TSTP Solution File: GRP004-2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP004-2 : 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 : n019.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 00:10:31 EDT 2023
% Result : Unsatisfiable 0.66s 0.94s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 20:10:43 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.57 start to proof:theBenchmark
% 0.66/0.93 %-------------------------------------------
% 0.66/0.93 % File :CSE---1.6
% 0.66/0.93 % Problem :theBenchmark
% 0.66/0.93 % Transform :cnf
% 0.66/0.93 % Format :tptp:raw
% 0.66/0.93 % Command :java -jar mcs_scs.jar %d %s
% 0.66/0.93
% 0.66/0.93 % Result :Theorem 0.120000s
% 0.66/0.93 % Output :CNFRefutation 0.120000s
% 0.66/0.93 %-------------------------------------------
% 0.66/0.93 %--------------------------------------------------------------------------
% 0.66/0.93 % File : GRP004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.66/0.93 % Domain : Group Theory
% 0.66/0.93 % Problem : Left inverse and identity => Right inverse exists
% 0.66/0.93 % Version : [Ver92] axioms.
% 0.66/0.93 % English : In a group with left inverses and left identity every element
% 0.66/0.93 % has a right inverse.
% 0.66/0.93
% 0.66/0.93 % Refs : [Ver92] Veroff (1992), Email to G. Sutcliffe
% 0.66/0.93 % Source : [TPTP]
% 0.66/0.93 % Names :
% 0.66/0.93
% 0.66/0.93 % Status : Unsatisfiable
% 0.66/0.93 % Rating : 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.00 v2.1.0, 0.00 v2.0.0
% 0.66/0.93 % Syntax : Number of clauses : 8 ( 4 unt; 0 nHn; 5 RR)
% 0.66/0.93 % Number of literals : 18 ( 0 equ; 11 neg)
% 0.66/0.93 % Maximal clause size : 4 ( 2 avg)
% 0.66/0.93 % Maximal term depth : 2 ( 1 avg)
% 0.66/0.93 % Number of predicates : 2 ( 2 usr; 0 prp; 2-3 aty)
% 0.66/0.93 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.66/0.93 % Number of variables : 24 ( 0 sgn)
% 0.66/0.93 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.66/0.93
% 0.66/0.94 % Comments :
% 0.66/0.94 %--------------------------------------------------------------------------
% 0.66/0.94 %----Include Veroff's minimal axiom set
% 0.66/0.94 include('Axioms/GRP005-0.ax').
% 0.66/0.94 %--------------------------------------------------------------------------
% 0.66/0.94 cnf(prove_right_inverse,negated_conjecture,
% 0.66/0.94 ~ product(a,inverse(a),identity) ).
% 0.66/0.94
% 0.66/0.94 %--------------------------------------------------------------------------
% 0.66/0.94 %-------------------------------------------
% 0.66/0.94 % Proof found
% 0.66/0.94 % SZS status Theorem for theBenchmark
% 0.66/0.94 % SZS output start Proof
% 0.66/0.94 %ClaNum:8(EqnAxiom:0)
% 0.66/0.94 %VarNum:48(SingletonVarNum:24)
% 0.66/0.94 %MaxLitNum:4
% 0.66/0.94 %MaxfuncDepth:1
% 0.66/0.94 %SharedTerms:4
% 0.66/0.94 %goalClause: 4
% 0.66/0.94 %singleGoalClaCount:1
% 0.66/0.94 [4]~P1(a2,f3(a2),a1)
% 0.66/0.94 [1]P1(a1,x11,x11)
% 0.66/0.94 [2]P1(f3(x21),x21,a1)
% 0.66/0.94 [3]P1(x31,x32,f4(x31,x32))
% 0.66/0.94 [5]~P1(x51,x52,x54)+P1(x51,x52,x53)+~P2(x54,x53)
% 0.66/0.94 [6]~P1(x63,x64,x61)+P2(x61,x62)+~P1(x63,x64,x62)
% 0.66/0.94 [7]~P1(x76,x74,x71)+P1(x71,x72,x73)+~P1(x74,x72,x75)+~P1(x76,x75,x73)
% 0.66/0.94 [8]~P1(x81,x86,x84)+P1(x81,x82,x83)+~P1(x84,x85,x83)+~P1(x86,x85,x82)
% 0.66/0.94 %EqnAxiom
% 0.66/0.94
% 0.66/0.94 %-------------------------------------------
% 0.66/0.94 cnf(10,plain,
% 0.66/0.94 (P1(a1,f4(a1,a1),a1)),
% 0.66/0.94 inference(scs_inference,[],[1,3,6,8])).
% 0.66/0.94 cnf(11,plain,
% 0.66/0.94 (P1(x111,x112,f4(x111,x112))),
% 0.66/0.94 inference(rename_variables,[],[3])).
% 0.66/0.94 cnf(13,plain,
% 0.66/0.94 (P1(a1,x131,x131)),
% 0.66/0.94 inference(rename_variables,[],[1])).
% 0.66/0.94 cnf(15,plain,
% 0.66/0.94 (P1(f4(f3(x151),a1),x151,a1)),
% 0.66/0.94 inference(scs_inference,[],[1,13,3,11,2,6,8,7])).
% 0.66/0.94 cnf(17,plain,
% 0.66/0.94 (P1(x171,x172,f4(x171,x172))),
% 0.66/0.94 inference(rename_variables,[],[3])).
% 0.66/0.94 cnf(19,plain,
% 0.66/0.94 (~P2(f4(a2,f3(a2)),a1)),
% 0.66/0.94 inference(scs_inference,[],[4,1,13,3,11,17,2,6,8,7,5])).
% 0.66/0.94 cnf(22,plain,
% 0.66/0.94 (P2(a1,f4(f3(x221),x221))),
% 0.66/0.94 inference(scs_inference,[],[3,2,6])).
% 0.66/0.94 cnf(23,plain,
% 0.66/0.94 (P1(f3(x231),x231,a1)),
% 0.66/0.94 inference(rename_variables,[],[2])).
% 0.66/0.94 cnf(24,plain,
% 0.66/0.94 (P1(x241,x242,f4(x241,x242))),
% 0.66/0.94 inference(rename_variables,[],[3])).
% 0.66/0.94 cnf(26,plain,
% 0.66/0.94 (P1(f4(a1,a1),a1,f4(a1,a1))),
% 0.66/0.94 inference(scs_inference,[],[3,24,2,1,6,7])).
% 0.66/0.94 cnf(28,plain,
% 0.66/0.94 (P1(x281,x282,f4(x281,x282))),
% 0.66/0.94 inference(rename_variables,[],[3])).
% 0.66/0.94 cnf(29,plain,
% 0.66/0.94 (P1(a1,x291,x291)),
% 0.66/0.94 inference(rename_variables,[],[1])).
% 0.66/0.94 cnf(31,plain,
% 0.66/0.94 (~P1(f4(a2,a1),f3(a2),a1)),
% 0.66/0.94 inference(scs_inference,[],[4,3,24,28,2,1,29,6,7,8])).
% 0.66/0.94 cnf(35,plain,
% 0.66/0.94 (P1(f3(x351),x351,f4(f3(x352),x352))),
% 0.66/0.94 inference(scs_inference,[],[4,3,24,28,2,23,1,29,6,7,8,5])).
% 0.66/0.94 cnf(37,plain,
% 0.66/0.94 (~P1(a1,a1,f4(a2,f3(a2)))),
% 0.66/0.94 inference(scs_inference,[],[1,19,6])).
% 0.66/0.94 cnf(38,plain,
% 0.66/0.94 (P1(a1,x381,x381)),
% 0.66/0.94 inference(rename_variables,[],[1])).
% 0.66/0.94 cnf(40,plain,
% 0.66/0.94 (~P2(f4(f4(a2,a1),f3(a2)),a1)),
% 0.66/0.94 inference(scs_inference,[],[1,3,19,31,6,5])).
% 0.66/0.94 cnf(43,plain,
% 0.66/0.94 (~P1(f3(f3(a2)),a1,f4(a2,a1))),
% 0.66/0.94 inference(scs_inference,[],[1,38,3,2,19,31,6,5,7])).
% 0.66/0.94 cnf(50,plain,
% 0.66/0.94 (P2(x501,f4(a1,x501))),
% 0.66/0.94 inference(scs_inference,[],[1,3,6])).
% 0.66/0.94 cnf(51,plain,
% 0.66/0.94 (P1(x511,x512,f4(x511,x512))),
% 0.66/0.94 inference(rename_variables,[],[3])).
% 0.66/0.94 cnf(54,plain,
% 0.66/0.94 (P1(a1,x541,x541)),
% 0.66/0.94 inference(rename_variables,[],[1])).
% 0.66/0.94 cnf(55,plain,
% 0.66/0.94 (P1(x551,x552,f4(x551,x552))),
% 0.66/0.94 inference(rename_variables,[],[3])).
% 0.66/0.94 cnf(57,plain,
% 0.66/0.94 (P1(f4(a1,f3(x571)),x571,a1)),
% 0.66/0.94 inference(scs_inference,[],[1,54,3,51,55,2,31,6,8,7])).
% 0.66/0.94 cnf(58,plain,
% 0.66/0.94 (P1(a1,x581,x581)),
% 0.66/0.94 inference(rename_variables,[],[1])).
% 0.66/0.94 cnf(61,plain,
% 0.66/0.94 (P1(a1,a1,f4(f3(x611),x611))),
% 0.66/0.94 inference(scs_inference,[],[1,54,58,3,51,55,2,22,31,6,8,7,5])).
% 0.66/0.94 cnf(66,plain,
% 0.66/0.94 (P1(a1,f4(a1,a1),f4(f3(a1),a1))),
% 0.66/0.94 inference(scs_inference,[],[2,10,3,35,6,7])).
% 0.66/0.94 cnf(67,plain,
% 0.66/0.94 (P1(x671,x672,f4(x671,x672))),
% 0.66/0.94 inference(rename_variables,[],[3])).
% 0.66/0.94 cnf(68,plain,
% 0.66/0.94 (P1(f3(x681),x681,a1)),
% 0.66/0.94 inference(rename_variables,[],[2])).
% 0.66/0.94 cnf(70,plain,
% 0.66/0.94 (~P2(a1,f4(a2,f3(a2)))),
% 0.66/0.94 inference(scs_inference,[],[2,10,3,35,37,1,6,7,5])).
% 0.66/0.94 cnf(73,plain,
% 0.66/0.94 (P1(f3(x731),f4(x731,f4(a1,a1)),a1)),
% 0.66/0.94 inference(scs_inference,[],[2,68,10,3,67,35,37,1,6,7,5,8])).
% 0.66/0.94 cnf(76,plain,
% 0.66/0.94 (~P1(f3(x761),x761,f4(f4(a2,a1),f3(a2)))),
% 0.66/0.94 inference(scs_inference,[],[2,40,6])).
% 0.66/0.94 cnf(78,plain,
% 0.66/0.94 (P1(a1,f4(f4(a1,a1),f4(a1,a1)),a1)),
% 0.66/0.94 inference(scs_inference,[],[2,10,3,40,6,8])).
% 0.66/0.94 cnf(85,plain,
% 0.66/0.94 (P2(f4(a1,x851),x851)),
% 0.66/0.94 inference(scs_inference,[],[3,1,6])).
% 0.66/0.94 cnf(86,plain,
% 0.66/0.94 (P1(a1,x861,x861)),
% 0.66/0.94 inference(rename_variables,[],[1])).
% 0.66/0.94 cnf(87,plain,
% 0.66/0.94 (P1(x871,x872,f4(x871,x872))),
% 0.66/0.94 inference(rename_variables,[],[3])).
% 0.66/0.94 cnf(92,plain,
% 0.66/0.94 (P1(a1,x921,x921)),
% 0.66/0.94 inference(rename_variables,[],[1])).
% 0.66/0.94 cnf(94,plain,
% 0.66/0.94 (~P1(f4(a1,a1),f3(f3(a2)),f4(a2,a1))),
% 0.66/0.94 inference(scs_inference,[],[3,87,10,76,1,86,92,6,7,8])).
% 0.66/0.94 cnf(97,plain,
% 0.66/0.94 (~P1(a1,f4(a1,a1),f4(a2,f3(a2)))),
% 0.66/0.94 inference(scs_inference,[],[10,70,6])).
% 0.66/0.95 cnf(99,plain,
% 0.66/0.95 (P1(f4(f3(a1),a1),f4(a1,x991),f4(a1,x991))),
% 0.66/0.95 inference(scs_inference,[],[3,15,10,70,6,8])).
% 0.66/0.95 cnf(100,plain,
% 0.66/0.95 (P1(x1001,x1002,f4(x1001,x1002))),
% 0.66/0.95 inference(rename_variables,[],[3])).
% 0.66/0.95 cnf(101,plain,
% 0.66/0.95 (P1(x1011,x1012,f4(x1011,x1012))),
% 0.66/0.95 inference(rename_variables,[],[3])).
% 0.66/0.95 cnf(104,plain,
% 0.66/0.95 (P1(f4(x1041,x1041),x1041,f4(x1041,f4(x1041,x1041)))),
% 0.66/0.95 inference(scs_inference,[],[3,101,100,15,10,70,6,8,7])).
% 0.66/0.95 cnf(109,plain,
% 0.66/0.95 (P1(f4(a1,a1),f4(a1,a1),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[10,26,7])).
% 0.66/0.95 cnf(113,plain,
% 0.66/0.95 (P1(f4(f3(x1131),a1),x1131,a1)),
% 0.66/0.95 inference(rename_variables,[],[15])).
% 0.66/0.95 cnf(115,plain,
% 0.66/0.95 (P1(f4(f3(x1151),a1),x1151,f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[15,113,10,26,50,61,7,8,5])).
% 0.66/0.95 cnf(117,plain,
% 0.66/0.95 (~P2(a1,f4(f4(a2,a1),f3(a2)))),
% 0.66/0.95 inference(scs_inference,[],[76,2,5])).
% 0.66/0.95 cnf(120,plain,
% 0.66/0.95 (~P1(a1,f3(f3(a2)),f4(a2,a1))),
% 0.66/0.95 inference(scs_inference,[],[94,76,2,3,1,5,7])).
% 0.66/0.95 cnf(122,plain,
% 0.66/0.95 (P1(a1,x1221,x1221)),
% 0.66/0.95 inference(rename_variables,[],[1])).
% 0.66/0.95 cnf(124,plain,
% 0.66/0.95 (~P1(f4(a1,a1),f4(a2,f3(a2)),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[10,94,97,76,2,3,1,122,5,7,8])).
% 0.66/0.95 cnf(129,plain,
% 0.66/0.95 (~P1(f4(a1,a1),f4(a1,a1),f4(a2,f3(a2)))),
% 0.66/0.95 inference(scs_inference,[],[10,109,124,40,6,8])).
% 0.66/0.95 cnf(153,plain,
% 0.66/0.95 (~P1(f4(a1,a1),a1,f4(a2,f3(a2)))),
% 0.66/0.95 inference(scs_inference,[],[26,129,78,109,7,8])).
% 0.66/0.95 cnf(155,plain,
% 0.66/0.95 (P1(f4(a1,a1),a1,a1)),
% 0.66/0.95 inference(scs_inference,[],[26,129,85,78,109,7,8,5])).
% 0.66/0.95 cnf(161,plain,
% 0.66/0.95 (P1(x1611,x1612,f4(x1611,x1612))),
% 0.66/0.95 inference(rename_variables,[],[3])).
% 0.66/0.95 cnf(163,plain,
% 0.66/0.95 (~P1(a2,a1,f3(f3(a2)))),
% 0.66/0.95 inference(scs_inference,[],[26,153,120,3,161,1,5,6,8])).
% 0.66/0.95 cnf(170,plain,
% 0.66/0.95 (P1(x1701,x1702,f4(x1701,x1702))),
% 0.66/0.95 inference(rename_variables,[],[3])).
% 0.66/0.95 cnf(175,plain,
% 0.66/0.95 (P1(f4(a1,a1),f4(f3(x1751),x1751),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[26,61,2,3,170,6,7,8])).
% 0.66/0.95 cnf(178,plain,
% 0.66/0.95 (~P1(f4(a1,a1),a1,f4(f4(a2,a1),f3(a2)))),
% 0.66/0.95 inference(scs_inference,[],[155,117,6])).
% 0.66/0.95 cnf(180,plain,
% 0.66/0.95 (P1(a1,f4(f3(a1),a1),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[115,155,117,61,6,8])).
% 0.66/0.95 cnf(184,plain,
% 0.66/0.95 (P1(f4(f3(x1841),x1841),a1,a1)),
% 0.66/0.95 inference(scs_inference,[],[35,26,115,155,117,61,2,6,8,7])).
% 0.66/0.95 cnf(188,plain,
% 0.66/0.95 (P2(f4(a1,a1),f4(f3(a1),a1))),
% 0.66/0.95 inference(scs_inference,[],[180,1,6])).
% 0.66/0.95 cnf(198,plain,
% 0.66/0.95 (~P1(f4(a1,a1),f4(a1,a1),f4(f4(a2,a1),f3(a2)))),
% 0.66/0.95 inference(scs_inference,[],[26,178,70,109,2,6,7])).
% 0.66/0.95 cnf(203,plain,
% 0.66/0.95 (P1(f4(a1,a1),a1,f4(f3(a1),a1))),
% 0.66/0.95 inference(scs_inference,[],[26,188,178,57,180,70,109,2,6,7,8,5])).
% 0.66/0.95 cnf(208,plain,
% 0.66/0.95 (P1(x2081,x2082,f4(x2081,x2082))),
% 0.66/0.95 inference(rename_variables,[],[3])).
% 0.66/0.95 cnf(215,plain,
% 0.66/0.95 (P1(a1,f4(f3(x2151),x2151),a1)),
% 0.66/0.95 inference(scs_inference,[],[198,184,76,61,109,3,208,1,5,6,7,8])).
% 0.66/0.95 cnf(218,plain,
% 0.66/0.95 (P2(f4(f3(a1),a1),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[66,1,6])).
% 0.66/0.95 cnf(228,plain,
% 0.66/0.95 (~P1(a1,f4(f4(a2,a1),f3(a2)),a1)),
% 0.66/0.95 inference(scs_inference,[],[40,1,6])).
% 0.66/0.95 cnf(231,plain,
% 0.66/0.95 (~P1(f3(f3(a2)),f4(a1,a1),a2)),
% 0.66/0.95 inference(scs_inference,[],[40,155,43,3,1,6,8])).
% 0.66/0.95 cnf(232,plain,
% 0.66/0.95 (P1(x2321,x2322,f4(x2321,x2322))),
% 0.66/0.95 inference(rename_variables,[],[3])).
% 0.66/0.95 cnf(234,plain,
% 0.66/0.95 (P1(f4(f3(x2341),x2341),f4(a1,a1),a1)),
% 0.66/0.95 inference(scs_inference,[],[40,35,155,43,73,3,232,1,6,8,7])).
% 0.66/0.95 cnf(249,plain,
% 0.66/0.95 (P1(f3(x2491),x2491,f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[35,104,218,175,115,8,5])).
% 0.66/0.95 cnf(252,plain,
% 0.66/0.95 (P1(f4(f3(x2521),x2521),f4(a1,a1),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[50,234,5])).
% 0.66/0.95 cnf(280,plain,
% 0.66/0.95 (P1(x2801,x2802,f4(x2801,x2802))),
% 0.66/0.95 inference(rename_variables,[],[3])).
% 0.66/0.95 cnf(282,plain,
% 0.66/0.95 (P1(f4(a1,a1),f4(a1,f4(a1,a1)),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[43,252,203,249,155,35,3,280,6,7,8])).
% 0.66/0.95 cnf(286,plain,
% 0.66/0.95 (P1(a1,f4(f3(x2861),x2861),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[50,43,252,203,215,249,155,35,3,280,6,7,8,5])).
% 0.66/0.95 cnf(293,plain,
% 0.66/0.95 (~P1(f4(a1,a1),f4(f4(a2,a1),f3(a2)),f4(a1,a1))),
% 0.66/0.95 inference(scs_inference,[],[228,234,249,35,1,8,7])).
% 0.66/0.95 cnf(303,plain,
% 0.66/0.95 (P1(a1,f4(a1,f4(a1,a1)),a1)),
% 0.66/0.95 inference(scs_inference,[],[57,282,293,163,155,3,1,5,8,7])).
% 0.66/0.95 cnf(314,plain,
% 0.66/0.95 ($false),
% 0.66/0.95 inference(scs_inference,[],[57,50,99,303,286,231,249,2,1,5,7,8]),
% 0.66/0.95 ['proof']).
% 0.66/0.95 % SZS output end Proof
% 0.66/0.95 % Total time :0.120000s
%------------------------------------------------------------------------------