%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP438-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:26:52 PM UTC 2026
% Result : Unsatisfiable 5.28s 1.26s
% Output : CNFRefutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 2
% Syntax : Number of clauses : 120 ( 120 unt; 0 nHn; 3 RR)
% Number of literals : 120 ( 119 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 411 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))) = X4,
inference(orient,[status(thm)],[t0]) ).
cnf(t3,plain,
X1 = multiply(X2,inverse(multiply(multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X1))),inverse(Y4))),multiply(Y4,multiply(X4,X2))))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t5,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),inverse(Y4))),multiply(Y4,multiply(X3,X1))))) = X4,
inference(orient,[status(thm)],[t3]) ).
cnf(t7,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X4))) = multiply(Y4,inverse(multiply(multiply(X4,multiply(X2,inverse(Y5))),multiply(Y5,multiply(X3,Y4))))),
inference(cp,[status(thm)],[t5,t1]) ).
cnf(t17,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X4))) = multiply(Y4,inverse(multiply(multiply(X4,multiply(X2,inverse(Y5))),multiply(Y5,multiply(X3,Y4))))),
inference(orient,[status(thm)],[t7]) ).
cnf(t40,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X4))) = multiply(Y4,multiply(multiply(inverse(Y4),inverse(multiply(X2,X3))),inverse(X4))),
inference(cp,[status(thm)],[t17,t17]) ).
cnf(t267,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X4))) = multiply(Y4,multiply(multiply(inverse(Y4),inverse(multiply(X2,X3))),inverse(X4))),
inference(orient,[status(thm)],[t40]) ).
cnf(t275,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),inverse(multiply(Y4,X3))),X2))))))),inverse(Y5))) = multiply(Y6,multiply(multiply(inverse(Y6),inverse(Y4)),inverse(Y5))),
inference(cp,[status(thm)],[t267,t1]) ).
cnf(t3958,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(Y4)),inverse(Y5))) = multiply(Y6,multiply(multiply(inverse(Y6),inverse(Y4)),inverse(Y5))),
inference(step,[status(thm)],[t275,t1]) ).
cnf(t301,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(X2)),inverse(X3))) = multiply(X4,multiply(multiply(inverse(X4),inverse(X2)),inverse(X3))),
inference(orient,[status(thm)],[t3958]) ).
cnf(t306,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),inverse(Y4)))))),inverse(Y5))) = multiply(Y4,multiply(X4,inverse(Y5))),
inference(cp,[status(thm)],[t301,t1]) ).
cnf(t807,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),inverse(Y4)))))),inverse(Y5))) = multiply(Y4,multiply(X4,inverse(Y5))),
inference(orient,[status(thm)],[t306]) ).
cnf(t29,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(inverse(X3),inverse(multiply(X4,multiply(Y4,multiply(X2,inverse(X3))))))))),inverse(Y4))) = X4,
inference(cp,[status(thm)],[t17,t1]) ).
cnf(t54,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(inverse(X3),inverse(multiply(X4,multiply(Y4,multiply(X2,inverse(X3))))))))),inverse(Y4))) = X4,
inference(orient,[status(thm)],[t29]) ).
cnf(t56,plain,
X1 = multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(multiply(inverse(X3),inverse(multiply(X4,X1))),X4))),inverse(X3))),
inference(cp,[status(thm)],[t54,t1]) ).
cnf(t71,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),X3))),inverse(X2))) = X4,
inference(orient,[status(thm)],[t56]) ).
cnf(t62,plain,
X1 = multiply(inverse(X2),inverse(multiply(multiply(inverse(X3),inverse(multiply(X4,multiply(X2,multiply(X1,inverse(X3)))))),X4))),
inference(cp,[status(thm)],[t1,t54]) ).
cnf(t87,plain,
multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,multiply(X1,multiply(X4,inverse(X2)))))),X3))) = X4,
inference(orient,[status(thm)],[t62]) ).
cnf(t145,plain,
multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,multiply(X1,multiply(X4,inverse(X2)))))),X3))) = X4,
inference(rw,[status(thm)],[t87]) ).
cnf(t94,plain,
multiply(inverse(X1),inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X1)))))) = multiply(Y4,inverse(multiply(X2,multiply(X3,multiply(X4,Y4))))),
inference(cp,[status(thm)],[t1,t87]) ).
cnf(t105,plain,
multiply(inverse(X1),inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X1)))))) = multiply(Y4,inverse(multiply(X2,multiply(X3,multiply(X4,Y4))))),
inference(orient,[status(thm)],[t94]) ).
cnf(t3957,plain,
multiply(inverse(X1),inverse(multiply(multiply(c3,inverse(multiply(X3,multiply(X1,multiply(X4,c3))))),X3))) = X4,
inference(step,[status(thm)],[t145,t105]) ).
cnf(t147,plain,
multiply(inverse(X1),inverse(multiply(multiply(c3,inverse(multiply(X2,multiply(X1,multiply(X3,c3))))),X2))) = X3,
inference(orient,[status(thm)],[t3957]) ).
cnf(t122,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X4,X1))))) = multiply(Y4,inverse(multiply(X2,multiply(X3,multiply(X4,Y4))))),
inference(cp,[status(thm)],[t105,t105]) ).
cnf(t161,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X4,X1))))) = multiply(Y4,inverse(multiply(X2,multiply(X3,multiply(X4,Y4))))),
inference(orient,[status(thm)],[t122]) ).
cnf(t174,plain,
X1 = multiply(inverse(X2),inverse(multiply(multiply(X3,inverse(multiply(X4,multiply(X2,multiply(X1,X3))))),X4))),
inference(cp,[status(thm)],[t147,t161]) ).
cnf(t185,plain,
multiply(inverse(X1),inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(X4,X2))))),X3))) = X4,
inference(orient,[status(thm)],[t174]) ).
cnf(t311,plain,
multiply(inverse(X1),inverse(X2)) = multiply(inverse(X1),inverse(multiply(multiply(inverse(X3),inverse(multiply(X4,multiply(Y4,multiply(multiply(inverse(Y4),inverse(X2)),inverse(X3)))))),X4))),
inference(cp,[status(thm)],[t185,t301]) ).
cnf(t3959,plain,
multiply(inverse(X1),inverse(X2)) = multiply(inverse(X1),inverse(multiply(multiply(c3,inverse(multiply(X4,multiply(Y4,multiply(multiply(inverse(Y4),inverse(X2)),c3))))),X4))),
inference(step,[status(thm)],[t311,t105]) ).
cnf(t326,plain,
multiply(inverse(X1),inverse(multiply(multiply(c3,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),c3))))),X2))) = multiply(inverse(X1),inverse(X4)),
inference(orient,[status(thm)],[t3959]) ).
cnf(t339,plain,
inverse(multiply(multiply(c3,inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),c3))))),X1)) = multiply(X4,multiply(multiply(inverse(X4),inverse(multiply(multiply(inverse(Y4),inverse(multiply(inverse(Y5),inverse(X3)))),inverse(Y5)))),inverse(Y4))),
inference(cp,[status(thm)],[t71,t326]) ).
cnf(t3960,plain,
inverse(multiply(multiply(c3,inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),c3))))),X1)) = inverse(X3),
inference(step,[status(thm)],[t339,t71]) ).
cnf(t351,plain,
inverse(multiply(multiply(c3,inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),c3))))),X1)) = inverse(X3),
inference(orient,[status(thm)],[t3960]) ).
cnf(t352,plain,
inverse(X1) = inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),inverse(X1)),X2))))),X3)),
inference(cp,[status(thm)],[t351,t161]) ).
cnf(t380,plain,
inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2)) = inverse(X4),
inference(orient,[status(thm)],[t352]) ).
cnf(t854,plain,
multiply(multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2),multiply(Y4,inverse(Y5))) = multiply(Y6,multiply(multiply(inverse(Y6),inverse(multiply(Y7,multiply(Y8,multiply(multiply(inverse(Y8),inverse(multiply(Y4,Y7))),inverse(X4)))))),inverse(Y5))),
inference(cp,[status(thm)],[t807,t380]) ).
cnf(t3962,plain,
multiply(multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2),multiply(Y4,inverse(Y5))) = multiply(X4,multiply(Y4,inverse(Y5))),
inference(step,[status(thm)],[t854,t807]) ).
cnf(t890,plain,
multiply(multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2),multiply(Y4,inverse(Y5))) = multiply(X4,multiply(Y4,inverse(Y5))),
inference(orient,[status(thm)],[t3962]) ).
cnf(t936,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2) = multiply(Y4,inverse(multiply(multiply(Y5,inverse(Y6)),multiply(Y7,multiply(multiply(inverse(Y7),inverse(multiply(X4,multiply(Y5,inverse(Y6))))),Y4))))),
inference(cp,[status(thm)],[t1,t890]) ).
cnf(t3963,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2) = X4,
inference(step,[status(thm)],[t936,t1]) ).
cnf(t954,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2) = X4,
inference(orient,[status(thm)],[t3963]) ).
cnf(t989,plain,
X1 = multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,X3)))),
inference(cp,[status(thm)],[t1,t954]) ).
cnf(t1028,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,X3)))) = X1,
inference(orient,[status(thm)],[t989]) ).
cnf(t1105,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(X2)),inverse(multiply(multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),inverse(Y4))),multiply(Y4,X4))))) = multiply(Y5,multiply(inverse(Y5),inverse(X2))),
inference(cp,[status(thm)],[t301,t1028]) ).
cnf(t3964,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = multiply(Y5,multiply(inverse(Y5),inverse(X2))),
inference(step,[status(thm)],[t1105,t1028]) ).
cnf(t1120,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = multiply(X3,multiply(inverse(X3),inverse(X2))),
inference(orient,[status(thm)],[t3964]) ).
cnf(t1122,plain,
multiply(X1,multiply(inverse(X1),inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,X3))))) = multiply(Y4,inverse(Y4)),
inference(cp,[status(thm)],[t1120,t1028]) ).
cnf(t3965,plain,
multiply(X1,inverse(X1)) = multiply(Y4,inverse(Y4)),
inference(step,[status(thm)],[t1122,t1028]) ).
cnf(t1164,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(orient,[status(thm)],[t3965]) ).
cnf(t1177,plain,
inverse(X1) = multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(multiply(X4,inverse(X4)),X2))))),X3),
inference(cp,[status(thm)],[t954,t1164]) ).
cnf(t1296,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),X1))))),X2) = inverse(X3),
inference(orient,[status(thm)],[t1177]) ).
cnf(t383,plain,
inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2)) = inverse(multiply(multiply(inverse(X1),inverse(multiply(X4,X3))),X4)),
inference(cp,[status(thm)],[t380,t71]) ).
cnf(t422,plain,
inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2)) = inverse(multiply(multiply(inverse(X1),inverse(multiply(X4,X3))),X4)),
inference(orient,[status(thm)],[t383]) ).
cnf(t1115,plain,
inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),inverse(Y4))),multiply(Y4,X4)))))),X2)) = inverse(multiply(multiply(inverse(X1),inverse(Y5)),Y5)),
inference(cp,[status(thm)],[t422,t1028]) ).
cnf(t3966,plain,
inverse(multiply(multiply(inverse(X1),inverse(X2)),X2)) = inverse(multiply(multiply(inverse(X1),inverse(Y5)),Y5)),
inference(step,[status(thm)],[t1115,t1028]) ).
cnf(t1372,plain,
inverse(multiply(multiply(inverse(X1),inverse(X2)),X2)) = inverse(multiply(multiply(inverse(X1),inverse(X3)),X3)),
inference(orient,[status(thm)],[t3966]) ).
cnf(t1401,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(X3,inverse(multiply(X4,multiply(Y4,multiply(multiply(inverse(Y4),inverse(multiply(multiply(inverse(X1),inverse(Y5)),Y5))),X3))))),X4),
inference(cp,[status(thm)],[t954,t1372]) ).
cnf(t3967,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(inverse(X1),inverse(Y5)),Y5),
inference(step,[status(thm)],[t1401,t954]) ).
cnf(t1453,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(inverse(X1),inverse(X3)),X3),
inference(orient,[status(thm)],[t3967]) ).
cnf(t1460,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(X3,inverse(X3)),inverse(X1)),
inference(cp,[status(thm)],[t1453,t1164]) ).
cnf(t1515,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(X3,inverse(X3)),inverse(X1)),
inference(orient,[status(thm)],[t1460]) ).
cnf(t1537,plain,
X1 = multiply(multiply(X1,X2),inverse(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(X3)))))),
inference(cp,[status(thm)],[t1,t1515]) ).
cnf(t1907,plain,
multiply(multiply(X1,X2),inverse(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(X3)))))) = X1,
inference(orient,[status(thm)],[t1537]) ).
cnf(t1911,plain,
multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(X1))) = multiply(X3,inverse(X3)),
inference(cp,[status(thm)],[t1907,t1164]) ).
cnf(t2002,plain,
multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(X1))) = multiply(X3,inverse(X3)),
inference(orient,[status(thm)],[t1911]) ).
cnf(t2032,plain,
X1 = multiply(X1,inverse(multiply(multiply(X2,inverse(X2)),multiply(X3,inverse(X3))))),
inference(cp,[status(thm)],[t1028,t2002]) ).
cnf(t2118,plain,
multiply(X1,inverse(multiply(multiply(X2,inverse(X2)),multiply(X3,inverse(X3))))) = X1,
inference(orient,[status(thm)],[t2032]) ).
cnf(t2129,plain,
X1 = multiply(X1,inverse(multiply(X2,inverse(X2)))),
inference(cp,[status(thm)],[t2118,t2002]) ).
cnf(t2216,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(orient,[status(thm)],[t2129]) ).
cnf(t2234,plain,
X1 = multiply(X2,inverse(multiply(inverse(X1),multiply(X3,multiply(inverse(X3),X2))))),
inference(cp,[status(thm)],[t1,t2216]) ).
cnf(t2288,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(X3,multiply(inverse(X3),X1))))) = X2,
inference(orient,[status(thm)],[t2234]) ).
cnf(t2037,plain,
inverse(X1) = multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(X3,inverse(X3))))),X2),
inference(cp,[status(thm)],[t1296,t2002]) ).
cnf(t2470,plain,
multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(X3,inverse(X3))))),X2) = inverse(X1),
inference(orient,[status(thm)],[t2037]) ).
cnf(t2479,plain,
inverse(X1) = multiply(inverse(X1),multiply(X2,inverse(X2))),
inference(cp,[status(thm)],[t2470,t2118]) ).
cnf(t2550,plain,
multiply(inverse(X1),multiply(X2,inverse(X2))) = inverse(X1),
inference(orient,[status(thm)],[t2479]) ).
cnf(t2572,plain,
X1 = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(X1),multiply(X3,inverse(X3))))),
inference(cp,[status(thm)],[t2288,t2550]) ).
cnf(t3970,plain,
X1 = multiply(multiply(X2,inverse(X2)),inverse(inverse(X1))),
inference(step,[status(thm)],[t2572,t2550]) ).
cnf(t2605,plain,
multiply(multiply(X1,inverse(X1)),inverse(inverse(X2))) = X2,
inference(orient,[status(thm)],[t3970]) ).
cnf(t2637,plain,
multiply(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(cp,[status(thm)],[t2002,t2605]) ).
cnf(t2645,plain,
multiply(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t2637]) ).
cnf(t2722,plain,
multiply(multiply(X1,inverse(X1)),inverse(inverse(X2))) = multiply(multiply(X3,inverse(X3)),X2),
inference(cp,[status(thm)],[t1515,t2645]) ).
cnf(t3974,plain,
X2 = multiply(multiply(X3,inverse(X3)),X2),
inference(step,[status(thm)],[t2722,t2605]) ).
cnf(t2848,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(orient,[status(thm)],[t3974]) ).
cnf(t3977,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,X1)))),X2) = inverse(X3),
inference(step,[status(thm)],[t1296,t2848]) ).
cnf(t2932,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,X1)))),X2) = inverse(X3),
inference(rw,[status(thm)],[t3977]) ).
cnf(t3857,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,X1)))),X2) = inverse(X3),
inference(orient,[status(thm)],[t2932]) ).
cnf(t2741,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X2,inverse(multiply(X3,inverse(X3)))),
inference(cp,[status(thm)],[t2288,t2645]) ).
cnf(t3978,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t2741,t2216]) ).
cnf(t2933,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t3978]) ).
cnf(t2754,plain,
X1 = multiply(multiply(X2,inverse(multiply(X3,multiply(inverse(X1),multiply(multiply(X4,inverse(X4)),X2))))),X3),
inference(cp,[status(thm)],[t954,t2645]) ).
cnf(t3971,plain,
X1 = inverse(inverse(X1)),
inference(step,[status(thm)],[t2754,t1296]) ).
cnf(t2780,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t3971]) ).
cnf(t2952,plain,
X1 = multiply(inverse(X2),multiply(X2,X1)),
inference(cp,[status(thm)],[t2933,t2780]) ).
cnf(t3230,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t2952]) ).
cnf(t3979,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = X2,
inference(step,[status(thm)],[t2288,t2933]) ).
cnf(t2996,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = X2,
inference(rw,[status(thm)],[t3979]) ).
cnf(t3392,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = X2,
inference(orient,[status(thm)],[t2996]) ).
cnf(t3397,plain,
X1 = multiply(multiply(X1,X2),inverse(X2)),
inference(cp,[status(thm)],[t3392,t3230]) ).
cnf(t3465,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(orient,[status(thm)],[t3397]) ).
cnf(t3492,plain,
inverse(X1) = multiply(inverse(multiply(X2,X1)),X2),
inference(cp,[status(thm)],[t3230,t3465]) ).
cnf(t3737,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(orient,[status(thm)],[t3492]) ).
cnf(t3868,plain,
inverse(inverse(multiply(X1,X2))) = multiply(multiply(X1,inverse(multiply(X3,inverse(X2)))),X3),
inference(cp,[status(thm)],[t3857,t3737]) ).
cnf(t4023,plain,
multiply(X1,X2) = multiply(multiply(X1,inverse(multiply(X3,inverse(X2)))),X3),
inference(step,[status(thm)],[t3868,t2780]) ).
cnf(t3419,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t3230,t3392]) ).
cnf(t3578,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t3419]) ).
cnf(t3598,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(cp,[status(thm)],[t3578,t2780]) ).
cnf(t3678,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t3598]) ).
cnf(t3684,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(cp,[status(thm)],[t3678,t2780]) ).
cnf(t3710,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t3684]) ).
cnf(t4024,plain,
multiply(X1,X2) = multiply(multiply(X1,multiply(X2,inverse(X3))),X3),
inference(step,[status(thm)],[t4023,t3710]) ).
cnf(t3893,plain,
multiply(multiply(X1,multiply(X2,inverse(X3))),X3) = multiply(X1,X2),
inference(orient,[status(thm)],[t4024]) ).
cnf(t3486,plain,
X1 = multiply(multiply(X1,inverse(X2)),X2),
inference(cp,[status(thm)],[t3465,t2780]) ).
cnf(t3521,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(orient,[status(thm)],[t3486]) ).
cnf(t3900,plain,
multiply(X1,multiply(X2,inverse(inverse(X3)))) = multiply(multiply(X1,X2),X3),
inference(cp,[status(thm)],[t3893,t3521]) ).
cnf(t4025,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t3900,t2780]) ).
cnf(t3930,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t4025]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[goal_0,t3930]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP438-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.01/0.36 % DateTime : Wed Sep 23 14:48:38 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.28/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.28/1.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------