TSTP Solution File: SET650+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET650+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 04:31:09 EDT 2022
% Result : Theorem 7.12s 7.43s
% Output : Refutation 7.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET650+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.31 % Computer : n024.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Mon Jul 11 09:01:43 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.70/1.02 ============================== Prover9 ===============================
% 0.70/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.02 Process 32189 was started by sandbox on n024.cluster.edu,
% 0.70/1.02 Mon Jul 11 09:01:44 2022
% 0.70/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32036_n024.cluster.edu".
% 0.70/1.02 ============================== end of head ===========================
% 0.70/1.02
% 0.70/1.02 ============================== INPUT =================================
% 0.70/1.02
% 0.70/1.02 % Reading from file /tmp/Prover9_32036_n024.cluster.edu
% 0.70/1.02
% 0.70/1.02 set(prolog_style_variables).
% 0.70/1.02 set(auto2).
% 0.70/1.02 % set(auto2) -> set(auto).
% 0.70/1.02 % set(auto) -> set(auto_inference).
% 0.70/1.02 % set(auto) -> set(auto_setup).
% 0.70/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.02 % set(auto) -> set(auto_limits).
% 0.70/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.02 % set(auto) -> set(auto_denials).
% 0.70/1.02 % set(auto) -> set(auto_process).
% 0.70/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.02 % 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 (27 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(ordered_pair(B,D),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,binary_relation_type) -> (member(B,range_of(C)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(D,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) -> (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(p3) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 4 (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(p4) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 5 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 6 (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(p6) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 7 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_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) -> (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(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) -> (exists D ilf_type(D,relation_type(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) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 11 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_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(ordered_pair(B,C),set_type))))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 13 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 14 (exists B ilf_type(B,binary_relation_type)) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 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].
% 0.74/1.02 16 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 17 (all B (ilf_type(B,set_type) -> subset(B,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) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p18) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 19 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 20 (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(p20) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 21 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 22 (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(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,subset_type(cross_product(B,C))) -> relation_like(D))))))) # label(p23) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 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].
% 0.74/1.02 25 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p25) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 26 (all B ilf_type(B,set_type)) # label(p26) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 27 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> subset(domain_of(D),B) & subset(range_of(D),C))))))) # label(prove_relset_1_12) # 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 28 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p13) # label(axiom). [clausify(13)].
% 0.74/1.02 29 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p25) # label(axiom). [clausify(25)].
% 0.74/1.02 30 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p13) # label(axiom). [clausify(13)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type). [resolve(28,c,29,c)].
% 0.74/1.02 31 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f12(A),set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | ilf_type(f12(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(31,b,28,c)].
% 0.74/1.02 32 -ilf_type(A,set_type) | relation_like(A) | member(f12(A),A) # label(p22) # label(axiom). [clausify(22)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | member(f12(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(32,b,28,c)].
% 0.74/1.02 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p23) # label(axiom). [clausify(23)].
% 0.74/1.02 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)].
% 0.74/1.02 34 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(34,b,29,c)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(34,b,30,c)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f12(A),set_type). [resolve(34,b,31,b)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(A,B),set_type) | -ilf_type(A,set_type) | member(f12(A),A). [resolve(34,b,32,b)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f10(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)].
% 0.74/1.02 35 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -empty(A) | -ilf_type(A,set_type). [resolve(35,b,29,c)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(35,b,30,c)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f12(A),set_type). [resolve(35,b,31,b)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(A,B),set_type) | -ilf_type(A,set_type) | member(f12(A),A). [resolve(35,b,32,b)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f11(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)].
% 0.74/1.02 36 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f12(A) # label(p22) # label(axiom). [clausify(22)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f12(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(36,b,28,c)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f12(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f10(A,D),set_type). [resolve(36,b,34,b)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f12(A) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f11(A,D),set_type). [resolve(36,b,35,b)].
% 0.74/1.02 37 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f10(A,B),f11(A,B)) = B # label(p22) # label(axiom). [clausify(22)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f10(A,B),f11(A,B)) = B | -empty(A) | -ilf_type(A,set_type). [resolve(37,b,29,c)].
% 0.74/1.02 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f10(A,B),f11(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(37,b,30,c)].
% 7.12/7.43 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f10(A,B),f11(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f12(A),set_type). [resolve(37,b,31,b)].
% 7.12/7.43 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f10(A,B),f11(A,B)) = B | -ilf_type(A,set_type) | member(f12(A),A). [resolve(37,b,32,b)].
% 7.12/7.43 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f10(A,B),f11(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)].
% 7.12/7.43 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f10(A,B),f11(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f12(A). [resolve(37,b,36,b)].
% 7.12/7.43
% 7.12/7.43 ============================== end predicate elimination =============
% 7.12/7.43
% 7.12/7.43 Auto_denials: (non-Horn, no changes).
% 7.12/7.43
% 7.12/7.43 Term ordering decisions:
% 7.12/7.43 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. ordered_pair=1. cross_product=1. relation_type=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f8=1. f10=1. f11=1. subset_type=1. domain_of=1. power_set=1. range_of=1. member_type=1. f7=1. f9=1. f12=1. f13=1.
% 7.12/7.43
% 7.12/7.43 ============================== end of process initial clauses ========
% 7.12/7.43
% 7.12/7.43 ============================== CLAUSES FOR SEARCH ====================
% 7.12/7.43
% 7.12/7.43 ============================== end of clauses for search =============
% 7.12/7.43
% 7.12/7.43 ============================== SEARCH ================================
% 7.12/7.43
% 7.12/7.43 % Starting search at 0.02 seconds.
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=81.000, iters=3337
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=72.000, iters=3336
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=49.000, iters=3334
% 7.12/7.43
% 7.12/7.43 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 37 (0.00 of 0.67 sec).
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=44.000, iters=3407
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=34.000, iters=3340
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=33.000, iters=3336
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=32.000, iters=3339
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=30.000, iters=3349
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=29.000, iters=3352
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=28.000, iters=3355
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=27.000, iters=3333
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=26.000, iters=3353
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=25.000, iters=3333
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=24.000, iters=3367
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=23.000, iters=3343
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=22.000, iters=3391
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=21.000, iters=3338
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=5192, wt=92.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=6056, wt=84.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=4700, wt=80.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=3789, wt=72.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=4645, wt=68.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=3511, wt=62.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=6092, wt=60.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=6101, wt=57.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=1727, wt=56.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=11274, wt=19.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=11276, wt=18.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=11342, wt=17.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=11852, wt=16.000
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=20.000, iters=3345
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=15465, wt=14.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=15475, wt=13.000
% 7.12/7.43
% 7.12/7.43 Low Water (displace): id=15476, wt=12.000
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=19.000, iters=3337
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=18.000, iters=5972
% 7.12/7.43
% 7.12/7.43 Low Water (keep): wt=17.000, iters=3438
% 7.12/7.43
% 7.12/7.43 ============================== PROOF =================================
% 7.12/7.43 % SZS status Theorem
% 7.12/7.43 % SZS output start Refutation
% 7.12/7.43
% 7.12/7.43 % Proof 1 at 6.20 (+ 0.21) seconds.
% 7.12/7.43 % Length of proof is 64.
% 7.12/7.43 % Level of proof is 19.
% 7.12/7.43 % Maximum clause weight is 21.000.
% 7.12/7.43 % Given clauses 2877.
% 7.12/7.43
% 7.12/7.43 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(ordered_pair(B,D),C)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (member(B,range_of(C)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(D,B),C)))))))) # label(p2) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 3 (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(p3) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 8 (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(p8) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 10 (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(p10) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 13 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 18 (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(p18) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 23 (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(p23) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 26 (all B ilf_type(B,set_type)) # label(p26) # label(axiom) # label(non_clause). [assumption].
% 7.12/7.43 27 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> subset(domain_of(D),B) & subset(range_of(D),C))))))) # label(prove_relset_1_12) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.12/7.43 28 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p13) # label(axiom). [clausify(13)].
% 7.12/7.43 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p23) # label(axiom). [clausify(23)].
% 7.12/7.43 39 ilf_type(A,set_type) # label(p26) # label(axiom). [clausify(26)].
% 7.12/7.43 40 ilf_type(c4,relation_type(c2,c3)) # label(prove_relset_1_12) # label(negated_conjecture). [clausify(27)].
% 7.12/7.43 43 -subset(domain_of(c4),c2) | -subset(range_of(c4),c3) # label(prove_relset_1_12) # label(negated_conjecture). [clausify(27)].
% 7.12/7.43 61 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f6(A,B),A) # label(p10) # label(axiom). [clausify(10)].
% 7.12/7.43 62 subset(A,B) | member(f6(A,B),A). [copy(61),unit_del(a,39),unit_del(b,39)].
% 7.12/7.43 63 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f6(A,B),B) # label(p10) # label(axiom). [clausify(10)].
% 7.12/7.43 64 subset(A,B) | -member(f6(A,B),B). [copy(63),unit_del(a,39),unit_del(b,39)].
% 7.12/7.43 74 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f8(A,B),A) # label(p18) # label(axiom). [clausify(18)].
% 7.12/7.43 75 member(A,power_set(B)) | member(f8(A,B),A). [copy(74),unit_del(a,39),unit_del(b,39)].
% 7.12/7.43 76 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f8(A,B),B) # label(p18) # label(axiom). [clausify(18)].
% 7.12/7.43 77 member(A,power_set(B)) | -member(f8(A,B),B). [copy(76),unit_del(a,39),unit_del(b,39)].
% 7.12/7.43 82 -ilf_type(A,set_type) | -ilf_type(B,binary_relation_type) | -member(A,domain_of(B)) | member(ordered_pair(A,f1(A,B)),B) # label(p1) # label(axiom). [clausify(1)].
% 7.12/7.43 83 -ilf_type(A,binary_relation_type) | -member(B,domain_of(A)) | member(ordered_pair(B,f1(B,A)),A). [copy(82),unit_del(a,39)].
% 7.12/7.43 84 -ilf_type(A,set_type) | -ilf_type(B,binary_relation_type) | -member(A,range_of(B)) | member(ordered_pair(f2(A,B),A),B) # label(p2) # label(axiom). [clausify(2)].
% 7.12/7.43 85 -ilf_type(A,binary_relation_type) | -member(B,range_of(A)) | member(ordered_pair(f2(B,A),B),A). [copy(84),unit_del(a,39)].
% 7.12/7.43 92 -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(p8) # label(axiom). [clausify(8)].
% 7.12/7.43 93 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(92),unit_del(a,39),unit_del(b,39)].
% 7.12/7.43 102 -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(p18) # label(axiom). [clausify(18)].
% 7.12/7.43 103 -member(A,power_set(B)) | -member(C,A) | member(C,B). [copy(102),unit_del(a,39),unit_del(b,39),unit_del(d,39)].
% 7.12/7.43 104 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(E,relation_type(A,B)) | -member(ordered_pair(C,D),E) | member(C,A) # label(p3) # label(axiom). [clausify(3)].
% 7.12/7.43 105 -ilf_type(A,relation_type(B,C)) | -member(ordered_pair(D,E),A) | member(D,B). [copy(104),unit_del(a,39),unit_del(b,39),unit_del(c,39),unit_del(d,39)].
% 7.12/7.43 106 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(E,relation_type(A,B)) | -member(ordered_pair(C,D),E) | member(D,B) # label(p3) # label(axiom). [clausify(3)].
% 7.12/7.43 107 -ilf_type(A,relation_type(B,C)) | -member(ordered_pair(D,E),A) | member(E,C). [copy(106),unit_del(a,39),unit_del(b,39),unit_del(c,39),unit_del(d,39)].
% 7.12/7.43 113 -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)].
% 7.12/7.43 114 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(113),unit_del(a,39),unit_del(b,39),unit_del(d,39)].
% 7.12/7.43 140 member(f6(range_of(c4),c3),range_of(c4)) | -subset(domain_of(c4),c2). [resolve(62,a,43,b)].
% 7.12/7.43 148 -ilf_type(A,binary_relation_type) | member(ordered_pair(f8(domain_of(A),B),f1(f8(domain_of(A),B),A)),A) | member(domain_of(A),power_set(B)). [resolve(83,b,75,b)].
% 7.12/7.43 150 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(f8(range_of(A),B),A),f8(range_of(A),B)),A) | member(range_of(A),power_set(B)). [resolve(85,b,75,b)].
% 7.12/7.43 158 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(93,a,40,a)].
% 7.12/7.43 181 member(f6(range_of(c4),c3),range_of(c4)) | member(f6(domain_of(c4),c2),domain_of(c4)). [resolve(140,b,62,a)].
% 7.12/7.43 229 ilf_type(c4,binary_relation_type). [resolve(158,a,114,a)].
% 7.12/7.43 232 member(ordered_pair(f8(domain_of(c4),A),f1(f8(domain_of(c4),A),c4)),c4) | member(domain_of(c4),power_set(A)). [resolve(148,a,229,a)].
% 7.12/7.43 262 member(ordered_pair(f2(f8(range_of(c4),A),c4),f8(range_of(c4),A)),c4) | member(range_of(c4),power_set(A)). [resolve(150,a,229,a)].
% 7.12/7.43 3492 member(domain_of(c4),power_set(A)) | -ilf_type(c4,relation_type(B,C)) | member(f8(domain_of(c4),A),B). [resolve(232,a,105,b)].
% 7.12/7.43 4362 member(range_of(c4),power_set(A)) | -ilf_type(c4,relation_type(B,C)) | member(f8(range_of(c4),A),C). [resolve(262,a,107,b)].
% 7.12/7.43 17585 member(domain_of(c4),power_set(A)) | member(f8(domain_of(c4),A),c2). [resolve(3492,b,40,a)].
% 7.12/7.43 17592 member(domain_of(c4),power_set(c2)). [resolve(17585,b,77,b),merge(b)].
% 7.12/7.43 17645 -member(A,domain_of(c4)) | member(A,c2). [resolve(17592,a,103,a)].
% 7.12/7.43 21038 member(range_of(c4),power_set(A)) | member(f8(range_of(c4),A),c3). [resolve(4362,b,40,a)].
% 7.12/7.43 21043 member(range_of(c4),power_set(c3)). [resolve(21038,b,77,b),merge(b)].
% 7.12/7.43 21102 -member(A,range_of(c4)) | member(A,c3). [resolve(21043,a,103,a)].
% 7.12/7.43 21591 member(f6(range_of(c4),c3),c3) | member(f6(domain_of(c4),c2),domain_of(c4)). [resolve(21102,a,181,a)].
% 7.12/7.43 22249 member(f6(range_of(c4),c3),c3) | member(f6(domain_of(c4),c2),c2). [resolve(21591,b,17645,a)].
% 7.12/7.43 22259 member(f6(domain_of(c4),c2),c2) | subset(range_of(c4),c3). [resolve(22249,a,64,b)].
% 7.12/7.43 22261 member(f6(domain_of(c4),c2),c2) | -subset(domain_of(c4),c2). [resolve(22259,b,43,b)].
% 7.12/7.43 22262 member(f6(domain_of(c4),c2),c2) | member(f6(domain_of(c4),c2),domain_of(c4)). [resolve(22261,b,62,a)].
% 7.12/7.43 22349 member(f6(domain_of(c4),c2),c2). [resolve(22262,b,17645,a),merge(b)].
% 7.12/7.43 22361 subset(domain_of(c4),c2). [resolve(22349,a,64,b)].
% 7.12/7.43 22367 member(f6(range_of(c4),c3),range_of(c4)). [back_unit_del(140),unit_del(b,22361)].
% 7.12/7.43 22368 -subset(range_of(c4),c3). [back_unit_del(43),unit_del(a,22361)].
% 7.12/7.43 22576 member(f6(range_of(c4),c3),c3). [resolve(22367,a,21102,a)].
% 7.12/7.43 23392 $F. [ur(64,a,22368,a),unit_del(a,22576)].
% 7.12/7.43
% 7.12/7.43 % SZS output end Refutation
% 7.12/7.43 ============================== end of proof ==========================
% 7.12/7.43
% 7.12/7.43 ============================== STATISTICS ============================
% 7.12/7.43
% 7.12/7.43 Given=2877. Generated=181866. Kept=23292. proofs=1.
% 7.12/7.43 Usable=2645. Sos=9708. Demods=4. Limbo=0, Disabled=11019. Hints=0.
% 7.12/7.43 Megabytes=24.84.
% 7.12/7.43 User_CPU=6.20, System_CPU=0.21, Wall_clock=6.
% 7.12/7.43
% 7.12/7.43 ============================== end of statistics =====================
% 7.12/7.43
% 7.12/7.43 ============================== end of search =========================
% 7.12/7.43
% 7.12/7.43 THEOREM PROVED
% 7.12/7.43 % SZS status Theorem
% 7.12/7.43
% 7.12/7.43 Exiting with 1 proof.
% 7.12/7.43
% 7.12/7.43 Process 32189 exit (max_proofs) Mon Jul 11 09:01:50 2022
% 7.12/7.43 Prover9 interrupted
%------------------------------------------------------------------------------