TSTP Solution File: SET143+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET143+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 04:27:42 EDT 2022
% Result : Theorem 204.73s 205.00s
% Output : Refutation 204.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET143+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n004.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 : Mon Jul 11 02:11:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.82/4.08 ============================== Prover9 ===============================
% 3.82/4.08 Prover9 (32) version 2009-11A, November 2009.
% 3.82/4.08 Process 27022 was started by sandbox2 on n004.cluster.edu,
% 3.82/4.08 Mon Jul 11 02:11:53 2022
% 3.82/4.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26867_n004.cluster.edu".
% 3.82/4.08 ============================== end of head ===========================
% 3.82/4.08
% 3.82/4.08 ============================== INPUT =================================
% 3.82/4.08
% 3.82/4.08 % Reading from file /tmp/Prover9_26867_n004.cluster.edu
% 3.82/4.08
% 3.82/4.08 set(prolog_style_variables).
% 3.82/4.08 set(auto2).
% 3.82/4.08 % set(auto2) -> set(auto).
% 3.82/4.08 % set(auto) -> set(auto_inference).
% 3.82/4.08 % set(auto) -> set(auto_setup).
% 3.82/4.08 % set(auto_setup) -> set(predicate_elim).
% 3.82/4.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.82/4.08 % set(auto) -> set(auto_limits).
% 3.82/4.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.82/4.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.82/4.08 % set(auto) -> set(auto_denials).
% 3.82/4.08 % set(auto) -> set(auto_process).
% 3.82/4.08 % set(auto2) -> assign(new_constants, 1).
% 3.82/4.08 % set(auto2) -> assign(fold_denial_max, 3).
% 3.82/4.08 % set(auto2) -> assign(max_weight, "200.000").
% 3.82/4.08 % set(auto2) -> assign(max_hours, 1).
% 3.82/4.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.82/4.08 % set(auto2) -> assign(max_seconds, 0).
% 3.82/4.08 % set(auto2) -> assign(max_minutes, 5).
% 3.82/4.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.82/4.08 % set(auto2) -> set(sort_initial_sos).
% 3.82/4.08 % set(auto2) -> assign(sos_limit, -1).
% 3.82/4.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.82/4.08 % set(auto2) -> assign(max_megs, 400).
% 3.82/4.08 % set(auto2) -> assign(stats, some).
% 3.82/4.08 % set(auto2) -> clear(echo_input).
% 3.82/4.08 % set(auto2) -> set(quiet).
% 3.82/4.08 % set(auto2) -> clear(print_initial_clauses).
% 3.82/4.08 % set(auto2) -> clear(print_given).
% 3.82/4.08 assign(lrs_ticks,-1).
% 3.82/4.08 assign(sos_limit,10000).
% 3.82/4.08 assign(order,kbo).
% 3.82/4.08 set(lex_order_vars).
% 3.82/4.08 clear(print_given).
% 3.82/4.08
% 3.82/4.08 % formulas(sos). % not echoed (7 formulas)
% 3.82/4.08
% 3.82/4.08 ============================== end of input ==========================
% 3.82/4.08
% 3.82/4.08 % From the command line: assign(max_seconds, 300).
% 3.82/4.08
% 3.82/4.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.82/4.08
% 3.82/4.08 % Formulas that are not ordinary clauses:
% 3.82/4.08 1 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption].
% 3.82/4.08 2 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 3.82/4.08 3 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 3.82/4.08 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].
% 3.82/4.08 5 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 3.82/4.08 6 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 3.82/4.08 7 -(all B all C all D intersection(intersection(B,C),D) = intersection(B,intersection(C,D))) # label(prove_associativity_of_intersection) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.82/4.08
% 3.82/4.08 ============================== end of process non-clausal formulas ===
% 3.82/4.08
% 3.82/4.08 ============================== PROCESS INITIAL CLAUSES ===============
% 3.82/4.08
% 3.82/4.08 ============================== PREDICATE ELIMINATION =================
% 3.82/4.08
% 3.82/4.08 ============================== end predicate elimination =============
% 3.82/4.08
% 3.82/4.08 Auto_denials: (non-Horn, no changes).
% 3.82/4.08
% 3.82/4.08 Term ordering decisions:
% 3.82/4.08 Function symbol KB weights: c1=1. c2=1. c3=1. intersection=1. f1=1. f2=1.
% 3.82/4.08
% 3.82/4.08 ============================== end of process initial clauses ========
% 3.82/4.08
% 3.82/4.08 ============================== CLAUSES FOR SEARCH ====================
% 3.82/4.08
% 3.82/4.08 ============================== end of clauses for search =============
% 3.82/4.08
% 3.82/4.08 ============================== SEARCH ================================
% 3.82/4.08
% 3.82/4.08 % Starting search at 0.01 seconds.
% 3.82/4.08
% 3.82/4.08 Low Water (keep): wt=61.000, iters=3348
% 3.82/4.08
% 3.82/4.08 Low Water (keep): wt=58.000, iters=3363
% 3.82/4.08
% 3.82/4.08 Low Water (keep): wt=55.000, iters=3357
% 3.82/4.08
% 3.82/4.08 Low Water (keep): wt=46.000, iters=3355
% 3.82/4.08
% 3.82/4.08 Low Water (keep): wt=44.000, iters=3401
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=41.000, iters=3370
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=39.000, iters=3333
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=38.000, iters=3390
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=37.000, iters=3333
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=36.000, iters=3341
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=35.000, iters=3337
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=34.000, iters=3338
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=33.000, iters=3343
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=32.000, iters=3338
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=31.000, iters=3338
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=30.000, iters=3339
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=29.000, iters=3335
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=28.000, iters=3371
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=27.000, iters=3334
% 204.73/205.00
% 204.73/205.00 Low Water (keep): wt=26.000, iters=3335
% 204.73/205.00
% 204.73/205.00 ============================== PROOF =================================
% 204.73/205.00 % SZS status Theorem
% 204.73/205.00 % SZS output start Refutation
% 204.73/205.00
% 204.73/205.00 % Proof 1 at 200.19 (+ 3.84) seconds.
% 204.73/205.00 % Length of proof is 56.
% 204.73/205.00 % Level of proof is 17.
% 204.73/205.00 % Maximum clause weight is 40.000.
% 204.73/205.00 % Given clauses 6711.
% 204.73/205.00
% 204.73/205.00 1 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption].
% 204.73/205.00 3 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 204.73/205.00 6 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 204.73/205.00 7 -(all B all C all D intersection(intersection(B,C),D) = intersection(B,intersection(C,D))) # label(prove_associativity_of_intersection) # label(negated_conjecture) # label(non_clause). [assumption].
% 204.73/205.00 9 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(3)].
% 204.73/205.00 11 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(6)].
% 204.73/205.00 12 intersection(intersection(c1,c2),c3) != intersection(c1,intersection(c2,c3)) # label(prove_associativity_of_intersection) # label(negated_conjecture). [clausify(7)].
% 204.73/205.00 13 intersection(c3,intersection(c1,c2)) != intersection(c1,intersection(c2,c3)). [copy(12),rewrite([9(5)])].
% 204.73/205.00 16 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(1)].
% 204.73/205.00 17 -member(A,intersection(B,C)) | member(A,C) # label(intersection_defn) # label(axiom). [clausify(1)].
% 204.73/205.00 23 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(1)].
% 204.73/205.00 24 A = B | -member(f2(B,A),B) | -member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(6)].
% 204.73/205.00 25 member(A,intersection(B,B)) | -member(A,B). [factor(23,b,c)].
% 204.73/205.00 26 member(f2(A,intersection(B,C)),B) | intersection(B,C) = A | member(f2(A,intersection(B,C)),A). [resolve(16,a,11,c)].
% 204.73/205.00 27 member(f2(intersection(A,B),C),A) | intersection(A,B) = C | member(f2(intersection(A,B),C),C). [resolve(16,a,11,b),flip(b)].
% 204.73/205.00 28 member(f2(A,intersection(A,B)),A) | intersection(A,B) = A. [factor(26,a,c)].
% 204.73/205.00 30 member(f2(A,intersection(B,C)),C) | intersection(B,C) = A | member(f2(A,intersection(B,C)),A). [resolve(17,a,11,c)].
% 204.73/205.00 31 member(f2(intersection(A,B),C),B) | intersection(A,B) = C | member(f2(intersection(A,B),C),C). [resolve(17,a,11,b),flip(b)].
% 204.73/205.00 32 member(f2(intersection(A,B),B),B) | intersection(A,B) = B. [factor(31,a,c)].
% 204.73/205.00 42 member(f2(A,B),intersection(B,C)) | -member(f2(A,B),C) | B = A | member(f2(A,B),A). [resolve(23,b,11,c)].
% 204.73/205.00 43 member(f2(A,B),intersection(A,C)) | -member(f2(A,B),C) | B = A | member(f2(A,B),B). [resolve(23,b,11,b)].
% 204.73/205.00 51 intersection(A,B) = C | member(f2(C,intersection(A,B)),C) | member(f2(C,intersection(A,B)),intersection(A,D)) | -member(f2(C,intersection(A,B)),D). [resolve(26,a,23,c),rewrite([9(8)])].
% 204.73/205.00 54 intersection(A,intersection(B,C)) = D | member(f2(D,intersection(A,intersection(B,C))),D) | member(f2(D,intersection(A,intersection(B,C))),C). [resolve(26,a,17,a),rewrite([9(2),9(5),9(9)])].
% 204.73/205.00 88 intersection(A,intersection(B,C)) = D | member(f2(intersection(A,intersection(B,C)),D),D) | member(f2(intersection(A,intersection(B,C)),D),C). [resolve(27,a,17,a),rewrite([9(2),9(5),9(9)])].
% 204.73/205.00 102 intersection(A,intersection(B,C)) = C | member(f2(intersection(A,intersection(B,C)),C),C). [factor(88,b,c)].
% 204.73/205.00 111 intersection(A,B) = A | member(f2(A,intersection(A,B)),intersection(A,A)). [resolve(28,a,25,b)].
% 204.73/205.00 128 intersection(A,B) = B | -member(f2(intersection(A,B),B),intersection(A,B)). [resolve(32,a,24,c),flip(b),merge(b)].
% 204.73/205.00 133 intersection(A,B) = C | member(f2(C,intersection(A,B)),C) | member(f2(C,intersection(A,B)),intersection(B,B)). [resolve(30,a,25,b)].
% 204.73/205.00 145 intersection(A,B) = intersection(B,B) | member(f2(intersection(B,B),intersection(A,B)),intersection(B,B)). [factor(133,b,c)].
% 204.73/205.00 225 intersection(A,A) = A | -member(f2(A,intersection(A,A)),A). [resolve(111,b,24,c),merge(b)].
% 204.73/205.00 228 intersection(A,A) = A. [resolve(225,b,28,a),merge(b)].
% 204.73/205.00 229 intersection(A,B) = B | member(f2(B,intersection(A,B)),B). [back_rewrite(145),rewrite([228(2),228(3),228(5)])].
% 204.73/205.00 230 member(f2(A,B),A) | A = B | member(f2(A,B),B). [para(228(a,1),27(a,1,1)),rewrite([228(3),228(4)])].
% 204.73/205.00 233 intersection(A,B) = B | -member(f2(B,intersection(A,B)),intersection(A,B)). [resolve(229,b,24,b),merge(b)].
% 204.73/205.00 246 member(f2(A,B),A) | A = B | member(f2(A,B),intersection(B,C)) | -member(f2(A,B),C). [resolve(230,c,23,c),rewrite([9(5)])].
% 204.73/205.00 269 member(f2(A,intersection(B,C)),intersection(C,intersection(B,C))) | intersection(B,C) = A | member(f2(A,intersection(B,C)),A). [resolve(42,b,30,a),rewrite([9(4)]),merge(d),merge(e)].
% 204.73/205.00 286 intersection(A,intersection(B,C)) = D | member(f2(D,intersection(A,intersection(B,C))),D) | member(f2(D,intersection(A,intersection(B,C))),intersection(A,C)). [resolve(54,c,51,d),merge(c),merge(d)].
% 204.73/205.00 356 intersection(A,intersection(B,C)) = C | -member(f2(intersection(A,intersection(B,C)),C),intersection(A,intersection(B,C))). [resolve(102,b,24,c),flip(b),merge(b)].
% 204.73/205.00 822 intersection(A,intersection(B,C)) = D | member(f2(intersection(A,intersection(B,C)),D),D) | member(f2(intersection(A,intersection(B,C)),D),intersection(C,intersection(A,intersection(B,C)))). [resolve(88,c,43,b),rewrite([9(13)]),flip(d),merge(d),merge(e)].
% 204.73/205.00 836 intersection(A,intersection(B,intersection(C,A))) = intersection(B,intersection(C,A)) | member(f2(intersection(B,intersection(C,A)),intersection(A,intersection(B,intersection(C,A)))),intersection(A,intersection(B,intersection(C,A)))). [factor(822,b,c),flip(a)].
% 204.73/205.00 2609 intersection(A,B) = C | member(f2(C,intersection(A,B)),C) | member(f2(C,intersection(A,B)),intersection(intersection(A,B),intersection(B,intersection(A,B)))). [resolve(269,a,246,d),flip(d),merge(c),merge(d)].
% 204.73/205.00 2632 intersection(intersection(A,B),intersection(B,intersection(A,B))) = intersection(A,B) | member(f2(intersection(intersection(A,B),intersection(B,intersection(A,B))),intersection(A,B)),intersection(intersection(A,B),intersection(B,intersection(A,B)))). [factor(2609,b,c),flip(a)].
% 204.73/205.00 3342 intersection(A,intersection(B,C)) = D | member(f2(D,intersection(A,intersection(B,C))),D) | member(f2(D,intersection(A,intersection(B,C))),intersection(intersection(A,C),intersection(A,intersection(B,C)))). [resolve(286,c,246,d),rewrite([9(21)]),flip(d),merge(c),merge(d)].
% 204.73/205.00 3356 intersection(intersection(A,B),intersection(A,intersection(C,B))) = intersection(A,intersection(C,B)) | member(f2(intersection(intersection(A,B),intersection(A,intersection(C,B))),intersection(A,intersection(C,B))),intersection(intersection(A,B),intersection(A,intersection(C,B)))). [factor(3342,b,c),flip(a)].
% 204.73/205.00 13341 intersection(A,intersection(B,intersection(A,C))) = intersection(B,intersection(A,C)). [resolve(836,b,233,b),rewrite([9(1),9(4),9(7),9(10)]),merge(b)].
% 204.73/205.00 13482 intersection(A,intersection(B,intersection(C,intersection(A,D)))) = intersection(B,intersection(C,intersection(A,D))). [para(13341(a,1),13341(a,1,2,2)),rewrite([13341(7)])].
% 204.73/205.00 18448 intersection(intersection(A,B),intersection(B,intersection(A,B))) = intersection(A,B). [resolve(2632,b,356,b),merge(b)].
% 204.73/205.00 18511 intersection(intersection(A,B),intersection(C,intersection(D,intersection(A,B)))) = intersection(C,intersection(D,intersection(A,B))). [para(18448(a,1),13482(a,1,2,2,2)),rewrite([18448(9)])].
% 204.73/205.00 19108 intersection(intersection(A,B),intersection(A,intersection(B,C))) = intersection(A,intersection(B,C)). [resolve(3356,b,128,b),rewrite([9(2),9(5),9(9),9(12)]),merge(b)].
% 204.73/205.00 19200 intersection(intersection(A,B),intersection(A,intersection(C,intersection(B,D)))) = intersection(A,intersection(C,intersection(B,D))). [para(13341(a,1),19108(a,1,2,2)),rewrite([13341(8)])].
% 204.73/205.00 19209 intersection(intersection(A,B),intersection(B,intersection(C,intersection(A,D)))) = intersection(B,intersection(C,intersection(A,D))). [para(13482(a,1),19108(a,1,2)),rewrite([13482(9)])].
% 204.73/205.00 19289 intersection(intersection(A,intersection(B,C)),intersection(A,intersection(D,intersection(B,C)))) = intersection(A,intersection(D,intersection(B,C))). [para(18511(a,1),19108(a,1,2)),rewrite([9(2),18511(11)])].
% 204.73/205.00 21764 intersection(intersection(A,intersection(B,intersection(C,D))),intersection(B,intersection(A,intersection(C,D)))) = intersection(A,intersection(B,intersection(C,D))). [para(19289(a,1),19200(a,1,2)),rewrite([9(3),9(7),19289(13)])].
% 204.73/205.00 21766 intersection(A,intersection(B,intersection(C,D))) = intersection(B,intersection(A,intersection(C,D))). [para(19289(a,1),19209(a,1,2)),rewrite([21764(7),19289(9)])].
% 204.73/205.00 21787 intersection(A,intersection(B,C)) = intersection(B,intersection(A,C)). [para(228(a,1),21766(a,1,2,2)),rewrite([228(3)])].
% 204.73/205.00 22465 $F. [back_rewrite(13),rewrite([21787(5),9(4)]),xx(a)].
% 204.73/205.00
% 204.73/205.00 % SZS output end Refutation
% 204.73/205.00 ============================== end of proof ==========================
% 204.73/205.00
% 204.73/205.00 ============================== STATISTICS ============================
% 204.73/205.00
% 204.73/205.00 Given=6711. Generated=7293031. Kept=22456. proofs=1.
% 204.73/205.00 Usable=4758. Sos=6628. Demods=5. Limbo=678, Disabled=10408. Hints=0.
% 204.73/205.00 Megabytes=15.09.
% 204.73/205.00 User_CPU=200.19, System_CPU=3.84, Wall_clock=204.
% 204.73/205.00
% 204.73/205.00 ============================== end of statistics =====================
% 204.73/205.00
% 204.73/205.00 ============================== end of search =========================
% 204.73/205.00
% 204.73/205.00 THEOREM PROVED
% 204.73/205.00 % SZS status Theorem
% 204.73/205.00
% 204.73/205.00 Exiting with 1 proof.
% 204.73/205.00
% 204.73/205.00 Process 27022 exit (max_proofs) Mon Jul 11 02:15:17 2022
% 204.73/205.00 Prover9 interrupted
%------------------------------------------------------------------------------