TSTP Solution File: SET655+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET655+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 04:31:11 EDT 2022
% Result : Theorem 0.76s 1.08s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET655+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n029.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 06:43:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.72/1.02 ============================== Prover9 ===============================
% 0.72/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.02 Process 16915 was started by sandbox2 on n029.cluster.edu,
% 0.72/1.02 Sun Jul 10 06:43:16 2022
% 0.72/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16762_n029.cluster.edu".
% 0.72/1.02 ============================== end of head ===========================
% 0.72/1.02
% 0.72/1.02 ============================== INPUT =================================
% 0.72/1.02
% 0.72/1.02 % Reading from file /tmp/Prover9_16762_n029.cluster.edu
% 0.72/1.02
% 0.72/1.02 set(prolog_style_variables).
% 0.72/1.02 set(auto2).
% 0.72/1.02 % set(auto2) -> set(auto).
% 0.72/1.02 % set(auto) -> set(auto_inference).
% 0.72/1.02 % set(auto) -> set(auto_setup).
% 0.72/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.02 % set(auto) -> set(auto_limits).
% 0.72/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.02 % set(auto) -> set(auto_denials).
% 0.72/1.02 % set(auto) -> set(auto_process).
% 0.72/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.02 % set(auto2) -> assign(stats, some).
% 0.72/1.02 % set(auto2) -> clear(echo_input).
% 0.72/1.02 % set(auto2) -> set(quiet).
% 0.72/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.02 % set(auto2) -> clear(print_given).
% 0.72/1.02 assign(lrs_ticks,-1).
% 0.72/1.02 assign(sos_limit,10000).
% 0.72/1.02 assign(order,kbo).
% 0.72/1.02 set(lex_order_vars).
% 0.72/1.02 clear(print_given).
% 0.72/1.02
% 0.72/1.02 % formulas(sos). % not echoed (20 formulas)
% 0.72/1.02
% 0.72/1.02 ============================== end of input ==========================
% 0.72/1.02
% 0.72/1.02 % From the command line: assign(max_seconds, 300).
% 0.72/1.02
% 0.72/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.02
% 0.72/1.02 % Formulas that are not ordinary clauses:
% 0.72/1.02 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (subset(B,C) & subset(C,D) -> subset(B,D)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (subset(B,C) & subset(D,E) -> subset(cross_product(B,D),cross_product(C,E))))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 3 (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(p3) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p4) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 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].
% 0.72/1.02 6 (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].
% 0.72/1.02 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].
% 0.72/1.02 8 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 9 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 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].
% 0.72/1.02 16 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 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].
% 0.72/1.02 18 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 19 (all B ilf_type(B,set_type)) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 20 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (all F (ilf_type(F,relation_type(B,D)) -> (subset(B,C) & subset(D,E) -> ilf_type(F,relation_type(C,E))))))))))))) # label(prove_relset_1_17) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.02
% 0.72/1.02 ============================== end of process non-clausal formulas ===
% 0.72/1.02
% 0.72/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.02
% 0.72/1.02 ============================== PREDICATE ELIMINATION =================
% 0.72/1.02 21 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) # label(p15) # label(axiom). [clausify(15)].
% 0.72/1.02 22 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p16) # label(axiom). [clausify(16)].
% 0.72/1.02 23 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f9(A),set_type) # label(p15) # label(axiom). [clausify(15)].
% 0.72/1.02 24 -ilf_type(A,set_type) | relation_like(A) | member(f9(A),A) # label(p15) # label(axiom). [clausify(15)].
% 0.72/1.02 25 -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)].
% 0.72/1.02 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(21,b,22,c)].
% 0.72/1.02 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(21,b,23,b)].
% 0.72/1.02 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(21,b,24,b)].
% 0.72/1.02 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(21,b,25,d)].
% 0.72/1.02 26 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p15) # label(axiom). [clausify(15)].
% 0.72/1.02 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(26,b,22,c)].
% 0.72/1.02 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(26,b,23,b)].
% 0.72/1.02 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(26,b,24,b)].
% 0.76/1.08 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(26,b,25,d)].
% 0.76/1.08 27 -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(p15) # label(axiom). [clausify(15)].
% 0.76/1.08 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(27,b,21,b)].
% 0.76/1.08 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(27,b,26,b)].
% 0.76/1.08 28 -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(p15) # label(axiom). [clausify(15)].
% 0.76/1.08 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(28,b,22,c)].
% 0.76/1.08 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(28,b,23,b)].
% 0.76/1.08 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(28,b,24,b)].
% 0.76/1.08 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(28,b,25,d)].
% 0.76/1.08 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(28,b,27,b)].
% 0.76/1.08
% 0.76/1.08 ============================== end predicate elimination =============
% 0.76/1.08
% 0.76/1.08 Auto_denials: (non-Horn, no changes).
% 0.76/1.08
% 0.76/1.08 Term ordering decisions:
% 0.76/1.08 Function symbol KB weights: set_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. ordered_pair=1. cross_product=1. relation_type=1. f1=1. f2=1. f4=1. f7=1. f8=1. subset_type=1. power_set=1. member_type=1. f3=1. f5=1. f6=1. f9=1.
% 0.76/1.08
% 0.76/1.08 ============================== end of process initial clauses ========
% 0.76/1.08
% 0.76/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.08
% 0.76/1.08 ============================== end of clauses for search =============
% 0.76/1.08
% 0.76/1.08 ============================== SEARCH ================================
% 0.76/1.08
% 0.76/1.08 % Starting search at 0.02 seconds.
% 0.76/1.08
% 0.76/1.08 ============================== PROOF =================================
% 0.76/1.08 % SZS status Theorem
% 0.76/1.08 % SZS output start Refutation
% 0.76/1.08
% 0.76/1.08 % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.76/1.08 % Length of proof is 71.
% 0.76/1.08 % Level of proof is 12.
% 0.76/1.08 % Maximum clause weight is 13.000.
% 0.76/1.08 % Given clauses 182.
% 0.76/1.08
% 0.76/1.08 2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (subset(B,C) & subset(D,E) -> subset(cross_product(B,D),cross_product(C,E))))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 3 (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(p3) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 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].
% 0.76/1.08 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].
% 0.76/1.08 9 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 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].
% 0.76/1.08 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].
% 0.76/1.08 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].
% 0.76/1.08 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].
% 0.76/1.08 19 (all B ilf_type(B,set_type)) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.08 20 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (all F (ilf_type(F,relation_type(B,D)) -> (subset(B,C) & subset(D,E) -> ilf_type(F,relation_type(C,E))))))))))))) # label(prove_relset_1_17) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.08 29 ilf_type(A,set_type) # label(p19) # label(axiom). [clausify(19)].
% 0.76/1.08 30 subset(c1,c2) # label(prove_relset_1_17) # label(negated_conjecture). [clausify(20)].
% 0.76/1.08 31 subset(c3,c4) # label(prove_relset_1_17) # label(negated_conjecture). [clausify(20)].
% 0.76/1.08 32 ilf_type(c5,relation_type(c1,c3)) # label(prove_relset_1_17) # label(negated_conjecture). [clausify(20)].
% 0.76/1.08 33 -ilf_type(c5,relation_type(c2,c4)) # label(prove_relset_1_17) # label(negated_conjecture). [clausify(20)].
% 0.76/1.08 34 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p11) # label(axiom). [clausify(11)].
% 0.76/1.08 35 -empty(power_set(A)). [copy(34),unit_del(a,29)].
% 0.76/1.08 36 -ilf_type(A,set_type) | -empty(A) | -ilf_type(B,set_type) | -member(B,A) # label(p14) # label(axiom). [clausify(14)].
% 0.76/1.08 37 -empty(A) | -member(B,A). [copy(36),unit_del(a,29),unit_del(c,29)].
% 0.76/1.08 38 -ilf_type(A,set_type) | subset(A,A) # label(p9) # label(axiom). [clausify(9)].
% 0.76/1.08 39 subset(A,A). [copy(38),unit_del(a,29)].
% 0.76/1.08 53 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f2(A,B),A) # label(p5) # label(axiom). [clausify(5)].
% 0.76/1.08 54 subset(A,B) | member(f2(A,B),A). [copy(53),unit_del(a,29),unit_del(b,29)].
% 0.76/1.08 55 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f2(A,B),B) # label(p5) # label(axiom). [clausify(5)].
% 0.76/1.08 56 subset(A,B) | -member(f2(A,B),B). [copy(55),unit_del(a,29),unit_del(b,29)].
% 0.76/1.08 57 -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)].
% 0.76/1.08 58 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))). [copy(57),unit_del(a,29),unit_del(b,29)].
% 0.76/1.08 59 -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)].
% 0.76/1.08 60 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [copy(59),unit_del(a,29),unit_del(b,29)].
% 0.76/1.08 62 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f4(A,B),A) # label(p10) # label(axiom). [clausify(10)].
% 0.76/1.08 63 member(A,power_set(B)) | member(f4(A,B),A). [copy(62),unit_del(a,29),unit_del(b,29)].
% 0.76/1.08 64 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f4(A,B),B) # label(p10) # label(axiom). [clausify(10)].
% 0.76/1.08 65 member(A,power_set(B)) | -member(f4(A,B),B). [copy(64),unit_del(a,29),unit_del(b,29)].
% 0.76/1.08 66 -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)].
% 0.76/1.08 67 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(66),unit_del(a,29),unit_del(c,29)].
% 0.76/1.08 68 -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)].
% 0.76/1.08 69 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [copy(68),unit_del(a,29),unit_del(c,29)].
% 0.76/1.08 70 -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(p3) # label(axiom). [clausify(3)].
% 0.76/1.08 71 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [copy(70),unit_del(a,29),unit_del(b,29)].
% 0.76/1.08 72 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))) # label(p3) # label(axiom). [clausify(3)].
% 0.76/1.08 73 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(72),unit_del(a,29),unit_del(b,29)].
% 0.76/1.08 76 -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)].
% 0.76/1.08 77 -subset(A,B) | -member(C,A) | member(C,B). [copy(76),unit_del(a,29),unit_del(b,29),unit_del(d,29)].
% 0.76/1.08 78 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(A,power_set(B)) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) # label(p10) # label(axiom). [clausify(10)].
% 0.76/1.08 79 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(78),unit_del(a,29),unit_del(b,29),unit_del(d,29)].
% 0.76/1.08 80 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -subset(A,B) | -subset(C,D) | subset(cross_product(A,C),cross_product(B,D)) # label(p2) # label(axiom). [clausify(2)].
% 0.76/1.08 81 -subset(A,B) | -subset(C,D) | subset(cross_product(A,C),cross_product(B,D)). [copy(80),unit_del(a,29),unit_del(b,29),unit_del(c,29),unit_del(d,29)].
% 0.76/1.08 104 member(A,power_set(B)) | -empty(A). [resolve(63,b,37,b)].
% 0.76/1.08 107 empty(A) | ilf_type(f4(A,B),member_type(A)) | member(A,power_set(B)). [resolve(69,c,63,b)].
% 0.76/1.08 110 -ilf_type(c5,subset_type(cross_product(c2,c4))). [ur(71,b,33,a)].
% 0.76/1.08 112 ilf_type(c5,subset_type(cross_product(c1,c3))). [resolve(73,a,32,a)].
% 0.76/1.08 128 -subset(A,B) | subset(cross_product(C,A),cross_product(C,B)). [resolve(81,a,39,a)].
% 0.76/1.08 130 -subset(A,B) | subset(cross_product(c1,A),cross_product(c2,B)). [resolve(81,a,30,a)].
% 0.76/1.08 145 -ilf_type(c5,member_type(power_set(cross_product(c2,c4)))). [ur(60,a,110,a)].
% 0.76/1.08 146 -member(c5,power_set(cross_product(c2,c4))). [ur(69,a,35,a,b,145,a)].
% 0.76/1.08 147 -member(f4(c5,cross_product(c2,c4)),cross_product(c2,c4)). [ur(65,a,146,a)].
% 0.76/1.08 181 -empty(c5). [ur(104,a,146,a)].
% 0.76/1.08 187 ilf_type(c5,member_type(power_set(cross_product(c1,c3)))). [resolve(112,a,58,a)].
% 0.76/1.08 190 ilf_type(f4(c5,cross_product(c2,c4)),member_type(c5)). [resolve(107,c,146,a),unit_del(a,181)].
% 0.76/1.08 322 member(c5,power_set(cross_product(c1,c3))). [resolve(187,a,67,b),unit_del(a,35)].
% 0.76/1.08 327 -member(A,c5) | member(A,cross_product(c1,c3)). [resolve(322,a,79,a)].
% 0.76/1.08 434 member(f4(c5,cross_product(c2,c4)),c5). [resolve(190,a,67,b),unit_del(a,181)].
% 0.76/1.08 442 -subset(c5,cross_product(c2,c4)). [ur(77,b,434,a,c,147,a)].
% 0.76/1.08 446 member(f2(c5,cross_product(c2,c4)),c5). [resolve(442,a,54,a)].
% 0.76/1.08 447 -member(f2(c5,cross_product(c2,c4)),cross_product(c2,c4)). [ur(56,a,442,a)].
% 0.76/1.08 532 member(f2(c5,cross_product(c2,c4)),cross_product(c1,c3)). [resolve(327,a,446,a)].
% 0.76/1.08 679 subset(cross_product(A,c3),cross_product(A,c4)). [resolve(128,a,31,a)].
% 0.76/1.08 715 -member(f2(c5,cross_product(c2,c4)),cross_product(c2,c3)). [ur(77,a,679,a,c,447,a)].
% 0.76/1.08 822 subset(cross_product(c1,A),cross_product(c2,A)). [resolve(130,a,39,a)].
% 0.76/1.08 846 $F. [ur(77,a,822,a,c,715,a),unit_del(a,532)].
% 0.76/1.08
% 0.76/1.08 % SZS output end Refutation
% 0.76/1.08 ============================== end of proof ==========================
% 0.76/1.08
% 0.76/1.08 ============================== STATISTICS ============================
% 0.76/1.08
% 0.76/1.08 Given=182. Generated=1192. Kept=775. proofs=1.
% 0.76/1.08 Usable=182. Sos=580. Demods=0. Limbo=12, Disabled=60. Hints=0.
% 0.76/1.08 Megabytes=0.99.
% 0.76/1.08 User_CPU=0.07, System_CPU=0.01, Wall_clock=0.
% 0.76/1.08
% 0.76/1.08 ============================== end of statistics =====================
% 0.76/1.08
% 0.76/1.08 ============================== end of search =========================
% 0.76/1.08
% 0.76/1.08 THEOREM PROVED
% 0.76/1.08 % SZS status Theorem
% 0.76/1.08
% 0.76/1.08 Exiting with 1 proof.
% 0.76/1.08
% 0.76/1.08 Process 16915 exit (max_proofs) Sun Jul 10 06:43:16 2022
% 0.76/1.08 Prover9 interrupted
%------------------------------------------------------------------------------