%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP423-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 01:26:49 PM UTC 2026
% Result : Unsatisfiable 19.58s 3.09s
% Output : CNFRefutation 19.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 2
% Syntax : Number of clauses : 160 ( 160 unt; 0 nHn; 3 RR)
% Number of literals : 160 ( 159 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 : 451 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X1,X3))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X1,X3))) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t2,plain,
multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))) = inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X1))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t6,plain,
multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))) = inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X1))),
inference(orient,[status(thm)],[t2]) ).
cnf(t16,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = inverse(multiply(inverse(multiply(Y3,X2)),multiply(Y3,X3))),
inference(cp,[status(thm)],[t6,t6]) ).
cnf(t33,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = inverse(multiply(inverse(multiply(Y3,X2)),multiply(Y3,X3))),
inference(orient,[status(thm)],[t16]) ).
cnf(t40,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = inverse(multiply(inverse(multiply(Y3,inverse(multiply(inverse(multiply(inverse(multiply(Y4,X2)),multiply(Y4,X3))),multiply(inverse(Y5),inverse(multiply(inverse(Y5),Y5))))))),multiply(Y3,Y5))),
inference(cp,[status(thm)],[t1,t33]) ).
cnf(t27211,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(Y4,X2)),multiply(Y4,X3)),
inference(step,[status(thm)],[t40,t1]) ).
cnf(t56,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(Y3,X2)),multiply(Y3,X3)),
inference(orient,[status(thm)],[t27211]) ).
cnf(t13,plain,
X1 = inverse(multiply(inverse(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3)))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))),
inference(cp,[status(thm)],[t1,t6]) ).
cnf(t78,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3)))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t57,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,Y3)) = multiply(Y4,multiply(inverse(multiply(X2,inverse(multiply(inverse(Y4),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),Y3)),
inference(cp,[status(thm)],[t56,t1]) ).
cnf(t649,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,Y3)) = multiply(Y4,multiply(inverse(multiply(X2,inverse(multiply(inverse(Y4),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),Y3)),
inference(orient,[status(thm)],[t57]) ).
cnf(t42,plain,
X1 = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),multiply(inverse(multiply(X3,Y3)),inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,Y3)))))))),multiply(X2,multiply(X3,Y3)))),
inference(cp,[status(thm)],[t1,t33]) ).
cnf(t454,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(multiply(X3,Y3)),inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,Y3)))))))),multiply(X1,multiply(X3,Y3)))) = X2,
inference(orient,[status(thm)],[t42]) ).
cnf(t3,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X1,X3)) = inverse(multiply(inverse(multiply(Y3,inverse(multiply(X2,multiply(inverse(Y4),inverse(multiply(inverse(Y4),Y4))))))),multiply(Y3,Y4))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t12044,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X1,X3)) = inverse(multiply(inverse(multiply(Y3,inverse(multiply(X2,multiply(inverse(Y4),inverse(multiply(inverse(Y4),Y4))))))),multiply(Y3,Y4))),
inference(orient,[status(thm)],[t3]) ).
cnf(t12219,plain,
X1 = inverse(inverse(multiply(inverse(multiply(X2,inverse(multiply(X1,multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X2,X3)))),
inference(cp,[status(thm)],[t454,t12044]) ).
cnf(t27213,plain,
X1 = inverse(multiply(inverse(multiply(c3,inverse(multiply(inverse(X1),multiply(inverse(c3),inverse(multiply(inverse(c3),c3))))))),multiply(c3,c3))),
inference(step,[status(thm)],[t12219,t12044]) ).
cnf(t27214,plain,
X1 = multiply(inverse(multiply(c3,inverse(multiply(inverse(inverse(X1)),multiply(inverse(c3),inverse(multiply(inverse(c3),c3))))))),multiply(c3,c3)),
inference(step,[status(thm)],[t27213,t12044]) ).
cnf(t12703,plain,
multiply(inverse(multiply(c3,inverse(multiply(inverse(inverse(X1)),multiply(inverse(c3),inverse(multiply(inverse(c3),c3))))))),multiply(c3,c3)) = X1,
inference(orient,[status(thm)],[t27214]) ).
cnf(t12910,plain,
multiply(inverse(multiply(X1,multiply(c3,c3))),multiply(X1,multiply(c3,c3))) = multiply(inverse(X2),X2),
inference(cp,[status(thm)],[t649,t12703]) ).
cnf(t12916,plain,
multiply(inverse(multiply(X1,multiply(c3,c3))),multiply(X1,multiply(c3,c3))) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t12910]) ).
cnf(t12928,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),multiply(inverse(multiply(c3,inverse(multiply(inverse(inverse(X2)),multiply(inverse(c3),inverse(multiply(inverse(c3),c3))))))),multiply(c3,c3))),
inference(cp,[status(thm)],[t12916,t12703]) ).
cnf(t27215,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(step,[status(thm)],[t12928,t12703]) ).
cnf(t13512,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t27215]) ).
cnf(t13544,plain,
X1 = inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),multiply(inverse(X1),inverse(multiply(inverse(X1),X1))))),
inference(cp,[status(thm)],[t78,t13512]) ).
cnf(t13747,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))) = X2,
inference(orient,[status(thm)],[t13544]) ).
cnf(t13778,plain,
X1 = inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),multiply(inverse(X1),inverse(multiply(inverse(X3),X3))))),
inference(cp,[status(thm)],[t13747,t13512]) ).
cnf(t13888,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(X2),inverse(multiply(inverse(X3),X3))))) = X2,
inference(orient,[status(thm)],[t13778]) ).
cnf(t18597,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(X2),inverse(multiply(inverse(X3),X3))))) = X2,
inference(rw,[status(thm)],[t13888]) ).
cnf(t13547,plain,
X1 = inverse(multiply(inverse(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3)))),multiply(inverse(X3),inverse(multiply(inverse(Y3),Y3))))),
inference(cp,[status(thm)],[t78,t13512]) ).
cnf(t16155,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3)))),multiply(inverse(X3),inverse(multiply(inverse(Y3),Y3))))) = X2,
inference(orient,[status(thm)],[t13547]) ).
cnf(t13948,plain,
multiply(inverse(X1),X1) = multiply(X2,multiply(inverse(inverse(multiply(inverse(X3),X3))),multiply(inverse(X2),inverse(multiply(inverse(Y3),Y3))))),
inference(cp,[status(thm)],[t13512,t13888]) ).
cnf(t17553,plain,
multiply(inverse(X1),X1) = multiply(X2,multiply(inverse(inverse(multiply(inverse(X3),X3))),multiply(inverse(X2),inverse(multiply(inverse(Y3),Y3))))),
inference(orient,[status(thm)],[t13948]) ).
cnf(t18100,plain,
X1 = inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),multiply(inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),X1))),inverse(multiply(inverse(Y3),Y3)))),inverse(multiply(inverse(Y4),Y4))))),
inference(cp,[status(thm)],[t16155,t17553]) ).
cnf(t27220,plain,
X1 = multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),X1))),inverse(multiply(inverse(Y3),Y3))),
inference(step,[status(thm)],[t18100,t13888]) ).
cnf(t18111,plain,
multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),X2))),inverse(multiply(inverse(X3),X3))) = X2,
inference(orient,[status(thm)],[t27220]) ).
cnf(t18116,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X2),X2),
inference(cp,[status(thm)],[t18111,t13512]) ).
cnf(t18331,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t18116]) ).
cnf(t27221,plain,
inverse(multiply(inverse(multiply(inverse(c3),c3)),multiply(inverse(X2),inverse(multiply(inverse(X3),X3))))) = X2,
inference(step,[status(thm)],[t18597,t18331]) ).
cnf(t27222,plain,
inverse(multiply(multiply(inverse(c3),c3),multiply(inverse(X2),inverse(multiply(inverse(X3),X3))))) = X2,
inference(step,[status(thm)],[t27221,t18331]) ).
cnf(t27223,plain,
inverse(multiply(multiply(inverse(c3),c3),multiply(inverse(X2),multiply(inverse(c3),c3)))) = X2,
inference(step,[status(thm)],[t27222,t18331]) ).
cnf(t18942,plain,
inverse(multiply(multiply(inverse(c3),c3),multiply(inverse(X1),multiply(inverse(c3),c3)))) = X1,
inference(orient,[status(thm)],[t27223]) ).
cnf(t18947,plain,
X1 = inverse(multiply(multiply(inverse(X2),X2),multiply(inverse(X1),multiply(inverse(c3),c3)))),
inference(cp,[status(thm)],[t18942,t13512]) ).
cnf(t19005,plain,
inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(X2),multiply(inverse(c3),c3)))) = X2,
inference(orient,[status(thm)],[t18947]) ).
cnf(t19034,plain,
X1 = inverse(multiply(multiply(inverse(X2),X2),multiply(inverse(X1),multiply(inverse(X3),X3)))),
inference(cp,[status(thm)],[t19005,t13512]) ).
cnf(t19088,plain,
inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(X2),multiply(inverse(X3),X3)))) = X2,
inference(orient,[status(thm)],[t19034]) ).
cnf(t20274,plain,
inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(X2),multiply(inverse(X3),X3)))) = X2,
inference(rw,[status(thm)],[t19088]) ).
cnf(t18362,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(multiply(inverse(Y3),Y3),multiply(inverse(X2),X3)),
inference(cp,[status(thm)],[t56,t18331]) ).
cnf(t19868,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(multiply(inverse(Y3),Y3),multiply(inverse(X2),X3)),
inference(orient,[status(thm)],[t18362]) ).
cnf(t27227,plain,
inverse(multiply(inverse(multiply(c3,X2)),multiply(c3,multiply(inverse(X3),X3)))) = X2,
inference(step,[status(thm)],[t20274,t19868]) ).
cnf(t20277,plain,
inverse(multiply(inverse(multiply(c3,X1)),multiply(c3,multiply(inverse(X2),X2)))) = X1,
inference(orient,[status(thm)],[t27227]) ).
cnf(t20278,plain,
X1 = inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X3),X3)))),
inference(cp,[status(thm)],[t20277,t33]) ).
cnf(t20371,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(inverse(X3),X3)))) = X2,
inference(orient,[status(thm)],[t20278]) ).
cnf(t20446,plain,
X1 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),X1)),multiply(inverse(X3),X3))),
inference(cp,[status(thm)],[t20371,t13512]) ).
cnf(t102,plain,
multiply(inverse(multiply(X1,multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))),multiply(X1,X3)) = multiply(Y3,multiply(inverse(inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,X2)))),X3)),
inference(cp,[status(thm)],[t56,t78]) ).
cnf(t836,plain,
multiply(inverse(multiply(X1,multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))),multiply(X1,X3)) = multiply(Y3,multiply(inverse(inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,X2)))),X3)),
inference(orient,[status(thm)],[t102]) ).
cnf(t846,plain,
multiply(X1,multiply(inverse(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3)))),Y3)) = multiply(Y4,multiply(inverse(inverse(multiply(inverse(multiply(Y5,Y4)),multiply(Y5,X3)))),Y3)),
inference(cp,[status(thm)],[t836,t78]) ).
cnf(t1047,plain,
multiply(X1,multiply(inverse(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3)))),Y3)) = multiply(Y4,multiply(inverse(inverse(multiply(inverse(multiply(Y5,Y4)),multiply(Y5,X3)))),Y3)),
inference(orient,[status(thm)],[t846]) ).
cnf(t20534,plain,
multiply(X1,multiply(inverse(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(inverse(X3),X3))))),Y3)) = multiply(Y4,multiply(inverse(Y4),Y3)),
inference(cp,[status(thm)],[t1047,t20371]) ).
cnf(t27228,plain,
multiply(X1,multiply(inverse(X1),Y3)) = multiply(Y4,multiply(inverse(Y4),Y3)),
inference(step,[status(thm)],[t20534,t20371]) ).
cnf(t20538,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(orient,[status(thm)],[t27228]) ).
cnf(t20544,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X2,multiply(inverse(X3),X3)),
inference(cp,[status(thm)],[t20538,t13512]) ).
cnf(t20705,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X2,multiply(inverse(X3),X3)),
inference(orient,[status(thm)],[t20544]) ).
cnf(t27232,plain,
X1 = inverse(multiply(c3,multiply(inverse(c3),inverse(multiply(inverse(multiply(inverse(X2),X2)),X1))))),
inference(step,[status(thm)],[t20446,t20705]) ).
cnf(t27233,plain,
X1 = inverse(multiply(c3,multiply(inverse(c3),inverse(multiply(multiply(inverse(c3),c3),X1))))),
inference(step,[status(thm)],[t27232,t18331]) ).
cnf(t22686,plain,
inverse(multiply(c3,multiply(inverse(c3),inverse(multiply(multiply(inverse(c3),c3),X1))))) = X1,
inference(orient,[status(thm)],[t27233]) ).
cnf(t22687,plain,
X1 = inverse(multiply(X2,multiply(inverse(X2),inverse(multiply(multiply(inverse(c3),c3),X1))))),
inference(cp,[status(thm)],[t22686,t20538]) ).
cnf(t22750,plain,
inverse(multiply(X1,multiply(inverse(X1),inverse(multiply(multiply(inverse(c3),c3),X2))))) = X2,
inference(orient,[status(thm)],[t22687]) ).
cnf(t22773,plain,
X1 = inverse(multiply(X2,multiply(inverse(X2),inverse(multiply(multiply(inverse(X3),X3),X1))))),
inference(cp,[status(thm)],[t22750,t13512]) ).
cnf(t22841,plain,
inverse(multiply(X1,multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),X2),X3))))) = X3,
inference(orient,[status(thm)],[t22773]) ).
cnf(t20576,plain,
X1 = inverse(multiply(inverse(multiply(X2,X1)),multiply(X3,multiply(inverse(X3),X2)))),
inference(cp,[status(thm)],[t20371,t20538]) ).
cnf(t21074,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X3,multiply(inverse(X3),X1)))) = X2,
inference(orient,[status(thm)],[t20576]) ).
cnf(t21102,plain,
X1 = inverse(multiply(multiply(inverse(X2),X2),multiply(X3,multiply(inverse(X3),inverse(X1))))),
inference(cp,[status(thm)],[t21074,t18331]) ).
cnf(t21339,plain,
inverse(multiply(multiply(inverse(X1),X1),multiply(X2,multiply(inverse(X2),inverse(X3))))) = X3,
inference(orient,[status(thm)],[t21102]) ).
cnf(t22854,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = inverse(multiply(X3,multiply(inverse(X3),X2))),
inference(cp,[status(thm)],[t22841,t21339]) ).
cnf(t22952,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = inverse(multiply(X3,multiply(inverse(X3),X2))),
inference(orient,[status(thm)],[t22854]) ).
cnf(t23102,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = inverse(multiply(X2,multiply(inverse(X3),X3))),
inference(cp,[status(thm)],[t22952,t20705]) ).
cnf(t23222,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = inverse(multiply(X2,multiply(inverse(X3),X3))),
inference(orient,[status(thm)],[t23102]) ).
cnf(t66,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,Y3))) = multiply(inverse(multiply(inverse(multiply(X3,Y4)),X2)),multiply(inverse(multiply(Y5,Y4)),multiply(Y5,Y3))),
inference(cp,[status(thm)],[t56,t56]) ).
cnf(t248,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,Y3))) = multiply(inverse(multiply(inverse(multiply(X3,Y4)),X2)),multiply(inverse(multiply(Y5,Y4)),multiply(Y5,Y3))),
inference(orient,[status(thm)],[t66]) ).
cnf(t58,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,Y3)) = multiply(inverse(multiply(inverse(multiply(Y4,Y5)),multiply(Y4,X3))),multiply(inverse(multiply(X2,Y5)),Y3)),
inference(cp,[status(thm)],[t56,t33]) ).
cnf(t150,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,Y3)) = multiply(inverse(multiply(inverse(multiply(Y4,Y5)),multiply(Y4,X3))),multiply(inverse(multiply(X2,Y5)),Y3)),
inference(orient,[status(thm)],[t58]) ).
cnf(t308,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,multiply(X2,Y3))) = multiply(inverse(multiply(Y4,multiply(Y5,X3))),multiply(Y4,multiply(Y5,Y3))),
inference(cp,[status(thm)],[t248,t150]) ).
cnf(t380,plain,
multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,multiply(X2,Y3))) = multiply(inverse(multiply(Y4,multiply(Y5,X3))),multiply(Y4,multiply(Y5,Y3))),
inference(orient,[status(thm)],[t308]) ).
cnf(t20386,plain,
multiply(inverse(X1),X2) = inverse(multiply(inverse(multiply(X3,multiply(Y3,X2))),multiply(X3,multiply(Y3,X1)))),
inference(cp,[status(thm)],[t20371,t380]) ).
cnf(t24555,plain,
inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,multiply(X2,Y3)))) = multiply(inverse(Y3),X3),
inference(orient,[status(thm)],[t20386]) ).
cnf(t20886,plain,
multiply(X1,multiply(inverse(X1),inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X3),X3),
inference(cp,[status(thm)],[t20705,t13512]) ).
cnf(t27230,plain,
multiply(X1,multiply(inverse(X1),multiply(inverse(c3),c3))) = multiply(inverse(X3),X3),
inference(step,[status(thm)],[t20886,t18331]) ).
cnf(t27231,plain,
multiply(X1,multiply(c3,multiply(inverse(c3),inverse(X1)))) = multiply(inverse(X3),X3),
inference(step,[status(thm)],[t27230,t20705]) ).
cnf(t21591,plain,
multiply(X1,multiply(c3,multiply(inverse(c3),inverse(X1)))) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t27231]) ).
cnf(t18599,plain,
multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),X2))),inverse(multiply(inverse(X3),X3))) = X2,
inference(rw,[status(thm)],[t18111]) ).
cnf(t27224,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(c3),c3)),X2))),inverse(multiply(inverse(X3),X3))) = X2,
inference(step,[status(thm)],[t18599,t18331]) ).
cnf(t27225,plain,
multiply(inverse(inverse(multiply(multiply(inverse(c3),c3),X2))),inverse(multiply(inverse(X3),X3))) = X2,
inference(step,[status(thm)],[t27224,t18331]) ).
cnf(t27226,plain,
multiply(inverse(inverse(multiply(multiply(inverse(c3),c3),X2))),multiply(inverse(c3),c3)) = X2,
inference(step,[status(thm)],[t27225,t18331]) ).
cnf(t19363,plain,
multiply(inverse(inverse(multiply(multiply(inverse(c3),c3),X1))),multiply(inverse(c3),c3)) = X1,
inference(orient,[status(thm)],[t27226]) ).
cnf(t19370,plain,
X1 = multiply(inverse(inverse(multiply(multiply(inverse(X2),X2),X1))),multiply(inverse(c3),c3)),
inference(cp,[status(thm)],[t19363,t13512]) ).
cnf(t19466,plain,
multiply(inverse(inverse(multiply(multiply(inverse(X1),X1),X2))),multiply(inverse(c3),c3)) = X2,
inference(orient,[status(thm)],[t19370]) ).
cnf(t19490,plain,
X1 = multiply(inverse(inverse(multiply(multiply(inverse(X2),X2),X1))),multiply(inverse(X3),X3)),
inference(cp,[status(thm)],[t19466,t13512]) ).
cnf(t19585,plain,
multiply(inverse(inverse(multiply(multiply(inverse(X1),X1),X2))),multiply(inverse(X3),X3)) = X2,
inference(orient,[status(thm)],[t19490]) ).
cnf(t21073,plain,
multiply(inverse(inverse(multiply(multiply(inverse(X1),X1),X2))),multiply(inverse(X3),X3)) = X2,
inference(rw,[status(thm)],[t19585]) ).
cnf(t27229,plain,
multiply(c3,multiply(inverse(c3),inverse(inverse(multiply(multiply(inverse(X1),X1),X2))))) = X2,
inference(step,[status(thm)],[t21073,t20705]) ).
cnf(t21232,plain,
multiply(c3,multiply(inverse(c3),inverse(inverse(multiply(multiply(inverse(X1),X1),X2))))) = X2,
inference(orient,[status(thm)],[t27229]) ).
cnf(t21233,plain,
X1 = multiply(X2,multiply(inverse(X2),inverse(inverse(multiply(multiply(inverse(X3),X3),X1))))),
inference(cp,[status(thm)],[t21232,t20538]) ).
cnf(t21434,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(multiply(multiply(inverse(X2),X2),X3))))) = X3,
inference(orient,[status(thm)],[t21233]) ).
cnf(t21595,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(multiply(inverse(X2),X2),X3)),X3),
inference(cp,[status(thm)],[t21591,t21434]) ).
cnf(t21924,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(multiply(inverse(X2),X2),X3)),X3),
inference(orient,[status(thm)],[t21595]) ).
cnf(t24708,plain,
multiply(inverse(X1),X2) = inverse(multiply(inverse(multiply(X3,multiply(inverse(multiply(multiply(inverse(Y3),Y3),X1)),X2))),multiply(X3,multiply(inverse(Y4),Y4)))),
inference(cp,[status(thm)],[t24555,t21924]) ).
cnf(t27237,plain,
multiply(inverse(X1),X2) = multiply(inverse(multiply(multiply(inverse(Y3),Y3),X1)),X2),
inference(step,[status(thm)],[t24708,t20371]) ).
cnf(t24821,plain,
multiply(inverse(multiply(multiply(inverse(X1),X1),X2)),X3) = multiply(inverse(X2),X3),
inference(orient,[status(thm)],[t27237]) ).
cnf(t24923,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(multiply(multiply(inverse(X2),X2),X3))))) = inverse(multiply(inverse(X3),multiply(inverse(Y3),Y3))),
inference(cp,[status(thm)],[t23222,t24821]) ).
cnf(t27239,plain,
X3 = inverse(multiply(inverse(X3),multiply(inverse(Y3),Y3))),
inference(step,[status(thm)],[t24923,t21434]) ).
cnf(t27240,plain,
X3 = multiply(c3,multiply(inverse(c3),inverse(inverse(X3)))),
inference(step,[status(thm)],[t27239,t23222]) ).
cnf(t25031,plain,
multiply(c3,multiply(inverse(c3),inverse(inverse(X1)))) = X1,
inference(orient,[status(thm)],[t27240]) ).
cnf(t25033,plain,
X1 = multiply(X2,multiply(inverse(X2),inverse(inverse(X1)))),
inference(cp,[status(thm)],[t25031,t20538]) ).
cnf(t25253,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))) = X2,
inference(orient,[status(thm)],[t25033]) ).
cnf(t25269,plain,
X1 = multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X3),X3),inverse(inverse(X1)))),
inference(cp,[status(thm)],[t25253,t18331]) ).
cnf(t25032,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(cp,[status(thm)],[t25031,t21434]) ).
cnf(t25119,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t25032]) ).
cnf(t27245,plain,
X1 = multiply(multiply(inverse(X3),X3),inverse(inverse(X1))),
inference(step,[status(thm)],[t25269,t25119]) ).
cnf(t27246,plain,
X1 = inverse(inverse(X1)),
inference(step,[status(thm)],[t27245,t25119]) ).
cnf(t25384,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t27246]) ).
cnf(t27250,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t25253,t25384]) ).
cnf(t25412,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[t27250]) ).
cnf(t25525,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t25412]) ).
cnf(t25529,plain,
X1 = multiply(X1,multiply(inverse(X2),X2)),
inference(cp,[status(thm)],[t25525,t13512]) ).
cnf(t25659,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(orient,[status(thm)],[t25529]) ).
cnf(t25694,plain,
X1 = multiply(X1,multiply(X2,inverse(X2))),
inference(cp,[status(thm)],[t25659,t25384]) ).
cnf(t25940,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(orient,[status(thm)],[t25694]) ).
cnf(t25392,plain,
X1 = multiply(multiply(X2,inverse(X2)),X1),
inference(cp,[status(thm)],[t25119,t25384]) ).
cnf(t25415,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(orient,[status(thm)],[t25392]) ).
cnf(t25942,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(cp,[status(thm)],[t25940,t25415]) ).
cnf(t27009,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(orient,[status(thm)],[t25942]) ).
cnf(t27018,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = multiply(inverse(multiply(Y3,inverse(Y3))),multiply(X2,X3)),
inference(cp,[status(thm)],[t56,t27009]) ).
cnf(t25556,plain,
multiply(inverse(X1),X2) = inverse(multiply(inverse(X2),multiply(X3,multiply(inverse(X3),X1)))),
inference(cp,[status(thm)],[t24555,t25525]) ).
cnf(t27258,plain,
multiply(inverse(X1),X2) = inverse(multiply(inverse(X2),X1)),
inference(step,[status(thm)],[t25556,t25525]) ).
cnf(t26059,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t27258]) ).
cnf(t26074,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(cp,[status(thm)],[t26059,t25384]) ).
cnf(t26109,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t26074]) ).
cnf(t26111,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(cp,[status(thm)],[t26109,t25384]) ).
cnf(t26146,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t26111]) ).
cnf(t27275,plain,
multiply(multiply(X2,inverse(X1)),multiply(X1,X3)) = multiply(inverse(multiply(Y3,inverse(Y3))),multiply(X2,X3)),
inference(step,[status(thm)],[t27018,t26146]) ).
cnf(t27276,plain,
multiply(multiply(X2,inverse(X1)),multiply(X1,X3)) = multiply(multiply(Y3,inverse(Y3)),multiply(X2,X3)),
inference(step,[status(thm)],[t27275,t26146]) ).
cnf(t27277,plain,
multiply(multiply(X2,inverse(X1)),multiply(X1,X3)) = multiply(X2,X3),
inference(step,[status(thm)],[t27276,t25415]) ).
cnf(t27053,plain,
multiply(multiply(X1,inverse(X2)),multiply(X2,X3)) = multiply(X1,X3),
inference(orient,[status(thm)],[t27277]) ).
cnf(t25550,plain,
X1 = multiply(inverse(X2),multiply(X2,X1)),
inference(cp,[status(thm)],[t25525,t25384]) ).
cnf(t25814,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t25550]) ).
cnf(t26060,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(cp,[status(thm)],[t26059,t25814]) ).
cnf(t26170,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(orient,[status(thm)],[t26060]) ).
cnf(t26175,plain,
inverse(inverse(X1)) = multiply(inverse(inverse(multiply(X1,X2))),inverse(X2)),
inference(cp,[status(thm)],[t26170,t26109]) ).
cnf(t27271,plain,
X1 = multiply(inverse(inverse(multiply(X1,X2))),inverse(X2)),
inference(step,[status(thm)],[t26175,t25384]) ).
cnf(t27272,plain,
X1 = inverse(multiply(X2,inverse(multiply(X1,X2)))),
inference(step,[status(thm)],[t27271,t26109]) ).
cnf(t27273,plain,
X1 = multiply(multiply(X1,X2),inverse(X2)),
inference(step,[status(thm)],[t27272,t26146]) ).
cnf(t26696,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(orient,[status(thm)],[t27273]) ).
cnf(t27055,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(cp,[status(thm)],[t27053,t26696]) ).
cnf(t27143,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t27055]) ).
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,t27143]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP423-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n006.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Wed Sep 23 14:42:41 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 19.58/3.09 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.58/3.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------