%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP443-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 01:26:53 PM UTC 2026
% Result : Unsatisfiable 6.73s 1.70s
% Output : CNFRefutation 6.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 2
% Syntax : Number of clauses : 89 ( 89 unt; 0 nHn; 3 RR)
% Number of literals : 89 ( 88 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 : 270 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2))))))) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2))))))) = X4,
inference(orient,[status(thm)],[t0]) ).
cnf(t3,plain,
X1 = inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2)))),multiply(multiply(Y4,inverse(Y4)),X4)))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t4,plain,
inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,X1)))),multiply(multiply(Y4,inverse(Y4)),X3)))) = X4,
inference(orient,[status(thm)],[t3]) ).
cnf(t11,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X4)))) = inverse(multiply(multiply(multiply(Y4,inverse(Y4)),X2),multiply(multiply(multiply(Y5,inverse(Y5)),X3),multiply(multiply(Y6,inverse(Y6)),X4)))),
inference(cp,[status(thm)],[t4,t4]) ).
cnf(t53,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X4)))) = inverse(multiply(multiply(multiply(Y4,inverse(Y4)),X2),multiply(multiply(multiply(Y5,inverse(Y5)),X3),multiply(multiply(Y6,inverse(Y6)),X4)))),
inference(orient,[status(thm)],[t11]) ).
cnf(t73,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(inverse(multiply(X3,multiply(X4,multiply(multiply(Y4,inverse(Y4)),X2)))),X3)))) = X4,
inference(cp,[status(thm)],[t53,t4]) ).
cnf(t99,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(inverse(multiply(X3,multiply(X4,multiply(multiply(Y4,inverse(Y4)),X2)))),X3)))) = X4,
inference(orient,[status(thm)],[t73]) ).
cnf(t105,plain,
X1 = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(multiply(X3,multiply(X4,X1))),multiply(X3,X4)))),
inference(cp,[status(thm)],[t99,t1]) ).
cnf(t257,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,X4))),multiply(X2,X3)))) = X4,
inference(orient,[status(thm)],[t105]) ).
cnf(t107,plain,
multiply(multiply(X1,inverse(X1)),X2) = multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(multiply(multiply(Y4,inverse(Y4)),inverse(multiply(Y5,multiply(X2,X4)))),multiply(multiply(Y6,inverse(Y6)),Y5))))),
inference(cp,[status(thm)],[t99,t53]) ).
cnf(t4098,plain,
multiply(multiply(X1,inverse(X1)),X2) = multiply(multiply(X3,inverse(X3)),X2),
inference(step,[status(thm)],[t107,t4]) ).
cnf(t126,plain,
multiply(multiply(X1,inverse(X1)),X2) = multiply(multiply(X3,inverse(X3)),X2),
inference(orient,[status(thm)],[t4098]) ).
cnf(t135,plain,
multiply(X1,inverse(X1)) = inverse(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(multiply(multiply(Y4,inverse(Y4)),multiply(X2,X3))))))),
inference(cp,[status(thm)],[t1,t126]) ).
cnf(t4099,plain,
multiply(X1,inverse(X1)) = multiply(Y4,inverse(Y4)),
inference(step,[status(thm)],[t135,t1]) ).
cnf(t169,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(orient,[status(thm)],[t4099]) ).
cnf(t175,plain,
X1 = inverse(multiply(X2,multiply(inverse(X2),multiply(multiply(X3,inverse(X3)),inverse(multiply(X1,multiply(X4,inverse(X4)))))))),
inference(cp,[status(thm)],[t1,t169]) ).
cnf(t387,plain,
inverse(multiply(X1,multiply(inverse(X1),multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,inverse(X4)))))))) = X3,
inference(orient,[status(thm)],[t175]) ).
cnf(t394,plain,
inverse(multiply(X1,multiply(inverse(X1),X2))) = inverse(multiply(X3,multiply(inverse(X3),X2))),
inference(cp,[status(thm)],[t387,t257]) ).
cnf(t442,plain,
inverse(multiply(X1,multiply(inverse(X1),X2))) = inverse(multiply(X3,multiply(inverse(X3),X2))),
inference(orient,[status(thm)],[t394]) ).
cnf(t456,plain,
X1 = inverse(multiply(inverse(X1),multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(inverse(X4),X2))))))),
inference(cp,[status(thm)],[t1,t442]) ).
cnf(t857,plain,
inverse(multiply(inverse(X1),multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(inverse(X4),X2))))))) = X1,
inference(orient,[status(thm)],[t456]) ).
cnf(t113,plain,
X1 = inverse(multiply(inverse(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),X1)))),multiply(X2,X3))),
inference(cp,[status(thm)],[t1,t99]) ).
cnf(t294,plain,
inverse(multiply(inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),X4)))),multiply(X1,X2))) = X4,
inference(orient,[status(thm)],[t113]) ).
cnf(t170,plain,
multiply(X1,inverse(X1)) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,inverse(X3)))),
inference(cp,[status(thm)],[t169,t126]) ).
cnf(t192,plain,
multiply(X1,inverse(X1)) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,inverse(X3)))),
inference(orient,[status(thm)],[t170]) ).
cnf(t301,plain,
inverse(multiply(X1,inverse(X1))) = inverse(multiply(inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X4))))),multiply(X2,X3))),
inference(cp,[status(thm)],[t294,t192]) ).
cnf(t2033,plain,
inverse(multiply(X1,inverse(X1))) = inverse(multiply(inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X4))))),multiply(X2,X3))),
inference(orient,[status(thm)],[t301]) ).
cnf(t2056,plain,
multiply(X1,inverse(X1)) = inverse(multiply(inverse(multiply(inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X4))))),multiply(X2,X3))),multiply(Y4,multiply(multiply(Y5,inverse(Y5)),inverse(multiply(Y6,multiply(inverse(Y6),Y4))))))),
inference(cp,[status(thm)],[t857,t2033]) ).
cnf(t4102,plain,
multiply(X1,inverse(X1)) = multiply(inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X4))))),multiply(X2,X3)),
inference(step,[status(thm)],[t2056,t857]) ).
cnf(t2237,plain,
multiply(X1,inverse(X1)) = multiply(inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X4))))),multiply(X2,X3)),
inference(orient,[status(thm)],[t4102]) ).
cnf(t2400,plain,
multiply(X1,X2) = multiply(multiply(X3,inverse(X3)),inverse(multiply(inverse(multiply(X4,multiply(Y4,inverse(Y4)))),multiply(X4,inverse(multiply(X1,multiply(X2,multiply(Y5,inverse(Y5))))))))),
inference(cp,[status(thm)],[t257,t2237]) ).
cnf(t272,plain,
inverse(X1) = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(multiply(X3,multiply(X4,inverse(X4)))),multiply(X3,X1)))),
inference(cp,[status(thm)],[t257,t169]) ).
cnf(t342,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,inverse(X3)))),multiply(X2,X4)))) = inverse(X4),
inference(orient,[status(thm)],[t272]) ).
cnf(t4103,plain,
multiply(X1,X2) = inverse(inverse(multiply(X1,multiply(X2,multiply(Y5,inverse(Y5)))))),
inference(step,[status(thm)],[t2400,t342]) ).
cnf(t2440,plain,
inverse(inverse(multiply(X1,multiply(X2,multiply(X3,inverse(X3)))))) = multiply(X1,X2),
inference(orient,[status(thm)],[t4103]) ).
cnf(t278,plain,
X1 = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(multiply(X3,multiply(inverse(X3),X1))),multiply(X4,inverse(X4))))),
inference(cp,[status(thm)],[t257,t169]) ).
cnf(t697,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),multiply(X4,inverse(X4))))) = X3,
inference(orient,[status(thm)],[t278]) ).
cnf(t871,plain,
X1 = inverse(multiply(inverse(X1),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3))),
inference(cp,[status(thm)],[t857,t697]) ).
cnf(t1136,plain,
inverse(multiply(inverse(X1),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3))) = X1,
inference(orient,[status(thm)],[t871]) ).
cnf(t1173,plain,
X1 = multiply(multiply(X2,inverse(X2)),multiply(inverse(inverse(inverse(multiply(X3,multiply(inverse(X3),X4))))),multiply(X4,X1))),
inference(cp,[status(thm)],[t257,t1136]) ).
cnf(t1931,plain,
multiply(multiply(X1,inverse(X1)),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),multiply(X3,X4))) = X4,
inference(orient,[status(thm)],[t1173]) ).
cnf(t2448,plain,
multiply(multiply(X1,inverse(X1)),inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3)))))) = inverse(inverse(inverse(X3))),
inference(cp,[status(thm)],[t2440,t1931]) ).
cnf(t3284,plain,
multiply(multiply(X1,inverse(X1)),inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3)))))) = inverse(inverse(inverse(X3))),
inference(orient,[status(thm)],[t2448]) ).
cnf(t1137,plain,
multiply(inverse(inverse(inverse(multiply(X1,multiply(inverse(X1),X2))))),multiply(X2,multiply(multiply(X3,inverse(X3)),X4))) = X4,
inference(cp,[status(thm)],[t1136,t294]) ).
cnf(t1634,plain,
multiply(inverse(inverse(inverse(multiply(X1,multiply(inverse(X1),X2))))),multiply(X2,multiply(multiply(X3,inverse(X3)),X4))) = X4,
inference(orient,[status(thm)],[t1137]) ).
cnf(t1701,plain,
X1 = inverse(inverse(multiply(X1,multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3)))),
inference(cp,[status(thm)],[t1,t1634]) ).
cnf(t1734,plain,
inverse(inverse(multiply(X1,multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3)))) = X1,
inference(orient,[status(thm)],[t1701]) ).
cnf(t2441,plain,
multiply(X1,inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),multiply(X3,inverse(X3)))))))) = X1,
inference(cp,[status(thm)],[t2440,t1734]) ).
cnf(t4104,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(step,[status(thm)],[t2441,t2440]) ).
cnf(t2547,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(orient,[status(thm)],[t4104]) ).
cnf(t2583,plain,
X1 = inverse(multiply(inverse(X1),inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),inverse(multiply(X3,inverse(X3)))))))))),
inference(cp,[status(thm)],[t1136,t2547]) ).
cnf(t4106,plain,
X1 = inverse(multiply(inverse(X1),inverse(inverse(inverse(multiply(X2,inverse(X2))))))),
inference(step,[status(thm)],[t2583,t2547]) ).
cnf(t2615,plain,
inverse(multiply(inverse(X1),inverse(inverse(inverse(multiply(X2,inverse(X2))))))) = X1,
inference(orient,[status(thm)],[t4106]) ).
cnf(t3563,plain,
inverse(multiply(inverse(X1),inverse(inverse(inverse(multiply(X2,inverse(X2))))))) = X1,
inference(rw,[status(thm)],[t2615]) ).
cnf(t3308,plain,
inverse(inverse(inverse(multiply(X1,inverse(X1))))) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,inverse(X3)))),
inference(cp,[status(thm)],[t3284,t2440]) ).
cnf(t4108,plain,
inverse(inverse(inverse(multiply(X1,inverse(X1))))) = multiply(X2,inverse(X2)),
inference(step,[status(thm)],[t3308,t2547]) ).
cnf(t3370,plain,
inverse(inverse(inverse(multiply(X1,inverse(X1))))) = multiply(X2,inverse(X2)),
inference(orient,[status(thm)],[t4108]) ).
cnf(t4109,plain,
inverse(multiply(inverse(X1),multiply(b2,inverse(b2)))) = X1,
inference(step,[status(thm)],[t3563,t3370]) ).
cnf(t3567,plain,
inverse(multiply(inverse(X1),multiply(b2,inverse(b2)))) = X1,
inference(orient,[status(thm)],[t4109]) ).
cnf(t3587,plain,
X1 = inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))),
inference(cp,[status(thm)],[t3567,t169]) ).
cnf(t3669,plain,
inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))) = X1,
inference(orient,[status(thm)],[t3587]) ).
cnf(t3723,plain,
inverse(inverse(inverse(inverse(inverse(inverse(X1)))))) = multiply(multiply(X2,inverse(X2)),inverse(inverse(X1))),
inference(cp,[status(thm)],[t3284,t3669]) ).
cnf(t3792,plain,
multiply(multiply(X1,inverse(X1)),inverse(inverse(X2))) = inverse(inverse(inverse(inverse(inverse(inverse(X2)))))),
inference(orient,[status(thm)],[t3723]) ).
cnf(t3814,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(X1,multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3)))))))) = multiply(multiply(X4,inverse(X4)),X1),
inference(cp,[status(thm)],[t3792,t1734]) ).
cnf(t4113,plain,
inverse(inverse(inverse(inverse(X1)))) = multiply(multiply(X4,inverse(X4)),X1),
inference(step,[status(thm)],[t3814,t1734]) ).
cnf(t3852,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(inverse(inverse(X2)))),
inference(orient,[status(thm)],[t4113]) ).
cnf(t2587,plain,
X1 = inverse(inverse(multiply(X1,inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),inverse(multiply(X3,inverse(X3))))))))))),
inference(cp,[status(thm)],[t1734,t2547]) ).
cnf(t4107,plain,
X1 = inverse(inverse(multiply(X1,inverse(inverse(inverse(multiply(X2,inverse(X2)))))))),
inference(step,[status(thm)],[t2587,t2547]) ).
cnf(t2710,plain,
inverse(inverse(multiply(X1,inverse(inverse(inverse(multiply(X2,inverse(X2)))))))) = X1,
inference(orient,[status(thm)],[t4107]) ).
cnf(t3564,plain,
inverse(inverse(multiply(X1,inverse(inverse(inverse(multiply(X2,inverse(X2)))))))) = X1,
inference(rw,[status(thm)],[t2710]) ).
cnf(t4132,plain,
inverse(inverse(multiply(X1,multiply(b2,inverse(b2))))) = X1,
inference(step,[status(thm)],[t3564,t3370]) ).
cnf(t3918,plain,
inverse(inverse(multiply(X1,multiply(b2,inverse(b2))))) = X1,
inference(orient,[status(thm)],[t4132]) ).
cnf(t3921,plain,
X1 = inverse(inverse(multiply(X1,multiply(X2,inverse(X2))))),
inference(cp,[status(thm)],[t3918,t169]) ).
cnf(t3960,plain,
inverse(inverse(multiply(X1,multiply(X2,inverse(X2))))) = X1,
inference(orient,[status(thm)],[t3921]) ).
cnf(t3976,plain,
X1 = inverse(inverse(multiply(X1,multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X3,inverse(X3)))))),
inference(cp,[status(thm)],[t3960,t3370]) ).
cnf(t4133,plain,
X1 = multiply(X1,inverse(inverse(multiply(X2,inverse(X2))))),
inference(step,[status(thm)],[t3976,t2440]) ).
cnf(t4010,plain,
multiply(X1,inverse(inverse(multiply(X2,inverse(X2))))) = X1,
inference(orient,[status(thm)],[t4133]) ).
cnf(t4028,plain,
X1 = inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(X2))))),
inference(cp,[status(thm)],[t3669,t4010]) ).
cnf(t4134,plain,
X1 = inverse(inverse(X1)),
inference(step,[status(thm)],[t4028,t2547]) ).
cnf(t4049,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t4134]) ).
cnf(t4135,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(step,[status(thm)],[t3852,t4049]) ).
cnf(t4136,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(step,[status(thm)],[t4135,t4049]) ).
cnf(t4050,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(orient,[status(thm)],[t4136]) ).
cnf(t4055,plain,
X1 = multiply(multiply(inverse(X2),X2),X1),
inference(cp,[status(thm)],[t4050,t4049]) ).
cnf(t4078,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t4055]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a2 != a2,
inference(rw,[status(thm)],[goal_0,t4078]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP443-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:46:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.73/1.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.73/1.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------