TSTP Solution File: SET647+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET647+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 04:31:07 EDT 2022
% Result : Theorem 0.75s 1.07s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET647+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n026.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 : Sun Jul 10 00:43:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.03 ============================== Prover9 ===============================
% 0.44/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.03 Process 14292 was started by sandbox2 on n026.cluster.edu,
% 0.44/1.03 Sun Jul 10 00:43:41 2022
% 0.44/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14139_n026.cluster.edu".
% 0.44/1.03 ============================== end of head ===========================
% 0.44/1.03
% 0.44/1.03 ============================== INPUT =================================
% 0.44/1.03
% 0.44/1.03 % Reading from file /tmp/Prover9_14139_n026.cluster.edu
% 0.44/1.03
% 0.44/1.03 set(prolog_style_variables).
% 0.44/1.03 set(auto2).
% 0.44/1.03 % set(auto2) -> set(auto).
% 0.44/1.03 % set(auto) -> set(auto_inference).
% 0.44/1.03 % set(auto) -> set(auto_setup).
% 0.44/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.03 % set(auto) -> set(auto_limits).
% 0.44/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.03 % set(auto) -> set(auto_denials).
% 0.44/1.03 % set(auto) -> set(auto_process).
% 0.44/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.03 % set(auto2) -> assign(stats, some).
% 0.44/1.03 % set(auto2) -> clear(echo_input).
% 0.44/1.03 % set(auto2) -> set(quiet).
% 0.44/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.03 % set(auto2) -> clear(print_given).
% 0.44/1.03 assign(lrs_ticks,-1).
% 0.44/1.03 assign(sos_limit,10000).
% 0.44/1.03 assign(order,kbo).
% 0.44/1.03 set(lex_order_vars).
% 0.44/1.03 clear(print_given).
% 0.44/1.03
% 0.44/1.03 % formulas(sos). % not echoed (27 formulas)
% 0.44/1.03
% 0.44/1.03 ============================== end of input ==========================
% 0.44/1.03
% 0.44/1.03 % From the command line: assign(max_seconds, 300).
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.03
% 0.44/1.03 % Formulas that are not ordinary clauses:
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 7 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p7) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 9 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 11 (exists B ilf_type(B,binary_relation_type)) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 16 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 17 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 25 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 26 (all B ilf_type(B,set_type)) # label(p26) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 27 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (subset(domain_of(C),B) -> ilf_type(C,relation_type(B,range_of(C)))))))) # label(prove_relset_1_9) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.03
% 0.44/1.03 ============================== end of process non-clausal formulas ===
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.03
% 0.44/1.03 ============================== PREDICATE ELIMINATION =================
% 0.44/1.03 28 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p10) # label(axiom). [clausify(10)].
% 0.44/1.03 29 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p25) # label(axiom). [clausify(25)].
% 0.44/1.03 30 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p10) # label(axiom). [clausify(10)].
% 0.44/1.03 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(28,c,29,c)].
% 0.44/1.03 31 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f8(A),set_type) # label(p18) # label(axiom). [clausify(18)].
% 0.44/1.03 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)].
% 0.44/1.03 32 -ilf_type(A,set_type) | relation_like(A) | member(f8(A),A) # label(p18) # label(axiom). [clausify(18)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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(35,b,29,c)].
% 0.44/1.03 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(A,binary_relation_type). [resolve(35,b,30,c)].
% 0.44/1.03 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(f8(A),set_type). [resolve(35,b,31,b)].
% 0.44/1.03 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(f8(A),A). [resolve(35,b,32,b)].
% 0.44/1.03 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(35,b,33,d)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.44/1.03 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)].
% 0.75/1.06 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)].
% 0.75/1.06 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)].
% 0.75/1.06 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)].
% 0.75/1.06
% 0.75/1.06 ============================== end predicate elimination =============
% 0.75/1.06
% 0.75/1.06 Auto_denials: (non-Horn, no changes).
% 0.75/1.06
% 0.75/1.06 Term ordering decisions:
% 0.75/1.06 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. domain_of=1. member_type=1. range_of=1. f5=1. f8=1. f10=1. f11=1.
% 0.75/1.07
% 0.75/1.07 ============================== end of process initial clauses ========
% 0.75/1.07
% 0.75/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.07
% 0.75/1.07 ============================== end of clauses for search =============
% 0.75/1.07
% 0.75/1.07 ============================== SEARCH ================================
% 0.75/1.07
% 0.75/1.07 % Starting search at 0.02 seconds.
% 0.75/1.07
% 0.75/1.07 ============================== PROOF =================================
% 0.75/1.07 % SZS status Theorem
% 0.75/1.07 % SZS output start Refutation
% 0.75/1.07
% 0.75/1.07 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.75/1.07 % Length of proof is 52.
% 0.75/1.07 % Level of proof is 10.
% 0.75/1.07 % Maximum clause weight is 12.000.
% 0.75/1.07 % Given clauses 133.
% 0.75/1.07
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 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].
% 0.75/1.07 26 (all B ilf_type(B,set_type)) # label(p26) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 27 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (subset(domain_of(C),B) -> ilf_type(C,relation_type(B,range_of(C)))))))) # label(prove_relset_1_9) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.07 39 ilf_type(A,set_type) # label(p26) # label(axiom). [clausify(26)].
% 0.75/1.07 40 ilf_type(c3,binary_relation_type) # label(prove_relset_1_9) # label(negated_conjecture). [clausify(27)].
% 0.75/1.07 41 subset(domain_of(c3),c2) # label(prove_relset_1_9) # label(negated_conjecture). [clausify(27)].
% 0.75/1.07 42 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p21) # label(axiom). [clausify(21)].
% 0.75/1.07 43 -empty(power_set(A)). [copy(42),unit_del(a,39)].
% 0.75/1.07 44 -ilf_type(c3,relation_type(c2,range_of(c3))) # label(prove_relset_1_9) # label(negated_conjecture). [clausify(27)].
% 0.75/1.07 45 -ilf_type(A,set_type) | -empty(A) | -ilf_type(B,set_type) | -member(B,A) # label(p24) # label(axiom). [clausify(24)].
% 0.75/1.07 46 -empty(A) | -member(B,A). [copy(45),unit_del(a,39),unit_del(c,39)].
% 0.75/1.07 55 -ilf_type(A,binary_relation_type) | subset(A,cross_product(domain_of(A),range_of(A))) # label(p2) # label(axiom). [clausify(2)].
% 0.75/1.07 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)].
% 0.75/1.07 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)].
% 0.75/1.07 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)].
% 0.75/1.07 75 member(A,power_set(B)) | member(f9(A,B),A). [copy(74),unit_del(a,39),unit_del(b,39)].
% 0.75/1.07 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)].
% 0.75/1.07 77 member(A,power_set(B)) | -member(f9(A,B),B). [copy(76),unit_del(a,39),unit_del(b,39)].
% 0.75/1.07 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)].
% 0.75/1.07 79 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(78),unit_del(a,39),unit_del(c,39)].
% 0.75/1.07 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)].
% 0.75/1.07 81 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [copy(80),unit_del(a,39),unit_del(c,39)].
% 0.75/1.07 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)].
% 0.75/1.07 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)].
% 0.75/1.07 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)].
% 0.75/1.07 91 -subset(A,B) | -subset(B,C) | subset(A,C). [copy(90),unit_del(a,39),unit_del(b,39),unit_del(c,39)].
% 0.75/1.07 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)].
% 0.75/1.07 97 -subset(A,B) | -member(C,A) | member(C,B). [copy(96),unit_del(a,39),unit_del(b,39),unit_del(d,39)].
% 0.75/1.07 98 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -subset(A,B) | subset(cross_product(A,C),cross_product(B,C)) # label(p3) # label(axiom). [clausify(3)].
% 0.75/1.07 99 -subset(A,B) | subset(cross_product(A,C),cross_product(B,C)). [copy(98),unit_del(a,39),unit_del(b,39),unit_del(c,39)].
% 0.75/1.07 136 subset(c3,cross_product(domain_of(c3),range_of(c3))). [resolve(55,a,40,a)].
% 0.75/1.07 140 member(A,power_set(B)) | -empty(A). [resolve(75,b,46,b)].
% 0.75/1.07 143 empty(A) | ilf_type(f9(A,B),member_type(A)) | member(A,power_set(B)). [resolve(81,c,75,b)].
% 0.75/1.07 146 -ilf_type(c3,subset_type(cross_product(c2,range_of(c3)))). [ur(83,b,44,a)].
% 0.75/1.07 159 subset(cross_product(domain_of(c3),A),cross_product(c2,A)). [resolve(99,a,41,a)].
% 0.75/1.07 186 -ilf_type(c3,member_type(power_set(cross_product(c2,range_of(c3))))). [ur(72,a,146,a)].
% 0.75/1.07 187 -member(c3,power_set(cross_product(c2,range_of(c3)))). [ur(81,a,43,a,b,186,a)].
% 0.75/1.07 188 -member(f9(c3,cross_product(c2,range_of(c3))),cross_product(c2,range_of(c3))). [ur(77,a,187,a)].
% 0.75/1.07 232 -empty(c3). [ur(140,a,187,a)].
% 0.75/1.07 254 ilf_type(f9(c3,cross_product(c2,range_of(c3))),member_type(c3)). [resolve(143,c,187,a),unit_del(a,232)].
% 0.75/1.07 519 member(f9(c3,cross_product(c2,range_of(c3))),c3). [resolve(254,a,79,b),unit_del(a,232)].
% 0.75/1.07 525 -subset(c3,cross_product(c2,range_of(c3))). [ur(97,b,519,a,c,188,a)].
% 0.75/1.07 533 $F. [ur(91,b,159,a,c,525,a),unit_del(a,136)].
% 0.75/1.07
% 0.75/1.07 % SZS output end Refutation
% 0.75/1.07 ============================== end of proof ==========================
% 0.75/1.07
% 0.75/1.07 ============================== STATISTICS ============================
% 0.75/1.07
% 0.75/1.07 Given=133. Generated=696. Kept=438. proofs=1.
% 0.75/1.07 Usable=133. Sos=301. Demods=1. Limbo=1, Disabled=79. Hints=0.
% 0.75/1.07 Megabytes=0.79.
% 0.75/1.07 User_CPU=0.05, System_CPU=0.01, Wall_clock=0.
% 0.75/1.07
% 0.75/1.07 ============================== end of statistics =====================
% 0.75/1.07
% 0.75/1.07 ============================== end of search =========================
% 0.75/1.07
% 0.75/1.07 THEOREM PROVED
% 0.75/1.07 % SZS status Theorem
% 0.75/1.07
% 0.75/1.07 Exiting with 1 proof.
% 0.75/1.07
% 0.75/1.07 Process 14292 exit (max_proofs) Sun Jul 10 00:43:41 2022
% 0.75/1.07 Prover9 interrupted
%------------------------------------------------------------------------------