TSTP Solution File: GRP012+5 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n009.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 00:10:34 EDT 2023
% Result : Theorem 0.56s 1.00s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 02:35:20 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.56/1.00 %-------------------------------------------
% 0.56/1.00 % File :CSE---1.6
% 0.56/1.00 % Problem :theBenchmark
% 0.56/1.00 % Transform :cnf
% 0.56/1.00 % Format :tptp:raw
% 0.56/1.00 % Command :java -jar mcs_scs.jar %d %s
% 0.56/1.00
% 0.56/1.00 % Result :Theorem 0.390000s
% 0.56/1.00 % Output :CNFRefutation 0.390000s
% 0.56/1.00 %-------------------------------------------
% 0.56/1.00 %------------------------------------------------------------------------------
% 0.56/1.00 % File : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% 0.56/1.00 % Domain : Group Theory
% 0.56/1.00 % Problem : Inverse of products = Product of inverses
% 0.56/1.00 % Version : Especial.
% 0.56/1.00 % English : The inverse of products equals the product of the inverse,
% 0.56/1.00 % in opposite order
% 0.56/1.00
% 0.56/1.00 % Refs : [Shu04] Shults (2004), Email to G. Sutcliffe
% 0.56/1.00 % Source : [Shu04]
% 0.56/1.00 % Names :
% 0.56/1.00
% 0.56/1.00 % Status : Theorem
% 0.56/1.00 % Rating : 0.20 v8.1.0, 0.21 v7.5.0, 0.33 v7.4.0, 0.12 v7.3.0, 0.14 v7.2.0, 0.17 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.07 v6.3.0, 0.08 v6.2.0, 0.09 v6.1.0, 0.24 v6.0.0, 0.25 v5.5.0, 0.29 v5.4.0, 0.22 v5.3.0, 0.35 v5.2.0, 0.07 v5.0.0, 0.15 v4.1.0, 0.17 v4.0.1, 0.21 v4.0.0, 0.20 v3.7.0, 0.29 v3.5.0, 0.25 v3.4.0, 0.00 v3.1.0
% 0.56/1.00 % Syntax : Number of formulae : 1 ( 0 unt; 0 def)
% 0.56/1.00 % Number of atoms : 16 ( 0 equ)
% 0.56/1.00 % Maximal formula atoms : 16 ( 16 avg)
% 0.56/1.00 % Number of connectives : 15 ( 0 ~; 0 |; 11 &)
% 0.56/1.00 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.56/1.00 % Maximal formula depth : 15 ( 15 avg)
% 0.56/1.00 % Maximal term depth : 2 ( 1 avg)
% 0.56/1.00 % Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% 0.56/1.00 % Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.56/1.00 % Number of variables : 24 ( 23 !; 1 ?)
% 0.56/1.00 % SPC : FOF_THM_RFO_NEQ
% 0.56/1.00
% 0.56/1.00 % Comments :
% 0.56/1.00 %------------------------------------------------------------------------------
% 0.56/1.00 fof(prove_distribution,conjecture,
% 0.56/1.00 ! [E] :
% 0.56/1.00 ( ( ! [X,Y] :
% 0.56/1.00 ? [Z] : product(X,Y,Z)
% 0.56/1.00 & ! [X,Y,Z,U,V,W] :
% 0.56/1.00 ( ( product(X,Y,U)
% 0.56/1.00 & product(Y,Z,V)
% 0.56/1.00 & product(U,Z,W) )
% 0.56/1.00 => product(X,V,W) )
% 0.56/1.00 & ! [X,Y,Z,U,V,W] :
% 0.56/1.00 ( ( product(X,Y,U)
% 0.56/1.00 & product(Y,Z,V)
% 0.56/1.00 & product(X,V,W) )
% 0.56/1.00 => product(U,Z,W) )
% 0.56/1.00 & ! [X] : product(X,E,X)
% 0.56/1.00 & ! [X] : product(E,X,X)
% 0.56/1.00 & ! [X] : product(X,inverse(X),E)
% 0.56/1.00 & ! [X] : product(inverse(X),X,E) )
% 0.56/1.00 => ! [U,V,W,X] :
% 0.56/1.00 ( ( product(inverse(U),inverse(V),W)
% 0.56/1.00 & product(V,U,X) )
% 0.56/1.00 => product(inverse(W),inverse(X),E) ) ) ).
% 0.56/1.00
% 0.56/1.00 %------------------------------------------------------------------------------
% 0.56/1.00 %-------------------------------------------
% 0.56/1.00 % Proof found
% 0.56/1.00 % SZS status Theorem for theBenchmark
% 0.56/1.00 % SZS output start Proof
% 0.56/1.00 %ClaNum:10(EqnAxiom:0)
% 0.56/1.00 %VarNum:36(SingletonVarNum:18)
% 0.56/1.00 %MaxLitNum:4
% 0.56/1.00 %MaxfuncDepth:1
% 0.56/1.00 %SharedTerms:12
% 0.56/1.00 %goalClause: 1 2 3 4 5 6 7 8 9 10
% 0.56/1.00 %singleGoalClaCount:8
% 0.56/1.00 [1]P1(a1,a2,a5)
% 0.56/1.00 [6]P1(f7(a2),f7(a1),a6)
% 0.56/1.00 [8]~P1(f7(a6),f7(a5),a3)
% 0.56/1.00 [2]P1(x21,a3,x21)
% 0.56/1.00 [3]P1(a3,x31,x31)
% 0.56/1.00 [4]P1(x41,f7(x41),a3)
% 0.56/1.00 [5]P1(f7(x51),x51,a3)
% 0.56/1.00 [7]P1(x71,x72,f4(x71,x72))
% 0.56/1.00 [9]~P1(x96,x94,x91)+P1(x91,x92,x93)+~P1(x94,x92,x95)+~P1(x96,x95,x93)
% 0.56/1.00 [10]~P1(x101,x106,x104)+P1(x101,x102,x103)+~P1(x104,x105,x103)+~P1(x106,x105,x102)
% 0.56/1.00 %EqnAxiom
% 0.56/1.00
% 0.56/1.00 %-------------------------------------------
% 0.56/1.01 cnf(11,plain,
% 0.56/1.01 (P1(a1,a2,f4(a5,a3))),
% 0.56/1.01 inference(scs_inference,[],[1,2,7,10])).
% 0.56/1.01 cnf(12,plain,
% 0.56/1.01 (P1(x121,a3,x121)),
% 0.56/1.01 inference(rename_variables,[],[2])).
% 0.56/1.01 cnf(14,plain,
% 0.56/1.01 (P1(a5,f7(a2),a1)),
% 0.56/1.01 inference(scs_inference,[],[1,2,12,7,4,10,9])).
% 0.56/1.01 cnf(18,plain,
% 0.56/1.01 (P1(a1,f4(a2,a3),a5)),
% 0.56/1.01 inference(scs_inference,[],[1,2,7,10])).
% 0.56/1.01 cnf(20,plain,
% 0.56/1.01 (P1(x201,x202,f4(x201,x202))),
% 0.56/1.01 inference(rename_variables,[],[7])).
% 0.56/1.01 cnf(22,plain,
% 0.56/1.01 (~P1(a3,f4(f7(a6),f7(a5)),a3)),
% 0.56/1.01 inference(scs_inference,[],[1,3,8,2,7,20,10,9])).
% 0.56/1.01 cnf(26,plain,
% 0.56/1.01 (~P1(a6,a3,f7(a5))),
% 0.56/1.01 inference(scs_inference,[],[2,5,8,10])).
% 0.56/1.01 cnf(27,plain,
% 0.56/1.01 (P1(x271,a3,x271)),
% 0.56/1.01 inference(rename_variables,[],[2])).
% 0.56/1.01 cnf(28,plain,
% 0.56/1.01 (P1(f7(x281),x281,a3)),
% 0.56/1.01 inference(rename_variables,[],[5])).
% 0.56/1.01 cnf(30,plain,
% 0.56/1.01 (~P1(a3,f7(f7(a5)),f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[2,27,5,28,8,10,9])).
% 0.56/1.01 cnf(37,plain,
% 0.56/1.01 (P1(f4(a3,a1),a2,f4(a5,a3))),
% 0.56/1.01 inference(scs_inference,[],[11,6,3,4,7,14,10,9])).
% 0.56/1.01 cnf(41,plain,
% 0.56/1.01 (~P1(f7(f7(a5)),a3,f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[3,30,2,10])).
% 0.56/1.01 cnf(43,plain,
% 0.56/1.01 (P1(a3,x431,x431)),
% 0.56/1.01 inference(rename_variables,[],[3])).
% 0.56/1.01 cnf(45,plain,
% 0.56/1.01 (~P1(f7(a6),f7(a5),f7(a3))),
% 0.56/1.01 inference(scs_inference,[],[3,43,4,8,30,2,10,9])).
% 0.56/1.01 cnf(49,plain,
% 0.56/1.01 (P1(a1,f7(a1),f4(a5,a6))),
% 0.56/1.01 inference(scs_inference,[],[14,6,7,9])).
% 0.56/1.01 cnf(65,plain,
% 0.56/1.01 (P1(f7(x651),x651,a3)),
% 0.56/1.01 inference(rename_variables,[],[5])).
% 0.56/1.01 cnf(68,plain,
% 0.56/1.01 (P1(f7(f7(a3)),a3,a3)),
% 0.56/1.01 inference(scs_inference,[],[4,18,5,65,7,2,9,10])).
% 0.56/1.01 cnf(73,plain,
% 0.56/1.01 (~P1(x731,f4(f7(a6),f7(a5)),x731)),
% 0.56/1.01 inference(scs_inference,[],[5,22,9])).
% 0.56/1.01 cnf(75,plain,
% 0.56/1.01 (P1(f7(a1),f4(a5,a3),f4(a3,a2))),
% 0.56/1.01 inference(scs_inference,[],[5,22,11,7,9,10])).
% 0.56/1.01 cnf(82,plain,
% 0.56/1.01 (~P1(f4(a2,a3),f7(a2),f4(f7(a6),f7(a5)))),
% 0.56/1.01 inference(scs_inference,[],[26,18,14,6,7,73,9,10])).
% 0.56/1.01 cnf(87,plain,
% 0.56/1.01 (P1(x871,a3,x871)),
% 0.56/1.01 inference(rename_variables,[],[2])).
% 0.56/1.01 cnf(89,plain,
% 0.56/1.01 (~P1(a6,f7(f7(a3)),f7(a5))),
% 0.56/1.01 inference(scs_inference,[],[26,7,45,68,2,87,9,10])).
% 0.56/1.01 cnf(92,plain,
% 0.56/1.01 (P1(a1,a2,f4(a3,f4(a5,a3)))),
% 0.56/1.01 inference(scs_inference,[],[11,7,3,9])).
% 0.56/1.01 cnf(93,plain,
% 0.56/1.01 (P1(x931,x932,f4(x931,x932))),
% 0.56/1.01 inference(rename_variables,[],[7])).
% 0.56/1.01 cnf(96,plain,
% 0.56/1.01 (P1(a5,a6,f4(a1,f7(a1)))),
% 0.56/1.01 inference(scs_inference,[],[6,11,14,7,93,3,9,10])).
% 0.56/1.01 cnf(99,plain,
% 0.56/1.01 (P1(f4(x991,f7(x991)),a3,a3)),
% 0.56/1.01 inference(scs_inference,[],[7,4,2,9])).
% 0.56/1.01 cnf(107,plain,
% 0.56/1.01 (~P1(a2,f7(a2),f4(f7(a6),f7(a5)))),
% 0.56/1.01 inference(scs_inference,[],[7,82,3,9])).
% 0.56/1.01 cnf(115,plain,
% 0.56/1.01 (~P1(f4(x1151,f7(x1151)),a5,f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[8,99,4,9])).
% 0.56/1.01 cnf(129,plain,
% 0.56/1.01 (P1(f4(a5,a3),f7(a2),a1)),
% 0.56/1.01 inference(scs_inference,[],[11,4,2,9])).
% 0.56/1.01 cnf(133,plain,
% 0.56/1.01 (P1(f7(a1),f4(a5,a3),a2)),
% 0.56/1.01 inference(scs_inference,[],[11,4,5,2,3,9,10])).
% 0.56/1.01 cnf(142,plain,
% 0.56/1.01 (~P1(f7(a5),f7(f7(a3)),a6)),
% 0.56/1.01 inference(scs_inference,[],[26,68,2,9])).
% 0.56/1.01 cnf(150,plain,
% 0.56/1.01 (P1(f7(x1501),x1501,a3)),
% 0.56/1.01 inference(rename_variables,[],[5])).
% 0.56/1.01 cnf(153,plain,
% 0.56/1.01 (P1(f7(a5),a1,f7(a2))),
% 0.56/1.01 inference(scs_inference,[],[14,5,150,3,7,9,10])).
% 0.56/1.01 cnf(161,plain,
% 0.56/1.01 (P1(f7(a5),a5,f4(f7(a2),f4(a2,a3)))),
% 0.56/1.01 inference(scs_inference,[],[18,153,4,2,7,9,10])).
% 0.56/1.01 cnf(176,plain,
% 0.56/1.01 (P1(f4(f4(a3,a1),f7(a1)),f4(a5,a3),f4(a5,a3))),
% 0.56/1.01 inference(scs_inference,[],[37,133,7,9])).
% 0.56/1.01 cnf(179,plain,
% 0.56/1.01 (P1(a3,f4(a5,a6),a3)),
% 0.56/1.01 inference(scs_inference,[],[49,37,133,4,3,7,9,10])).
% 0.56/1.01 cnf(183,plain,
% 0.56/1.01 (P1(f4(a5,a6),a3,a3)),
% 0.56/1.01 inference(scs_inference,[],[49,4,2,9])).
% 0.56/1.01 cnf(187,plain,
% 0.56/1.01 (P1(f7(a5),f4(a5,a6),a6)),
% 0.56/1.01 inference(scs_inference,[],[49,153,6,4,2,9,10])).
% 0.56/1.01 cnf(204,plain,
% 0.56/1.01 (P1(f4(f4(a3,a1),f7(a1)),a1,a1)),
% 0.56/1.01 inference(scs_inference,[],[176,153,129,7,9,10])).
% 0.56/1.01 cnf(223,plain,
% 0.56/1.01 (P1(a3,f4(a5,a6),f4(a1,f7(a1)))),
% 0.56/1.01 inference(scs_inference,[],[187,96,4,9])).
% 0.56/1.01 cnf(255,plain,
% 0.56/1.01 (P1(f4(a3,a2),f7(a2),a3)),
% 0.56/1.01 inference(scs_inference,[],[75,129,5,9])).
% 0.56/1.01 cnf(258,plain,
% 0.56/1.01 (P1(a1,f4(a3,a2),f4(f4(a5,a6),f4(a5,a3)))),
% 0.56/1.01 inference(scs_inference,[],[75,129,49,5,7,9,10])).
% 0.56/1.01 cnf(276,plain,
% 0.56/1.01 (P1(f7(a2),a2,f4(f7(a2),f4(a2,a3)))),
% 0.56/1.01 inference(scs_inference,[],[161,153,1,9])).
% 0.56/1.01 cnf(278,plain,
% 0.56/1.01 (P1(f4(f4(a3,a1),f7(a1)),a5,a5)),
% 0.56/1.01 inference(scs_inference,[],[161,204,153,1,9,10])).
% 0.56/1.01 cnf(294,plain,
% 0.56/1.01 (P1(a3,f7(f7(a3)),a3)),
% 0.56/1.01 inference(scs_inference,[],[68,5,4,9])).
% 0.56/1.01 cnf(304,plain,
% 0.56/1.01 (P1(f7(f7(a5)),f7(a2),a1)),
% 0.56/1.01 inference(scs_inference,[],[153,5,3,10])).
% 0.56/1.01 cnf(312,plain,
% 0.56/1.01 (P1(f4(a3,f4(a5,a3)),f7(a2),a1)),
% 0.56/1.01 inference(scs_inference,[],[92,4,2,9])).
% 0.56/1.01 cnf(323,plain,
% 0.56/1.01 (P1(f7(x3231),x3231,a3)),
% 0.56/1.01 inference(rename_variables,[],[5])).
% 0.56/1.01 cnf(325,plain,
% 0.56/1.01 (P1(f7(a5),f4(a3,f4(a5,a3)),a3)),
% 0.56/1.01 inference(scs_inference,[],[73,92,153,4,5,323,9,10])).
% 0.56/1.01 cnf(331,plain,
% 0.56/1.01 (P1(a5,a3,f4(a3,f4(a5,a3)))),
% 0.56/1.01 inference(scs_inference,[],[89,325,294,4,2,3,9,10])).
% 0.56/1.01 cnf(335,plain,
% 0.56/1.01 (P1(f4(f7(a2),f4(a2,a3)),a3,a3)),
% 0.56/1.01 inference(scs_inference,[],[331,161,325,9])).
% 0.56/1.01 cnf(337,plain,
% 0.56/1.01 (~P1(a3,f7(a6),a5)),
% 0.56/1.01 inference(scs_inference,[],[99,331,161,325,115,3,9,10])).
% 0.56/1.01 cnf(345,plain,
% 0.56/1.01 (~P1(f4(f4(a3,a1),f7(a1)),a5,f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[96,278,337,4,2,3,9,10])).
% 0.56/1.01 cnf(352,plain,
% 0.56/1.01 (P1(f7(a1),f4(a3,f4(a5,a3)),a2)),
% 0.56/1.01 inference(scs_inference,[],[92,223,115,5,7,3,9,10])).
% 0.56/1.01 cnf(364,plain,
% 0.56/1.01 (~P1(a1,f7(f7(a2)),f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[304,352,331,41,4,7,9,10])).
% 0.56/1.01 cnf(367,plain,
% 0.56/1.01 (P1(f4(a1,f7(a1)),f7(a6),f4(a5,a3))),
% 0.56/1.01 inference(scs_inference,[],[96,4,7,9])).
% 0.56/1.01 cnf(386,plain,
% 0.56/1.01 (P1(f4(a5,a6),f4(a5,a3),f4(a3,f4(a5,a3)))),
% 0.56/1.01 inference(scs_inference,[],[92,133,49,9])).
% 0.56/1.01 cnf(388,plain,
% 0.56/1.01 (~P1(a5,a3,f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[92,345,278,133,49,2,9,10])).
% 0.56/1.01 cnf(397,plain,
% 0.56/1.01 (~P1(f4(a3,f4(a5,a3)),a3,f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[364,312,4,9])).
% 0.56/1.01 cnf(406,plain,
% 0.56/1.01 (P1(f4(a3,a2),f4(f7(a2),f4(a2,a3)),a2)),
% 0.56/1.01 inference(scs_inference,[],[107,276,255,2,3,9,10])).
% 0.56/1.01 cnf(412,plain,
% 0.56/1.01 (~P1(f4(a1,f7(a1)),f7(a6),f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[96,386,388,352,4,7,9,10])).
% 0.56/1.01 cnf(423,plain,
% 0.56/1.01 (~P1(f4(a5,a6),f4(a5,a3),f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[397,386,2,9])).
% 0.56/1.01 cnf(433,plain,
% 0.56/1.01 (P1(f4(a3,a2),a3,a2)),
% 0.56/1.01 inference(scs_inference,[],[406,412,335,367,2,3,9,10])).
% 0.56/1.01 cnf(453,plain,
% 0.56/1.01 (~P1(f4(f4(a5,a6),f4(a5,a3)),a3,f7(a6))),
% 0.56/1.01 inference(scs_inference,[],[133,258,423,433,49,9,10])).
% 0.56/1.01 cnf(497,plain,
% 0.56/1.01 (~P1(a3,f7(a6),f4(f4(a5,a6),f4(a5,a3)))),
% 0.56/1.01 inference(scs_inference,[],[453,3,2,9])).
% 0.56/1.01 cnf(515,plain,
% 0.56/1.01 (~P1(f4(a5,a6),f4(a1,f7(a1)),a3)),
% 0.56/1.01 inference(scs_inference,[],[142,153,497,367,6,7,10,9])).
% 0.56/1.01 cnf(606,plain,
% 0.56/1.01 ($false),
% 0.56/1.01 inference(scs_inference,[],[179,183,515,223,10]),
% 0.56/1.01 ['proof']).
% 0.56/1.01 % SZS output end Proof
% 0.56/1.01 % Total time :0.390000s
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