TSTP Solution File: SET597+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 04:30:34 EDT 2022
% Result : Theorem 0.97s 1.25s
% Output : Refutation 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 15:43:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 32223 was started by sandbox2 on n014.cluster.edu,
% 0.42/0.97 Sun Jul 10 15:43:50 2022
% 0.42/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32070_n014.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_32070_n014.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.97 % set(auto2) -> assign(stats, some).
% 0.42/0.97 % set(auto2) -> clear(echo_input).
% 0.42/0.97 % set(auto2) -> set(quiet).
% 0.42/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.97 % set(auto2) -> clear(print_given).
% 0.42/0.97 assign(lrs_ticks,-1).
% 0.42/0.97 assign(sos_limit,10000).
% 0.42/0.97 assign(order,kbo).
% 0.42/0.97 set(lex_order_vars).
% 0.42/0.97 clear(print_given).
% 0.42/0.97
% 0.42/0.97 % formulas(sos). % not echoed (9 formulas)
% 0.42/0.97
% 0.42/0.97 ============================== end of input ==========================
% 0.42/0.97
% 0.42/0.97 % From the command line: assign(max_seconds, 300).
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.97
% 0.42/0.97 % Formulas that are not ordinary clauses:
% 0.42/0.97 1 (all B all C subset(B,union(B,C))) # label(subset_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 2 (all B all C all D (subset(B,C) & subset(D,C) -> subset(union(B,D),C))) # label(union_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 3 (all B all C all D (member(D,union(B,C)) <-> member(D,B) | member(D,C))) # label(union_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 4 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 5 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 6 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 7 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 8 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 9 -(all B all C all D (B = union(C,D) <-> subset(C,B) & subset(D,B) & (all E (subset(C,E) & subset(D,E) -> subset(B,E))))) # label(prove_th56) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.97
% 0.42/0.97 ============================== end of process non-clausal formulas ===
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.97
% 0.42/0.97 ============================== PREDICATE ELIMINATION =================
% 0.42/0.97
% 0.42/0.97 ============================== end predicate elimination =============
% 0.42/0.97
% 0.42/0.97 Auto_denials: (non-Horn, no changes).
% 0.42/0.97
% 0.42/0.97 Term ordering decisions:
% 0.42/0.97 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. union=1. f1=1. f2=1.
% 0.42/0.97
% 0.42/0.97 ============================== end of process initial clauses ========
% 0.42/0.97
% 0.42/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.42/0.97
% 0.42/0.97 ============================== end of clauses for search =============
% 0.42/0.97
% 0.42/0.97 ============================== SEARCH ================================
% 0.97/1.25
% 0.97/1.25 % Starting search at 0.01 seconds.
% 0.97/1.25
% 0.97/1.25 ============================== PROOF =================================
% 0.97/1.25 % SZS status Theorem
% 0.97/1.25 % SZS output start Refutation
% 0.97/1.25
% 0.97/1.25 % Proof 1 at 0.29 (+ 0.01) seconds.
% 0.97/1.25 % Length of proof is 97.
% 0.97/1.25 % Level of proof is 20.
% 0.97/1.25 % Maximum clause weight is 22.000.
% 0.97/1.25 % Given clauses 368.
% 0.97/1.25
% 0.97/1.25 1 (all B all C subset(B,union(B,C))) # label(subset_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.25 2 (all B all C all D (subset(B,C) & subset(D,C) -> subset(union(B,D),C))) # label(union_subset) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.25 3 (all B all C all D (member(D,union(B,C)) <-> member(D,B) | member(D,C))) # label(union_defn) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.25 4 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.25 5 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.25 6 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.25 7 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.25 9 -(all B all C all D (B = union(C,D) <-> subset(C,B) & subset(D,B) & (all E (subset(C,E) & subset(D,E) -> subset(B,E))))) # label(prove_th56) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.97/1.25 10 subset(A,A) # label(reflexivity_of_subset) # label(axiom). [clausify(7)].
% 0.97/1.25 11 subset(A,union(A,B)) # label(subset_of_union) # label(axiom). [clausify(1)].
% 0.97/1.25 12 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(6)].
% 0.97/1.25 13 subset(A,B) | member(f1(A,B),A) # label(subset_defn) # label(axiom). [clausify(4)].
% 0.97/1.25 14 union(c2,c3) = c1 | subset(c2,c1) # label(prove_th56) # label(negated_conjecture). [clausify(9)].
% 0.97/1.25 15 union(c2,c3) = c1 | subset(c3,c1) # label(prove_th56) # label(negated_conjecture). [clausify(9)].
% 0.97/1.25 17 union(c2,c3) != c1 | -subset(c2,c1) | -subset(c3,c1) | -subset(c1,c4) # label(prove_th56) # label(negated_conjecture). [clausify(9)].
% 0.97/1.25 20 member(A,union(B,C)) | -member(A,B) # label(union_defn) # label(axiom). [clausify(3)].
% 0.97/1.25 21 member(A,union(B,C)) | -member(A,C) # label(union_defn) # label(axiom). [clausify(3)].
% 0.97/1.25 22 subset(A,B) | -member(f1(A,B),B) # label(subset_defn) # label(axiom). [clausify(4)].
% 0.97/1.25 23 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(4)].
% 0.97/1.25 24 A = B | -subset(B,A) | -subset(A,B) # label(equal_defn) # label(axiom). [clausify(5)].
% 0.97/1.25 27 -subset(A,B) | -subset(C,B) | subset(union(A,C),B) # label(union_subset) # label(axiom). [clausify(2)].
% 0.97/1.25 28 -member(A,union(B,C)) | member(A,B) | member(A,C) # label(union_defn) # label(axiom). [clausify(3)].
% 0.97/1.25 30 union(c2,c3) = c1 | -subset(c2,A) | -subset(c3,A) | subset(c1,A) # label(prove_th56) # label(negated_conjecture). [clausify(9)].
% 0.97/1.25 31 union(c2,c3) != c1 | -subset(c2,c1) | -subset(c3,c1) | subset(c2,c4) # label(prove_th56) # label(negated_conjecture). [clausify(9)].
% 0.97/1.25 32 union(c2,c3) != c1 | -subset(c2,c1) | -subset(c3,c1) | subset(c3,c4) # label(prove_th56) # label(negated_conjecture). [clausify(9)].
% 0.97/1.25 33 -subset(A,B) | subset(union(A,A),B). [factor(27,a,b)].
% 0.97/1.25 37 member(f1(A,B),union(A,C)) | subset(A,B). [resolve(20,b,13,b)].
% 0.97/1.25 47 union(A,B) = A | -subset(union(A,B),A). [resolve(24,b,11,a)].
% 0.97/1.25 56 -subset(A,c1) | subset(union(A,c3),c1) | union(c2,c3) = c1. [resolve(27,a,15,b),rewrite([12(4)])].
% 0.97/1.25 58 -subset(A,union(B,C)) | subset(union(A,B),union(B,C)). [resolve(27,a,11,a),rewrite([12(3)])].
% 0.97/1.25 59 -subset(A,B) | subset(union(A,B),B). [resolve(27,a,10,a),rewrite([12(2)])].
% 0.97/1.25 62 member(f1(union(A,B),C),A) | member(f1(union(A,B),C),B) | subset(union(A,B),C). [resolve(28,a,13,b)].
% 0.97/1.25 71 union(c2,c3) = c1 | -subset(c2,union(A,c3)) | subset(c1,union(A,c3)). [resolve(30,c,11,a),rewrite([12(8),12(12)])].
% 0.97/1.25 76 subset(union(A,A),A). [resolve(33,a,10,a)].
% 0.97/1.25 95 union(A,A) = A. [resolve(76,a,24,c),unit_del(b,11)].
% 0.97/1.25 98 subset(union(c1,c3),c1) | union(c2,c3) = c1. [resolve(59,a,15,b),rewrite([12(3)])].
% 0.97/1.25 99 subset(union(c1,c2),c1) | union(c2,c3) = c1. [resolve(59,a,14,b),rewrite([12(3)])].
% 0.97/1.25 119 subset(A,B) | member(f1(A,B),union(C,union(A,D))). [resolve(37,a,21,b)].
% 0.97/1.25 121 union(c2,c3) = c1 | union(c1,c3) = c1. [resolve(98,a,47,b)].
% 0.97/1.25 124 union(c2,c3) = c1 | union(c1,c2) = c1. [resolve(99,a,47,b)].
% 0.97/1.25 150 union(c1,c2) = c1 | subset(c2,c1). [para(124(a,1),11(a,2))].
% 0.97/1.25 162 union(c1,c2) = c1 | subset(union(c1,c2),c1). [resolve(150,b,59,a),rewrite([12(8)])].
% 0.97/1.25 198 union(c1,c2) = c1. [resolve(162,b,47,b),merge(b)].
% 0.97/1.25 215 -subset(A,union(B,C)) | subset(union(A,C),union(B,C)). [para(12(a,1),58(a,2)),rewrite([12(4)])].
% 0.97/1.25 229 subset(A,union(B,union(A,C))). [resolve(119,b,22,b),merge(b)].
% 0.97/1.25 234 subset(union(A,B),union(B,union(A,C))). [resolve(229,a,58,a)].
% 0.97/1.25 236 -subset(A,union(B,union(C,D))) | subset(union(A,C),union(B,union(C,D))). [resolve(229,a,27,b)].
% 0.97/1.25 239 subset(c1,union(A,c1)). [para(198(a,1),229(a,2,2))].
% 0.97/1.25 240 subset(union(c1,union(A,c1)),union(A,c1)). [resolve(239,a,59,a)].
% 0.97/1.25 275 union(c1,union(A,c1)) = union(A,c1). [resolve(240,a,24,c),unit_del(b,234)].
% 0.97/1.25 285 subset(union(A,c1),union(A,union(B,c1))). [para(275(a,1),234(a,2,2)),rewrite([12(2)])].
% 0.97/1.25 288 subset(union(c2,c3),c1) | union(c2,c3) = c1. [resolve(56,a,14,b),merge(c)].
% 0.97/1.25 324 union(c2,c3) = c1 | -subset(c1,union(c2,c3)). [resolve(288,a,24,c),merge(b)].
% 0.97/1.25 522 subset(union(A,union(A,B)),union(C,union(A,B))). [resolve(215,a,229,a)].
% 0.97/1.25 526 subset(union(A,union(B,A)),union(B,A)). [resolve(215,a,10,a),rewrite([12(2)])].
% 0.97/1.25 541 union(A,union(B,A)) = union(B,A). [resolve(526,a,24,b),flip(a),unit_del(b,234)].
% 0.97/1.25 543 union(A,union(A,B)) = union(A,B). [para(12(a,1),541(a,1,2)),rewrite([12(3)])].
% 0.97/1.25 544 union(c1,c3) = c1 | union(c2,c3) = union(c1,c3). [para(121(a,1),541(a,1,2)),rewrite([12(8)]),flip(b)].
% 0.97/1.25 547 subset(union(A,B),union(C,union(A,B))). [back_rewrite(522),rewrite([543(2)])].
% 0.97/1.25 623 union(c2,c3) = c1 | subset(c1,union(c2,c3)). [resolve(71,b,11,a)].
% 0.97/1.25 625 union(c2,c3) = c1. [resolve(623,b,324,b),merge(b)].
% 0.97/1.25 627 union(c1,c3) = c1. [back_rewrite(544),rewrite([625(8)]),flip(b),merge(b)].
% 0.97/1.25 628 -subset(c2,c1) | -subset(c3,c1) | subset(c3,c4). [back_rewrite(32),rewrite([625(3)]),xx(a)].
% 0.97/1.25 629 -subset(c2,c1) | -subset(c3,c1) | subset(c2,c4). [back_rewrite(31),rewrite([625(3)]),xx(a)].
% 0.97/1.25 630 -subset(c2,c1) | -subset(c3,c1) | -subset(c1,c4). [back_rewrite(17),rewrite([625(3)]),xx(a)].
% 0.97/1.25 631 subset(c2,c1). [para(625(a,1),11(a,2))].
% 0.97/1.25 640 subset(c2,union(A,c1)). [para(625(a,1),229(a,2,2))].
% 0.97/1.25 641 subset(c1,union(c3,union(A,c2))). [para(625(a,1),234(a,1)),rewrite([12(4)])].
% 0.97/1.25 642 subset(union(A,c2),union(A,c1)). [para(625(a,1),234(a,2,2)),rewrite([12(2)])].
% 0.97/1.25 647 member(f1(c1,A),c2) | member(f1(c1,A),c3) | subset(c1,A). [para(625(a,1),62(a,1,1)),rewrite([625(7),625(11)])].
% 0.97/1.25 651 -subset(c3,c1) | -subset(c1,c4). [back_unit_del(630),unit_del(a,631)].
% 0.97/1.25 652 -subset(c3,c1) | subset(c2,c4). [back_unit_del(629),unit_del(a,631)].
% 0.97/1.25 653 -subset(c3,c1) | subset(c3,c4). [back_unit_del(628),unit_del(a,631)].
% 0.97/1.25 660 subset(union(c2,union(A,c1)),union(A,c1)). [resolve(640,a,59,a)].
% 0.97/1.25 673 subset(union(c1,union(A,c2)),union(c3,union(A,c2))). [resolve(641,a,215,a)].
% 0.97/1.25 682 subset(union(c1,union(A,c2)),union(A,c1)). [resolve(642,a,215,a),rewrite([12(4)])].
% 0.97/1.25 792 union(c2,union(A,c1)) = union(A,c1). [resolve(660,a,24,c),unit_del(b,547)].
% 0.97/1.25 801 union(c1,union(A,c2)) = union(A,c1). [resolve(682,a,24,c),unit_del(b,234)].
% 0.97/1.25 802 subset(union(A,c1),union(c3,union(A,c2))). [back_rewrite(673),rewrite([801(4)])].
% 0.97/1.25 804 subset(c2,union(A,union(B,c1))). [para(792(a,1),229(a,2,2))].
% 0.97/1.25 836 subset(union(c3,union(A,c1)),union(c3,union(A,c2))). [resolve(802,a,58,a),rewrite([12(4)])].
% 0.97/1.25 982 union(c3,union(A,c2)) = union(c3,union(A,c1)) | -subset(union(c3,union(A,c2)),union(c3,union(A,c1))). [resolve(836,a,24,c),flip(a)].
% 0.97/1.25 1594 subset(union(A,c2),union(B,union(A,c1))). [resolve(236,a,804,a),rewrite([12(2)])].
% 0.97/1.25 1596 subset(union(A,union(B,c1)),union(B,union(A,c1))). [resolve(236,a,285,a),rewrite([12(3)])].
% 0.97/1.25 1626 subset(union(A,union(B,c2)),union(A,union(B,c1))). [resolve(1594,a,58,a),rewrite([12(3)])].
% 0.97/1.25 1632 union(c3,union(A,c2)) = union(c3,union(A,c1)). [back_unit_del(982),unit_del(b,1626)].
% 0.97/1.25 1808 union(A,union(B,c1)) = union(B,union(A,c1)). [resolve(1596,a,24,c),unit_del(b,1596)].
% 0.97/1.25 1823 union(c3,union(A,c2)) = union(A,c1). [back_rewrite(1632),rewrite([1808(8),12(7),627(7)])].
% 0.97/1.25 1845 subset(c3,union(A,c1)). [para(1823(a,1),11(a,2))].
% 0.97/1.25 1932 subset(c3,c1). [para(95(a,1),1845(a,2))].
% 0.97/1.25 1933 subset(c3,c4). [back_unit_del(653),unit_del(a,1932)].
% 0.97/1.25 1934 subset(c2,c4). [back_unit_del(652),unit_del(a,1932)].
% 0.97/1.25 1935 -subset(c1,c4). [back_unit_del(651),unit_del(a,1932)].
% 0.97/1.25 1975 -member(f1(c1,c4),c4). [ur(22,a,1935,a)].
% 0.97/1.25 1981 -member(f1(c1,c4),c2). [ur(23,a,1934,a,c,1975,a)].
% 0.97/1.25 1982 -member(f1(c1,c4),c3). [ur(23,a,1933,a,c,1975,a)].
% 0.97/1.25 2245 $F. [resolve(1982,a,647,b),unit_del(a,1981),unit_del(b,1935)].
% 0.97/1.25
% 0.97/1.25 % SZS output end Refutation
% 0.97/1.25 ============================== end of proof ==========================
% 0.97/1.25
% 0.97/1.25 ============================== STATISTICS ============================
% 0.97/1.25
% 0.97/1.25 Given=368. Generated=8253. Kept=2235. proofs=1.
% 0.97/1.25 Usable=230. Sos=1181. Demods=17. Limbo=0, Disabled=847. Hints=0.
% 0.97/1.25 Megabytes=1.54.
% 0.97/1.25 User_CPU=0.29, System_CPU=0.01, Wall_clock=1.
% 0.97/1.25
% 0.97/1.25 ============================== end of statistics =====================
% 0.97/1.25
% 0.97/1.25 ============================== end of search =========================
% 0.97/1.25
% 0.97/1.25 THEOREM PROVED
% 0.97/1.25 % SZS status Theorem
% 0.97/1.25
% 0.97/1.25 Exiting with 1 proof.
% 0.97/1.25
% 0.97/1.25 Process 32223 exit (max_proofs) Sun Jul 10 15:43:51 2022
% 0.97/1.25 Prover9 interrupted
%------------------------------------------------------------------------------