
% 0.41/0.99
% 0.41/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.99
% 0.41/0.99 % Formulas that are not ordinary clauses:
% 0.41/0.99 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> subset(empty_set,cross_product(B,C)))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 2 (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(p2) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 4 (all B (ilf_type(B,set_type) -> -member(B,empty_set))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 6 (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].
% 0.41/0.99 7 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 8 (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(p9) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 9 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 10 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 11 (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(p12) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 12 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 13 (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(p14) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 14 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 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(p16) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 16 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 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(p18) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 18 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 19 (all B ilf_type(B,set_type)) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 20 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(empty_set,relation_type(B,C)))))) # label(prove_relset_1_25) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/0.99
% 0.41/0.99 ============================== end of process non-clausal formulas ===
% 0.41/0.99
% 0.41/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.99
% 0.41/0.99 ============================== PREDICATE ELIMINATION =================
% 0.41/0.99 21 -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(p9) # label(axiom). [clausify(8)].
% 0.41/0.99 22 -ilf_type(A,set_type) | subset(A,A) # label(p10) # label(axiom). [clausify(9)].
% 0.41/0.99 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(empty_set,cross_product(A,B)) # label(p1) # label(axiom). [clausify(1)].
% 0.41/0.99 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f3(A,B),set_type) # label(p9) # label(axiom). [clausify(8)].
% 0.41/0.99 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f3(A,B),A) # label(p9) # label(axiom). [clausify(8)].
% 0.41/0.99 26 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f3(A,B),B) # label(p9) # label(axiom). [clausify(8)].
% 0.41/0.99 Derived: -ilf_type(empty_set,set_type) | -ilf_type(cross_product(A,B),set_type) | -ilf_type(C,set_type) | -member(C,empty_set) | member(C,cross_product(A,B)) | -ilf_type(A,set_type) | -ilf_type(B,set_type). [resolve(21,c,23,c)].
% 0.41/0.99 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(f3(A,B),set_type). [resolve(21,c,24,c)].
% 0.41/0.99 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(f3(A,B),A). [resolve(21,c,25,c)].
% 0.41/0.99 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(f3(A,B),B). [resolve(21,c,26,c)].
% 0.41/0.99 27 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) # label(p16) # label(axiom). [clausify(15)].
% 0.41/0.99 28 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p17) # label(axiom). [clausify(16)].
% 0.41/0.99 29 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f9(A),set_type) # label(p16) # label(axiom). [clausify(15)].
% 0.41/0.99 30 -ilf_type(A,set_type) | relation_like(A) | member(f9(A),A) # label(p16) # label(axiom). [clausify(15)].
% 0.41/0.99 31 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p18) # label(axiom). [clausify(17)].
% 0.41/0.99 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(27,b,28,c)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f9(A),set_type). [resolve(27,b,29,b)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | member(f9(A),A). [resolve(27,b,30,b)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(27,b,31,d)].
% 0.41/1.00 32 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p16) # label(axiom). [clausify(15)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(32,b,28,c)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f9(A),set_type). [resolve(32,b,29,b)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(A,set_type) | member(f9(A),A). [resolve(32,b,30,b)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(32,b,31,d)].
% 0.41/1.00 33 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) # label(p16) # label(axiom). [clausify(15)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f7(A,D),set_type). [resolve(33,b,27,b)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f8(A,D),set_type). [resolve(33,b,32,b)].
% 0.41/1.00 34 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B # label(p16) # label(axiom). [clausify(15)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -empty(A) | -ilf_type(A,set_type). [resolve(34,b,28,c)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f9(A),set_type). [resolve(34,b,29,b)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | member(f9(A),A). [resolve(34,b,30,b)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(34,b,31,d)].
% 0.41/1.00 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f9(A). [resolve(34,b,33,b)].
% 0.41/1.00
% 0.41/1.00 ============================== end predicate elimination =============
% 0.41/1.00
% 0.41/1.00 Auto_denials: (non-Horn, no changes).
% 0.41/1.00
% 0.41/1.00 Term ordering decisions:
% 0.41/1.00 Function symbol KB weights: set_type=1. empty_set=1. c1=1. c2=1. ordered_pair=1. cross_product=1. relation_type=1. f1=1. f3=1. f5=1. f7=1. f8=1. subset_type=1. power_set=1. member_type=1. f2=1. f4=1. f6=1. f9=1.
% 0.41/1.00
% 0.41/1.00 ============================== end of process initial clauses ========
% 0.41/1.00
% 0.41/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.41/1.00
% 0.41/1.00 ============================== end of clauses for search =============
% 0.41/1.00
% 0.41/1.00 ============================== SEARCH ================================
% 0.41/1.00
% 0.41/1.00 % Starting search at 0.02 seconds.
% 0.41/1.00
% 0.41/1.00 ============================== PROOF =================================
% 0.41/1.00 % SZS status Theorem
% 0.41/1.00 % SZS output start Refutation
% 0.41/1.00
% 0.41/1.00 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.41/1.00 % Length of proof is 27.
% 0.41/1.00 % Level of proof is 5.
% 0.41/1.00 % Maximum clause weight is 11.000.
% 0.41/1.00 % Given clauses 31.
% 0.41/1.00
% 0.41/1.00 2 (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(p2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 4 (all B (ilf_type(B,set_type) -> -member(B,empty_set))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 6 (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].
% 0.41/1.00 11 (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(p12) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 12 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 13 (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(p14) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 19 (all B ilf_type(B,set_type)) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 20 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(empty_set,relation_type(B,C)))))) # label(prove_relset_1_25) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/1.00 36 ilf_type(A,set_type) # label(p20) # label(axiom). [clausify(19)].
% 0.41/1.00 37 -ilf_type(empty_set,relation_type(c1,c2)) # label(prove_relset_1_25) # label(negated_conjecture). [clausify(20)].
% 0.41/1.00 38 -ilf_type(A,set_type) | -member(A,empty_set) # label(p4) # label(axiom). [clausify(4)].
% 0.41/1.00 39 -member(A,empty_set). [copy(38),unit_del(a,36)].
% 0.41/1.00 40 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p13) # label(axiom). [clausify(12)].
% 0.41/1.00 41 -empty(power_set(A)). [copy(40),unit_del(a,36)].
% 0.41/1.00 58 -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(6)].
% 0.41/1.00 59 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [copy(58),unit_del(a,36),unit_del(b,36)].
% 0.41/1.00 61 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f5(A,B),A) # label(p12) # label(axiom). [clausify(11)].
% 0.41/1.00 62 member(A,power_set(B)) | member(f5(A,B),A). [copy(61),unit_del(a,36),unit_del(b,36)].
% 0.41/1.00 67 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B) # label(p14) # label(axiom). [clausify(13)].
% 0.41/1.00 68 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [copy(67),unit_del(a,36),unit_del(c,36)].
% 0.41/1.00 69 -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(p2) # label(axiom). [clausify(2)].
% 0.41/1.00 70 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [copy(69),unit_del(a,36),unit_del(b,36)].
% 0.41/1.00 103 member(empty_set,power_set(A)). [resolve(62,b,39,a)].
% 0.41/1.00 109 -ilf_type(empty_set,subset_type(cross_product(c1,c2))). [ur(70,b,37,a)].
% 0.41/1.00 129 -ilf_type(empty_set,member_type(power_set(cross_product(c1,c2)))). [ur(59,a,109,a)].
% 0.41/1.00 137 ilf_type(empty_set,member_type(power_set(A))). [resolve(103,a,68,c),unit_del(a,41)].
% 0.41/1.00 138 $F. [resolve(137,a,129,a)].
% 0.41/1.00
% 0.41/1.00 % SZS output end Refutation
% 0.41/1.00 ============================== end of proof ==========================
% 0.41/1.00
% 0.41/1.00 ============================== STATISTICS ============================
% 0.41/1.00
% 0.41/1.00 Given=31. Generated=97. Kept=63. proofs=1.
% 0.41/1.00 Usable=31. Sos=25. Demods=0. Limbo=6, Disabled=60. Hints=0.
% 0.41/1.00 Megabytes=0.16.
% 0.41/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.41/1.00
% 0.41/1.00 ============================== end of statistics =====================
% 0.41/1.00
% 0.41/1.00 ============================== end of search =========================
% 0.41/1.00
% 0.41/1.00 THEOREM PROVED
% 0.41/1.00 % SZS status Theorem
% 0.41/1.00
% 0.41/1.00 Exiting with 1 proof.
% 0.41/1.00
% 0.41/1.00 Process 30885 exit (max_proofs) Sun Jul 10 03:53:18 2022
% 0.41/1.00 Prover9 interrupted
%------------------------------------------------------------------------------