TSTP Solution File: LCL132-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL132-1 : 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 : n001.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 06:48:05 EDT 2023
% Result : Unsatisfiable 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL132-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n001.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 : 300
% 0.13/0.34 % DateTime : Fri Aug 25 05:21:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % File :CSE---1.6
% 0.20/0.66 % Problem :theBenchmark
% 0.20/0.66 % Transform :cnf
% 0.20/0.66 % Format :tptp:raw
% 0.20/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.66
% 0.20/0.66 % Result :Theorem 0.050000s
% 0.20/0.66 % Output :CNFRefutation 0.050000s
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 % File : LCL132-1 : TPTP v8.1.2. Released v1.0.0.
% 0.20/0.66 % Domain : Logic Calculi (Wajsberg Algebra)
% 0.20/0.66 % Problem : A lemma in Wajsberg algebras
% 0.20/0.66 % Version : [Bon91] (equality) axioms.
% 0.20/0.66 % English :
% 0.20/0.66
% 0.20/0.66 % Refs : [FRT84] Font et al. (1984), Wajsberg Algebras
% 0.20/0.66 % : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic
% 0.20/0.66 % Source : [Bon91]
% 0.20/0.66 % Names : Lemma 1 [Bon91]
% 0.20/0.66
% 0.20/0.66 % Status : Unsatisfiable
% 0.20/0.66 % Rating : 0.00 v7.4.0, 0.09 v7.3.0, 0.05 v7.1.0, 0.06 v7.0.0, 0.05 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.06 v6.0.0, 0.14 v5.5.0, 0.11 v5.4.0, 0.00 v5.1.0, 0.07 v5.0.0, 0.00 v2.0.0
% 0.20/0.66 % Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 1 RR)
% 0.20/0.66 % Number of literals : 5 ( 5 equ; 1 neg)
% 0.20/0.66 % Maximal clause size : 1 ( 1 avg)
% 0.20/0.66 % Maximal term depth : 4 ( 2 avg)
% 0.20/0.66 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.20/0.66 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.20/0.66 % Number of variables : 8 ( 0 sgn)
% 0.20/0.66 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.20/0.66
% 0.20/0.66 % Comments :
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 %----Include Wajsberg algebra axioms
% 0.20/0.66 include('Axioms/LCL001-0.ax').
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 cnf(prove_wajsberg_lemma,negated_conjecture,
% 0.20/0.66 implies(x,x) != truth ).
% 0.20/0.66
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark
% 0.20/0.66 % SZS output start Proof
% 0.20/0.67 %ClaNum:11(EqnAxiom:6)
% 0.20/0.67 %VarNum:18(SingletonVarNum:8)
% 0.20/0.67 %MaxLitNum:1
% 0.20/0.67 %MaxfuncDepth:3
% 0.20/0.67 %SharedTerms:4
% 0.20/0.67 %goalClause: 11
% 0.20/0.67 %singleGoalClaCount:1
% 0.20/0.67 [11]~E(f2(a4,a4),a1)
% 0.20/0.67 [7]E(f2(a1,x71),x71)
% 0.20/0.67 [8]E(f2(f2(x81,x82),x82),f2(f2(x82,x81),x81))
% 0.20/0.67 [9]E(f2(f2(f3(x91),f3(x92)),f2(x92,x91)),a1)
% 0.20/0.67 [10]E(f2(f2(x101,x102),f2(f2(x102,x103),f2(x101,x103))),a1)
% 0.20/0.67 %EqnAxiom
% 0.20/0.67 [1]E(x11,x11)
% 0.20/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.67 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.67 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.67 [6]~E(x61,x62)+E(f3(x61),f3(x62))
% 0.20/0.67
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 cnf(12,plain,
% 0.20/0.67 (E(x121,f2(a1,x121))),
% 0.20/0.67 inference(scs_inference,[],[7,2])).
% 0.20/0.67 cnf(13,plain,
% 0.20/0.67 (~E(f2(a4,a4),f2(a1,a1))),
% 0.20/0.67 inference(scs_inference,[],[11,7,2,3])).
% 0.20/0.67 cnf(14,plain,
% 0.20/0.67 (E(f2(a1,x141),x141)),
% 0.20/0.67 inference(rename_variables,[],[7])).
% 0.20/0.67 cnf(15,plain,
% 0.20/0.67 (E(f3(f2(a1,x151)),f3(x151))),
% 0.20/0.67 inference(scs_inference,[],[11,7,14,2,3,6])).
% 0.20/0.67 cnf(16,plain,
% 0.20/0.67 (E(f2(x161,f2(a1,x162)),f2(x161,x162))),
% 0.20/0.67 inference(scs_inference,[],[11,7,14,2,3,6,5])).
% 0.20/0.67 cnf(17,plain,
% 0.20/0.67 (E(f2(f2(a1,x171),x172),f2(x171,x172))),
% 0.20/0.67 inference(scs_inference,[],[11,7,14,2,3,6,5,4])).
% 0.20/0.67 cnf(18,plain,
% 0.20/0.67 (~E(a1,f2(a4,a4))),
% 0.20/0.67 inference(scs_inference,[],[11,2])).
% 0.20/0.67 cnf(19,plain,
% 0.20/0.67 (~E(f2(a1,f2(a4,a4)),a1)),
% 0.20/0.67 inference(scs_inference,[],[11,12,2,3])).
% 0.20/0.67 cnf(21,plain,
% 0.20/0.67 (E(a1,f2(f2(f3(x211),f3(x212)),f2(x212,x211)))),
% 0.20/0.67 inference(scs_inference,[],[9,2])).
% 0.20/0.67 cnf(22,plain,
% 0.20/0.67 (E(f2(a1,f2(f2(x221,x222),x222)),f2(f2(x222,x221),x221))),
% 0.20/0.67 inference(scs_inference,[],[7,8,9,2,3])).
% 0.20/0.67 cnf(24,plain,
% 0.20/0.67 (~E(a1,f2(a1,f2(a4,a4)))),
% 0.20/0.67 inference(scs_inference,[],[19,2])).
% 0.20/0.67 cnf(25,plain,
% 0.20/0.67 (~E(f2(a1,f2(a4,a4)),f2(a1,a1))),
% 0.20/0.67 inference(scs_inference,[],[7,19,2,3])).
% 0.20/0.67 cnf(27,plain,
% 0.20/0.67 (E(a1,f2(f2(x271,x272),f2(f2(x272,x273),f2(x271,x273))))),
% 0.20/0.67 inference(scs_inference,[],[10,2])).
% 0.20/0.67 cnf(29,plain,
% 0.20/0.67 (E(x291,f2(a1,x291))),
% 0.20/0.67 inference(rename_variables,[],[12])).
% 0.20/0.67 cnf(30,plain,
% 0.20/0.67 (E(f2(x301,x302),f2(f2(a1,x301),x302))),
% 0.20/0.67 inference(scs_inference,[],[10,12,29,25,2,3,4])).
% 0.20/0.67 cnf(31,plain,
% 0.20/0.67 (E(f3(x311),f3(f2(a1,x311)))),
% 0.20/0.67 inference(scs_inference,[],[10,12,29,25,2,3,4,6])).
% 0.20/0.67 cnf(33,plain,
% 0.20/0.67 (~E(f2(a1,a1),f2(a4,a4))),
% 0.20/0.67 inference(scs_inference,[],[13,2])).
% 0.20/0.67 cnf(34,plain,
% 0.20/0.67 (E(f2(f2(f3(x341),f3(x342)),f2(x342,x341)),f2(a1,a1))),
% 0.20/0.67 inference(scs_inference,[],[13,9,12,2,3])).
% 0.20/0.67 cnf(37,plain,
% 0.20/0.67 (~E(f2(a1,f2(a4,a4)),f2(f2(f3(x371),f3(x372)),f2(x372,x371)))),
% 0.20/0.67 inference(scs_inference,[],[9,34,19,2,3])).
% 0.20/0.67 cnf(40,plain,
% 0.20/0.67 (~E(f2(f2(f3(x401),f3(x402)),f2(x402,x401)),f2(a1,f2(a4,a4)))),
% 0.20/0.67 inference(scs_inference,[],[9,37,4,2])).
% 0.20/0.67 cnf(41,plain,
% 0.20/0.67 (~E(f2(a1,f2(a1,a1)),f2(a4,a4))),
% 0.20/0.67 inference(scs_inference,[],[9,12,37,33,4,2,3])).
% 0.20/0.67 cnf(43,plain,
% 0.20/0.67 (~E(f2(f3(a4),f3(a4)),a1)),
% 0.20/0.67 inference(scs_inference,[],[40,4])).
% 0.20/0.67 cnf(48,plain,
% 0.20/0.67 (E(f2(x481,f2(x482,f2(a1,x483))),f2(x481,f2(x482,x483)))),
% 0.20/0.67 inference(scs_inference,[],[10,16,12,40,22,4,2,3,5])).
% 0.20/0.67 cnf(50,plain,
% 0.20/0.67 (E(f2(f3(f2(a1,x501)),x502),f2(f3(x501),x502))),
% 0.20/0.67 inference(scs_inference,[],[15,4])).
% 0.20/0.67 cnf(52,plain,
% 0.20/0.67 (~E(f2(f3(a4),f3(a4)),f2(f2(x521,x522),f2(f2(x522,x523),f2(x521,x523))))),
% 0.20/0.67 inference(scs_inference,[],[10,15,41,43,4,2,3])).
% 0.20/0.67 cnf(59,plain,
% 0.20/0.67 (E(f2(f2(f2(a1,x591),x592),x593),f2(f2(x591,x592),x593))),
% 0.20/0.67 inference(scs_inference,[],[17,4])).
% 0.20/0.67 cnf(62,plain,
% 0.20/0.67 (E(f2(f2(a1,x621),x622),f2(x621,x622))),
% 0.20/0.67 inference(rename_variables,[],[17])).
% 0.20/0.67 cnf(64,plain,
% 0.20/0.67 (E(f2(x641,f2(f2(a1,x642),x643)),f2(x641,f2(x642,x643)))),
% 0.20/0.67 inference(scs_inference,[],[13,17,62,48,4,2,3,6,5])).
% 0.20/0.67 cnf(66,plain,
% 0.20/0.67 (~E(f2(f2(a1,a4),a4),f2(a1,a1))),
% 0.20/0.67 inference(scs_inference,[],[13,30,52,2,3])).
% 0.20/0.67 cnf(68,plain,
% 0.20/0.67 (E(f2(f2(x681,x682),x683),f2(f2(f2(a1,x681),x682),x683))),
% 0.20/0.67 inference(scs_inference,[],[59,2])).
% 0.20/0.67 cnf(69,plain,
% 0.20/0.67 (E(f2(f2(a1,x691),f2(a1,x692)),f2(x691,x692))),
% 0.20/0.67 inference(scs_inference,[],[16,17,59,2,3])).
% 0.20/0.67 cnf(71,plain,
% 0.20/0.67 (~E(f2(a1,a1),f2(f2(a1,a4),a4))),
% 0.20/0.67 inference(scs_inference,[],[66,2])).
% 0.20/0.67 cnf(79,plain,
% 0.20/0.67 (E(f2(f2(x791,f2(a1,x792)),x793),f2(f2(x791,x792),x793))),
% 0.20/0.67 inference(scs_inference,[],[16,21,18,64,2,3,5,6,4])).
% 0.20/0.67 cnf(85,plain,
% 0.20/0.67 (~E(a1,f2(f2(a1,a4),a4))),
% 0.20/0.67 inference(scs_inference,[],[17,18,79,2,3])).
% 0.20/0.67 cnf(93,plain,
% 0.20/0.67 (E(f2(x931,f3(x932)),f2(x931,f3(f2(a1,x932))))),
% 0.20/0.67 inference(scs_inference,[],[21,68,50,31,2,3,5])).
% 0.20/0.67 cnf(99,plain,
% 0.20/0.67 (~E(a1,f2(f2(a4,a1),a1))),
% 0.20/0.67 inference(scs_inference,[],[22,71,85,2,3,5])).
% 0.20/0.67 cnf(100,plain,
% 0.20/0.67 (E(f2(x1001,f2(f2(a1,x1002),f2(a1,x1003))),f2(x1001,f2(x1002,x1003)))),
% 0.20/0.67 inference(scs_inference,[],[69,5])).
% 0.20/0.67 cnf(110,plain,
% 0.20/0.67 (E(f3(f3(x1101)),f3(f3(f2(a1,x1101))))),
% 0.20/0.67 inference(scs_inference,[],[22,93,99,31,2,3,6])).
% 0.20/0.67 cnf(111,plain,
% 0.20/0.67 (E(f2(f2(f2(a1,x1111),f2(a1,x1112)),x1113),f2(f2(x1111,x1112),x1113))),
% 0.20/0.67 inference(scs_inference,[],[22,93,99,31,69,2,3,6,4])).
% 0.20/0.67 cnf(117,plain,
% 0.20/0.67 (E(f2(x1171,f2(x1172,x1173)),f2(x1171,f2(f2(a1,x1172),f2(a1,x1173))))),
% 0.20/0.67 inference(scs_inference,[],[100,9,5,2])).
% 0.20/0.67 cnf(126,plain,
% 0.20/0.67 (~E(f2(f2(x1261,x1262),f2(f2(x1262,x1263),f2(x1261,x1263))),f2(a1,f2(a4,a4)))),
% 0.20/0.67 inference(scs_inference,[],[24,27,111,2,3])).
% 0.20/0.67 cnf(129,plain,
% 0.20/0.67 (~E(f2(a1,f2(a4,a4)),f2(f2(x1291,x1292),f2(f2(x1292,x1293),f2(x1291,x1293))))),
% 0.20/0.67 inference(scs_inference,[],[126,2])).
% 0.20/0.67 cnf(134,plain,
% 0.20/0.67 ($false),
% 0.20/0.67 inference(scs_inference,[],[30,129,117,110,2,3]),
% 0.20/0.67 ['proof']).
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time :0.050000s
%------------------------------------------------------------------------------