TSTP Solution File: GRP022-2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP022-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n003.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 00:10:37 EDT 2023
% Result : Unsatisfiable 1.59s 1.71s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.10 % Problem : GRP022-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 29 02:46:25 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.52 start to proof:theBenchmark
% 1.59/1.70 %-------------------------------------------
% 1.59/1.70 % File :CSE---1.6
% 1.59/1.70 % Problem :theBenchmark
% 1.59/1.70 % Transform :cnf
% 1.59/1.70 % Format :tptp:raw
% 1.59/1.70 % Command :java -jar mcs_scs.jar %d %s
% 1.59/1.70
% 1.59/1.70 % Result :Theorem 1.140000s
% 1.59/1.70 % Output :CNFRefutation 1.140000s
% 1.59/1.70 %-------------------------------------------
% 1.59/1.70 %--------------------------------------------------------------------------
% 1.59/1.70 % File : GRP022-2 : TPTP v8.1.2. Released v1.0.0.
% 1.59/1.70 % Domain : Group Theory
% 1.59/1.70 % Problem : Inverse is an involution
% 1.59/1.70 % Version : [MOW76] (equality) axioms : Augmented.
% 1.59/1.71 % English :
% 1.59/1.71
% 1.59/1.71 % Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 1.59/1.71 % : [LO85] Lusk & Overbeek (1985), Reasoning about Equality
% 1.59/1.71 % Source : [TPTP]
% 1.59/1.71 % Names : Established lemma [MOW76]
% 1.59/1.71 % : Problem 2 [LO85]
% 1.59/1.71
% 1.59/1.71 % Status : Unsatisfiable
% 1.59/1.71 % Rating : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 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
% 1.59/1.71 % Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 1 RR)
% 1.59/1.71 % Number of literals : 6 ( 6 equ; 1 neg)
% 1.59/1.71 % Maximal clause size : 1 ( 1 avg)
% 1.59/1.71 % Maximal term depth : 3 ( 2 avg)
% 1.59/1.71 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 1.59/1.71 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 1.59/1.71 % Number of variables : 7 ( 0 sgn)
% 1.59/1.71 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 1.59/1.71
% 1.59/1.71 % Comments :
% 1.59/1.71 %--------------------------------------------------------------------------
% 1.59/1.71 %----Include equality group theory axioms
% 1.59/1.71 include('Axioms/GRP004-0.ax').
% 1.59/1.71 %--------------------------------------------------------------------------
% 1.59/1.71 %----Redundant two axioms
% 1.59/1.71 cnf(right_identity,axiom,
% 1.59/1.71 multiply(X,identity) = X ).
% 1.59/1.71
% 1.59/1.71 cnf(right_inverse,axiom,
% 1.59/1.71 multiply(X,inverse(X)) = identity ).
% 1.59/1.71
% 1.59/1.71 cnf(prove_inverse_of_inverse_is_original,negated_conjecture,
% 1.59/1.71 inverse(inverse(a)) != a ).
% 1.59/1.71
% 1.59/1.71 %--------------------------------------------------------------------------
% 1.59/1.71 %-------------------------------------------
% 1.59/1.71 % Proof found
% 1.59/1.71 % SZS status Theorem for theBenchmark
% 1.59/1.71 % SZS output start Proof
% 1.59/1.71 %ClaNum:12(EqnAxiom:6)
% 1.59/1.71 %VarNum:14(SingletonVarNum:7)
% 1.59/1.71 %MaxLitNum:1
% 1.59/1.71 %MaxfuncDepth:2
% 1.59/1.71 %SharedTerms:5
% 1.59/1.71 %goalClause: 12
% 1.59/1.71 %singleGoalClaCount:1
% 1.59/1.71 [12]~E(f4(f4(a2)),a2)
% 1.59/1.71 [7]E(f3(x71,a1),x71)
% 1.59/1.71 [8]E(f3(a1,x81),x81)
% 1.59/1.71 [9]E(f3(x91,f4(x91)),a1)
% 1.59/1.71 [10]E(f3(f4(x101),x101),a1)
% 1.59/1.71 [11]E(f3(f3(x111,x112),x113),f3(x111,f3(x112,x113)))
% 1.59/1.71 %EqnAxiom
% 1.59/1.71 [1]E(x11,x11)
% 1.59/1.71 [2]E(x22,x21)+~E(x21,x22)
% 1.59/1.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.59/1.71 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 1.59/1.71 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 1.59/1.71 [6]~E(x61,x62)+E(f4(x61),f4(x62))
% 1.59/1.71
% 1.59/1.71 %-------------------------------------------
% 1.59/1.71 cnf(13,plain,
% 1.59/1.71 (E(x131,f3(x131,a1))),
% 1.59/1.71 inference(scs_inference,[],[7,2])).
% 1.59/1.71 cnf(14,plain,
% 1.59/1.71 (~E(f4(f4(a2)),f3(a2,a1))),
% 1.59/1.71 inference(scs_inference,[],[12,7,2,3])).
% 1.59/1.71 cnf(15,plain,
% 1.59/1.71 (E(f3(x151,a1),x151)),
% 1.59/1.71 inference(rename_variables,[],[7])).
% 1.59/1.71 cnf(16,plain,
% 1.59/1.71 (E(f4(f3(x161,a1)),f4(x161))),
% 1.59/1.71 inference(scs_inference,[],[12,7,15,2,3,6])).
% 1.59/1.71 cnf(17,plain,
% 1.59/1.71 (E(f3(x171,f3(x172,a1)),f3(x171,x172))),
% 1.59/1.71 inference(scs_inference,[],[12,7,15,2,3,6,5])).
% 1.59/1.71 cnf(18,plain,
% 1.59/1.71 (E(f3(f3(x181,a1),x182),f3(x181,x182))),
% 1.59/1.71 inference(scs_inference,[],[12,7,15,2,3,6,5,4])).
% 1.59/1.71 cnf(19,plain,
% 1.59/1.72 (~E(a2,f4(f4(a2)))),
% 1.59/1.72 inference(scs_inference,[],[12,2])).
% 1.59/1.72 cnf(20,plain,
% 1.59/1.72 (~E(f3(f4(f4(a2)),a1),a2)),
% 1.59/1.72 inference(scs_inference,[],[12,13,2,3])).
% 1.59/1.72 cnf(22,plain,
% 1.59/1.72 (E(x221,f3(a1,x221))),
% 1.59/1.72 inference(scs_inference,[],[8,2])).
% 1.59/1.72 cnf(23,plain,
% 1.59/1.72 (E(f3(f3(a1,x231),a1),x231)),
% 1.59/1.72 inference(scs_inference,[],[7,8,2,3])).
% 1.59/1.72 cnf(25,plain,
% 1.59/1.72 (~E(a2,f3(f4(f4(a2)),a1))),
% 1.59/1.72 inference(scs_inference,[],[20,2])).
% 1.59/1.72 cnf(26,plain,
% 1.59/1.72 (~E(f3(f4(f4(a2)),a1),f3(a2,a1))),
% 1.59/1.72 inference(scs_inference,[],[7,20,2,3])).
% 1.59/1.72 cnf(28,plain,
% 1.59/1.72 (E(a1,f3(x281,f4(x281)))),
% 1.59/1.72 inference(scs_inference,[],[9,2])).
% 1.59/1.72 cnf(31,plain,
% 1.59/1.72 (E(f4(f3(a1,x311)),f4(x311))),
% 1.59/1.72 inference(scs_inference,[],[8,9,13,25,2,3,6])).
% 1.59/1.72 cnf(32,plain,
% 1.59/1.72 (E(f3(f3(a1,x321),x322),f3(x321,x322))),
% 1.59/1.72 inference(scs_inference,[],[8,9,13,25,2,3,6,4])).
% 1.59/1.72 cnf(33,plain,
% 1.59/1.72 (E(f3(x331,f3(a1,x332)),f3(x331,x332))),
% 1.59/1.72 inference(scs_inference,[],[8,9,13,25,2,3,6,4,5])).
% 1.59/1.72 cnf(34,plain,
% 1.59/1.72 (~E(f3(a2,a1),f4(f4(a2)))),
% 1.59/1.72 inference(scs_inference,[],[14,2])).
% 1.59/1.72 cnf(35,plain,
% 1.59/1.72 (E(f3(a1,f3(f4(x351),x351)),a1)),
% 1.59/1.72 inference(scs_inference,[],[8,14,10,2,3])).
% 1.59/1.72 cnf(41,plain,
% 1.59/1.72 (~E(f3(f3(a2,a1),a1),f4(f4(a2)))),
% 1.59/1.72 inference(scs_inference,[],[13,34,3])).
% 1.59/1.72 cnf(44,plain,
% 1.59/1.72 (E(a1,f3(f4(x441),x441))),
% 1.59/1.72 inference(scs_inference,[],[10,2])).
% 1.59/1.72 cnf(45,plain,
% 1.59/1.72 (E(f3(f4(x451),x451),f3(a1,a1))),
% 1.59/1.72 inference(scs_inference,[],[10,13,2,3])).
% 1.59/1.72 cnf(49,plain,
% 1.59/1.72 (E(f3(f3(f4(x491),x491),x492),f3(a1,x492))),
% 1.59/1.72 inference(scs_inference,[],[10,13,2,3,6,5,4])).
% 1.59/1.72 cnf(50,plain,
% 1.59/1.72 (E(f3(f3(x501,x502),f3(x503,a1)),f3(x501,f3(x502,x503)))),
% 1.59/1.72 inference(scs_inference,[],[11,17,3])).
% 1.59/1.72 cnf(55,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(a2,f3(a1,a1)))),
% 1.59/1.72 inference(scs_inference,[],[11,41,3,2])).
% 1.59/1.72 cnf(56,plain,
% 1.59/1.72 (E(f3(x561,f3(x562,x563)),f3(f3(x561,x562),x563))),
% 1.59/1.72 inference(scs_inference,[],[11,2])).
% 1.59/1.72 cnf(59,plain,
% 1.59/1.72 (~E(a2,f4(f3(f4(a2),a1)))),
% 1.59/1.72 inference(scs_inference,[],[19,16,3])).
% 1.59/1.72 cnf(62,plain,
% 1.59/1.72 (E(f3(x621,x622),f3(f3(x621,a1),x622))),
% 1.59/1.72 inference(scs_inference,[],[13,19,16,22,3,6,4])).
% 1.59/1.72 cnf(63,plain,
% 1.59/1.72 (E(f3(x631,x632),f3(x631,f3(x632,a1)))),
% 1.59/1.72 inference(scs_inference,[],[13,19,16,22,3,6,4,5])).
% 1.59/1.72 cnf(65,plain,
% 1.59/1.72 (E(f3(x651,x652),f3(f3(a1,x651),x652))),
% 1.59/1.72 inference(scs_inference,[],[32,2])).
% 1.59/1.72 cnf(66,plain,
% 1.59/1.72 (~E(f3(a2,a1),f4(f3(f4(a2),a1)))),
% 1.59/1.72 inference(scs_inference,[],[13,32,59,2,3])).
% 1.59/1.72 cnf(69,plain,
% 1.59/1.72 (E(f3(f3(x691,a1),f3(x692,a1)),f3(x691,x692))),
% 1.59/1.72 inference(scs_inference,[],[18,17,66,2,3])).
% 1.59/1.72 cnf(72,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(f3(a2,a1),f3(a1,a1)))),
% 1.59/1.72 inference(scs_inference,[],[55,33,50,2,3])).
% 1.59/1.72 cnf(75,plain,
% 1.59/1.72 (~E(f3(a1,a2),f4(f4(a2)))),
% 1.59/1.72 inference(scs_inference,[],[19,22,72,2,3])).
% 1.59/1.72 cnf(83,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(a1,a2))),
% 1.59/1.72 inference(scs_inference,[],[75,2])).
% 1.59/1.72 cnf(84,plain,
% 1.59/1.72 (E(f3(x841,f3(x842,a1)),f3(f3(a1,x841),x842))),
% 1.59/1.72 inference(scs_inference,[],[17,65,75,2,3])).
% 1.59/1.72 cnf(87,plain,
% 1.59/1.72 (~E(f3(a1,f4(f4(a2))),f3(a1,a2))),
% 1.59/1.72 inference(scs_inference,[],[22,23,83,2,3])).
% 1.59/1.72 cnf(90,plain,
% 1.59/1.72 (E(f3(f3(x901,a1),x902),f3(a1,f3(x901,x902)))),
% 1.59/1.72 inference(scs_inference,[],[18,22,87,2,3])).
% 1.59/1.72 cnf(96,plain,
% 1.59/1.72 (~E(a2,f4(f3(a1,f4(a2))))),
% 1.59/1.72 inference(scs_inference,[],[19,31,69,2,3])).
% 1.59/1.72 cnf(99,plain,
% 1.59/1.72 (~E(f3(a1,a2),f3(f4(f4(a2)),a1))),
% 1.59/1.72 inference(scs_inference,[],[25,22,96,2,3])).
% 1.59/1.72 cnf(101,plain,
% 1.59/1.72 (E(f3(f3(a1,x1011),x1012),f3(x1011,f3(x1012,a1)))),
% 1.59/1.72 inference(scs_inference,[],[84,2])).
% 1.59/1.72 cnf(102,plain,
% 1.59/1.72 (E(f3(a1,f3(x1021,a1)),x1021)),
% 1.59/1.72 inference(scs_inference,[],[23,56,84,2,3])).
% 1.59/1.72 cnf(104,plain,
% 1.59/1.72 (~E(f3(f4(f4(a2)),a1),f3(a1,a2))),
% 1.59/1.72 inference(scs_inference,[],[99,2])).
% 1.59/1.72 cnf(108,plain,
% 1.59/1.72 (E(f3(f3(a1,f3(x1081,a1)),x1082),f3(x1081,x1082))),
% 1.59/1.72 inference(scs_inference,[],[28,23,99,102,2,3,6,4])).
% 1.59/1.72 cnf(111,plain,
% 1.59/1.72 (~E(f3(a1,f3(a2,a1)),f4(f4(a2)))),
% 1.59/1.72 inference(scs_inference,[],[22,108,34,2,3])).
% 1.59/1.72 cnf(113,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(a1,f3(a2,a1)))),
% 1.59/1.72 inference(scs_inference,[],[111,2])).
% 1.59/1.72 cnf(114,plain,
% 1.59/1.72 (E(x1141,f3(f3(a1,a1),x1141))),
% 1.59/1.72 inference(scs_inference,[],[22,62,111,2,3])).
% 1.59/1.72 cnf(117,plain,
% 1.59/1.72 (E(f3(f3(a1,a1),x1171),x1171)),
% 1.59/1.72 inference(scs_inference,[],[114,2])).
% 1.59/1.72 cnf(118,plain,
% 1.59/1.72 (E(x1181,f3(f3(a1,a1),f3(a1,x1181)))),
% 1.59/1.72 inference(scs_inference,[],[22,114,2,3])).
% 1.59/1.72 cnf(122,plain,
% 1.59/1.72 (E(f4(f3(f3(a1,a1),x1221)),f4(x1221))),
% 1.59/1.72 inference(scs_inference,[],[26,117,63,3,6])).
% 1.59/1.72 cnf(123,plain,
% 1.59/1.72 (E(f3(f3(f3(a1,a1),x1231),x1232),f3(x1231,x1232))),
% 1.59/1.72 inference(scs_inference,[],[26,117,63,3,6,4])).
% 1.59/1.72 cnf(124,plain,
% 1.59/1.72 (E(f3(x1241,f3(f3(a1,a1),x1242)),f3(x1241,x1242))),
% 1.59/1.72 inference(scs_inference,[],[26,117,63,3,6,4,5])).
% 1.59/1.72 cnf(129,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(f3(a1,a1),a2))),
% 1.59/1.72 inference(scs_inference,[],[124,113,101,2,3])).
% 1.59/1.72 cnf(132,plain,
% 1.59/1.72 (~E(f3(f3(a1,a1),f3(a1,a2)),f4(f4(a2)))),
% 1.59/1.72 inference(scs_inference,[],[118,129,19,2,3])).
% 1.59/1.72 cnf(139,plain,
% 1.59/1.72 (E(f3(x1391,a1),f3(x1391,f3(f4(x1392),x1392)))),
% 1.59/1.72 inference(scs_inference,[],[32,33,122,44,2,3,6,4,5])).
% 1.59/1.72 cnf(140,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(f3(a1,a1),f3(a1,a2)))),
% 1.59/1.72 inference(scs_inference,[],[132,2])).
% 1.59/1.72 cnf(151,plain,
% 1.59/1.72 (~E(f3(a2,a1),f4(f3(a1,f4(a2))))),
% 1.59/1.72 inference(scs_inference,[],[35,31,34,2,3])).
% 1.59/1.72 cnf(154,plain,
% 1.59/1.72 (E(f3(x1541,x1542),f3(f3(f3(a1,a1),f3(a1,x1541)),x1542))),
% 1.59/1.72 inference(scs_inference,[],[35,31,34,118,2,3,6,4])).
% 1.59/1.72 cnf(155,plain,
% 1.59/1.72 (E(f3(x1551,x1552),f3(x1551,f3(f3(a1,a1),f3(a1,x1552))))),
% 1.59/1.72 inference(scs_inference,[],[35,31,34,118,2,3,6,4,5])).
% 1.59/1.72 cnf(161,plain,
% 1.59/1.72 (~E(f3(a1,a2),f3(f4(f4(a2)),f3(a1,a1)))),
% 1.59/1.72 inference(scs_inference,[],[33,154,99,2,3])).
% 1.59/1.72 cnf(163,plain,
% 1.59/1.72 (~E(f3(f4(f4(a2)),f3(a1,a1)),f3(a1,a2))),
% 1.59/1.72 inference(scs_inference,[],[161,2])).
% 1.59/1.72 cnf(173,plain,
% 1.59/1.72 (~E(f3(f4(f4(a2)),f3(a1,a1)),f3(f3(a1,a1),a2))),
% 1.59/1.72 inference(scs_inference,[],[32,163,151,2,3])).
% 1.59/1.72 cnf(175,plain,
% 1.59/1.72 (E(f3(x1751,f3(f3(a1,a1),f3(a1,x1752))),f3(x1751,x1752))),
% 1.59/1.72 inference(scs_inference,[],[155,2])).
% 1.59/1.72 cnf(179,plain,
% 1.59/1.72 (~E(f3(f3(a1,a1),a2),f3(f4(f4(a2)),f3(a1,a1)))),
% 1.59/1.72 inference(scs_inference,[],[173,2])).
% 1.59/1.72 cnf(210,plain,
% 1.59/1.72 (~E(f3(a1,f3(a1,a2)),f3(f4(f4(a2)),f3(a1,a1)))),
% 1.59/1.72 inference(scs_inference,[],[50,179,90,2,3])).
% 1.59/1.72 cnf(213,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(f3(f3(a1,a1),a1),f3(a2,a1)))),
% 1.59/1.72 inference(scs_inference,[],[50,140,210,2,3])).
% 1.59/1.72 cnf(220,plain,
% 1.59/1.72 (E(f3(f4(x2201),f3(f3(a1,a1),f3(a1,x2201))),f3(a1,a1))),
% 1.59/1.72 inference(scs_inference,[],[45,175,213,2,3])).
% 1.59/1.72 cnf(222,plain,
% 1.59/1.72 (E(f3(a1,a1),f3(f4(x2221),f3(f3(a1,a1),f3(a1,x2221))))),
% 1.59/1.72 inference(scs_inference,[],[220,2])).
% 1.59/1.72 cnf(223,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(f3(f3(a1,a1),a2),f3(a1,a1)))),
% 1.59/1.72 inference(scs_inference,[],[55,123,3])).
% 1.59/1.72 cnf(226,plain,
% 1.59/1.72 (E(f3(a1,a1),f3(f3(f4(x2261),f3(a1,a1)),f3(a1,x2261)))),
% 1.59/1.72 inference(scs_inference,[],[56,222,223,2,3])).
% 1.59/1.72 cnf(229,plain,
% 1.59/1.72 (~E(f4(f4(a2)),f3(a1,f3(a1,a2)))),
% 1.59/1.72 inference(scs_inference,[],[56,226,129,2,3])).
% 1.59/1.72 cnf(232,plain,
% 1.59/1.72 (E(f3(f4(x2321),f3(x2321,x2322)),f3(a1,x2322))),
% 1.59/1.72 inference(scs_inference,[],[49,56,229,2,3])).
% 1.59/1.72 cnf(275,plain,
% 1.59/1.72 ($false),
% 1.59/1.72 inference(scs_inference,[],[104,139,232,3]),
% 1.59/1.72 ['proof']).
% 1.59/1.72 % SZS output end Proof
% 1.59/1.72 % Total time :1.140000s
%------------------------------------------------------------------------------