TSTP Solution File: SET653+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET653+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 04:31:11 EDT 2022
% Result : Theorem 0.76s 1.03s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET653+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 : n010.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 : Sun Jul 10 22:58:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.76/1.02 ============================== Prover9 ===============================
% 0.76/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.02 Process 24592 was started by sandbox2 on n010.cluster.edu,
% 0.76/1.02 Sun Jul 10 22:58:16 2022
% 0.76/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24439_n010.cluster.edu".
% 0.76/1.02 ============================== end of head ===========================
% 0.76/1.02
% 0.76/1.02 ============================== INPUT =================================
% 0.76/1.02
% 0.76/1.02 % Reading from file /tmp/Prover9_24439_n010.cluster.edu
% 0.76/1.02
% 0.76/1.02 set(prolog_style_variables).
% 0.76/1.02 set(auto2).
% 0.76/1.02 % set(auto2) -> set(auto).
% 0.76/1.02 % set(auto) -> set(auto_inference).
% 0.76/1.02 % set(auto) -> set(auto_setup).
% 0.76/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.02 % set(auto) -> set(auto_limits).
% 0.76/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.02 % set(auto) -> set(auto_denials).
% 0.76/1.02 % set(auto) -> set(auto_process).
% 0.76/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.02 % set(auto2) -> assign(stats, some).
% 0.76/1.02 % set(auto2) -> clear(echo_input).
% 0.76/1.02 % set(auto2) -> set(quiet).
% 0.76/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.02 % set(auto2) -> clear(print_given).
% 0.76/1.02 assign(lrs_ticks,-1).
% 0.76/1.02 assign(sos_limit,10000).
% 0.76/1.02 assign(order,kbo).
% 0.76/1.02 set(lex_order_vars).
% 0.76/1.02 clear(print_given).
% 0.76/1.02
% 0.76/1.02 % formulas(sos). % not echoed (23 formulas)
% 0.76/1.02
% 0.76/1.02 ============================== end of input ==========================
% 0.76/1.02
% 0.76/1.02 % From the command line: assign(max_seconds, 300).
% 0.76/1.02
% 0.76/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.02
% 0.76/1.02 % Formulas that are not ordinary clauses:
% 0.76/1.02 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].
% 0.76/1.02 2 (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(p2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 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,relation_type(B,D)) -> (subset(domain_of(E),C) -> ilf_type(E,relation_type(C,D))))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 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].
% 0.76/1.02 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p5) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 6 (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(p6) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 7 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p7) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 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].
% 0.76/1.02 9 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p9) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))) # label(p10) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 11 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p11) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 12 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p12) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p13) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 14 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p14) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 15 (all B (ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))) # label(p15) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 16 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p16) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 17 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p17) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 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].
% 0.76/1.02 19 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p19) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 20 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> relation_like(D))))))) # label(p20) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 21 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p21) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 22 (all B ilf_type(B,set_type)) # label(p22) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.02 23 -(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,relation_type(B,D)) -> (subset(B,C) -> ilf_type(E,relation_type(C,D))))))))))) # label(prove_relset_1_15) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.02
% 0.76/1.02 ============================== end of process non-clausal formulas ===
% 0.76/1.02
% 0.76/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.02
% 0.76/1.02 ============================== PREDICATE ELIMINATION =================
% 0.76/1.02 24 -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)].
% 0.76/1.02 25 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p19) # label(axiom). [clausify(19)].
% 0.76/1.02 26 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f9(A),set_type) # label(p18) # label(axiom). [clausify(18)].
% 0.76/1.02 27 -ilf_type(A,set_type) | relation_like(A) | member(f9(A),A) # label(p18) # label(axiom). [clausify(18)].
% 0.76/1.02 28 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p20) # label(axiom). [clausify(20)].
% 0.76/1.02 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(24,b,25,c)].
% 0.76/1.02 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(24,b,26,b)].
% 0.76/1.02 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(24,b,27,b)].
% 0.76/1.02 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(24,b,28,d)].
% 0.76/1.02 29 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p18) # label(axiom). [clausify(18)].
% 0.76/1.03 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(29,b,25,c)].
% 0.76/1.03 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(29,b,26,b)].
% 0.76/1.03 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(29,b,27,b)].
% 0.76/1.03 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(29,b,28,d)].
% 0.76/1.03 30 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f9(A) # label(p18) # label(axiom). [clausify(18)].
% 0.76/1.03 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(30,b,24,b)].
% 0.76/1.03 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(30,b,29,b)].
% 0.76/1.03 31 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B # label(p18) # label(axiom). [clausify(18)].
% 0.76/1.03 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(31,b,25,c)].
% 0.76/1.03 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(31,b,26,b)].
% 0.76/1.03 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(31,b,27,b)].
% 0.76/1.03 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(31,b,28,d)].
% 0.76/1.03 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(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f9(A). [resolve(31,b,30,b)].
% 0.76/1.03
% 0.76/1.03 ============================== end predicate elimination =============
% 0.76/1.03
% 0.76/1.03 Auto_denials: (non-Horn, no changes).
% 0.76/1.03
% 0.76/1.03 Term ordering decisions:
% 0.76/1.03 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. ordered_pair=1. relation_type=1. cross_product=1. f1=1. f2=1. f4=1. f7=1. f8=1. subset_type=1. power_set=1. member_type=1. domain_of=1. range_of=1. f3=1. f5=1. f6=1. f9=1.
% 0.76/1.03
% 0.76/1.03 ============================== end of process initial clauses ========
% 0.76/1.03
% 0.76/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.03
% 0.76/1.03 ============================== end of clauses for search =============
% 0.76/1.03
% 0.76/1.03 ============================== SEARCH ================================
% 0.76/1.03
% 0.76/1.03 % Starting search at 0.02 seconds.
% 0.76/1.03
% 0.76/1.03 ============================== PROOF =================================
% 0.76/1.03 % SZS status Theorem
% 0.76/1.03 % SZS output start Refutation
% 0.76/1.03
% 0.76/1.03 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.76/1.03 % Length of proof is 18.
% 0.76/1.03 % Level of proof is 4.
% 0.76/1.03 % Maximum clause weight is 14.000.
% 0.76/1.03 % Given clauses 33.
% 0.76/1.03
% 0.76/1.03 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].
% 0.76/1.03 2 (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(p2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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,relation_type(B,D)) -> (subset(domain_of(E),C) -> ilf_type(E,relation_type(C,D))))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 22 (all B ilf_type(B,set_type)) # label(p22) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 23 -(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,relation_type(B,D)) -> (subset(B,C) -> ilf_type(E,relation_type(C,D))))))))))) # label(prove_relset_1_15) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.03 32 ilf_type(A,set_type) # label(p22) # label(axiom). [clausify(22)].
% 0.76/1.03 33 subset(c1,c2) # label(prove_relset_1_15) # label(negated_conjecture). [clausify(23)].
% 0.76/1.03 34 ilf_type(c4,relation_type(c1,c3)) # label(prove_relset_1_15) # label(negated_conjecture). [clausify(23)].
% 0.76/1.03 35 -ilf_type(c4,relation_type(c2,c3)) # label(prove_relset_1_15) # label(negated_conjecture). [clausify(23)].
% 0.76/1.03 59 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | subset(domain_of(C),A) # label(p2) # label(axiom). [clausify(2)].
% 0.76/1.03 60 -ilf_type(A,relation_type(B,C)) | subset(domain_of(A),B). [copy(59),unit_del(a,32),unit_del(b,32)].
% 0.76/1.03 80 -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)].
% 0.76/1.03 81 -subset(A,B) | -subset(B,C) | subset(A,C). [copy(80),unit_del(a,32),unit_del(b,32),unit_del(c,32)].
% 0.76/1.03 86 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,C)) | -subset(domain_of(D),B) | ilf_type(D,relation_type(B,C)) # label(p3) # label(axiom). [clausify(3)].
% 0.76/1.03 87 -ilf_type(A,relation_type(B,C)) | -subset(domain_of(A),D) | ilf_type(A,relation_type(D,C)). [copy(86),unit_del(a,32),unit_del(b,32),unit_del(c,32)].
% 0.76/1.03 108 subset(domain_of(c4),c1). [resolve(60,a,34,a)].
% 0.76/1.03 135 -subset(domain_of(c4),c2). [ur(87,a,34,a,c,35,a)].
% 0.76/1.03 148 $F. [ur(81,b,33,a,c,135,a),unit_del(a,108)].
% 0.76/1.03
% 0.76/1.03 % SZS output end Refutation
% 0.76/1.03 ============================== end of proof ==========================
% 0.76/1.03
% 0.76/1.03 ============================== STATISTICS ============================
% 0.76/1.03
% 0.76/1.03 Given=33. Generated=103. Kept=72. proofs=1.
% 0.76/1.03 Usable=33. Sos=37. Demods=0. Limbo=2, Disabled=61. Hints=0.
% 0.76/1.03 Megabytes=0.19.
% 0.76/1.03 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.76/1.03
% 0.76/1.03 ============================== end of statistics =====================
% 0.76/1.03
% 0.76/1.03 ============================== end of search =========================
% 0.76/1.03
% 0.76/1.03 THEOREM PROVED
% 0.76/1.03 % SZS status Theorem
% 0.76/1.03
% 0.76/1.03 Exiting with 1 proof.
% 0.76/1.03
% 0.76/1.03 Process 24592 exit (max_proofs) Sun Jul 10 22:58:16 2022
% 0.76/1.03 Prover9 interrupted
%------------------------------------------------------------------------------