TSTP Solution File: ROB002-1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ROB002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n008.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 : 300s
% DateTime : Thu Aug 31 14:07:06 EDT 2023
% Result : Unsatisfiable 61.22s 61.40s
% Output : CNFRefutation 61.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ROB002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 07:01:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 61.22/61.39 %-------------------------------------------
% 61.22/61.39 % File :CSE---1.6
% 61.22/61.39 % Problem :theBenchmark
% 61.22/61.39 % Transform :cnf
% 61.22/61.39 % Format :tptp:raw
% 61.22/61.39 % Command :java -jar mcs_scs.jar %d %s
% 61.22/61.39
% 61.22/61.39 % Result :Theorem 60.750000s
% 61.22/61.39 % Output :CNFRefutation 60.750000s
% 61.22/61.39 %-------------------------------------------
% 61.22/61.40 %--------------------------------------------------------------------------
% 61.22/61.40 % File : ROB002-1 : TPTP v8.1.2. Released v1.0.0.
% 61.22/61.40 % Domain : Robbins Algebra
% 61.22/61.40 % Problem : --X = X => Boolean
% 61.22/61.40 % Version : [Win90] (equality) axioms.
% 61.22/61.40 % English : If --X = X then the algebra is Boolean.
% 61.22/61.40
% 61.22/61.40 % Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras
% 61.22/61.40 % : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% 61.22/61.40 % Source : [Win90]
% 61.22/61.40 % Names : Lemma 2.1 [Win90]
% 61.22/61.40
% 61.22/61.40 % Status : Unsatisfiable
% 61.22/61.40 % Rating : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 v6.1.0, 0.06 v6.0.0, 0.24 v5.5.0, 0.21 v5.4.0, 0.07 v5.3.0, 0.00 v5.2.0, 0.07 v5.1.0, 0.13 v5.0.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0
% 61.22/61.40 % Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 1 RR)
% 61.22/61.40 % Number of literals : 5 ( 5 equ; 1 neg)
% 61.22/61.40 % Maximal clause size : 1 ( 1 avg)
% 61.22/61.40 % Maximal term depth : 6 ( 2 avg)
% 61.22/61.40 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 61.22/61.40 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 61.22/61.40 % Number of variables : 8 ( 0 sgn)
% 61.22/61.40 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 61.22/61.40
% 61.22/61.40 % Comments : Commutativity, associativity, and Huntington's axiom
% 61.22/61.40 % axiomatize Boolean algebra.
% 61.22/61.40 %--------------------------------------------------------------------------
% 61.22/61.40 %----Include axioms for Robbins algebra
% 61.22/61.40 include('Axioms/ROB001-0.ax').
% 61.22/61.40 %--------------------------------------------------------------------------
% 61.22/61.40 cnf(double_negation,hypothesis,
% 61.22/61.40 negate(negate(X)) = X ).
% 61.22/61.40
% 61.22/61.40 cnf(prove_huntingtons_axiom,negated_conjecture,
% 61.22/61.40 add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ).
% 61.22/61.40
% 61.22/61.40 %--------------------------------------------------------------------------
% 61.22/61.40 %-------------------------------------------
% 61.22/61.40 % Proof found
% 61.22/61.40 % SZS status Theorem for theBenchmark
% 61.22/61.40 % SZS output start Proof
% 61.22/61.41 %ClaNum:11(EqnAxiom:6)
% 61.22/61.41 %VarNum:17(SingletonVarNum:8)
% 61.22/61.41 %MaxLitNum:1
% 61.22/61.41 %MaxfuncDepth:5
% 61.22/61.41 %SharedTerms:10
% 61.22/61.41 %goalClause: 11
% 61.22/61.41 %singleGoalClaCount:1
% 61.22/61.41 [11]~E(f2(f1(f2(a3,f1(a4))),f1(f2(f1(a3),f1(a4)))),a4)
% 61.22/61.41 [7]E(f1(f1(x71)),x71)
% 61.22/61.41 [8]E(f2(x81,x82),f2(x82,x81))
% 61.22/61.41 [10]E(f1(f2(f1(f2(x101,x102)),f1(f2(x101,f1(x102))))),x101)
% 61.22/61.41 [9]E(f2(f2(x91,x92),x93),f2(x91,f2(x92,x93)))
% 61.22/61.41 %EqnAxiom
% 61.22/61.41 [1]E(x11,x11)
% 61.22/61.41 [2]E(x22,x21)+~E(x21,x22)
% 61.22/61.41 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 61.22/61.41 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 61.22/61.41 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 61.22/61.41 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 61.22/61.41
% 61.22/61.41 %-------------------------------------------
% 61.22/61.42 cnf(12,plain,
% 61.22/61.42 (E(x121,f1(f1(x121)))),
% 61.22/61.42 inference(scs_inference,[],[7,2])).
% 61.22/61.42 cnf(13,plain,
% 61.22/61.42 (~E(f2(f1(f2(a3,f1(a4))),f1(f2(f1(a3),f1(a4)))),f1(f1(a4)))),
% 61.22/61.42 inference(scs_inference,[],[11,7,2,3])).
% 61.22/61.42 cnf(15,plain,
% 61.22/61.42 (E(f2(x151,f2(x152,x153)),f2(x151,f2(x153,x152)))),
% 61.22/61.42 inference(scs_inference,[],[11,8,7,2,3,6])).
% 61.22/61.42 cnf(16,plain,
% 61.22/61.42 (E(f2(f2(x161,x162),x163),f2(f2(x162,x161),x163))),
% 61.22/61.42 inference(scs_inference,[],[11,8,7,2,3,6,5])).
% 61.22/61.42 cnf(17,plain,
% 61.22/61.42 (E(f1(f2(x171,x172)),f1(f2(x172,x171)))),
% 61.22/61.42 inference(scs_inference,[],[11,8,7,2,3,6,5,4])).
% 61.22/61.42 cnf(18,plain,
% 61.22/61.42 (~E(f2(f1(f2(f1(a3),f1(a4))),f1(f2(a3,f1(a4)))),a4)),
% 61.22/61.42 inference(scs_inference,[],[11,8,3])).
% 61.22/61.42 cnf(20,plain,
% 61.22/61.42 (~E(a4,f2(f1(f2(a3,f1(a4))),f1(f2(f1(a3),f1(a4)))))),
% 61.22/61.42 inference(scs_inference,[],[11,8,3,2])).
% 61.22/61.42 cnf(21,plain,
% 61.22/61.42 (E(f2(f2(x211,x212),x213),f1(f1(f2(x211,f2(x212,x213)))))),
% 61.22/61.42 inference(scs_inference,[],[12,9,3])).
% 61.22/61.42 cnf(23,plain,
% 61.22/61.42 (E(f2(x231,f2(x232,x233)),f2(f2(x231,x232),x233))),
% 61.22/61.42 inference(scs_inference,[],[12,9,3,2])).
% 61.22/61.42 cnf(24,plain,
% 61.22/61.42 (E(f1(f1(f2(f2(x241,x242),x243))),f2(x241,f2(x242,x243)))),
% 61.22/61.42 inference(scs_inference,[],[7,9,3])).
% 61.22/61.42 cnf(26,plain,
% 61.22/61.42 (~E(f1(f1(a4)),f2(f1(f2(a3,f1(a4))),f1(f2(f1(a3),f1(a4)))))),
% 61.22/61.42 inference(scs_inference,[],[7,9,13,3,2])).
% 61.22/61.42 cnf(27,plain,
% 61.22/61.42 (~E(f2(f1(f2(f1(a3),f1(a4))),f1(f2(a3,f1(a4)))),f1(f1(a4)))),
% 61.22/61.42 inference(scs_inference,[],[8,13,3])).
% 61.22/61.42 cnf(29,plain,
% 61.22/61.42 (E(x291,f1(f2(f1(f2(x291,x292)),f1(f2(x291,f1(x292))))))),
% 61.22/61.42 inference(scs_inference,[],[8,10,13,3,2])).
% 61.22/61.43 cnf(30,plain,
% 61.22/61.43 (E(f2(x301,x302),f2(f1(f1(x301)),x302))),
% 61.22/61.43 inference(scs_inference,[],[8,10,12,13,3,2,5])).
% 61.22/61.43 cnf(31,plain,
% 61.22/61.43 (E(f2(x311,x312),f2(x311,f1(f1(x312))))),
% 61.22/61.43 inference(scs_inference,[],[8,10,12,13,3,2,5,6])).
% 61.22/61.43 cnf(32,plain,
% 61.22/61.43 (E(f1(f2(f2(x321,x322),x323)),f1(f2(x321,f2(x322,x323))))),
% 61.22/61.43 inference(scs_inference,[],[8,10,12,13,9,3,2,5,6,4])).
% 61.22/61.43 cnf(33,plain,
% 61.22/61.43 (E(f2(f2(x331,x332),x333),f2(f2(x332,x333),x331))),
% 61.22/61.43 inference(scs_inference,[],[8,9,3])).
% 61.22/61.43 cnf(36,plain,
% 61.22/61.43 (~E(f1(f1(a4)),f2(f1(f2(f1(a3),f1(a4))),f1(f2(a3,f1(a4)))))),
% 61.22/61.43 inference(scs_inference,[],[8,9,27,3,2])).
% 61.22/61.43 cnf(37,plain,
% 61.22/61.43 (E(f2(f2(x371,x372),f2(x373,x374)),f2(x371,f2(x372,f2(x374,x373))))),
% 61.22/61.43 inference(scs_inference,[],[9,15,3])).
% 61.22/61.43 cnf(42,plain,
% 61.22/61.43 (E(f2(f2(x421,x422),x423),f2(x421,f2(x423,x422)))),
% 61.22/61.43 inference(scs_inference,[],[9,15,18,2,3])).
% 61.22/61.43 cnf(50,plain,
% 61.22/61.43 (E(f2(x501,f1(f2(x502,x503))),f2(x501,f1(f2(x503,x502))))),
% 61.22/61.43 inference(scs_inference,[],[17,6])).
% 61.22/61.43 cnf(51,plain,
% 61.22/61.43 (E(f2(f1(f2(x511,x512)),x513),f2(f1(f2(x512,x511)),x513))),
% 61.22/61.43 inference(scs_inference,[],[17,6,5])).
% 61.22/61.43 cnf(52,plain,
% 61.22/61.43 (E(f1(f1(f2(x521,x522))),f1(f1(f2(x522,x521))))),
% 61.22/61.43 inference(scs_inference,[],[17,6,5,4])).
% 61.22/61.43 cnf(56,plain,
% 61.22/61.43 (E(f2(f1(f1(x561)),x562),f2(x561,x562))),
% 61.22/61.43 inference(scs_inference,[],[17,30,32,6,5,4,3,2])).
% 61.22/61.43 cnf(57,plain,
% 61.22/61.43 (~E(a4,f2(f1(f2(a3,f1(a4))),f1(f2(f1(a4),f1(a3)))))),
% 61.22/61.43 inference(scs_inference,[],[20,50,3])).
% 61.22/61.43 cnf(59,plain,
% 61.22/61.43 (~E(f2(f1(f2(a3,f1(a4))),f1(f2(f1(a4),f1(a3)))),a4)),
% 61.22/61.43 inference(scs_inference,[],[57,2])).
% 61.22/61.43 cnf(62,plain,
% 61.22/61.43 (E(f2(f2(x621,x622),x623),f2(f2(x623,x621),x622))),
% 61.22/61.43 inference(scs_inference,[],[33,2])).
% 61.22/61.43 cnf(63,plain,
% 61.22/61.43 (E(f2(f2(f2(x631,x632),x633),f2(x634,x635)),f2(f2(x632,x631),f2(x633,f2(x635,x634))))),
% 61.22/61.43 inference(scs_inference,[],[16,33,37,2,3])).
% 61.22/61.43 cnf(66,plain,
% 61.22/61.43 (~E(a4,f2(f1(f2(f1(a4),a3)),f1(f2(f1(a3),f1(a4)))))),
% 61.22/61.43 inference(scs_inference,[],[20,51,3])).
% 61.22/61.43 cnf(68,plain,
% 61.22/61.43 (E(f2(x681,f2(f2(x682,x683),x684)),f2(x681,f2(x682,f2(x684,x683))))),
% 61.22/61.43 inference(scs_inference,[],[20,42,51,3,6])).
% 61.22/61.43 cnf(78,plain,
% 61.22/61.43 (~E(f1(f1(a4)),f2(f1(f2(a3,f1(a4))),f1(f2(f1(a4),f1(a3)))))),
% 61.22/61.43 inference(scs_inference,[],[26,50,3])).
% 61.22/61.43 cnf(85,plain,
% 61.22/61.43 (E(f2(f2(x851,f2(x852,x853)),x854),f2(f2(f2(x851,x852),x853),x854))),
% 61.22/61.43 inference(scs_inference,[],[24,21,23,78,2,3,6,5])).
% 61.22/61.43 cnf(93,plain,
% 61.22/61.43 (E(f2(f2(x931,x932),f2(x933,f2(x934,x935))),f2(f2(f2(x932,x931),x933),f2(x935,x934)))),
% 61.22/61.43 inference(scs_inference,[],[26,63,51,3,2])).
% 61.22/61.43 cnf(98,plain,
% 61.22/61.43 (E(f2(f2(x981,f2(x982,x983)),x984),f1(f1(f2(f2(x981,x982),f2(x983,x984)))))),
% 61.22/61.43 inference(scs_inference,[],[21,68,85,2,3])).
% 61.22/61.43 cnf(110,plain,
% 61.22/61.43 (~E(f2(f1(f2(f1(a3),f1(a4))),f1(f2(f1(a4),a3))),f1(f1(a4)))),
% 61.22/61.43 inference(scs_inference,[],[27,50,3])).
% 61.22/61.43 cnf(159,plain,
% 61.22/61.43 (~E(f2(f1(f2(f1(a4),a3)),f1(f2(f1(a4),f1(a3)))),a4)),
% 61.22/61.43 inference(scs_inference,[],[51,98,59,2,3])).
% 61.22/61.43 cnf(160,plain,
% 61.22/61.43 (E(f2(f1(f2(x1601,x1602)),x1603),f2(f1(f2(x1602,x1601)),x1603))),
% 61.22/61.43 inference(rename_variables,[],[51])).
% 61.22/61.43 cnf(163,plain,
% 61.22/61.43 (E(f1(f2(f1(f2(x1631,x1632)),x1633)),f1(f2(f1(f2(x1632,x1631)),x1633)))),
% 61.22/61.43 inference(scs_inference,[],[51,160,98,59,2,3,6,5,4])).
% 61.22/61.43 cnf(165,plain,
% 61.22/61.43 (~E(f1(f1(a4)),f2(f1(f2(f1(a4),f1(a3))),f1(f2(a3,f1(a4)))))),
% 61.22/61.43 inference(scs_inference,[],[51,36,159,2,3])).
% 61.22/61.43 cnf(188,plain,
% 61.22/61.43 (~E(f1(f1(a4)),f2(f1(f2(f1(a4),f1(a3))),f1(f2(f1(a4),a3))))),
% 61.22/61.43 inference(scs_inference,[],[50,165,3])).
% 61.22/61.43 cnf(191,plain,
% 61.22/61.43 (E(f2(f1(f1(f2(x1911,x1912))),f2(x1913,f2(x1914,x1915))),f2(f2(f2(x1912,x1911),x1913),f2(x1915,x1914)))),
% 61.22/61.43 inference(scs_inference,[],[56,93,188,2,3])).
% 61.22/61.43 cnf(193,plain,
% 61.22/61.43 (E(f2(x1931,f2(f2(x1932,x1933),x1934)),f2(x1931,f2(f2(x1934,x1932),x1933)))),
% 61.22/61.43 inference(scs_inference,[],[56,62,93,188,2,3,6])).
% 61.22/61.43 cnf(504,plain,
% 61.22/61.43 (E(f2(f2(x5041,f2(x5042,x5043)),x5044),f2(f2(x5041,f2(x5043,x5042)),x5044))),
% 61.22/61.43 inference(scs_inference,[],[15,6,5])).
% 61.22/61.43 cnf(516,plain,
% 61.22/61.43 (E(f2(f1(f1(f2(x5161,x5162))),f2(x5163,f2(x5164,x5165))),f2(f2(f2(x5162,x5161),x5163),f2(x5165,x5164)))),
% 61.22/61.43 inference(rename_variables,[],[191])).
% 61.22/61.43 cnf(518,plain,
% 61.22/61.43 (E(f2(f2(f2(x5181,x5182),x5183),f2(x5184,x5185)),f2(f1(f1(f2(x5182,x5181))),f2(x5183,f2(x5185,x5184))))),
% 61.22/61.43 inference(scs_inference,[],[191,516,193,3,2])).
% 61.22/61.43 cnf(519,plain,
% 61.22/61.43 (E(f2(x5191,f2(f2(x5192,f2(x5193,x5194)),x5195)),f2(x5191,f2(f2(x5192,f2(x5194,x5193)),x5195)))),
% 61.22/61.43 inference(scs_inference,[],[504,6])).
% 61.22/61.43 cnf(538,plain,
% 61.22/61.43 (E(f1(f2(x5381,f1(f2(x5382,x5383)))),f1(f2(x5381,f1(f2(x5383,x5382)))))),
% 61.22/61.43 inference(scs_inference,[],[31,50,5,6,4])).
% 61.22/61.43 cnf(1020,plain,
% 61.22/61.43 (~E(f1(f2(f1(f2(a4,x10201)),f1(f2(a4,f1(x10201))))),f2(f1(f2(f1(a4),a3)),f1(f2(f1(a3),f1(a4)))))),
% 61.22/61.43 inference(scs_inference,[],[66,29,3])).
% 61.22/61.43 cnf(1033,plain,
% 61.22/61.43 (~E(f1(f1(f2(f1(f2(f1(a3),f1(a4))),f1(f2(f1(a4),a3))))),f1(f1(a4)))),
% 61.22/61.43 inference(scs_inference,[],[110,12,3])).
% 61.22/61.43 cnf(1096,plain,
% 61.22/61.43 (~E(f1(f1(f2(f1(f2(f1(a4),a3)),f1(f2(f1(a3),f1(a4)))))),f1(f1(a4)))),
% 61.22/61.43 inference(scs_inference,[],[1033,52,3])).
% 61.22/61.43 cnf(1105,plain,
% 61.22/61.43 (~E(f1(f1(a4)),f1(f1(f2(f1(f2(f1(a4),a3)),f1(f2(f1(a3),f1(a4)))))))),
% 61.22/61.43 inference(scs_inference,[],[519,518,1096,3,4,2])).
% 61.22/61.43 cnf(1114,plain,
% 61.22/61.43 (~E(f1(a4),f1(f2(f1(f2(f1(a4),a3)),f1(f2(f1(a3),f1(a4))))))),
% 61.22/61.43 inference(scs_inference,[],[163,1020,1105,3,4])).
% 61.22/61.43 cnf(1127,plain,
% 61.22/61.43 ($false),
% 61.22/61.43 inference(scs_inference,[],[1114,538,29,3]),
% 61.22/61.43 ['proof']).
% 61.22/61.43 % SZS output end Proof
% 61.22/61.43 % Total time :60.750000s
%------------------------------------------------------------------------------