TSTP Solution File: SET682+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET682+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 04:31:22 EDT 2022
% Result : Theorem 0.74s 1.04s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET682+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 : n024.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 : Mon Jul 11 09:00:58 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.74/1.02 ============================== Prover9 ===============================
% 0.74/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.02 Process 30296 was started by sandbox2 on n024.cluster.edu,
% 0.74/1.02 Mon Jul 11 09:00:59 2022
% 0.74/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30142_n024.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_30142_n024.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 (25 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,binary_relation_type) -> (member(B,domain_of(C)) -> (exists D (ilf_type(D,set_type) & member(D,range_of(C))))))))) # 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,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 4 (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(p4) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 5 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 6 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p6) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 7 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p7) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p8) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 9 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 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].
% 0.74/1.02 11 (exists B ilf_type(B,binary_relation_type)) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 12 (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(p12) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 13 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 14 (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(p14) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 15 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 16 (all B (ilf_type(B,set_type) -> (relation_like(B) <-> (all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & C = ordered_pair(D,E))))))))))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 17 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 18 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> relation_like(D))))))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 19 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 20 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 21 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(domain(B,C,D),subset_type(B)))))))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 22 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range(B,C,D) = range_of(D))))))) # label(p22) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 23 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(range(B,C,D),subset_type(C)))))))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 24 (all B ilf_type(B,set_type)) # label(p24) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 25 -(all B (-empty(B) & ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> (all E (ilf_type(E,member_type(B)) -> (member(E,domain(B,C,D)) -> (exists F (ilf_type(F,member_type(C)) & member(F,range(B,C,D))))))))))))) # label(prove_relset_1_49) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.02
% 0.74/1.02 ============================== end of process non-clausal formulas ===
% 0.74/1.02
% 0.74/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.02
% 0.74/1.02 ============================== PREDICATE ELIMINATION =================
% 0.74/1.02 26 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p10) # label(axiom). [clausify(10)].
% 0.74/1.02 27 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p17) # label(axiom). [clausify(17)].
% 0.74/1.02 28 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p10) # label(axiom). [clausify(10)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(26,c,27,c)].
% 0.74/1.02 29 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f9(A),set_type) # label(p16) # label(axiom). [clausify(16)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | ilf_type(f9(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(29,b,26,c)].
% 0.74/1.02 30 -ilf_type(A,set_type) | relation_like(A) | member(f9(A),A) # label(p16) # label(axiom). [clausify(16)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | member(f9(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(30,b,26,c)].
% 0.74/1.02 31 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p18) # label(axiom). [clausify(18)].
% 0.74/1.03 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(31,d,26,c)].
% 0.74/1.03 32 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) # label(p16) # label(axiom). [clausify(16)].
% 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(32,b,27,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(A,binary_relation_type). [resolve(32,b,28,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(32,b,29,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(32,b,30,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(32,b,31,d)].
% 0.74/1.03 33 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p16) # label(axiom). [clausify(16)].
% 0.74/1.03 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(33,b,27,c)].
% 0.74/1.03 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(A,binary_relation_type). [resolve(33,b,28,c)].
% 0.74/1.03 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(33,b,29,b)].
% 0.74/1.03 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(33,b,30,b)].
% 0.74/1.03 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(33,b,31,d)].
% 0.74/1.03 34 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) # label(p16) # label(axiom). [clausify(16)].
% 0.74/1.03 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(A,binary_relation_type). [resolve(34,b,26,c)].
% 0.74/1.03 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(34,b,32,b)].
% 0.74/1.03 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(34,b,33,b)].
% 0.74/1.03 35 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B # label(p16) # label(axiom). [clausify(16)].
% 0.74/1.03 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(35,b,27,c)].
% 0.74/1.03 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(A,binary_relation_type). [resolve(35,b,28,c)].
% 0.74/1.03 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(35,b,29,b)].
% 0.74/1.03 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(35,b,30,b)].
% 0.74/1.03 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(35,b,31,d)].
% 0.74/1.04 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(35,b,34,b)].
% 0.74/1.04
% 0.74/1.04 ============================== end predicate elimination =============
% 0.74/1.04
% 0.74/1.04 Auto_denials: (non-Horn, no changes).
% 0.74/1.04
% 0.74/1.04 Term ordering decisions:
% 0.74/1.04 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. ordered_pair=1. relation_type=1. cross_product=1. f1=1. f2=1. f6=1. f7=1. f8=1. subset_type=1. power_set=1. member_type=1. domain_of=1. range_of=1. f3=1. f4=1. f5=1. f9=1. domain=1. range=1.
% 0.74/1.04
% 0.74/1.04 ============================== end of process initial clauses ========
% 0.74/1.04
% 0.74/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.04
% 0.74/1.04 ============================== end of clauses for search =============
% 0.74/1.04
% 0.74/1.04 ============================== SEARCH ================================
% 0.74/1.04
% 0.74/1.04 % Starting search at 0.02 seconds.
% 0.74/1.04
% 0.74/1.04 ============================== PROOF =================================
% 0.74/1.04 % SZS status Theorem
% 0.74/1.04 % SZS output start Refutation
% 0.74/1.04
% 0.74/1.04 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.74/1.04 % Length of proof is 56.
% 0.74/1.04 % Level of proof is 9.
% 0.74/1.04 % Maximum clause weight is 13.000.
% 0.74/1.04 % Given clauses 73.
% 0.74/1.04
% 0.74/1.04 1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (member(B,domain_of(C)) -> (exists D (ilf_type(D,set_type) & member(D,range_of(C))))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 4 (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(p4) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 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].
% 0.74/1.04 12 (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(p12) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 14 (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(p14) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 15 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 18 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> relation_like(D))))))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 20 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 22 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range(B,C,D) = range_of(D))))))) # label(p22) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 23 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(range(B,C,D),subset_type(C)))))))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 24 (all B ilf_type(B,set_type)) # label(p24) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.04 25 -(all B (-empty(B) & ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> (all E (ilf_type(E,member_type(B)) -> (member(E,domain(B,C,D)) -> (exists F (ilf_type(F,member_type(C)) & member(F,range(B,C,D))))))))))))) # label(prove_relset_1_49) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.04 26 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p10) # label(axiom). [clausify(10)].
% 0.74/1.04 31 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p18) # label(axiom). [clausify(18)].
% 0.74/1.04 37 ilf_type(A,set_type) # label(p24) # label(axiom). [clausify(24)].
% 0.74/1.04 39 ilf_type(c4,relation_type(c2,c3)) # label(prove_relset_1_49) # label(negated_conjecture). [clausify(25)].
% 0.74/1.04 40 member(c5,domain(c2,c3,c4)) # label(prove_relset_1_49) # label(negated_conjecture). [clausify(25)].
% 0.74/1.04 42 -empty(c3) # label(prove_relset_1_49) # label(negated_conjecture). [clausify(25)].
% 0.74/1.04 43 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p15) # label(axiom). [clausify(15)].
% 0.74/1.04 44 -empty(power_set(A)). [copy(43),unit_del(a,37)].
% 0.74/1.04 45 -ilf_type(A,member_type(c3)) | -member(A,range(c2,c3,c4)) # label(prove_relset_1_49) # label(negated_conjecture). [clausify(25)].
% 0.74/1.04 61 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | -ilf_type(A,member_type(B)) | member(A,B) # label(p4) # label(axiom). [clausify(4)].
% 0.74/1.04 62 empty(A) | -ilf_type(B,member_type(A)) | member(B,A). [copy(61),unit_del(a,37),unit_del(c,37)].
% 0.74/1.04 63 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B) # label(p4) # label(axiom). [clausify(4)].
% 0.74/1.04 64 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [copy(63),unit_del(a,37),unit_del(c,37)].
% 0.74/1.04 65 -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(p12) # label(axiom). [clausify(12)].
% 0.74/1.04 66 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))). [copy(65),unit_del(a,37),unit_del(b,37)].
% 0.74/1.04 74 -ilf_type(A,set_type) | -ilf_type(B,binary_relation_type) | -member(A,domain_of(B)) | member(f1(A,B),range_of(B)) # label(p1) # label(axiom). [clausify(1)].
% 0.74/1.04 75 -ilf_type(A,binary_relation_type) | -member(B,domain_of(A)) | member(f1(B,A),range_of(A)). [copy(74),unit_del(a,37)].
% 0.74/1.04 78 -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(p2) # label(axiom). [clausify(2)].
% 0.74/1.04 79 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(78),unit_del(a,37),unit_del(b,37)].
% 0.74/1.04 80 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C) # label(p20) # label(axiom). [clausify(20)].
% 0.74/1.04 81 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [copy(80),unit_del(a,37),unit_del(b,37)].
% 0.74/1.04 84 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C) # label(p22) # label(axiom). [clausify(22)].
% 0.74/1.04 85 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [copy(84),unit_del(a,37),unit_del(b,37)].
% 0.74/1.04 86 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)) # label(p23) # label(axiom). [clausify(23)].
% 0.74/1.04 87 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [copy(86),unit_del(a,37),unit_del(b,37)].
% 0.74/1.04 88 -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(p14) # label(axiom). [clausify(14)].
% 0.74/1.04 89 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(88),unit_del(a,37),unit_del(b,37),unit_del(d,37)].
% 0.74/1.04 95 -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(31,d,26,c)].
% 0.74/1.04 96 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(95),unit_del(a,37),unit_del(b,37),unit_del(d,37)].
% 0.74/1.04 138 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(79,a,39,a)].
% 0.74/1.04 140 domain(c2,c3,c4) = domain_of(c4). [resolve(81,a,39,a)].
% 0.74/1.04 143 member(c5,domain_of(c4)). [back_rewrite(40),rewrite([140(5)])].
% 0.74/1.04 147 range(c2,c3,c4) = range_of(c4). [resolve(85,a,39,a)].
% 0.74/1.04 150 -ilf_type(A,member_type(c3)) | -member(A,range_of(c4)). [back_rewrite(45),rewrite([147(7)])].
% 0.74/1.04 152 ilf_type(range_of(c4),subset_type(c3)). [resolve(87,a,39,a),rewrite([147(4)])].
% 0.74/1.04 196 -ilf_type(c4,binary_relation_type) | member(f1(c5,c4),range_of(c4)). [resolve(143,a,75,b)].
% 0.74/1.04 199 ilf_type(range_of(c4),member_type(power_set(c3))). [resolve(152,a,66,a)].
% 0.74/1.04 222 ilf_type(c4,binary_relation_type). [resolve(138,a,96,a)].
% 0.74/1.04 224 member(f1(c5,c4),range_of(c4)). [back_unit_del(196),unit_del(a,222)].
% 0.74/1.04 239 member(range_of(c4),power_set(c3)). [resolve(199,a,62,b),unit_del(a,44)].
% 0.74/1.04 250 -ilf_type(f1(c5,c4),member_type(c3)). [resolve(224,a,150,b)].
% 0.74/1.04 270 -member(f1(c5,c4),c3). [ur(64,a,42,a,b,250,a)].
% 0.74/1.04 271 $F. [ur(89,b,224,a,c,270,a),unit_del(a,239)].
% 0.74/1.04
% 0.74/1.04 % SZS output end Refutation
% 0.74/1.04 ============================== end of proof ==========================
% 0.74/1.04
% 0.74/1.04 ============================== STATISTICS ============================
% 0.74/1.04
% 0.74/1.04 Given=73. Generated=255. Kept=186. proofs=1.
% 0.74/1.04 Usable=71. Sos=103. Demods=6. Limbo=0, Disabled=83. Hints=0.
% 0.74/1.04 Megabytes=0.36.
% 0.74/1.04 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.74/1.04
% 0.74/1.04 ============================== end of statistics =====================
% 0.74/1.04
% 0.74/1.04 ============================== end of search =========================
% 0.74/1.04
% 0.74/1.04 THEOREM PROVED
% 0.74/1.04 % SZS status Theorem
% 0.74/1.04
% 0.74/1.04 Exiting with 1 proof.
% 0.74/1.04
% 0.74/1.04 Process 30296 exit (max_proofs) Mon Jul 11 09:00:59 2022
% 0.74/1.04 Prover9 interrupted
%------------------------------------------------------------------------------