%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP431-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 01:26:51 PM UTC 2026
% Result : Unsatisfiable 5.59s 6.21s
% Output : CNFRefutation 5.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 2
% Syntax : Number of clauses : 85 ( 85 unt; 0 nHn; 3 RR)
% Number of literals : 85 ( 84 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 249 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
multiply(X1,inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X1)))) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1,plain,
multiply(X1,inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X1)))) = X4,
inference(orient,[status(thm)],[t0]) ).
cnf(t3,plain,
X1 = multiply(X2,inverse(multiply(multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X1))),multiply(Y4,inverse(Y4))),multiply(X4,X2)))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t5,plain,
multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X4))),multiply(Y4,inverse(Y4))),multiply(X3,X1)))) = X4,
inference(orient,[status(thm)],[t3]) ).
cnf(t6,plain,
multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),multiply(X4,inverse(X4))) = multiply(Y4,inverse(multiply(multiply(X2,multiply(Y5,inverse(Y5))),multiply(X3,Y4)))),
inference(cp,[status(thm)],[t5,t1]) ).
cnf(t15,plain,
multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),multiply(X4,inverse(X4))) = multiply(Y4,inverse(multiply(multiply(X2,multiply(Y5,inverse(Y5))),multiply(X3,Y4)))),
inference(orient,[status(thm)],[t6]) ).
cnf(t19,plain,
X1 = multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,inverse(multiply(multiply(X1,multiply(Y4,inverse(Y4))),multiply(X3,X4))))))),
inference(cp,[status(thm)],[t1,t15]) ).
cnf(t35,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,inverse(multiply(multiply(X4,multiply(Y4,inverse(Y4))),multiply(X2,X3))))))) = X4,
inference(orient,[status(thm)],[t19]) ).
cnf(t43,plain,
X1 = multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(multiply(X4,multiply(Y4,inverse(Y4))),multiply(X1,X3)))),multiply(X4,X2)))),
inference(cp,[status(thm)],[t1,t35]) ).
cnf(t49,plain,
multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(multiply(X3,multiply(X4,inverse(X4))),multiply(Y4,X2)))),multiply(X3,X1)))) = Y4,
inference(orient,[status(thm)],[t43]) ).
cnf(t51,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X4)))))) = multiply(Y4,inverse(multiply(X2,multiply(X3,Y4)))),
inference(cp,[status(thm)],[t49,t1]) ).
cnf(t71,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X4)))))) = multiply(Y4,inverse(multiply(X2,multiply(X3,Y4)))),
inference(orient,[status(thm)],[t51]) ).
cnf(t75,plain,
X1 = multiply(X2,inverse(multiply(multiply(X3,multiply(X4,inverse(X4))),multiply(multiply(Y4,inverse(multiply(X1,multiply(X3,Y4)))),X2)))),
inference(cp,[status(thm)],[t1,t71]) ).
cnf(t132,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),multiply(multiply(X4,inverse(multiply(Y4,multiply(X2,X4)))),X1)))) = Y4,
inference(orient,[status(thm)],[t75]) ).
cnf(t161,plain,
X1 = multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X3,inverse(multiply(X4,multiply(X1,X3)))),X4))),
inference(cp,[status(thm)],[t35,t132]) ).
cnf(t171,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X4,X2)))),X3))) = X4,
inference(orient,[status(thm)],[t161]) ).
cnf(t174,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))) = multiply(multiply(X4,inverse(X4)),inverse(multiply(X2,X3))),
inference(cp,[status(thm)],[t171,t1]) ).
cnf(t239,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))) = multiply(multiply(X4,inverse(X4)),inverse(multiply(X2,X3))),
inference(orient,[status(thm)],[t174]) ).
cnf(t260,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(multiply(inverse(multiply(X3,X4)),multiply(multiply(multiply(Y4,inverse(Y4)),inverse(multiply(multiply(Y5,inverse(Y5)),inverse(multiply(X3,X4))))),X2)))),
inference(cp,[status(thm)],[t1,t239]) ).
cnf(t1620,plain,
multiply(X1,inverse(X1)) = multiply(Y5,inverse(Y5)),
inference(step,[status(thm)],[t260,t1]) ).
cnf(t290,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(orient,[status(thm)],[t1620]) ).
cnf(t293,plain,
X1 = multiply(X2,inverse(multiply(inverse(X1),multiply(multiply(X3,inverse(X3)),X2)))),
inference(cp,[status(thm)],[t1,t290]) ).
cnf(t316,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(multiply(X3,inverse(X3)),X1)))) = X2,
inference(orient,[status(thm)],[t293]) ).
cnf(t332,plain,
inverse(X1) = multiply(X2,inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X4,inverse(X4))),multiply(X1,X2)))),
inference(cp,[status(thm)],[t1,t316]) ).
cnf(t440,plain,
multiply(X1,inverse(multiply(multiply(multiply(X2,inverse(X2)),multiply(X3,inverse(X3))),multiply(X4,X1)))) = inverse(X4),
inference(orient,[status(thm)],[t332]) ).
cnf(t441,plain,
inverse(multiply(X1,inverse(multiply(X2,multiply(multiply(X3,inverse(X3)),X1))))) = X2,
inference(cp,[status(thm)],[t440,t132]) ).
cnf(t491,plain,
inverse(multiply(X1,inverse(multiply(X2,multiply(multiply(X3,inverse(X3)),X1))))) = X2,
inference(orient,[status(thm)],[t441]) ).
cnf(t492,plain,
multiply(multiply(X1,inverse(X1)),multiply(X2,inverse(X2))) = inverse(inverse(multiply(X3,inverse(X3)))),
inference(cp,[status(thm)],[t491,t440]) ).
cnf(t585,plain,
multiply(multiply(X1,inverse(X1)),multiply(X2,inverse(X2))) = inverse(inverse(multiply(X3,inverse(X3)))),
inference(orient,[status(thm)],[t492]) ).
cnf(t599,plain,
X1 = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(X1),inverse(inverse(multiply(X3,inverse(X3))))))),
inference(cp,[status(thm)],[t316,t585]) ).
cnf(t664,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(X2),inverse(inverse(multiply(X3,inverse(X3))))))) = X2,
inference(orient,[status(thm)],[t599]) ).
cnf(t686,plain,
inverse(X1) = multiply(X2,inverse(multiply(inverse(inverse(multiply(X3,inverse(X3)))),multiply(X1,X2)))),
inference(cp,[status(thm)],[t1,t664]) ).
cnf(t712,plain,
multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X3,X1)))) = inverse(X3),
inference(orient,[status(thm)],[t686]) ).
cnf(t734,plain,
inverse(X1) = multiply(inverse(X1),inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X3,inverse(X3))))),
inference(cp,[status(thm)],[t712,t290]) ).
cnf(t823,plain,
multiply(inverse(X1),inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X3,inverse(X3))))) = inverse(X1),
inference(orient,[status(thm)],[t734]) ).
cnf(t605,plain,
X1 = inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X1,inverse(inverse(multiply(X3,inverse(X3)))))))),
inference(cp,[status(thm)],[t491,t585]) ).
cnf(t767,plain,
inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(inverse(multiply(X3,inverse(X3)))))))) = X2,
inference(orient,[status(thm)],[t605]) ).
cnf(t828,plain,
inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(inverse(multiply(X3,inverse(X3)))))))) = multiply(X2,inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),multiply(Y4,inverse(Y4))))),
inference(cp,[status(thm)],[t823,t767]) ).
cnf(t1621,plain,
X2 = multiply(X2,inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),multiply(Y4,inverse(Y4))))),
inference(step,[status(thm)],[t828,t767]) ).
cnf(t863,plain,
multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X3,inverse(X3))))) = X1,
inference(orient,[status(thm)],[t1621]) ).
cnf(t869,plain,
multiply(inverse(inverse(multiply(X1,inverse(X1)))),multiply(X2,inverse(X2))) = multiply(X3,inverse(X3)),
inference(cp,[status(thm)],[t863,t290]) ).
cnf(t940,plain,
multiply(inverse(inverse(multiply(X1,inverse(X1)))),multiply(X2,inverse(X2))) = multiply(X3,inverse(X3)),
inference(orient,[status(thm)],[t869]) ).
cnf(t964,plain,
X1 = multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X1,inverse(inverse(multiply(X3,inverse(X3)))))))),inverse(multiply(X4,inverse(X4)))),
inference(cp,[status(thm)],[t1,t940]) ).
cnf(t1622,plain,
X1 = multiply(X1,inverse(multiply(X4,inverse(X4)))),
inference(step,[status(thm)],[t964,t767]) ).
cnf(t1056,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(orient,[status(thm)],[t1622]) ).
cnf(t188,plain,
X1 = multiply(inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X4,X2)))),X3)),inverse(multiply(inverse(X1),X4))),
inference(cp,[status(thm)],[t1,t171]) ).
cnf(t202,plain,
multiply(inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(X3,X1)))),X2)),inverse(multiply(inverse(X4),X3))) = X4,
inference(orient,[status(thm)],[t188]) ).
cnf(t1057,plain,
inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(inverse(inverse(X3)),X1)))),X2)) = X3,
inference(cp,[status(thm)],[t1056,t202]) ).
cnf(t1099,plain,
inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(inverse(inverse(X3)),X1)))),X2)) = X3,
inference(orient,[status(thm)],[t1057]) ).
cnf(t1149,plain,
inverse(inverse(X1)) = multiply(multiply(X2,inverse(X2)),X1),
inference(cp,[status(thm)],[t171,t1099]) ).
cnf(t1180,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(orient,[status(thm)],[t1149]) ).
cnf(t1192,plain,
X1 = multiply(X1,inverse(inverse(inverse(inverse(multiply(X2,inverse(X2))))))),
inference(cp,[status(thm)],[t1056,t1180]) ).
cnf(t1317,plain,
multiply(X1,inverse(inverse(inverse(inverse(multiply(X2,inverse(X2))))))) = X1,
inference(orient,[status(thm)],[t1192]) ).
cnf(t1145,plain,
X1 = multiply(X2,inverse(multiply(inverse(X1),inverse(inverse(X2))))),
inference(cp,[status(thm)],[t202,t1099]) ).
cnf(t1229,plain,
multiply(X1,inverse(multiply(inverse(X2),inverse(inverse(X1))))) = X2,
inference(orient,[status(thm)],[t1145]) ).
cnf(t1330,plain,
X1 = multiply(inverse(inverse(multiply(X2,inverse(X2)))),inverse(inverse(X1))),
inference(cp,[status(thm)],[t1229,t1317]) ).
cnf(t1352,plain,
multiply(inverse(inverse(multiply(X1,inverse(X1)))),inverse(inverse(X2))) = X2,
inference(orient,[status(thm)],[t1330]) ).
cnf(t1370,plain,
X1 = multiply(inverse(inverse(inverse(multiply(X2,inverse(X2))))),inverse(inverse(X1))),
inference(cp,[status(thm)],[t1352,t1352]) ).
cnf(t1191,plain,
inverse(inverse(X1)) = multiply(inverse(inverse(inverse(multiply(X2,inverse(X2))))),X1),
inference(cp,[status(thm)],[t1180,t1180]) ).
cnf(t1272,plain,
multiply(inverse(inverse(inverse(multiply(X1,inverse(X1))))),X2) = inverse(inverse(X2)),
inference(orient,[status(thm)],[t1191]) ).
cnf(t1636,plain,
X1 = inverse(inverse(inverse(inverse(X1)))),
inference(step,[status(thm)],[t1370,t1272]) ).
cnf(t1390,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(orient,[status(thm)],[t1636]) ).
cnf(t1637,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(step,[status(thm)],[t1317,t1390]) ).
cnf(t1420,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[t1637]) ).
cnf(t1421,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(orient,[status(thm)],[t1420]) ).
cnf(t1426,plain,
X1 = multiply(X1,multiply(inverse(inverse(inverse(X2))),X2)),
inference(cp,[status(thm)],[t1421,t1390]) ).
cnf(t1486,plain,
multiply(X1,multiply(inverse(inverse(inverse(X2))),X2)) = X1,
inference(orient,[status(thm)],[t1426]) ).
cnf(t1501,plain,
inverse(X1) = inverse(multiply(multiply(X1,inverse(X2)),X2)),
inference(cp,[status(thm)],[t1099,t1486]) ).
cnf(t1505,plain,
inverse(multiply(multiply(X1,inverse(X2)),X2)) = inverse(X1),
inference(orient,[status(thm)],[t1501]) ).
cnf(t1506,plain,
inverse(X1) = inverse(inverse(inverse(X1))),
inference(cp,[status(thm)],[t1505,t1180]) ).
cnf(t1543,plain,
inverse(inverse(inverse(X1))) = inverse(X1),
inference(orient,[status(thm)],[t1506]) ).
cnf(t1203,plain,
X1 = multiply(X2,inverse(multiply(inverse(inverse(multiply(X3,inverse(X3)))),multiply(multiply(X4,inverse(multiply(X1,multiply(multiply(Y4,inverse(Y4)),X4)))),X2)))),
inference(cp,[status(thm)],[t132,t1180]) ).
cnf(t1634,plain,
X1 = inverse(multiply(X4,inverse(multiply(X1,multiply(multiply(Y4,inverse(Y4)),X4))))),
inference(step,[status(thm)],[t1203,t712]) ).
cnf(t1635,plain,
X1 = inverse(multiply(X4,inverse(multiply(X1,inverse(inverse(X4)))))),
inference(step,[status(thm)],[t1634,t1180]) ).
cnf(t1245,plain,
inverse(multiply(X1,inverse(multiply(X2,inverse(inverse(X1)))))) = X2,
inference(orient,[status(thm)],[t1635]) ).
cnf(t1544,plain,
inverse(multiply(X1,inverse(multiply(X2,inverse(inverse(X1)))))) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t1543,t1245]) ).
cnf(t1645,plain,
X2 = inverse(inverse(X2)),
inference(step,[status(thm)],[t1544,t1245]) ).
cnf(t1567,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t1645]) ).
cnf(t1646,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(step,[status(thm)],[t1180,t1567]) ).
cnf(t1568,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(orient,[status(thm)],[t1646]) ).
cnf(t1573,plain,
X1 = multiply(multiply(inverse(X2),X2),X1),
inference(cp,[status(thm)],[t1568,t1567]) ).
cnf(t1605,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t1573]) ).
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,t1605]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP431-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n005.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 14:43:53 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.59/6.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.59/6.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------