TSTP Solution File: SET015-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET015-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 04:25:43 EDT 2022
% Result : Unsatisfiable 169.88s 170.15s
% Output : Refutation 169.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET015-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n011.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 22:48:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.72/3.97 ============================== Prover9 ===============================
% 3.72/3.97 Prover9 (32) version 2009-11A, November 2009.
% 3.72/3.97 Process 4981 was started by sandbox on n011.cluster.edu,
% 3.72/3.97 Sun Jul 10 22:48:12 2022
% 3.72/3.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4827_n011.cluster.edu".
% 3.72/3.97 ============================== end of head ===========================
% 3.72/3.97
% 3.72/3.97 ============================== INPUT =================================
% 3.72/3.97
% 3.72/3.97 % Reading from file /tmp/Prover9_4827_n011.cluster.edu
% 3.72/3.97
% 3.72/3.97 set(prolog_style_variables).
% 3.72/3.97 set(auto2).
% 3.72/3.97 % set(auto2) -> set(auto).
% 3.72/3.97 % set(auto) -> set(auto_inference).
% 3.72/3.97 % set(auto) -> set(auto_setup).
% 3.72/3.97 % set(auto_setup) -> set(predicate_elim).
% 3.72/3.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.72/3.97 % set(auto) -> set(auto_limits).
% 3.72/3.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.72/3.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.72/3.97 % set(auto) -> set(auto_denials).
% 3.72/3.97 % set(auto) -> set(auto_process).
% 3.72/3.97 % set(auto2) -> assign(new_constants, 1).
% 3.72/3.97 % set(auto2) -> assign(fold_denial_max, 3).
% 3.72/3.97 % set(auto2) -> assign(max_weight, "200.000").
% 3.72/3.97 % set(auto2) -> assign(max_hours, 1).
% 3.72/3.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.72/3.97 % set(auto2) -> assign(max_seconds, 0).
% 3.72/3.97 % set(auto2) -> assign(max_minutes, 5).
% 3.72/3.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.72/3.97 % set(auto2) -> set(sort_initial_sos).
% 3.72/3.97 % set(auto2) -> assign(sos_limit, -1).
% 3.72/3.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.72/3.97 % set(auto2) -> assign(max_megs, 400).
% 3.72/3.97 % set(auto2) -> assign(stats, some).
% 3.72/3.97 % set(auto2) -> clear(echo_input).
% 3.72/3.97 % set(auto2) -> set(quiet).
% 3.72/3.97 % set(auto2) -> clear(print_initial_clauses).
% 3.72/3.97 % set(auto2) -> clear(print_given).
% 3.72/3.97 assign(lrs_ticks,-1).
% 3.72/3.97 assign(sos_limit,10000).
% 3.72/3.97 assign(order,kbo).
% 3.72/3.97 set(lex_order_vars).
% 3.72/3.97 clear(print_given).
% 3.72/3.97
% 3.72/3.97 % formulas(sos). % not echoed (15 formulas)
% 3.72/3.97
% 3.72/3.97 ============================== end of input ==========================
% 3.72/3.97
% 3.72/3.97 % From the command line: assign(max_seconds, 300).
% 3.72/3.97
% 3.72/3.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.72/3.97
% 3.72/3.97 % Formulas that are not ordinary clauses:
% 3.72/3.97
% 3.72/3.97 ============================== end of process non-clausal formulas ===
% 3.72/3.97
% 3.72/3.97 ============================== PROCESS INITIAL CLAUSES ===============
% 3.72/3.97
% 3.72/3.97 ============================== PREDICATE ELIMINATION =================
% 3.72/3.97 1 member(A,universal_set) | -little_set(A) # label(universal_set) # label(axiom). [assumption].
% 3.72/3.97 2 little_set(f1(A,B)) | A = B # label(extensionality1) # label(axiom). [assumption].
% 3.72/3.97 3 -member(A,B) | little_set(A) # label(a2) # label(axiom). [assumption].
% 3.72/3.97 Derived: member(f1(A,B),universal_set) | A = B. [resolve(1,b,2,a)].
% 3.72/3.97 Derived: member(A,universal_set) | -member(A,B). [resolve(1,b,3,b)].
% 3.72/3.97 4 member(A,complement(B)) | -little_set(A) | member(A,B) # label(complement2) # label(axiom). [assumption].
% 3.72/3.97 Derived: member(f1(A,B),complement(C)) | member(f1(A,B),C) | A = B. [resolve(4,b,2,a)].
% 3.72/3.97 Derived: member(A,complement(B)) | member(A,B) | -member(A,C). [resolve(4,b,3,b)].
% 3.72/3.97
% 3.72/3.97 ============================== end predicate elimination =============
% 3.72/3.97
% 3.72/3.97 Auto_denials: (non-Horn, no changes).
% 3.72/3.97
% 3.72/3.97 Term ordering decisions:
% 3.72/3.97
% 3.72/3.97 % Assigning unary symbol complement kb_weight 0 and highest precedence (12).
% 3.72/3.97 Function symbol KB weights: as=1. bs=1. universal_set=1. cs=1. ds=1. empty_set=1. f1=1. intersection=1. union=1. complement=0.
% 3.72/3.97
% 3.72/3.97 ============================== end of process initial clauses ========
% 3.72/3.97
% 3.72/3.97 ============================== CLAUSES FOR SEARCH ====================
% 3.72/3.97
% 3.72/3.97 ============================== end of clauses for search =============
% 3.72/3.97
% 3.72/3.97 ============================== SEARCH ================================
% 3.72/3.97
% 3.72/3.97 % Starting search at 0.01 seconds.
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=59.000, iters=3345
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=57.000, iters=3344
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=56.000, iters=3345
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=53.000, iters=3375
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=51.000, iters=3347
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=49.000, iters=3360
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=48.000, iters=3337
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=47.000, iters=3345
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=44.000, iters=3333
% 3.72/3.97
% 3.72/3.97 Low Water (keep): wt=43.000, iters=3343
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=40.000, iters=3348
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=39.000, iters=3400
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=38.000, iters=3336
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=37.000, iters=3338
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=36.000, iters=3340
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=35.000, iters=3360
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=34.000, iters=3343
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=32.000, iters=3350
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=31.000, iters=3356
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=30.000, iters=3333
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=29.000, iters=3335
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=28.000, iters=3353
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=27.000, iters=3336
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=26.000, iters=3402
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=25.000, iters=3346
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=24.000, iters=3346
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=6644, wt=78.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=6852, wt=56.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=8603, wt=53.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=8747, wt=51.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=8635, wt=49.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=4869, wt=48.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=8742, wt=47.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=6762, wt=46.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=8897, wt=45.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=8899, wt=44.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=8933, wt=43.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=16588, wt=21.000
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=23.000, iters=3358
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=17230, wt=20.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=17278, wt=19.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=17332, wt=18.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=19227, wt=17.000
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=19326, wt=16.000
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=22.000, iters=3333
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=21.000, iters=3355
% 169.88/170.15
% 169.88/170.15 Low Water (displace): id=65740, wt=14.000
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=20.000, iters=3341
% 169.88/170.15
% 169.88/170.15 Low Water (keep): wt=19.000, iters=3333
% 169.88/170.15
% 169.88/170.15 ============================== PROOF =================================
% 169.88/170.15 % SZS status Unsatisfiable
% 169.88/170.15 % SZS output start Refutation
% 169.88/170.15
% 169.88/170.15 % Proof 1 at 158.73 (+ 10.42) seconds.
% 169.88/170.15 % Length of proof is 55.
% 169.88/170.15 % Level of proof is 11.
% 169.88/170.15 % Maximum clause weight is 36.000.
% 169.88/170.15 % Given clauses 4888.
% 169.88/170.15
% 169.88/170.15 2 little_set(f1(A,B)) | A = B # label(extensionality1) # label(axiom). [assumption].
% 169.88/170.15 4 member(A,complement(B)) | -little_set(A) | member(A,B) # label(complement2) # label(axiom). [assumption].
% 169.88/170.15 5 union(as,bs) = cs # label(a_union_b_is_c) # label(hypothesis). [assumption].
% 169.88/170.15 6 cs = union(as,bs). [copy(5),flip(a)].
% 169.88/170.15 7 union(bs,as) = ds # label(b_union_a_is_d) # label(hypothesis). [assumption].
% 169.88/170.15 8 ds = union(bs,as). [copy(7),flip(a)].
% 169.88/170.15 9 union(A,B) = complement(intersection(complement(A),complement(B))) # label(union) # label(axiom). [assumption].
% 169.88/170.15 10 member(f1(A,B),A) | member(f1(A,B),B) | A = B # label(extensionality2) # label(axiom). [assumption].
% 169.88/170.15 11 -member(A,empty_set) # label(empty_set) # label(axiom). [assumption].
% 169.88/170.15 12 cs != ds # label(prove_c_equals_d) # label(negated_conjecture). [assumption].
% 169.88/170.15 13 complement(intersection(complement(bs),complement(as))) != complement(intersection(complement(as),complement(bs))). [copy(12),rewrite([6(1),9(3),8(7),9(9)]),flip(a)].
% 169.88/170.15 14 -member(A,complement(B)) | -member(A,B) # label(complement1) # label(axiom). [assumption].
% 169.88/170.15 15 -member(A,intersection(B,C)) | member(A,B) # label(intersection1) # label(axiom). [assumption].
% 169.88/170.15 16 -member(A,intersection(B,C)) | member(A,C) # label(intersection2) # label(axiom). [assumption].
% 169.88/170.15 17 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection3) # label(axiom). [assumption].
% 169.88/170.15 18 -member(f1(A,B),A) | -member(f1(A,B),B) | A = B # label(extensionality3) # label(axiom). [assumption].
% 169.88/170.15 21 member(f1(A,B),complement(C)) | member(f1(A,B),C) | A = B. [resolve(4,b,2,a)].
% 169.88/170.15 27 member(f1(empty_set,A),A) | empty_set = A. [resolve(11,a,10,a)].
% 169.88/170.15 28 -member(f1(A,complement(B)),B) | member(f1(A,complement(B)),A) | complement(B) = A. [resolve(14,a,10,b),flip(c)].
% 169.88/170.15 30 member(f1(A,intersection(B,C)),B) | member(f1(A,intersection(B,C)),A) | intersection(B,C) = A. [resolve(15,a,10,b),flip(c)].
% 169.88/170.15 31 member(f1(intersection(A,B),C),A) | member(f1(intersection(A,B),C),C) | intersection(A,B) = C. [resolve(15,a,10,a)].
% 169.88/170.15 34 member(f1(intersection(A,B),A),A) | intersection(A,B) = A. [factor(31,a,b)].
% 169.88/170.15 36 member(f1(intersection(A,B),C),B) | member(f1(intersection(A,B),C),C) | intersection(A,B) = C. [resolve(16,a,10,a)].
% 169.88/170.15 39 member(f1(intersection(A,B),B),B) | intersection(A,B) = B. [factor(36,a,b)].
% 169.88/170.15 52 member(f1(A,complement(B)),B) | complement(B) = A | -member(f1(A,complement(B)),A). [resolve(21,a,18,b),flip(b),flip(d),merge(d)].
% 169.88/170.15 54 member(f1(A,B),C) | A = B | member(f1(A,B),intersection(D,complement(C))) | -member(f1(A,B),D). [resolve(21,a,17,c)].
% 169.88/170.15 55 member(f1(A,B),C) | A = B | member(f1(A,B),intersection(complement(C),D)) | -member(f1(A,B),D). [resolve(21,a,17,b)].
% 169.88/170.15 75 intersection(A,B) = empty_set | member(f1(empty_set,intersection(A,B)),B). [resolve(27,a,16,a),flip(a)].
% 169.88/170.15 76 intersection(A,B) = empty_set | member(f1(empty_set,intersection(A,B)),A). [resolve(27,a,15,a),flip(a)].
% 169.88/170.15 80 member(f1(A,complement(complement(B))),A) | complement(complement(B)) = A | member(f1(A,complement(complement(B))),B). [resolve(28,a,21,a),flip(d),merge(d)].
% 169.88/170.15 83 member(f1(A,complement(complement(A))),A) | complement(complement(A)) = A. [factor(80,a,c)].
% 169.88/170.15 107 member(f1(A,intersection(intersection(B,C),D)),A) | intersection(intersection(B,C),D) = A | member(f1(A,intersection(intersection(B,C),D)),C). [resolve(30,a,16,a)].
% 169.88/170.15 188 intersection(A,B) = A | -member(f1(intersection(A,B),A),intersection(A,B)). [resolve(34,a,18,b),merge(c)].
% 169.88/170.15 190 intersection(A,B) = A | member(f1(intersection(A,B),A),intersection(A,C)) | -member(f1(intersection(A,B),A),C). [resolve(34,a,17,b)].
% 169.88/170.15 204 intersection(A,B) = B | -member(f1(intersection(A,B),B),intersection(A,B)). [resolve(39,a,18,b),merge(c)].
% 169.88/170.15 206 intersection(A,B) = B | member(f1(intersection(A,B),B),intersection(B,C)) | -member(f1(intersection(A,B),B),C). [resolve(39,a,17,b)].
% 169.88/170.15 256 intersection(A,complement(B)) = empty_set | -member(f1(empty_set,intersection(A,complement(B))),B). [resolve(75,b,14,a)].
% 169.88/170.15 261 intersection(intersection(A,B),C) = empty_set | member(f1(empty_set,intersection(intersection(A,B),C)),A). [resolve(76,b,15,a)].
% 169.88/170.15 603 member(f1(A,complement(complement(A))),complement(A)) | complement(complement(A)) = A. [resolve(52,c,83,a),merge(c)].
% 169.88/170.15 713 member(f1(intersection(A,B),A),C) | intersection(A,B) = A | member(f1(intersection(A,B),A),intersection(A,complement(C))). [resolve(54,d,34,a),merge(d)].
% 169.88/170.15 817 member(f1(intersection(A,B),B),C) | intersection(A,B) = B | member(f1(intersection(A,B),B),intersection(complement(C),B)). [resolve(55,d,39,a),merge(d)].
% 169.88/170.15 947 complement(complement(A)) = A | -member(f1(A,complement(complement(A))),A). [resolve(603,a,14,a)].
% 169.88/170.15 948 complement(complement(A)) = A. [resolve(947,b,83,a),merge(b)].
% 169.88/170.15 1318 member(f1(A,intersection(intersection(B,C),D)),A) | intersection(intersection(B,C),D) = A | member(f1(A,intersection(intersection(B,C),D)),intersection(C,E)) | -member(f1(A,intersection(intersection(B,C),D)),E). [resolve(107,c,17,b)].
% 169.88/170.15 5658 member(f1(intersection(A,complement(B)),A),B) | intersection(A,complement(B)) = A. [resolve(713,c,188,b),merge(c)].
% 169.88/170.15 5682 member(f1(intersection(A,B),A),complement(B)) | intersection(A,B) = A. [para(948(a,1),5658(a,1,1,2)),rewrite([948(6)])].
% 169.88/170.15 5734 intersection(A,B) = A | member(f1(intersection(A,B),A),intersection(A,complement(B))). [resolve(5682,a,190,c),merge(b)].
% 169.88/170.15 8477 member(f1(intersection(complement(A),B),B),A) | intersection(complement(A),B) = B. [resolve(817,c,204,b),merge(c)].
% 169.88/170.15 10606 member(f1(intersection(A,B),B),complement(A)) | intersection(A,B) = B. [para(948(a,1),8477(a,1,1,1)),rewrite([948(6)])].
% 169.88/170.15 10636 intersection(A,B) = B | member(f1(intersection(A,B),B),intersection(B,complement(A))). [resolve(10606,a,206,c),merge(b)].
% 169.88/170.15 14001 intersection(intersection(A,B),C) = empty_set | member(f1(empty_set,intersection(intersection(A,B),C)),intersection(B,A)). [resolve(1318,d,261,b),merge(d),unit_del(a,11)].
% 169.88/170.15 92829 intersection(intersection(A,B),complement(intersection(B,A))) = empty_set. [resolve(14001,b,256,b),merge(b)].
% 169.88/170.15 92835 intersection(intersection(A,B),intersection(B,A)) = intersection(A,B). [para(92829(a,1),5734(b,2)),unit_del(b,11)].
% 169.88/170.15 92838 intersection(A,B) = intersection(B,A). [para(92829(a,1),10636(b,2)),rewrite([92835(3),92835(6)]),unit_del(b,11)].
% 169.88/170.15 93052 $F. [back_rewrite(13),rewrite([92838(5)]),xx(a)].
% 169.88/170.15
% 169.88/170.15 % SZS output end Refutation
% 169.88/170.15 ============================== end of proof ==========================
% 169.88/170.15
% 169.88/170.15 ============================== STATISTICS ============================
% 169.88/170.15
% 169.88/170.15 Given=4888. Generated=20032239. Kept=93044. proofs=1.
% 169.88/170.15 Usable=878. Sos=754. Demods=340. Limbo=214, Disabled=91217. Hints=0.
% 169.88/170.15 Megabytes=55.93.
% 169.88/170.15 User_CPU=158.73, System_CPU=10.42, Wall_clock=169.
% 169.88/170.15
% 169.88/170.15 ============================== end of statistics =====================
% 169.88/170.15
% 169.88/170.15 ============================== end of search =========================
% 169.88/170.15
% 169.88/170.15 THEOREM PROVED
% 169.88/170.15 % SZS status Unsatisfiable
% 169.88/170.15
% 169.88/170.15 Exiting with 1 proof.
% 169.88/170.15
% 169.88/170.15 Process 4981 exit (max_proofs) Sun Jul 10 22:51:01 2022
% 169.88/170.15 Prover9 interrupted
%------------------------------------------------------------------------------