TSTP Solution File: SET648+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET648+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 04:31:08 EDT 2022
% Result : Theorem 0.72s 1.02s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SET648+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n024.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 : Mon Jul 11 04:16:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.98 ============================== Prover9 ===============================
% 0.41/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.98 Process 14963 was started by sandbox on n024.cluster.edu,
% 0.41/0.98 Mon Jul 11 04:16:29 2022
% 0.41/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14810_n024.cluster.edu".
% 0.41/0.98 ============================== end of head ===========================
% 0.41/0.98
% 0.41/0.98 ============================== INPUT =================================
% 0.41/0.98
% 0.41/0.98 % Reading from file /tmp/Prover9_14810_n024.cluster.edu
% 0.41/0.98
% 0.41/0.98 set(prolog_style_variables).
% 0.41/0.98 set(auto2).
% 0.41/0.98 % set(auto2) -> set(auto).
% 0.41/0.98 % set(auto) -> set(auto_inference).
% 0.41/0.98 % set(auto) -> set(auto_setup).
% 0.41/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.98 % set(auto) -> set(auto_limits).
% 0.41/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.98 % set(auto) -> set(auto_denials).
% 0.41/0.98 % set(auto) -> set(auto_process).
% 0.41/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.98 % set(auto2) -> assign(stats, some).
% 0.41/0.98 % set(auto2) -> clear(echo_input).
% 0.41/0.98 % set(auto2) -> set(quiet).
% 0.41/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.98 % set(auto2) -> clear(print_given).
% 0.41/0.98 assign(lrs_ticks,-1).
% 0.41/0.98 assign(sos_limit,10000).
% 0.41/0.98 assign(order,kbo).
% 0.41/0.98 set(lex_order_vars).
% 0.41/0.98 clear(print_given).
% 0.41/0.98
% 0.41/0.98 % formulas(sos). % not echoed (27 formulas)
% 0.41/0.98
% 0.41/0.98 ============================== end of input ==========================
% 0.41/0.98
% 0.41/0.98 % From the command line: assign(max_seconds, 300).
% 0.41/0.98
% 0.41/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.98
% 0.41/0.98 % Formulas that are not ordinary clauses:
% 0.41/0.98 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].
% 0.41/0.98 2 (all B (ilf_type(B,binary_relation_type) -> subset(B,cross_product(domain_of(B),range_of(B))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 3 (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(cross_product(B,D),cross_product(C,D)) & subset(cross_product(D,B),cross_product(D,C))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 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].
% 0.41/0.98 6 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,set_type) -> (member(C,domain_of(B)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(C,D),B)))))))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 7 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p7) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 8 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,set_type) -> (member(C,range_of(B)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B)))))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 9 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 10 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 11 (exists B ilf_type(B,binary_relation_type)) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 12 (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(p12) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 14 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 15 (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(p15) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 16 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 17 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 19 (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(p19) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 20 (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(p20) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 21 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 22 (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(p22) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 23 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 24 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p24) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 25 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 26 (all B ilf_type(B,set_type)) # label(p26) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 27 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (subset(range_of(C),B) -> ilf_type(C,relation_type(domain_of(C),B))))))) # label(prove_relset_1_10) # 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 28 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p10) # label(axiom). [clausify(10)].
% 0.41/0.98 29 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p25) # label(axiom). [clausify(25)].
% 0.41/0.98 30 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p10) # label(axiom). [clausify(10)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(28,c,29,c)].
% 0.41/0.98 31 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f8(A),set_type) # label(p18) # label(axiom). [clausify(18)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | ilf_type(f8(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(31,b,28,c)].
% 0.41/0.98 32 -ilf_type(A,set_type) | relation_like(A) | member(f8(A),A) # label(p18) # label(axiom). [clausify(18)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | member(f8(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(32,b,28,c)].
% 0.41/0.98 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p19) # label(axiom). [clausify(19)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(33,d,28,c)].
% 0.41/0.98 34 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f6(A,B),set_type) # label(p18) # label(axiom). [clausify(18)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f6(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(34,b,29,c)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f6(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(34,b,30,c)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f6(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f8(A),set_type). [resolve(34,b,31,b)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f6(A,B),set_type) | -ilf_type(A,set_type) | member(f8(A),A). [resolve(34,b,32,b)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f6(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(34,b,33,d)].
% 0.41/0.98 35 -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)].
% 0.41/0.98 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(35,b,29,c)].
% 0.41/0.98 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(A,binary_relation_type). [resolve(35,b,30,c)].
% 0.41/0.98 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(f8(A),set_type). [resolve(35,b,31,b)].
% 0.41/0.98 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(f8(A),A). [resolve(35,b,32,b)].
% 0.41/0.98 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(35,b,33,d)].
% 0.41/0.98 36 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f8(A) # label(p18) # label(axiom). [clausify(18)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f8(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(36,b,28,c)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f8(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f6(A,D),set_type). [resolve(36,b,34,b)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f8(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f7(A,D),set_type). [resolve(36,b,35,b)].
% 0.41/0.98 37 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f6(A,B),f7(A,B)) = B # label(p18) # label(axiom). [clausify(18)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f6(A,B),f7(A,B)) = B | -empty(A) | -ilf_type(A,set_type). [resolve(37,b,29,c)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f6(A,B),f7(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(37,b,30,c)].
% 0.41/0.98 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f6(A,B),f7(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f8(A),set_type). [resolve(37,b,31,b)].
% 0.72/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f6(A,B),f7(A,B)) = B | -ilf_type(A,set_type) | member(f8(A),A). [resolve(37,b,32,b)].
% 0.72/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f6(A,B),f7(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(37,b,33,d)].
% 0.72/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f6(A,B),f7(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f8(A). [resolve(37,b,36,b)].
% 0.72/1.02
% 0.72/1.02 ============================== end predicate elimination =============
% 0.72/1.02
% 0.72/1.02 Auto_denials: (non-Horn, no changes).
% 0.72/1.02
% 0.72/1.02 Term ordering decisions:
% 0.72/1.02 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. ordered_pair=1. cross_product=1. relation_type=1. f1=1. f2=1. f3=1. f4=1. f6=1. f7=1. f9=1. subset_type=1. power_set=1. range_of=1. domain_of=1. member_type=1. f5=1. f8=1. f10=1. f11=1.
% 0.72/1.02
% 0.72/1.02 ============================== end of process initial clauses ========
% 0.72/1.02
% 0.72/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.02
% 0.72/1.02 ============================== end of clauses for search =============
% 0.72/1.02
% 0.72/1.02 ============================== SEARCH ================================
% 0.72/1.02
% 0.72/1.02 % Starting search at 0.02 seconds.
% 0.72/1.02
% 0.72/1.02 ============================== PROOF =================================
% 0.72/1.02 % SZS status Theorem
% 0.72/1.02 % SZS output start Refutation
% 0.72/1.02
% 0.72/1.02 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.72/1.02 % Length of proof is 52.
% 0.72/1.02 % Level of proof is 10.
% 0.72/1.02 % Maximum clause weight is 12.000.
% 0.72/1.02 % Given clauses 133.
% 0.72/1.02
% 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,binary_relation_type) -> subset(B,cross_product(domain_of(B),range_of(B))))) # 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,set_type) -> (subset(B,C) -> subset(cross_product(B,D),cross_product(C,D)) & subset(cross_product(D,B),cross_product(D,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) -> (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].
% 0.72/1.02 12 (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(p12) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 15 (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(p15) # 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) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 21 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 22 (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(p22) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 24 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p24) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 26 (all B ilf_type(B,set_type)) # label(p26) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.02 27 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (subset(range_of(C),B) -> ilf_type(C,relation_type(domain_of(C),B))))))) # label(prove_relset_1_10) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.02 39 ilf_type(A,set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.72/1.02 40 ilf_type(c3,binary_relation_type) # label(prove_relset_1_10) # label(negated_conjecture). [clausify(27)].
% 0.72/1.02 41 subset(range_of(c3),c2) # label(prove_relset_1_10) # label(negated_conjecture). [clausify(27)].
% 0.72/1.02 42 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p21) # label(axiom). [clausify(21)].
% 0.72/1.02 43 -empty(power_set(A)). [copy(42),unit_del(a,39)].
% 0.72/1.02 44 -ilf_type(c3,relation_type(domain_of(c3),c2)) # label(prove_relset_1_10) # label(negated_conjecture). [clausify(27)].
% 0.72/1.02 45 -ilf_type(A,set_type) | -empty(A) | -ilf_type(B,set_type) | -member(B,A) # label(p24) # label(axiom). [clausify(24)].
% 0.72/1.02 46 -empty(A) | -member(B,A). [copy(45),unit_del(a,39),unit_del(c,39)].
% 0.72/1.02 55 -ilf_type(A,binary_relation_type) | subset(A,cross_product(domain_of(A),range_of(A))) # label(p2) # label(axiom). [clausify(2)].
% 0.72/1.02 71 -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(p15) # label(axiom). [clausify(15)].
% 0.72/1.02 72 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [copy(71),unit_del(a,39),unit_del(b,39)].
% 0.72/1.02 74 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f9(A,B),A) # label(p20) # label(axiom). [clausify(20)].
% 0.72/1.02 75 member(A,power_set(B)) | member(f9(A,B),A). [copy(74),unit_del(a,39),unit_del(b,39)].
% 0.72/1.02 76 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f9(A,B),B) # label(p20) # label(axiom). [clausify(20)].
% 0.72/1.02 77 member(A,power_set(B)) | -member(f9(A,B),B). [copy(76),unit_del(a,39),unit_del(b,39)].
% 0.72/1.02 78 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p22) # label(axiom). [clausify(22)].
% 0.72/1.02 79 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(78),unit_del(a,39),unit_del(c,39)].
% 0.72/1.02 80 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B) # label(p22) # label(axiom). [clausify(22)].
% 0.72/1.02 81 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [copy(80),unit_del(a,39),unit_del(c,39)].
% 0.72/1.02 82 -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(p4) # label(axiom). [clausify(4)].
% 0.72/1.02 83 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [copy(82),unit_del(a,39),unit_del(b,39)].
% 0.72/1.02 90 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -subset(A,B) | -subset(B,C) | subset(A,C) # label(p1) # label(axiom). [clausify(1)].
% 0.72/1.02 91 -subset(A,B) | -subset(B,C) | subset(A,C). [copy(90),unit_del(a,39),unit_del(b,39),unit_del(c,39)].
% 0.72/1.02 96 -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(p12) # label(axiom). [clausify(12)].
% 0.72/1.02 97 -subset(A,B) | -member(C,A) | member(C,B). [copy(96),unit_del(a,39),unit_del(b,39),unit_del(d,39)].
% 0.72/1.02 100 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -subset(A,B) | subset(cross_product(C,A),cross_product(C,B)) # label(p3) # label(axiom). [clausify(3)].
% 0.72/1.02 101 -subset(A,B) | subset(cross_product(C,A),cross_product(C,B)). [copy(100),unit_del(a,39),unit_del(b,39),unit_del(c,39)].
% 0.72/1.02 136 subset(c3,cross_product(domain_of(c3),range_of(c3))). [resolve(55,a,40,a)].
% 0.72/1.02 140 member(A,power_set(B)) | -empty(A). [resolve(75,b,46,b)].
% 0.72/1.02 143 empty(A) | ilf_type(f9(A,B),member_type(A)) | member(A,power_set(B)). [resolve(81,c,75,b)].
% 0.72/1.02 146 -ilf_type(c3,subset_type(cross_product(domain_of(c3),c2))). [ur(83,b,44,a)].
% 0.72/1.02 161 subset(cross_product(A,range_of(c3)),cross_product(A,c2)). [resolve(101,a,41,a)].
% 0.72/1.02 186 -ilf_type(c3,member_type(power_set(cross_product(domain_of(c3),c2)))). [ur(72,a,146,a)].
% 0.72/1.02 187 -member(c3,power_set(cross_product(domain_of(c3),c2))). [ur(81,a,43,a,b,186,a)].
% 0.72/1.02 188 -member(f9(c3,cross_product(domain_of(c3),c2)),cross_product(domain_of(c3),c2)). [ur(77,a,187,a)].
% 0.72/1.02 232 -empty(c3). [ur(140,a,187,a)].
% 0.72/1.02 254 ilf_type(f9(c3,cross_product(domain_of(c3),c2)),member_type(c3)). [resolve(143,c,187,a),unit_del(a,232)].
% 0.72/1.02 519 member(f9(c3,cross_product(domain_of(c3),c2)),c3). [resolve(254,a,79,b),unit_del(a,232)].
% 0.72/1.02 525 -subset(c3,cross_product(domain_of(c3),c2)). [ur(97,b,519,a,c,188,a)].
% 0.72/1.02 533 $F. [ur(91,b,161,a,c,525,a),unit_del(a,136)].
% 0.72/1.02
% 0.72/1.02 % SZS output end Refutation
% 0.72/1.02 ============================== end of proof ==========================
% 0.72/1.02
% 0.72/1.02 ============================== STATISTICS ============================
% 0.72/1.02
% 0.72/1.02 Given=133. Generated=696. Kept=438. proofs=1.
% 0.72/1.02 Usable=133. Sos=301. Demods=1. Limbo=1, Disabled=79. Hints=0.
% 0.72/1.02 Megabytes=0.79.
% 0.72/1.02 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.72/1.02
% 0.72/1.02 ============================== end of statistics =====================
% 0.72/1.02
% 0.72/1.02 ============================== end of search =========================
% 0.72/1.02
% 0.72/1.02 THEOREM PROVED
% 0.72/1.02 % SZS status Theorem
% 0.72/1.02
% 0.72/1.02 Exiting with 1 proof.
% 0.72/1.02
% 0.72/1.02 Process 14963 exit (max_proofs) Mon Jul 11 04:16:29 2022
% 0.72/1.02 Prover9 interrupted
%------------------------------------------------------------------------------