TSTP Solution File: SET645+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 04:31:06 EDT 2022
% Result : Theorem 0.74s 1.06s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 19:25:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.02 ============================== Prover9 ===============================
% 0.74/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.02 Process 23930 was started by sandbox2 on n023.cluster.edu,
% 0.74/1.02 Sat Jul 9 19:25:56 2022
% 0.74/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23775_n023.cluster.edu".
% 0.74/1.02 ============================== end of head ===========================
% 0.74/1.02
% 0.74/1.02 ============================== INPUT =================================
% 0.74/1.02
% 0.74/1.02 % Reading from file /tmp/Prover9_23775_n023.cluster.edu
% 0.74/1.02
% 0.74/1.02 set(prolog_style_variables).
% 0.74/1.02 set(auto2).
% 0.74/1.02 % set(auto2) -> set(auto).
% 0.74/1.02 % set(auto) -> set(auto_inference).
% 0.74/1.02 % set(auto) -> set(auto_setup).
% 0.74/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.02 % set(auto) -> set(auto_limits).
% 0.74/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.02 % set(auto) -> set(auto_denials).
% 0.74/1.02 % set(auto) -> set(auto_process).
% 0.74/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.02 % set(auto2) -> assign(stats, some).
% 0.74/1.02 % set(auto2) -> clear(echo_input).
% 0.74/1.02 % set(auto2) -> set(quiet).
% 0.74/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.02 % set(auto2) -> clear(print_given).
% 0.74/1.02 assign(lrs_ticks,-1).
% 0.74/1.02 assign(sos_limit,10000).
% 0.74/1.02 assign(order,kbo).
% 0.74/1.02 set(lex_order_vars).
% 0.74/1.02 clear(print_given).
% 0.74/1.02
% 0.74/1.02 % formulas(sos). % not echoed (22 formulas)
% 0.74/1.02
% 0.74/1.02 ============================== end of input ==========================
% 0.74/1.02
% 0.74/1.02 % From the command line: assign(max_seconds, 300).
% 0.74/1.02
% 0.74/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.02
% 0.74/1.02 % Formulas that are not ordinary clauses:
% 0.74/1.02 1 (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) -> (member(ordered_pair(B,C),cross_product(D,E)) <-> member(B,D) & member(C,E)))))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 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) -> (all F (ilf_type(F,set_type) -> (F = ordered_pair(D,E) <-> F = unordered_pair(unordered_pair(D,E),singleton(D))))))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 4 (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(p4) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 6 (all B (ilf_type(B,set_type) -> ilf_type(singleton(B),set_type))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 7 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p7) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(unordered_pair(B,C),set_type))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 9 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> unordered_pair(B,C) = unordered_pair(C,B))))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 10 (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(p10) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 11 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (B = C <-> (all D (ilf_type(D,set_type) -> (member(D,B) <-> member(D,C))))))))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 13 (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(p13) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 14 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 15 (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(p15) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 16 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 17 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 18 (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(p18) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 19 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 20 (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(p20) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 21 (all B ilf_type(B,set_type)) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.03 22 -(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,C)) -> (member(ordered_pair(D,E),F) -> member(D,B) & member(E,C)))))))))))) # label(prove_relset_1_7) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.03
% 0.74/1.03 ============================== end of process non-clausal formulas ===
% 0.74/1.03
% 0.74/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.03
% 0.74/1.03 ============================== PREDICATE ELIMINATION =================
% 0.74/1.03 23 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) # label(p18) # label(axiom). [clausify(18)].
% 0.74/1.03 24 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p19) # label(axiom). [clausify(19)].
% 0.74/1.03 25 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f9(A),set_type) # label(p18) # label(axiom). [clausify(18)].
% 0.74/1.03 26 -ilf_type(A,set_type) | relation_like(A) | member(f9(A),A) # label(p18) # label(axiom). [clausify(18)].
% 0.74/1.03 27 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p20) # label(axiom). [clausify(20)].
% 0.74/1.03 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(23,b,24,c)].
% 0.74/1.03 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(23,b,25,b)].
% 0.74/1.03 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(23,b,26,b)].
% 0.74/1.03 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(23,b,27,d)].
% 0.74/1.03 28 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p18) # label(axiom). [clausify(18)].
% 0.74/1.06 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(28,b,24,c)].
% 0.74/1.06 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(28,b,25,b)].
% 0.74/1.06 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(28,b,26,b)].
% 0.74/1.06 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(28,b,27,d)].
% 0.74/1.06 29 -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(p18) # label(axiom). [clausify(18)].
% 0.74/1.06 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(29,b,23,b)].
% 0.74/1.06 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(29,b,28,b)].
% 0.74/1.06 30 -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(p18) # label(axiom). [clausify(18)].
% 0.74/1.06 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(30,b,24,c)].
% 0.74/1.06 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(30,b,25,b)].
% 0.74/1.06 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(30,b,26,b)].
% 0.74/1.06 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(30,b,27,d)].
% 0.74/1.06 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(30,b,29,b)].
% 0.74/1.06
% 0.74/1.06 ============================== end predicate elimination =============
% 0.74/1.06
% 0.74/1.06 Auto_denials: (non-Horn, no changes).
% 0.74/1.06
% 0.74/1.06 Term ordering decisions:
% 0.74/1.06 Function symbol KB weights: set_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. ordered_pair=1. cross_product=1. unordered_pair=1. relation_type=1. f1=1. f3=1. f4=1. f7=1. f8=1. subset_type=1. power_set=1. member_type=1. singleton=1. f2=1. f5=1. f6=1. f9=1.
% 0.74/1.06
% 0.74/1.06 ============================== end of process initial clauses ========
% 0.74/1.06
% 0.74/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.06
% 0.74/1.06 ============================== end of clauses for search =============
% 0.74/1.06
% 0.74/1.06 ============================== SEARCH ================================
% 0.74/1.06
% 0.74/1.06 % Starting search at 0.03 seconds.
% 0.74/1.06
% 0.74/1.06 ============================== PROOF =================================
% 0.74/1.06 % SZS status Theorem
% 0.74/1.06 % SZS output start Refutation
% 0.74/1.06
% 0.74/1.06 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.74/1.06 % Length of proof is 34.
% 0.74/1.06 % Level of proof is 9.
% 0.74/1.06 % Maximum clause weight is 11.000.
% 0.74/1.06 % Given clauses 73.
% 0.74/1.06
% 0.74/1.06 1 (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) -> (member(ordered_pair(B,C),cross_product(D,E)) <-> member(B,D) & member(C,E)))))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 4 (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(p4) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 10 (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(p10) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 13 (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(p13) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 14 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 15 (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(p15) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 21 (all B ilf_type(B,set_type)) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.06 22 -(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,C)) -> (member(ordered_pair(D,E),F) -> member(D,B) & member(E,C)))))))))))) # label(prove_relset_1_7) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.06 31 ilf_type(A,set_type) # label(p21) # label(axiom). [clausify(21)].
% 0.74/1.06 32 ilf_type(c5,relation_type(c1,c2)) # label(prove_relset_1_7) # label(negated_conjecture). [clausify(22)].
% 0.74/1.06 33 member(ordered_pair(c3,c4),c5) # label(prove_relset_1_7) # label(negated_conjecture). [clausify(22)].
% 0.74/1.06 34 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p14) # label(axiom). [clausify(14)].
% 0.74/1.06 35 -empty(power_set(A)). [copy(34),unit_del(a,31)].
% 0.74/1.06 36 -member(c3,c1) | -member(c4,c2) # label(prove_relset_1_7) # label(negated_conjecture). [clausify(22)].
% 0.74/1.06 56 -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(p10) # label(axiom). [clausify(10)].
% 0.74/1.06 57 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))). [copy(56),unit_del(a,31),unit_del(b,31)].
% 0.74/1.06 65 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p15) # label(axiom). [clausify(15)].
% 0.74/1.06 66 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(65),unit_del(a,31),unit_del(c,31)].
% 0.74/1.06 71 -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(p4) # label(axiom). [clausify(4)].
% 0.74/1.06 72 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(71),unit_del(a,31),unit_del(b,31)].
% 0.74/1.06 81 -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(p13) # label(axiom). [clausify(13)].
% 0.74/1.06 82 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(81),unit_del(a,31),unit_del(b,31),unit_del(d,31)].
% 0.74/1.06 83 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(A,B),cross_product(C,D)) | member(A,C) # label(p1) # label(axiom). [clausify(1)].
% 0.74/1.06 84 -member(ordered_pair(A,B),cross_product(C,D)) | member(A,C). [copy(83),unit_del(a,31),unit_del(b,31),unit_del(c,31),unit_del(d,31)].
% 0.74/1.06 85 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(A,B),cross_product(C,D)) | member(B,D) # label(p1) # label(axiom). [clausify(1)].
% 0.74/1.06 86 -member(ordered_pair(A,B),cross_product(C,D)) | member(B,D). [copy(85),unit_del(a,31),unit_del(b,31),unit_del(c,31),unit_del(d,31)].
% 0.74/1.06 124 ilf_type(c5,subset_type(cross_product(c1,c2))). [resolve(72,a,32,a)].
% 0.74/1.06 232 ilf_type(c5,member_type(power_set(cross_product(c1,c2)))). [resolve(124,a,57,a)].
% 0.74/1.06 253 member(c5,power_set(cross_product(c1,c2))). [resolve(232,a,66,b),unit_del(a,35)].
% 0.74/1.06 261 -member(A,c5) | member(A,cross_product(c1,c2)). [resolve(253,a,82,a)].
% 0.74/1.06 323 member(ordered_pair(c3,c4),cross_product(c1,c2)). [resolve(261,a,33,a)].
% 0.74/1.06 352 member(c4,c2). [resolve(323,a,86,a)].
% 0.74/1.06 353 member(c3,c1). [resolve(323,a,84,a)].
% 0.74/1.06 357 $F. [back_unit_del(36),unit_del(a,353),unit_del(b,352)].
% 0.74/1.06
% 0.74/1.06 % SZS output end Refutation
% 0.74/1.06 ============================== end of proof ==========================
% 0.74/1.06
% 0.74/1.06 ============================== STATISTICS ============================
% 0.74/1.06
% 0.74/1.06 Given=73. Generated=379. Kept=278. proofs=1.
% 0.74/1.06 Usable=71. Sos=198. Demods=2. Limbo=5, Disabled=68. Hints=0.
% 0.74/1.06 Megabytes=0.45.
% 0.74/1.06 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.74/1.06
% 0.74/1.06 ============================== end of statistics =====================
% 0.74/1.06
% 0.74/1.06 ============================== end of search =========================
% 0.74/1.06
% 0.74/1.06 THEOREM PROVED
% 0.74/1.06 % SZS status Theorem
% 0.74/1.06
% 0.74/1.06 Exiting with 1 proof.
% 0.74/1.06
% 0.74/1.06 Process 23930 exit (max_proofs) Sat Jul 9 19:25:56 2022
% 0.74/1.06 Prover9 interrupted
%------------------------------------------------------------------------------