%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:26:17 PM UTC 2026
% Result : Unsatisfiable 30.17s 4.49s
% Output : CNFRefutation 30.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 98
% Number of leaves : 2
% Syntax : Number of clauses : 140 ( 140 unt; 0 nHn; 3 RR)
% Number of literals : 140 ( 139 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 428 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1)))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1)))))) = X3,
inference(orient,[status(thm)],[t0]) ).
cnf(t3,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1))))) = inverse(multiply(Y3,inverse(multiply(inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,X3))),inverse(multiply(inverse(Y3),Y3)))))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t5,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1))))) = inverse(multiply(Y3,inverse(multiply(inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,X3))),inverse(multiply(inverse(Y3),Y3)))))),
inference(orient,[status(thm)],[t3]) ).
cnf(t17,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1))))) = multiply(Y3,inverse(multiply(inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,inverse(X3)))),inverse(multiply(inverse(Y3),Y3))))),
inference(cp,[status(thm)],[t5,t5]) ).
cnf(t38,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1))))) = multiply(Y3,inverse(multiply(inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,inverse(X3)))),inverse(multiply(inverse(Y3),Y3))))),
inference(orient,[status(thm)],[t17]) ).
cnf(t18,plain,
inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X1),X1)))))) = X3,
inference(rw,[status(thm)],[t1]) ).
cnf(t11106,plain,
multiply(b2,inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(inverse(X3))))),inverse(multiply(inverse(b2),b2))))) = X3,
inference(step,[status(thm)],[t18,t5]) ).
cnf(t19,plain,
multiply(b2,inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(inverse(X1))))),inverse(multiply(inverse(b2),b2))))) = X1,
inference(orient,[status(thm)],[t11106]) ).
cnf(t39,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))),inverse(multiply(inverse(X1),X1))))) = X3,
inference(cp,[status(thm)],[t38,t19]) ).
cnf(t59,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))),inverse(multiply(inverse(X1),X1))))) = X3,
inference(orient,[status(thm)],[t39]) ).
cnf(t8988,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))),inverse(multiply(inverse(X1),X1))))) = X3,
inference(rw,[status(thm)],[t59]) ).
cnf(t72,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(multiply(inverse(multiply(inverse(multiply(X3,Y3)),multiply(X3,inverse(inverse(Y4))))),inverse(multiply(inverse(Y3),Y3)))))))),inverse(multiply(inverse(X1),X1))))) = inverse(multiply(Y5,inverse(multiply(inverse(multiply(inverse(multiply(Y3,Y5)),Y4)),inverse(multiply(inverse(Y5),Y5)))))),
inference(cp,[status(thm)],[t5,t59]) ).
cnf(t11107,plain,
multiply(inverse(multiply(inverse(multiply(X3,Y3)),multiply(X3,inverse(inverse(Y4))))),inverse(multiply(inverse(Y3),Y3))) = inverse(multiply(Y5,inverse(multiply(inverse(multiply(inverse(multiply(Y3,Y5)),Y4)),inverse(multiply(inverse(Y5),Y5)))))),
inference(step,[status(thm)],[t72,t59]) ).
cnf(t224,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(X3))))),inverse(multiply(inverse(X2),X2))) = inverse(multiply(Y3,inverse(multiply(inverse(multiply(inverse(multiply(X2,Y3)),X3)),inverse(multiply(inverse(Y3),Y3)))))),
inference(orient,[status(thm)],[t11107]) ).
cnf(t234,plain,
X1 = multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X1)),inverse(multiply(inverse(X3),X3)))))))),
inference(cp,[status(thm)],[t59,t224]) ).
cnf(t311,plain,
multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(inverse(X2),X2)))))))) = X3,
inference(orient,[status(thm)],[t234]) ).
cnf(t319,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(inverse(Y3))))),inverse(multiply(inverse(inverse(multiply(X2,X3))),inverse(multiply(X2,X3)))))) = multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(inverse(Y3),inverse(multiply(inverse(X3),X3)))))))),
inference(cp,[status(thm)],[t311,t59]) ).
cnf(t11108,plain,
inverse(inverse(multiply(b2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),b2)),Y3)),inverse(multiply(inverse(b2),b2))))))) = multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(inverse(Y3),inverse(multiply(inverse(X3),X3)))))))),
inference(step,[status(thm)],[t319,t224]) ).
cnf(t394,plain,
inverse(inverse(multiply(b2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),b2)),X3)),inverse(multiply(inverse(b2),b2))))))) = multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))))),
inference(orient,[status(thm)],[t11108]) ).
cnf(t415,plain,
X1 = multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(inverse(X3),X3))))))))),
inference(cp,[status(thm)],[t311,t394]) ).
cnf(t486,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2))))))))) = X3,
inference(orient,[status(thm)],[t415]) ).
cnf(t68,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,Y3)),multiply(X3,inverse(inverse(Y4))))),inverse(multiply(inverse(Y3),Y3))))))),inverse(multiply(inverse(X1),X1))))) = multiply(Y5,inverse(multiply(inverse(multiply(inverse(multiply(Y3,Y5)),Y4)),inverse(multiply(inverse(Y5),Y5))))),
inference(cp,[status(thm)],[t38,t59]) ).
cnf(t73,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,Y3)),multiply(X3,inverse(inverse(Y4))))),inverse(multiply(inverse(Y3),Y3))))))),inverse(multiply(inverse(X1),X1))))) = multiply(Y5,inverse(multiply(inverse(multiply(inverse(multiply(Y3,Y5)),Y4)),inverse(multiply(inverse(Y5),Y5))))),
inference(orient,[status(thm)],[t68]) ).
cnf(t80,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),X3)),inverse(multiply(inverse(X1),X1))))) = multiply(Y3,inverse(multiply(inverse(multiply(inverse(multiply(X2,Y3)),X3)),inverse(multiply(inverse(Y3),Y3))))),
inference(cp,[status(thm)],[t73,t59]) ).
cnf(t130,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),X3)),inverse(multiply(inverse(X1),X1))))) = multiply(Y3,inverse(multiply(inverse(multiply(inverse(multiply(X2,Y3)),X3)),inverse(multiply(inverse(Y3),Y3))))),
inference(orient,[status(thm)],[t80]) ).
cnf(t503,plain,
multiply(inverse(multiply(X1,X2)),X3) = multiply(inverse(multiply(Y3,X2)),multiply(Y3,inverse(inverse(multiply(Y4,inverse(multiply(inverse(multiply(inverse(multiply(X1,Y4)),X3)),inverse(multiply(inverse(Y4),Y4))))))))),
inference(cp,[status(thm)],[t486,t130]) ).
cnf(t1018,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(Y3,X3)),Y4)),inverse(multiply(inverse(X3),X3))))))))) = multiply(inverse(multiply(Y3,X2)),Y4),
inference(orient,[status(thm)],[t503]) ).
cnf(t499,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),b2)),X3) = multiply(inverse(multiply(Y3,b2)),multiply(Y3,multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))))))),
inference(cp,[status(thm)],[t486,t394]) ).
cnf(t589,plain,
multiply(inverse(multiply(X1,b2)),multiply(X1,multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(inverse(Y3),inverse(multiply(inverse(X3),X3)))))))))) = multiply(inverse(multiply(inverse(multiply(X2,X3)),b2)),Y3),
inference(orient,[status(thm)],[t499]) ).
cnf(t591,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),b2)),multiply(inverse(multiply(X1,X2)),X3)) = multiply(inverse(multiply(Y3,b2)),multiply(Y3,X3)),
inference(cp,[status(thm)],[t589,t311]) ).
cnf(t631,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),b2)),multiply(inverse(multiply(X1,X2)),X3)) = multiply(inverse(multiply(Y3,b2)),multiply(Y3,X3)),
inference(orient,[status(thm)],[t591]) ).
cnf(t719,plain,
multiply(inverse(multiply(X1,b2)),multiply(X1,X2)) = multiply(inverse(multiply(X3,b2)),multiply(X3,X2)),
inference(cp,[status(thm)],[t631,t631]) ).
cnf(t781,plain,
multiply(inverse(multiply(X1,b2)),multiply(X1,X2)) = multiply(inverse(multiply(X3,b2)),multiply(X3,X2)),
inference(orient,[status(thm)],[t719]) ).
cnf(t1053,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(Y3,X2)),multiply(Y3,inverse(inverse(multiply(b2,inverse(multiply(inverse(multiply(inverse(multiply(Y4,b2)),multiply(Y4,X3))),inverse(multiply(inverse(b2),b2))))))))),
inference(cp,[status(thm)],[t1018,t781]) ).
cnf(t11109,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(Y4,X2)),multiply(Y4,X3)),
inference(step,[status(thm)],[t1053,t1018]) ).
cnf(t1132,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(Y3,X2)),multiply(Y3,X3)),
inference(orient,[status(thm)],[t11109]) ).
cnf(t1172,plain,
X1 = multiply(X2,inverse(inverse(multiply(multiply(X3,Y3),inverse(multiply(inverse(multiply(inverse(multiply(X2,multiply(X3,Y3))),X1)),inverse(multiply(inverse(multiply(Y4,Y3)),multiply(Y4,Y3))))))))),
inference(cp,[status(thm)],[t311,t1132]) ).
cnf(t2849,plain,
multiply(X1,inverse(inverse(multiply(multiply(X2,X3),inverse(multiply(inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),Y3)),inverse(multiply(inverse(multiply(Y4,X3)),multiply(Y4,X3))))))))) = Y3,
inference(orient,[status(thm)],[t1172]) ).
cnf(t2889,plain,
multiply(X1,X2) = multiply(X1,inverse(inverse(multiply(multiply(X3,Y3),inverse(multiply(inverse(multiply(inverse(multiply(Y4,multiply(X3,Y3))),multiply(Y4,X2))),inverse(multiply(inverse(multiply(Y5,Y3)),multiply(Y5,Y3))))))))),
inference(cp,[status(thm)],[t2849,t1132]) ).
cnf(t3874,plain,
multiply(X1,inverse(inverse(multiply(multiply(X2,X3),inverse(multiply(inverse(multiply(inverse(multiply(Y3,multiply(X2,X3))),multiply(Y3,Y4))),inverse(multiply(inverse(multiply(Y5,X3)),multiply(Y5,X3))))))))) = multiply(X1,Y4),
inference(orient,[status(thm)],[t2889]) ).
cnf(t3877,plain,
multiply(X1,X2) = multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X3,Y3)),multiply(X3,inverse(inverse(multiply(Y3,X2)))))),inverse(multiply(inverse(Y3),Y3))))),
inference(cp,[status(thm)],[t3874,t224]) ).
cnf(t4169,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(inverse(multiply(X3,Y3)))))),inverse(multiply(inverse(X3),X3))))) = multiply(X1,Y3),
inference(orient,[status(thm)],[t3877]) ).
cnf(t4281,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X3)))))),inverse(multiply(inverse(X2),X2)))) = multiply(Y3,inverse(inverse(multiply(Y4,inverse(multiply(inverse(multiply(inverse(multiply(Y3,Y4)),X3)),inverse(multiply(inverse(Y4),Y4)))))))),
inference(cp,[status(thm)],[t311,t4169]) ).
cnf(t11113,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X3)))))),inverse(multiply(inverse(X2),X2)))) = X3,
inference(step,[status(thm)],[t4281,t311]) ).
cnf(t4368,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X3)))))),inverse(multiply(inverse(X2),X2)))) = X3,
inference(orient,[status(thm)],[t11113]) ).
cnf(t4516,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,X3)) = multiply(Y3,multiply(inverse(multiply(inverse(multiply(Y4,X2)),multiply(Y4,inverse(inverse(multiply(X2,Y3)))))),X3)),
inference(cp,[status(thm)],[t1132,t4368]) ).
cnf(t5911,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,X3)) = multiply(Y3,multiply(inverse(multiply(inverse(multiply(Y4,X2)),multiply(Y4,inverse(inverse(multiply(X2,Y3)))))),X3)),
inference(orient,[status(thm)],[t4516]) ).
cnf(t265,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(inverse(X3)))))))),inverse(multiply(inverse(X2),X2))) = inverse(X3),
inference(cp,[status(thm)],[t224,t59]) ).
cnf(t358,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(inverse(X3)))))))),inverse(multiply(inverse(X2),X2))) = inverse(X3),
inference(orient,[status(thm)],[t265]) ).
cnf(t4467,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X3)))))),inverse(multiply(inverse(X2),X2)))) = multiply(inverse(multiply(inverse(multiply(Y3,Y4)),multiply(Y3,inverse(inverse(multiply(Y4,inverse(X3))))))),inverse(multiply(inverse(Y4),Y4))),
inference(cp,[status(thm)],[t358,t4368]) ).
cnf(t11114,plain,
X3 = multiply(inverse(multiply(inverse(multiply(Y3,Y4)),multiply(Y3,inverse(inverse(multiply(Y4,inverse(X3))))))),inverse(multiply(inverse(Y4),Y4))),
inference(step,[status(thm)],[t4467,t4368]) ).
cnf(t4547,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X3))))))),inverse(multiply(inverse(X2),X2))) = X3,
inference(orient,[status(thm)],[t11114]) ).
cnf(t6123,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X3),X3),
inference(cp,[status(thm)],[t5911,t4547]) ).
cnf(t6313,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X3),X3),
inference(orient,[status(thm)],[t6123]) ).
cnf(t6319,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),multiply(inverse(multiply(inverse(multiply(X3,Y3)),multiply(X3,inverse(inverse(multiply(Y3,inverse(X2))))))),inverse(multiply(inverse(Y3),Y3)))),
inference(cp,[status(thm)],[t6313,t4547]) ).
cnf(t11119,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(step,[status(thm)],[t6319,t4547]) ).
cnf(t6690,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t11119]) ).
cnf(t6736,plain,
multiply(X1,X2) = multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))))))),
inference(cp,[status(thm)],[t311,t6690]) ).
cnf(t8036,plain,
multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))))))) = multiply(X1,X2),
inference(orient,[status(thm)],[t6736]) ).
cnf(t8102,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X1),X1))))))) = inverse(multiply(inverse(multiply(inverse(multiply(X3,Y3)),multiply(X3,inverse(inverse(multiply(Y3,X1)))))),inverse(multiply(inverse(Y3),Y3)))),
inference(cp,[status(thm)],[t4368,t8036]) ).
cnf(t11126,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X1),X1))))))) = X1,
inference(step,[status(thm)],[t8102,t4368]) ).
cnf(t8189,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X1),X1))))))) = X1,
inference(orient,[status(thm)],[t11126]) ).
cnf(t8215,plain,
X1 = inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3))))))),
inference(cp,[status(thm)],[t8189,t6690]) ).
cnf(t8294,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3))))))) = X1,
inference(orient,[status(thm)],[t8215]) ).
cnf(t8300,plain,
inverse(inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))))) = inverse(inverse(multiply(inverse(X3),X3))),
inference(cp,[status(thm)],[t8294,t6690]) ).
cnf(t8384,plain,
inverse(inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))))) = inverse(inverse(multiply(inverse(X3),X3))),
inference(orient,[status(thm)],[t8300]) ).
cnf(t8443,plain,
multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(Y3,X3)),multiply(Y3,inverse(inverse(multiply(inverse(Y4),Y4)))))),inverse(multiply(inverse(X3),X3))))),
inference(cp,[status(thm)],[t59,t8384]) ).
cnf(t11127,plain,
multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(Y4),Y4),
inference(step,[status(thm)],[t8443,t59]) ).
cnf(t8584,plain,
multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(X3),X3),
inference(orient,[status(thm)],[t11127]) ).
cnf(t8663,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(inverse(Y3),Y3))))))),
inference(cp,[status(thm)],[t486,t8584]) ).
cnf(t6741,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(multiply(X1,inverse(multiply(inverse(X3),X3))))))),
inference(cp,[status(thm)],[t486,t6690]) ).
cnf(t7889,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),X3))))))) = inverse(multiply(inverse(X2),X2)),
inference(orient,[status(thm)],[t6741]) ).
cnf(t11128,plain,
multiply(inverse(X1),X1) = inverse(multiply(inverse(X3),X3)),
inference(step,[status(thm)],[t8663,t7889]) ).
cnf(t8905,plain,
multiply(inverse(X1),X1) = inverse(multiply(inverse(X2),X2)),
inference(orient,[status(thm)],[t11128]) ).
cnf(t11138,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))),multiply(inverse(b2),b2)))) = X3,
inference(step,[status(thm)],[t8988,t8905]) ).
cnf(t6776,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(inverse(X3),X2)),multiply(inverse(Y3),Y3)),
inference(cp,[status(thm)],[t1132,t6690]) ).
cnf(t7508,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(inverse(X3),X2)),multiply(inverse(Y3),Y3)),
inference(orient,[status(thm)],[t6776]) ).
cnf(t11139,plain,
multiply(X1,inverse(multiply(inverse(multiply(b2,multiply(X2,inverse(inverse(X3))))),multiply(b2,multiply(X2,X1))))) = X3,
inference(step,[status(thm)],[t11138,t7508]) ).
cnf(t10168,plain,
multiply(X1,inverse(multiply(inverse(multiply(b2,multiply(X2,inverse(inverse(X3))))),multiply(b2,multiply(X2,X1))))) = X3,
inference(orient,[status(thm)],[t11139]) ).
cnf(t10169,plain,
X1 = multiply(inverse(inverse(X1)),multiply(inverse(X2),X2)),
inference(cp,[status(thm)],[t10168,t8905]) ).
cnf(t10246,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X2),X2)) = X1,
inference(orient,[status(thm)],[t10169]) ).
cnf(t10588,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X2),X2)) = X1,
inference(rw,[status(thm)],[t10246]) ).
cnf(t8904,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3))))))) = X1,
inference(rw,[status(thm)],[t8294]) ).
cnf(t11129,plain,
inverse(inverse(multiply(X1,inverse(multiply(multiply(inverse(b2),b2),inverse(multiply(inverse(X3),X3))))))) = X1,
inference(step,[status(thm)],[t8904,t8905]) ).
cnf(t11130,plain,
inverse(inverse(multiply(X1,inverse(multiply(multiply(inverse(b2),b2),multiply(inverse(b2),b2)))))) = X1,
inference(step,[status(thm)],[t11129,t8905]) ).
cnf(t8959,plain,
multiply(inverse(X1),X1) = multiply(multiply(inverse(X2),X2),multiply(inverse(X3),X3)),
inference(cp,[status(thm)],[t6690,t8905]) ).
cnf(t9002,plain,
multiply(inverse(X1),X1) = multiply(multiply(inverse(X2),X2),multiply(inverse(X3),X3)),
inference(orient,[status(thm)],[t8959]) ).
cnf(t11131,plain,
inverse(inverse(multiply(X1,inverse(multiply(inverse(b2),b2))))) = X1,
inference(step,[status(thm)],[t11130,t9002]) ).
cnf(t11132,plain,
inverse(inverse(multiply(X1,multiply(inverse(b2),b2)))) = X1,
inference(step,[status(thm)],[t11131,t8905]) ).
cnf(t9096,plain,
inverse(inverse(multiply(X1,multiply(inverse(b2),b2)))) = X1,
inference(orient,[status(thm)],[t11132]) ).
cnf(t9105,plain,
X1 = inverse(inverse(multiply(X1,multiply(inverse(X2),X2)))),
inference(cp,[status(thm)],[t9096,t6690]) ).
cnf(t9114,plain,
inverse(inverse(multiply(X1,multiply(inverse(X2),X2)))) = X1,
inference(orient,[status(thm)],[t9105]) ).
cnf(t9117,plain,
inverse(multiply(inverse(X1),X2)) = inverse(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X1)))),
inference(cp,[status(thm)],[t9114,t7508]) ).
cnf(t9143,plain,
inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3)))) = inverse(multiply(inverse(X3),X2)),
inference(orient,[status(thm)],[t9117]) ).
cnf(t10187,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = multiply(Y3,inverse(multiply(inverse(multiply(b2,multiply(Y4,inverse(inverse(multiply(inverse(X3),X2)))))),multiply(b2,multiply(Y4,Y3))))),
inference(cp,[status(thm)],[t10168,t9143]) ).
cnf(t11140,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = multiply(inverse(X3),X2),
inference(step,[status(thm)],[t10187,t10168]) ).
cnf(t10309,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = multiply(inverse(X3),X2),
inference(orient,[status(thm)],[t11140]) ).
cnf(t9137,plain,
multiply(inverse(X1),X1) = multiply(X2,inverse(multiply(X2,multiply(inverse(X3),X3)))),
inference(cp,[status(thm)],[t6690,t9114]) ).
cnf(t9186,plain,
multiply(inverse(X1),X1) = multiply(X2,inverse(multiply(X2,multiply(inverse(X3),X3)))),
inference(orient,[status(thm)],[t9137]) ).
cnf(t10336,plain,
multiply(inverse(inverse(multiply(X1,multiply(inverse(X2),X2)))),X3) = inverse(multiply(inverse(multiply(X1,X3)),multiply(inverse(Y3),Y3))),
inference(cp,[status(thm)],[t10309,t9186]) ).
cnf(t11144,plain,
multiply(X1,X3) = inverse(multiply(inverse(multiply(X1,X3)),multiply(inverse(Y3),Y3))),
inference(step,[status(thm)],[t10336,t9114]) ).
cnf(t10382,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(inverse(X3),X3))) = multiply(X1,X2),
inference(orient,[status(thm)],[t11144]) ).
cnf(t10393,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X2),X2)) = inverse(multiply(inverse(X1),multiply(inverse(X3),X3))),
inference(cp,[status(thm)],[t10382,t10246]) ).
cnf(t11145,plain,
X1 = inverse(multiply(inverse(X1),multiply(inverse(X3),X3))),
inference(step,[status(thm)],[t10393,t10246]) ).
cnf(t10443,plain,
inverse(multiply(inverse(X1),multiply(inverse(X2),X2))) = X1,
inference(orient,[status(thm)],[t11145]) ).
cnf(t10473,plain,
multiply(inverse(multiply(inverse(X1),multiply(inverse(X2),X2))),multiply(inverse(X3),X3)) = multiply(Y3,multiply(inverse(Y3),X1)),
inference(cp,[status(thm)],[t7508,t10443]) ).
cnf(t11146,plain,
multiply(X1,multiply(inverse(X3),X3)) = multiply(Y3,multiply(inverse(Y3),X1)),
inference(step,[status(thm)],[t10473,t10443]) ).
cnf(t10491,plain,
multiply(X1,multiply(inverse(X2),X2)) = multiply(X3,multiply(inverse(X3),X1)),
inference(orient,[status(thm)],[t11146]) ).
cnf(t11147,plain,
multiply(b2,multiply(inverse(b2),inverse(inverse(X1)))) = X1,
inference(step,[status(thm)],[t10588,t10491]) ).
cnf(t10617,plain,
multiply(b2,multiply(inverse(b2),inverse(inverse(X1)))) = X1,
inference(orient,[status(thm)],[t11147]) ).
cnf(t10517,plain,
X1 = inverse(inverse(multiply(X2,multiply(inverse(X2),X1)))),
inference(cp,[status(thm)],[t9114,t10491]) ).
cnf(t10590,plain,
inverse(inverse(multiply(X1,multiply(inverse(X1),X2)))) = X2,
inference(orient,[status(thm)],[t10517]) ).
cnf(t10622,plain,
inverse(multiply(X1,multiply(inverse(X1),X2))) = multiply(b2,multiply(inverse(b2),inverse(X2))),
inference(cp,[status(thm)],[t10617,t10590]) ).
cnf(t10704,plain,
inverse(multiply(X1,multiply(inverse(X1),X2))) = multiply(b2,multiply(inverse(b2),inverse(X2))),
inference(orient,[status(thm)],[t10622]) ).
cnf(t11143,plain,
multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))) = X3,
inference(step,[status(thm)],[t10168,t10309]) ).
cnf(t10381,plain,
multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))) = X3,
inference(rw,[status(thm)],[t11143]) ).
cnf(t10935,plain,
multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X3))))) = X3,
inference(orient,[status(thm)],[t10381]) ).
cnf(t10546,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(cp,[status(thm)],[t10491,t10491]) ).
cnf(t10739,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(orient,[status(thm)],[t10546]) ).
cnf(t10740,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))) = X2,
inference(cp,[status(thm)],[t10739,t10617]) ).
cnf(t10784,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))) = X2,
inference(orient,[status(thm)],[t10740]) ).
cnf(t10798,plain,
multiply(inverse(multiply(inverse(X1),inverse(inverse(X2)))),X3) = inverse(multiply(inverse(multiply(X1,X3)),X2)),
inference(cp,[status(thm)],[t10309,t10784]) ).
cnf(t10875,plain,
multiply(inverse(multiply(inverse(X1),inverse(inverse(X2)))),X3) = inverse(multiply(inverse(multiply(X1,X3)),X2)),
inference(orient,[status(thm)],[t10798]) ).
cnf(t10938,plain,
X1 = multiply(inverse(inverse(X2)),inverse(multiply(inverse(multiply(X3,multiply(inverse(X3),inverse(inverse(X1))))),X2))),
inference(cp,[status(thm)],[t10935,t10875]) ).
cnf(t11150,plain,
X1 = multiply(inverse(inverse(X2)),inverse(multiply(multiply(b2,multiply(inverse(b2),inverse(inverse(inverse(X1))))),X2))),
inference(step,[status(thm)],[t10938,t10704]) ).
cnf(t11151,plain,
X1 = multiply(inverse(inverse(X2)),inverse(multiply(inverse(X1),X2))),
inference(step,[status(thm)],[t11150,t10617]) ).
cnf(t10996,plain,
multiply(inverse(inverse(X1)),inverse(multiply(inverse(X2),X1))) = X2,
inference(orient,[status(thm)],[t11151]) ).
cnf(t11027,plain,
multiply(b2,multiply(inverse(b2),inverse(inverse(multiply(inverse(X1),X2))))) = inverse(multiply(inverse(X2),X1)),
inference(cp,[status(thm)],[t10704,t10996]) ).
cnf(t11152,plain,
multiply(inverse(X1),X2) = inverse(multiply(inverse(X2),X1)),
inference(step,[status(thm)],[t11027,t10617]) ).
cnf(t11045,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t11152]) ).
cnf(t10621,plain,
inverse(multiply(X1,multiply(inverse(X2),X2))) = multiply(b2,multiply(inverse(b2),inverse(X1))),
inference(cp,[status(thm)],[t10617,t9114]) ).
cnf(t10663,plain,
inverse(multiply(X1,multiply(inverse(X2),X2))) = multiply(b2,multiply(inverse(b2),inverse(X1))),
inference(orient,[status(thm)],[t10621]) ).
cnf(t11048,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = multiply(b2,multiply(inverse(b2),inverse(inverse(X2)))),
inference(cp,[status(thm)],[t11045,t10663]) ).
cnf(t11163,plain,
multiply(multiply(inverse(X1),X1),X2) = multiply(b2,multiply(inverse(b2),inverse(inverse(X2)))),
inference(step,[status(thm)],[t11048,t11045]) ).
cnf(t11164,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(step,[status(thm)],[t11163,t10617]) ).
cnf(t11087,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t11164]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a2 != a2,
inference(rw,[status(thm)],[goal_0,t11087]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.57 % Computer : n006.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Wed Sep 23 14:41:58 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 30.17/4.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.17/4.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------