TSTP Solution File: LCL109-5 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL109-5 : 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 06:48:00 EDT 2023
% Result : Unsatisfiable 0.20s 0.71s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL109-5 : 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 : Thu Aug 24 16:53:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.70 %-------------------------------------------
% 0.20/0.70 % File :CSE---1.6
% 0.20/0.70 % Problem :theBenchmark
% 0.20/0.70 % Transform :cnf
% 0.20/0.70 % Format :tptp:raw
% 0.20/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.70
% 0.20/0.70 % Result :Theorem 0.070000s
% 0.20/0.70 % Output :CNFRefutation 0.070000s
% 0.20/0.70 %-------------------------------------------
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 % File : LCL109-5 : TPTP v8.1.2. Released v1.0.0.
% 0.20/0.71 % Domain : Logic Calculi (Wajsberg Algebra)
% 0.20/0.71 % Problem : A theorem in the lattice structure of Wajsberg algebras
% 0.20/0.71 % Version : [Bon91] (equality) axioms : Augmented.
% 0.20/0.71 % Theorem formulation : Wajsberg algebras lattice structure.
% 0.20/0.71 % English :
% 0.20/0.71
% 0.20/0.71 % Refs : [FRT84] Font et al. (1984), Wajsberg Algebras
% 0.20/0.71 % : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic
% 0.20/0.71 % Source : [Bon91]
% 0.20/0.71 % Names : Lattice structure theorem 8 [Bon91]
% 0.20/0.71
% 0.20/0.71 % Status : Unsatisfiable
% 0.20/0.71 % Rating : 0.00 v6.0.0, 0.11 v5.5.0, 0.19 v5.4.0, 0.20 v5.3.0, 0.25 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.29 v4.1.0, 0.11 v4.0.1, 0.17 v3.7.0, 0.00 v3.3.0, 0.14 v3.2.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.29 v2.5.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.60 v2.0.0
% 0.20/0.71 % Syntax : Number of clauses : 17 ( 11 unt; 0 nHn; 5 RR)
% 0.20/0.71 % Number of literals : 23 ( 13 equ; 7 neg)
% 0.20/0.71 % Maximal clause size : 2 ( 1 avg)
% 0.20/0.71 % Maximal term depth : 4 ( 2 avg)
% 0.20/0.71 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.20/0.71 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.20/0.71 % Number of variables : 38 ( 0 sgn)
% 0.20/0.71 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.20/0.71
% 0.20/0.71 % Comments :
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 %----Include Wajsberg algebra axioms
% 0.20/0.71 include('Axioms/LCL001-0.ax').
% 0.20/0.71 %----Include Wajsberg algebra lattice structure axioms
% 0.20/0.71 include('Axioms/LCL001-1.ax').
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 %----Lemmas in Wajsberg algebra lattice structures.
% 0.20/0.71 cnf(lemma_1,axiom,
% 0.20/0.71 ( ~ ordered(X,Y)
% 0.20/0.71 | ordered(implies(X,Z),implies(Y,Z)) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(lemma_2,axiom,
% 0.20/0.71 ( ~ ordered(X,Y)
% 0.20/0.71 | ordered(implies(Z,X),implies(Z,Y)) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(lemma_3_1,axiom,
% 0.20/0.71 ( ~ ordered(X,implies(Y,Z))
% 0.20/0.71 | ordered(Y,implies(X,Z)) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(lemma_3_2,axiom,
% 0.20/0.71 ( ~ ordered(Y,implies(X,Z))
% 0.20/0.71 | ordered(X,implies(Y,Z)) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(lemma_4,axiom,
% 0.20/0.71 not(big_V(X,Y)) = big_hat(not(X),not(Y)) ).
% 0.20/0.71
% 0.20/0.71 cnf(lemma_5,axiom,
% 0.20/0.71 not(big_hat(X,Y)) = big_V(not(X),not(Y)) ).
% 0.20/0.71
% 0.20/0.71 cnf(lemma_6,axiom,
% 0.20/0.71 implies(big_V(X,Y),Z) = big_hat(implies(X,Z),implies(Y,Z)) ).
% 0.20/0.71
% 0.20/0.71 cnf(lemma_7,axiom,
% 0.20/0.71 implies(X,big_hat(Y,Z)) = big_hat(implies(X,Y),implies(X,Z)) ).
% 0.20/0.71
% 0.20/0.71 cnf(prove_mv_4,negated_conjecture,
% 0.20/0.71 big_V(implies(x,y),implies(y,x)) != truth ).
% 0.20/0.71
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 %-------------------------------------------
% 0.20/0.71 % Proof found
% 0.20/0.71 % SZS status Theorem for theBenchmark
% 0.20/0.71 % SZS output start Proof
% 0.20/0.71 %ClaNum:23(EqnAxiom:8)
% 0.20/0.71 %VarNum:76(SingletonVarNum:31)
% 0.20/0.71 %MaxLitNum:2
% 0.20/0.71 %MaxfuncDepth:4
% 0.20/0.71 %SharedTerms:8
% 0.20/0.71 %goalClause: 17
% 0.20/0.71 %singleGoalClaCount:1
% 0.20/0.71 [17]~E(f2(f2(f2(a4,a5),f2(a5,a4)),f2(a5,a4)),a1)
% 0.20/0.71 [9]E(f2(a1,x91),x91)
% 0.20/0.71 [10]E(f2(f2(x101,x102),x102),f2(f2(x102,x101),x101))
% 0.20/0.71 [11]E(f2(f2(f3(x111),f3(x112)),f2(x112,x111)),a1)
% 0.20/0.71 [13]E(f3(f2(f2(f3(f3(x131)),f3(f3(x132))),f3(f3(x132)))),f3(f2(f2(x131,x132),x132)))
% 0.20/0.71 [14]E(f3(f3(f2(f2(f3(x141),f3(x142)),f3(x142)))),f2(f2(f3(x141),f3(x142)),f3(x142)))
% 0.20/0.71 [12]E(f2(f2(x121,x122),f2(f2(x122,x123),f2(x121,x123))),a1)
% 0.20/0.71 [15]E(f3(f2(f2(f3(f2(x151,x152)),f3(f2(x153,x152))),f3(f2(x153,x152)))),f2(f2(f2(x151,x153),x153),x152))
% 0.20/0.71 [16]E(f3(f2(f2(f3(f2(x161,x162)),f3(f2(x161,x163))),f3(f2(x161,x163)))),f2(x161,f3(f2(f2(f3(x162),f3(x163)),f3(x163)))))
% 0.20/0.71 [18]~P1(x181,x182)+E(f2(x181,x182),a1)
% 0.20/0.71 [19]P1(x191,x192)+~E(f2(x191,x192),a1)
% 0.20/0.71 [20]~P1(x202,x203)+P1(f2(x201,x202),f2(x201,x203))
% 0.20/0.71 [21]~P1(x211,x213)+P1(f2(x211,x212),f2(x213,x212))
% 0.20/0.71 [23]~P1(x232,f2(x231,x233))+P1(x231,f2(x232,x233))
% 0.20/0.71 %EqnAxiom
% 0.20/0.71 [1]E(x11,x11)
% 0.20/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.71 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.71 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.71 [6]~E(x61,x62)+E(f3(x61),f3(x62))
% 0.20/0.71 [7]P1(x72,x73)+~E(x71,x72)+~P1(x71,x73)
% 0.20/0.71 [8]P1(x83,x82)+~E(x81,x82)+~P1(x83,x81)
% 0.20/0.71
% 0.20/0.71 %-------------------------------------------
% 0.20/0.72 cnf(24,plain,
% 0.20/0.72 (E(x241,f2(a1,x241))),
% 0.20/0.72 inference(scs_inference,[],[9,2])).
% 0.20/0.72 cnf(25,plain,
% 0.20/0.72 (P1(a1,a1)),
% 0.20/0.72 inference(scs_inference,[],[9,2,19])).
% 0.20/0.72 cnf(26,plain,
% 0.20/0.72 (E(f2(a1,x261),x261)),
% 0.20/0.72 inference(rename_variables,[],[9])).
% 0.20/0.72 cnf(28,plain,
% 0.20/0.72 (~P1(f2(f2(a4,a5),f2(a5,a4)),f2(a5,a4))),
% 0.20/0.72 inference(scs_inference,[],[17,9,2,19,18])).
% 0.20/0.72 cnf(30,plain,
% 0.20/0.72 (~P1(a5,f2(f2(f2(a4,a5),f2(a5,a4)),a4))),
% 0.20/0.72 inference(scs_inference,[],[17,9,2,19,18,23])).
% 0.20/0.72 cnf(32,plain,
% 0.20/0.72 (P1(a1,f2(a1,a1))),
% 0.20/0.72 inference(scs_inference,[],[17,9,2,19,18,23,8])).
% 0.20/0.72 cnf(34,plain,
% 0.20/0.72 (~E(f2(f2(f2(a4,a5),f2(a5,a4)),f2(a5,a4)),f2(a1,a1))),
% 0.20/0.72 inference(scs_inference,[],[17,9,26,2,19,18,23,8,7,3])).
% 0.20/0.72 cnf(35,plain,
% 0.20/0.72 (E(f2(a1,x351),x351)),
% 0.20/0.72 inference(rename_variables,[],[9])).
% 0.20/0.72 cnf(37,plain,
% 0.20/0.72 (E(f2(x371,f2(a1,x372)),f2(x371,x372))),
% 0.20/0.72 inference(scs_inference,[],[17,9,26,35,2,19,18,23,8,7,3,6,5])).
% 0.20/0.72 cnf(38,plain,
% 0.20/0.72 (E(f2(f2(a1,x381),x382),f2(x381,x382))),
% 0.20/0.72 inference(scs_inference,[],[17,9,26,35,2,19,18,23,8,7,3,6,5,4])).
% 0.20/0.72 cnf(39,plain,
% 0.20/0.72 (P1(f2(a1,x391),f2(a1,x391))),
% 0.20/0.72 inference(scs_inference,[],[17,9,26,35,2,19,18,23,8,7,3,6,5,4,21])).
% 0.20/0.72 cnf(41,plain,
% 0.20/0.72 (P1(f2(x411,a1),f2(x411,a1))),
% 0.20/0.72 inference(scs_inference,[],[17,9,26,35,2,19,18,23,8,7,3,6,5,4,21,20])).
% 0.20/0.72 cnf(49,plain,
% 0.20/0.72 (~P1(f2(f2(a4,a5),f2(a5,a4)),f2(a1,f2(a5,a4)))),
% 0.20/0.72 inference(scs_inference,[],[9,39,28,30,18,19,23,8])).
% 0.20/0.72 cnf(50,plain,
% 0.20/0.72 (E(f2(a1,x501),x501)),
% 0.20/0.72 inference(rename_variables,[],[9])).
% 0.20/0.72 cnf(52,plain,
% 0.20/0.72 (~P1(f2(a1,f2(f2(a4,a5),f2(a5,a4))),f2(a5,a4))),
% 0.20/0.72 inference(scs_inference,[],[17,9,50,39,28,30,18,19,23,8,2,7])).
% 0.20/0.72 cnf(54,plain,
% 0.20/0.72 (~E(f2(f2(f2(a5,a4),f2(a4,a5)),f2(a4,a5)),a1)),
% 0.20/0.72 inference(scs_inference,[],[17,10,9,50,39,28,30,18,19,23,8,2,7,3])).
% 0.20/0.72 cnf(56,plain,
% 0.20/0.72 (~P1(f2(a4,a5),a1)),
% 0.20/0.72 inference(scs_inference,[],[17,10,9,50,39,28,30,18,19,23,8,2,7,3,21])).
% 0.20/0.72 cnf(58,plain,
% 0.20/0.72 (~P1(f2(f2(a5,a4),f2(a4,a5)),f2(a4,a5))),
% 0.20/0.72 inference(scs_inference,[],[54,18])).
% 0.20/0.72 cnf(60,plain,
% 0.20/0.72 (~P1(a1,f2(f2(f2(a4,a5),f2(a5,a4)),f2(a5,a4)))),
% 0.20/0.72 inference(scs_inference,[],[49,54,18,23])).
% 0.20/0.72 cnf(62,plain,
% 0.20/0.72 (P1(f2(f2(x621,a1),x622),f2(f2(x621,a1),x622))),
% 0.20/0.72 inference(scs_inference,[],[41,49,54,18,23,21])).
% 0.20/0.72 cnf(64,plain,
% 0.20/0.72 (P1(f2(f3(x641),f3(x642)),f2(x642,x641))),
% 0.20/0.72 inference(scs_inference,[],[11,41,49,54,18,23,21,19])).
% 0.20/0.72 cnf(75,plain,
% 0.20/0.72 (P1(x751,f2(f2(f3(x752),f3(x751)),x752))),
% 0.20/0.72 inference(scs_inference,[],[64,62,18,23])).
% 0.20/0.72 cnf(79,plain,
% 0.20/0.72 (~E(f2(a1,a1),f2(f2(f2(a4,a5),f2(a5,a4)),f2(a5,a4)))),
% 0.20/0.72 inference(scs_inference,[],[64,62,34,52,18,23,19,2])).
% 0.20/0.72 cnf(80,plain,
% 0.20/0.72 (P1(f2(f3(x801),f3(a1)),x801)),
% 0.20/0.72 inference(scs_inference,[],[9,64,62,34,52,18,23,19,2,8])).
% 0.20/0.72 cnf(81,plain,
% 0.20/0.72 (P1(f2(f3(x811),f3(x812)),f2(x812,x811))),
% 0.20/0.72 inference(rename_variables,[],[64])).
% 0.20/0.72 cnf(84,plain,
% 0.20/0.72 (~E(f2(f3(a4),f3(a5)),f2(a1,f2(f2(a4,a5),f2(a5,a4))))),
% 0.20/0.72 inference(scs_inference,[],[9,64,81,62,34,52,18,23,19,2,8,3,7])).
% 0.20/0.72 cnf(88,plain,
% 0.20/0.72 (P1(f2(x881,x882),f2(f2(x882,x883),f2(x881,x883)))),
% 0.20/0.72 inference(scs_inference,[],[12,58,23,19])).
% 0.20/0.72 cnf(90,plain,
% 0.20/0.72 (~P1(f2(a4,a5),f2(f2(x901,x902),f2(f2(x902,x903),f2(x901,x903))))),
% 0.20/0.72 inference(scs_inference,[],[12,56,58,23,19,8])).
% 0.20/0.72 cnf(94,plain,
% 0.20/0.72 (~P1(f2(a4,f2(a1,a5)),a1)),
% 0.20/0.72 inference(scs_inference,[],[12,24,79,37,56,58,23,19,8,2,3,7])).
% 0.20/0.72 cnf(98,plain,
% 0.20/0.72 (P1(f2(x981,x982),f2(x981,f2(f2(f3(x983),f3(x982)),x983)))),
% 0.20/0.72 inference(scs_inference,[],[10,12,24,75,79,37,56,58,23,19,8,2,3,7,5,4,20])).
% 0.20/0.72 cnf(105,plain,
% 0.20/0.72 (~E(f2(f2(a4,a5),f2(f2(x1051,x1052),f2(f2(x1052,x1053),f2(x1051,x1053)))),a1)),
% 0.20/0.72 inference(scs_inference,[],[88,90,23,19])).
% 0.20/0.72 cnf(112,plain,
% 0.20/0.72 (E(f2(f2(x1121,x1122),x1122),f2(f2(x1122,x1121),x1121))),
% 0.20/0.72 inference(rename_variables,[],[10])).
% 0.20/0.72 cnf(113,plain,
% 0.20/0.72 (P1(f2(f2(x1131,x1132),x1132),f2(f2(x1131,x1133),f2(f2(x1132,x1131),x1133)))),
% 0.20/0.72 inference(scs_inference,[],[10,112,15,88,80,84,90,23,19,8,2,3,7])).
% 0.20/0.72 cnf(116,plain,
% 0.20/0.72 (P1(f2(f2(f2(x1161,x1162),x1162),x1163),f2(f2(f2(x1161,x1164),f2(f2(x1162,x1161),x1164)),x1163))),
% 0.20/0.72 inference(scs_inference,[],[113,21])).
% 0.20/0.72 cnf(118,plain,
% 0.20/0.72 (~P1(f2(x1181,x1182),f2(f2(a4,a5),f2(f2(x1182,x1183),f2(x1181,x1183))))),
% 0.20/0.72 inference(scs_inference,[],[113,90,21,23])).
% 0.20/0.72 cnf(120,plain,
% 0.20/0.72 (~E(f2(f2(x1201,x1202),f2(f2(x1203,x1201),x1202)),f2(f2(a4,a5),f2(f2(x1203,x1204),f2(f2(x1201,x1203),x1204))))),
% 0.20/0.72 inference(scs_inference,[],[113,90,21,23,8])).
% 0.20/0.72 cnf(122,plain,
% 0.20/0.72 (~E(f2(f2(a4,a5),f2(f2(x1221,x1222),f2(f2(x1222,x1223),f2(x1221,x1223)))),f2(f2(f3(x1224),f3(x1225)),f2(x1225,x1224)))),
% 0.20/0.72 inference(scs_inference,[],[11,113,105,90,21,23,8,3])).
% 0.20/0.72 cnf(129,plain,
% 0.20/0.72 (~E(f2(a1,f2(f2(f2(a4,a5),f2(a5,a4)),f2(a5,a4))),a1)),
% 0.20/0.72 inference(scs_inference,[],[11,25,13,113,60,105,94,90,21,23,8,3,2,7,20,5,4,19])).
% 0.20/0.72 cnf(139,plain,
% 0.20/0.72 (~E(f2(f2(a4,a5),f2(f2(x1391,x1392),f2(f2(x1393,x1391),x1392))),f2(f2(x1393,x1394),f2(f2(x1391,x1393),x1394)))),
% 0.20/0.72 inference(scs_inference,[],[11,28,116,120,38,20,4,5,23,8,2])).
% 0.20/0.72 cnf(144,plain,
% 0.20/0.72 (~P1(x1441,f2(f2(x1441,x1442),f2(f2(a4,a5),x1442)))),
% 0.20/0.72 inference(scs_inference,[],[118,20])).
% 0.20/0.72 cnf(147,plain,
% 0.20/0.72 (~P1(x1471,f2(f2(x1471,f2(f2(a4,a5),x1472)),x1472))),
% 0.20/0.72 inference(scs_inference,[],[118,20,21])).
% 0.20/0.72 cnf(150,plain,
% 0.20/0.72 (~E(f2(f2(a4,a5),f2(f2(x1501,x1502),f2(f2(x1503,x1501),x1502))),f2(f2(x1503,x1504),f2(f2(x1501,x1503),x1504)))),
% 0.20/0.72 inference(rename_variables,[],[139])).
% 0.20/0.72 cnf(151,plain,
% 0.20/0.72 (~E(f2(a4,a5),f2(x1511,f2(f2(x1511,x1512),x1511)))),
% 0.20/0.72 inference(scs_inference,[],[139,150,118,20,21,5,4])).
% 0.20/0.72 cnf(176,plain,
% 0.20/0.72 (~P1(x1761,f2(f2(x1761,f2(f2(a4,a5),x1762)),x1762))),
% 0.20/0.72 inference(rename_variables,[],[147])).
% 0.20/0.72 cnf(179,plain,
% 0.20/0.72 (~E(f2(f2(x1791,f2(f2(a4,a5),f2(f2(f3(x1792),f3(x1793)),x1792))),x1793),x1791)),
% 0.20/0.72 inference(scs_inference,[],[12,25,98,147,176,122,129,20,21,5,4,23,8,2,3,7])).
% 0.20/0.72 cnf(182,plain,
% 0.20/0.72 (~P1(f2(a1,f2(f2(a4,a5),f2(f2(f3(x1821),f3(x1822)),x1821))),x1822)),
% 0.20/0.72 inference(scs_inference,[],[12,25,98,147,176,122,129,20,21,5,4,23,8,2,3,7,18])).
% 0.20/0.72 cnf(193,plain,
% 0.20/0.72 ($false),
% 0.20/0.72 inference(scs_inference,[],[32,179,144,151,182,113,20,18,5,4,23]),
% 0.20/0.72 ['proof']).
% 0.20/0.72 % SZS output end Proof
% 0.20/0.72 % Total time :0.070000s
%------------------------------------------------------------------------------