TSTP Solution File: GRP481-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP481-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n010.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 00:12:13 EDT 2023
% Result : Unsatisfiable 1.15s 1.25s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP481-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n010.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 : Mon Aug 28 20:36:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 1.15/1.25 %-------------------------------------------
% 1.15/1.25 % File :CSE---1.6
% 1.15/1.25 % Problem :theBenchmark
% 1.15/1.25 % Transform :cnf
% 1.15/1.25 % Format :tptp:raw
% 1.15/1.25 % Command :java -jar mcs_scs.jar %d %s
% 1.15/1.25
% 1.15/1.25 % Result :Theorem 0.650000s
% 1.15/1.25 % Output :CNFRefutation 0.650000s
% 1.15/1.25 %-------------------------------------------
% 1.15/1.25 %--------------------------------------------------------------------------
% 1.15/1.25 % File : GRP481-1 : TPTP v8.1.2. Released v2.6.0.
% 1.15/1.25 % Domain : Group Theory
% 1.15/1.25 % Problem : Axiom for group theory, in double division and identity, part 1
% 1.15/1.25 % Version : [McC93] (equality) axioms.
% 1.15/1.25 % English :
% 1.15/1.25
% 1.15/1.25 % Refs : [Neu86] Neumann (1986), Yet Another Single Law for Groups
% 1.15/1.25 % : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr
% 1.15/1.25 % Source : [TPTP]
% 1.15/1.25 % Names :
% 1.15/1.25
% 1.15/1.25 % Status : Unsatisfiable
% 1.15/1.25 % Rating : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 v7.0.0, 0.05 v6.3.0, 0.06 v6.2.0, 0.07 v6.1.0, 0.06 v6.0.0, 0.14 v5.5.0, 0.11 v5.4.0, 0.00 v2.6.0
% 1.15/1.25 % Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 1 RR)
% 1.15/1.25 % Number of literals : 5 ( 5 equ; 1 neg)
% 1.15/1.25 % Maximal clause size : 1 ( 1 avg)
% 1.15/1.25 % Maximal term depth : 7 ( 2 avg)
% 1.15/1.25 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 1.15/1.25 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 1.15/1.25 % Number of variables : 8 ( 0 sgn)
% 1.15/1.25 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 1.15/1.25
% 1.15/1.25 % Comments : A UEQ part of GRP075-1
% 1.15/1.25 %--------------------------------------------------------------------------
% 1.15/1.25 cnf(single_axiom,axiom,
% 1.15/1.25 double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = C ).
% 1.15/1.25
% 1.15/1.25 cnf(multiply,axiom,
% 1.15/1.25 multiply(A,B) = double_divide(double_divide(B,A),identity) ).
% 1.15/1.25
% 1.15/1.25 cnf(inverse,axiom,
% 1.15/1.25 inverse(A) = double_divide(A,identity) ).
% 1.15/1.25
% 1.15/1.25 cnf(identity,axiom,
% 1.15/1.25 identity = double_divide(A,inverse(A)) ).
% 1.15/1.25
% 1.15/1.25 cnf(prove_these_axioms_1,negated_conjecture,
% 1.15/1.25 multiply(inverse(a1),a1) != identity ).
% 1.15/1.25
% 1.15/1.25 %--------------------------------------------------------------------------
% 1.15/1.25 %-------------------------------------------
% 1.15/1.25 % Proof found
% 1.15/1.25 % SZS status Theorem for theBenchmark
% 1.15/1.25 % SZS output start Proof
% 1.15/1.25 %ClaNum:8(EqnAxiom:5)
% 1.15/1.25 %VarNum:10(SingletonVarNum:5)
% 1.15/1.25 %MaxLitNum:1
% 1.15/1.25 %MaxfuncDepth:4
% 1.15/1.25 %SharedTerms:6
% 1.15/1.25 %goalClause: 8
% 1.15/1.25 %singleGoalClaCount:1
% 1.15/1.25 [8]~E(f2(f2(a3,f2(a3,a1)),a1),a1)
% 1.15/1.25 [6]E(f2(x61,f2(x61,a1)),a1)
% 1.15/1.25 [7]E(f2(f2(f2(x71,f2(x72,a1)),f2(f2(x73,f2(x74,f2(x74,a1))),f2(x71,a1))),x72),x73)
% 1.15/1.25 %EqnAxiom
% 1.15/1.25 [1]E(x11,x11)
% 1.15/1.25 [2]E(x22,x21)+~E(x21,x22)
% 1.15/1.25 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.15/1.26 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 1.15/1.26 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 1.15/1.26
% 1.15/1.26 %-------------------------------------------
% 1.15/1.26 cnf(9,plain,
% 1.15/1.26 (E(a1,f2(x91,f2(x91,a1)))),
% 1.15/1.26 inference(scs_inference,[],[6,2])).
% 1.15/1.26 cnf(10,plain,
% 1.15/1.26 (~E(f2(f2(a3,f2(a3,a1)),a1),f2(x101,f2(x101,a1)))),
% 1.15/1.26 inference(scs_inference,[],[8,6,2,3])).
% 1.15/1.26 cnf(11,plain,
% 1.15/1.26 (E(f2(x111,f2(x112,f2(x112,a1))),f2(x111,a1))),
% 1.15/1.26 inference(scs_inference,[],[8,6,2,3,5])).
% 1.15/1.26 cnf(12,plain,
% 1.15/1.26 (E(f2(f2(x121,f2(x121,a1)),x122),f2(a1,x122))),
% 1.15/1.26 inference(scs_inference,[],[8,6,2,3,5,4])).
% 1.15/1.26 cnf(13,plain,
% 1.15/1.26 (~E(a1,f2(f2(a3,f2(a3,a1)),a1))),
% 1.15/1.26 inference(scs_inference,[],[10,5])).
% 1.15/1.26 cnf(15,plain,
% 1.15/1.26 (~E(f2(a1,a1),a1)),
% 1.15/1.26 inference(scs_inference,[],[8,12,10,5,3])).
% 1.15/1.26 cnf(18,plain,
% 1.15/1.26 (E(f2(x181,f2(x181,a1)),f2(x182,f2(x182,a1)))),
% 1.15/1.26 inference(scs_inference,[],[6,9,3])).
% 1.15/1.26 cnf(19,plain,
% 1.15/1.26 (E(f2(x191,a1),f2(x191,f2(x192,f2(x192,a1))))),
% 1.15/1.26 inference(scs_inference,[],[6,9,3,5])).
% 1.15/1.26 cnf(20,plain,
% 1.15/1.26 (E(x201,f2(f2(f2(x202,f2(x203,a1)),f2(f2(x201,f2(x204,f2(x204,a1))),f2(x202,a1))),x203))),
% 1.15/1.26 inference(scs_inference,[],[6,9,7,3,5,2])).
% 1.15/1.26 cnf(21,plain,
% 1.15/1.26 (~E(f2(a1,a1),f2(x211,f2(x211,a1)))),
% 1.15/1.26 inference(scs_inference,[],[6,15,3])).
% 1.15/1.26 cnf(23,plain,
% 1.15/1.26 (~E(f2(a1,f2(a1,a1)),f2(a1,a1))),
% 1.15/1.26 inference(scs_inference,[],[6,15,3,5,2])).
% 1.15/1.26 cnf(26,plain,
% 1.15/1.26 (~E(f2(f2(f2(x261,f2(x262,a1)),f2(f2(f2(a1,f2(a1,a1)),f2(x263,f2(x263,a1))),f2(x261,a1))),x262),f2(a1,a1))),
% 1.15/1.26 inference(scs_inference,[],[20,18,23,12,5,2,3])).
% 1.15/1.26 cnf(30,plain,
% 1.15/1.26 (~E(f2(f2(f2(x301,f2(x302,a1)),f2(f2(f2(a1,f2(a1,a1)),f2(x303,f2(x303,a1))),f2(x301,a1))),x302),f2(a1,a1))),
% 1.15/1.26 inference(rename_variables,[],[26])).
% 1.15/1.26 cnf(31,plain,
% 1.15/1.26 (~E(f2(a1,a1),f2(f2(f2(x311,f2(x312,a1)),f2(f2(f2(a1,f2(a1,a1)),f2(x313,f2(x313,a1))),f2(x311,a1))),x312))),
% 1.15/1.26 inference(scs_inference,[],[26,30,4,2])).
% 1.15/1.26 cnf(32,plain,
% 1.15/1.26 (E(f2(f2(f2(x321,f2(x322,a1)),f2(f2(a1,f2(x323,f2(x323,a1))),f2(x321,a1))),x322),f2(x324,f2(x324,a1)))),
% 1.15/1.26 inference(scs_inference,[],[7,9,26,30,4,2,3])).
% 1.15/1.26 cnf(34,plain,
% 1.15/1.26 (E(f2(f2(x341,f2(x342,f2(x342,a1))),x343),f2(f2(x341,a1),x343))),
% 1.15/1.26 inference(scs_inference,[],[11,4])).
% 1.15/1.26 cnf(35,plain,
% 1.15/1.26 (E(f2(x351,f2(x351,a1)),f2(f2(f2(x352,f2(x353,a1)),f2(f2(a1,f2(x354,f2(x354,a1))),f2(x352,a1))),x353))),
% 1.15/1.26 inference(scs_inference,[],[11,32,4,2])).
% 1.15/1.26 cnf(36,plain,
% 1.15/1.26 (~E(a1,f2(f2(a3,f2(a3,a1)),f2(x361,f2(x361,a1))))),
% 1.15/1.26 inference(scs_inference,[],[11,13,32,4,2,3])).
% 1.15/1.26 cnf(38,plain,
% 1.15/1.26 (~E(a1,f2(f2(x381,f2(a1,a1)),f2(f2(f2(a1,f2(a1,a1)),f2(x382,f2(x382,a1))),f2(x381,a1))))),
% 1.15/1.26 inference(scs_inference,[],[31,4])).
% 1.15/1.26 cnf(40,plain,
% 1.15/1.26 (~E(f2(x401,f2(x401,a1)),f2(a1,a1))),
% 1.15/1.26 inference(scs_inference,[],[31,21,4,2])).
% 1.15/1.26 cnf(44,plain,
% 1.15/1.26 (E(f2(f2(f2(x441,f2(x441,a1)),x442),x443),f2(f2(a1,x442),x443))),
% 1.15/1.26 inference(scs_inference,[],[12,4])).
% 1.15/1.26 cnf(45,plain,
% 1.15/1.26 (E(f2(x451,f2(x452,f2(x453,f2(x453,a1)))),f2(x451,f2(x452,a1)))),
% 1.15/1.26 inference(scs_inference,[],[11,12,4,5])).
% 1.15/1.26 cnf(46,plain,
% 1.15/1.26 (E(f2(f2(x461,a1),x462),f2(f2(x461,f2(x463,f2(x463,a1))),x462))),
% 1.15/1.26 inference(scs_inference,[],[11,12,34,4,5,2])).
% 1.15/1.26 cnf(47,plain,
% 1.15/1.26 (E(f2(f2(x471,f2(x471,a1)),f2(x472,f2(x472,a1))),f2(a1,a1))),
% 1.15/1.26 inference(scs_inference,[],[11,12,34,4,5,2,3])).
% 1.15/1.26 cnf(55,plain,
% 1.15/1.26 (E(f2(a1,a1),f2(f2(x551,f2(x551,a1)),f2(x552,f2(x552,a1))))),
% 1.15/1.26 inference(scs_inference,[],[19,47,5,2])).
% 1.15/1.26 cnf(62,plain,
% 1.15/1.26 (E(f2(x621,f2(a1,a1)),f2(x621,f2(f2(x622,f2(x622,a1)),f2(x623,f2(x623,a1)))))),
% 1.15/1.26 inference(scs_inference,[],[18,55,44,36,2,3,5])).
% 1.15/1.26 cnf(66,plain,
% 1.15/1.26 (E(f2(x661,f2(f2(x662,f2(x662,a1)),f2(x663,f2(x663,a1)))),f2(x661,f2(a1,a1)))),
% 1.15/1.26 inference(scs_inference,[],[19,62,38,3,2])).
% 1.15/1.26 cnf(72,plain,
% 1.15/1.26 (E(f2(f2(a1,a1),x721),f2(f2(f2(x722,f2(x722,a1)),f2(x723,f2(x723,a1))),x721))),
% 1.15/1.26 inference(scs_inference,[],[55,4])).
% 1.15/1.26 cnf(73,plain,
% 1.15/1.26 (E(x731,f2(f2(f2(x732,f2(a1,a1)),f2(f2(x731,f2(x733,f2(x733,a1))),f2(x732,a1))),f2(x734,f2(x734,a1))))),
% 1.15/1.26 inference(scs_inference,[],[19,20,55,4,3])).
% 1.15/1.26 cnf(77,plain,
% 1.15/1.26 (~E(f2(a1,a1),f2(a1,f2(f2(x771,f2(x771,a1)),f2(x772,f2(x772,a1)))))),
% 1.15/1.26 inference(scs_inference,[],[21,66,3])).
% 1.15/1.26 cnf(85,plain,
% 1.15/1.26 (E(f2(f2(f2(x851,f2(a1,a1)),f2(f2(x852,f2(x853,f2(x853,a1))),f2(x851,a1))),f2(x854,f2(x854,a1))),x852)),
% 1.15/1.26 inference(scs_inference,[],[73,77,47,5,4,2])).
% 1.15/1.26 cnf(86,plain,
% 1.15/1.26 (~E(f2(f2(f2(x861,f2(x862,a1)),f2(f2(f2(a1,a1),f2(x863,f2(x863,a1))),f2(x861,a1))),x862),f2(x864,f2(x864,a1)))),
% 1.15/1.26 inference(scs_inference,[],[20,21,73,77,47,5,4,2,3])).
% 1.15/1.26 cnf(88,plain,
% 1.15/1.26 (E(f2(x881,f2(f2(x882,f2(x882,a1)),x883)),f2(x881,f2(a1,x883)))),
% 1.15/1.26 inference(scs_inference,[],[12,5])).
% 1.15/1.26 cnf(90,plain,
% 1.15/1.26 (~E(f2(f2(f2(x901,f2(x902,a1)),f2(f2(f2(a1,a1),f2(x903,f2(x903,a1))),f2(x901,a1))),x902),f2(x904,f2(x904,a1)))),
% 1.15/1.26 inference(rename_variables,[],[86])).
% 1.15/1.26 cnf(91,plain,
% 1.15/1.26 (~E(f2(x911,f2(x911,a1)),f2(f2(f2(x912,f2(x913,a1)),f2(f2(f2(a1,a1),f2(x914,f2(x914,a1))),f2(x912,a1))),x913))),
% 1.15/1.26 inference(scs_inference,[],[86,90,12,5,4,2])).
% 1.15/1.26 cnf(155,plain,
% 1.15/1.26 (E(f2(f2(x1551,f2(x1552,f2(x1552,a1))),f2(f2(x1553,f2(x1553,a1)),x1554)),f2(f2(x1551,a1),f2(a1,x1554)))),
% 1.15/1.26 inference(scs_inference,[],[34,88,3])).
% 1.15/1.26 cnf(160,plain,
% 1.15/1.26 (E(f2(f2(x1601,a1),f2(a1,x1602)),f2(f2(x1601,f2(x1603,f2(x1603,a1))),f2(f2(x1604,f2(x1604,a1)),x1602)))),
% 1.15/1.26 inference(scs_inference,[],[155,2])).
% 1.15/1.26 cnf(167,plain,
% 1.15/1.26 (E(f2(f2(a1,a1),f2(a1,f2(x1671,f2(x1671,a1)))),f2(x1672,f2(x1672,a1)))),
% 1.15/1.26 inference(scs_inference,[],[32,72,3])).
% 1.15/1.26 cnf(170,plain,
% 1.15/1.26 (E(f2(x1701,f2(x1701,a1)),f2(f2(a1,a1),f2(a1,f2(x1702,f2(x1702,a1)))))),
% 1.15/1.26 inference(scs_inference,[],[167,2])).
% 1.15/1.26 cnf(179,plain,
% 1.15/1.26 (E(f2(x1791,f2(x1791,a1)),f2(f2(a1,f2(x1792,f2(x1792,a1))),f2(f2(x1793,f2(x1793,a1)),f2(x1794,f2(x1794,a1)))))),
% 1.15/1.26 inference(scs_inference,[],[170,160,3])).
% 1.15/1.26 cnf(182,plain,
% 1.15/1.26 (E(f2(f2(a1,f2(x1821,f2(x1821,a1))),f2(f2(x1822,f2(x1822,a1)),f2(x1823,f2(x1823,a1)))),f2(x1824,f2(x1824,a1)))),
% 1.15/1.26 inference(scs_inference,[],[179,2])).
% 1.15/1.26 cnf(183,plain,
% 1.15/1.26 (~E(f2(x1831,f2(x1831,a1)),f2(f2(f2(x1832,f2(a1,a1)),f2(f2(f2(a1,a1),f2(x1833,f2(x1833,a1))),f2(x1832,a1))),f2(x1834,f2(x1834,a1))))),
% 1.15/1.26 inference(scs_inference,[],[40,85,179,2,3])).
% 1.15/1.26 cnf(185,plain,
% 1.15/1.26 (~E(f2(f2(f2(x1851,f2(a1,a1)),f2(f2(f2(a1,a1),f2(x1852,f2(x1852,a1))),f2(x1851,a1))),f2(x1853,f2(x1853,a1))),f2(x1854,f2(x1854,a1)))),
% 1.15/1.26 inference(scs_inference,[],[183,2])).
% 1.15/1.26 cnf(191,plain,
% 1.15/1.26 (E(f2(f2(a1,f2(x1911,f2(x1911,a1))),f2(a1,a1)),f2(x1912,f2(x1912,a1)))),
% 1.15/1.26 inference(scs_inference,[],[182,62,3])).
% 1.15/1.26 cnf(193,plain,
% 1.15/1.26 (E(f2(x1931,f2(f2(a1,f2(x1932,f2(x1932,a1))),f2(a1,a1))),f2(x1931,f2(x1933,f2(x1933,a1))))),
% 1.15/1.26 inference(scs_inference,[],[191,5])).
% 1.15/1.26 cnf(203,plain,
% 1.15/1.26 (E(f2(x2031,f2(x2031,a1)),f2(f2(a1,f2(f2(a1,f2(x2032,f2(x2032,a1))),f2(x2033,a1))),x2033))),
% 1.15/1.26 inference(scs_inference,[],[44,193,35,2,3])).
% 1.15/1.26 cnf(212,plain,
% 1.15/1.26 (~E(f2(f2(a1,f2(f2(f2(a1,a1),f2(x2121,f2(x2121,a1))),f2(a1,a1))),f2(x2122,f2(x2122,a1))),f2(x2123,f2(x2123,a1)))),
% 1.15/1.26 inference(scs_inference,[],[44,185,203,2,3])).
% 1.15/1.26 cnf(216,plain,
% 1.15/1.26 (E(f2(f2(f2(x2161,f2(x2161,a1)),x2162),f2(x2163,f2(x2164,f2(x2164,a1)))),f2(f2(a1,x2162),f2(x2163,a1)))),
% 1.15/1.27 inference(scs_inference,[],[45,44,212,2,3])).
% 1.15/1.27 cnf(219,plain,
% 1.15/1.27 (E(f2(f2(a1,x2191),f2(x2192,a1)),f2(f2(f2(x2193,f2(x2193,a1)),x2191),f2(x2192,f2(x2194,f2(x2194,a1)))))),
% 1.15/1.27 inference(scs_inference,[],[216,2])).
% 1.15/1.27 cnf(240,plain,
% 1.15/1.27 ($false),
% 1.15/1.27 inference(scs_inference,[],[46,219,91,3]),
% 1.15/1.27 ['proof']).
% 1.15/1.27 % SZS output end Proof
% 1.15/1.27 % Total time :0.650000s
%------------------------------------------------------------------------------