%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 12:59:44 PM UTC 2026
% Result : Unsatisfiable 5.69s 1.36s
% Output : CNFRefutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 2
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 3 RR)
% Number of literals : 84 ( 83 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 309 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t2,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(multiply(X3,X1,X2),inverse(multiply(multiply(X5,X6,X7),Y7,multiply(X5,X6,Y8))),multiply(X6,multiply(Y8,Y7,X7),X5)),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t6,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(multiply(X3,X1,X2),inverse(multiply(multiply(X5,X6,X7),Y7,multiply(X5,X6,Y8))),multiply(X6,multiply(Y8,Y7,X7),X5)),
inference(orient,[status(thm)],[t2]) ).
cnf(t37,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(X1,multiply(X2,inverse(multiply(X3,X1,X5)),X5),X3),
inference(cp,[status(thm)],[t6,t6]) ).
cnf(t51,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(X1,multiply(X2,inverse(multiply(X3,X1,X5)),X5),X3),
inference(orient,[status(thm)],[t37]) ).
cnf(t21,plain,
multiply(inverse(X1),multiply(X2,inverse(multiply(X1,inverse(X1),X3)),X3),X1) = X2,
inference(cp,[status(thm)],[t6,t1]) ).
cnf(t38,plain,
multiply(inverse(X1),multiply(X2,inverse(multiply(X1,inverse(X1),X3)),X3),X1) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(t44,plain,
X1 = multiply(multiply(X2,inverse(X2),X1),inverse(multiply(multiply(X3,X4,X5),multiply(X6,inverse(multiply(X5,inverse(X5),X7)),X7),multiply(X3,X4,inverse(X5)))),multiply(X4,X6,X3)),
inference(cp,[status(thm)],[t1,t38]) ).
cnf(t123,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,X5),multiply(X6,inverse(multiply(X5,inverse(X5),X7)),X7),multiply(X3,X4,inverse(X5)))),multiply(X4,X6,X3)) = X2,
inference(orient,[status(thm)],[t44]) ).
cnf(t149,plain,
X1 = multiply(multiply(X2,inverse(X2),X1),inverse(X3),multiply(inverse(X4),multiply(X5,inverse(multiply(multiply(X5,X4,X6),multiply(inverse(X4),inverse(multiply(X6,inverse(X6),X7)),X7),multiply(X5,X4,inverse(X6)))),X3),X4)),
inference(cp,[status(thm)],[t1,t123]) ).
cnf(t443,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(X3),multiply(inverse(X4),multiply(X5,inverse(multiply(multiply(X5,X4,X6),multiply(inverse(X4),inverse(multiply(X6,inverse(X6),X7)),X7),multiply(X5,X4,inverse(X6)))),X3),X4)) = X2,
inference(orient,[status(thm)],[t149]) ).
cnf(t449,plain,
X1 = multiply(multiply(X2,inverse(X2),X1),inverse(multiply(X3,inverse(X3),multiply(X4,inverse(X4),X5))),multiply(inverse(X3),X5,X3)),
inference(cp,[status(thm)],[t443,t123]) ).
cnf(t522,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(X3,inverse(X3),multiply(X4,inverse(X4),X5))),multiply(inverse(X3),X5,X3)) = X2,
inference(orient,[status(thm)],[t449]) ).
cnf(t542,plain,
multiply(inverse(X1),X2,X1) = multiply(multiply(X3,inverse(X3),X2),inverse(multiply(multiply(X4,X5,X6),X7,multiply(X4,X5,Y7))),multiply(X5,multiply(Y7,X7,X6),X4)),
inference(cp,[status(thm)],[t1,t522]) ).
cnf(t1419,plain,
multiply(inverse(X1),X2,X1) = X2,
inference(step,[status(thm)],[t542,t1]) ).
cnf(t587,plain,
multiply(inverse(X1),X2,X1) = X2,
inference(orient,[status(thm)],[t1419]) ).
cnf(t43,plain,
X1 = multiply(multiply(X2,inverse(X2),X1),inverse(multiply(multiply(X3,inverse(X3),X4),inverse(multiply(X3,inverse(X3),X4)),multiply(X3,inverse(X3),X5))),X5),
inference(cp,[status(thm)],[t1,t38]) ).
cnf(t71,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,inverse(X3),X4),inverse(multiply(X3,inverse(X3),X4)),multiply(X3,inverse(X3),X5))),X5) = X2,
inference(orient,[status(thm)],[t43]) ).
cnf(t85,plain,
X1 = multiply(multiply(X2,inverse(X2),X1),inverse(multiply(X3,inverse(X3),multiply(multiply(X3,inverse(X3),X4),inverse(multiply(X3,inverse(X3),X4)),X5))),X5),
inference(cp,[status(thm)],[t71,t71]) ).
cnf(t96,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(X3,inverse(X3),multiply(multiply(X3,inverse(X3),X4),inverse(multiply(X3,inverse(X3),X4)),X5))),X5) = X2,
inference(orient,[status(thm)],[t85]) ).
cnf(t97,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(multiply(X3,X1,X2),inverse(multiply(X5,inverse(X5),multiply(multiply(X5,inverse(X5),X6),inverse(multiply(X5,inverse(X5),X6)),X7))),X7),
inference(cp,[status(thm)],[t96,t1]) ).
cnf(t332,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(multiply(X3,X1,X2),inverse(multiply(X5,inverse(X5),multiply(multiply(X5,inverse(X5),X6),inverse(multiply(X5,inverse(X5),X6)),X7))),X7),
inference(orient,[status(thm)],[t97]) ).
cnf(t588,plain,
multiply(X1,inverse(multiply(X2,inverse(X2),X3)),X3) = multiply(multiply(X2,inverse(X2),X1),inverse(multiply(X4,inverse(X4),multiply(multiply(X4,inverse(X4),X5),inverse(multiply(X4,inverse(X4),X5)),X6))),X6),
inference(cp,[status(thm)],[t587,t332]) ).
cnf(t1423,plain,
multiply(X1,inverse(multiply(X2,inverse(X2),X3)),X3) = X1,
inference(step,[status(thm)],[t588,t96]) ).
cnf(t640,plain,
multiply(X1,inverse(multiply(X2,inverse(X2),X3)),X3) = X1,
inference(orient,[status(thm)],[t1423]) ).
cnf(t641,plain,
inverse(X1) = inverse(multiply(X2,inverse(X2),X1)),
inference(cp,[status(thm)],[t640,t587]) ).
cnf(t681,plain,
inverse(multiply(X1,inverse(X1),X2)) = inverse(X2),
inference(orient,[status(thm)],[t641]) ).
cnf(t1431,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(X3,inverse(X3),X5)),X5) = X2,
inference(step,[status(thm)],[t71,t681]) ).
cnf(t1432,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(X5),X5) = X2,
inference(step,[status(thm)],[t1431,t681]) ).
cnf(t696,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(X5),X5) = X2,
inference(rw,[status(thm)],[t1432]) ).
cnf(t690,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = multiply(inverse(X1),multiply(X2,inverse(Y7),Y7),X1),
inference(cp,[status(thm)],[t6,t681]) ).
cnf(t1435,plain,
X2 = multiply(inverse(X1),multiply(X2,inverse(Y7),Y7),X1),
inference(step,[status(thm)],[t690,t1]) ).
cnf(t1436,plain,
X2 = multiply(X2,inverse(Y7),Y7),
inference(step,[status(thm)],[t1435,t587]) ).
cnf(t702,plain,
multiply(X1,inverse(X2),X2) = X1,
inference(orient,[status(thm)],[t1436]) ).
cnf(t1437,plain,
multiply(X1,inverse(X1),X2) = X2,
inference(step,[status(thm)],[t696,t702]) ).
cnf(t776,plain,
multiply(X1,inverse(X1),X2) = X2,
inference(orient,[status(thm)],[t1437]) ).
cnf(t683,plain,
inverse(X1) = inverse(inverse(inverse(X1))),
inference(cp,[status(thm)],[t681,t587]) ).
cnf(t698,plain,
inverse(inverse(inverse(X1))) = inverse(X1),
inference(orient,[status(thm)],[t683]) ).
cnf(t704,plain,
X1 = multiply(X1,inverse(X2),inverse(inverse(X2))),
inference(cp,[status(thm)],[t702,t698]) ).
cnf(t734,plain,
multiply(X1,inverse(X2),inverse(inverse(X2))) = X1,
inference(orient,[status(thm)],[t704]) ).
cnf(t777,plain,
inverse(inverse(X1)) = X1,
inference(cp,[status(thm)],[t776,t734]) ).
cnf(t791,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t777]) ).
cnf(t792,plain,
X1 = multiply(X2,X1,inverse(X2)),
inference(cp,[status(thm)],[t587,t791]) ).
cnf(t795,plain,
multiply(X1,X2,inverse(X1)) = X2,
inference(orient,[status(thm)],[t792]) ).
cnf(t798,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(X1,inverse(multiply(X3,X1,inverse(X2))),X3),
inference(cp,[status(thm)],[t51,t795]) ).
cnf(t824,plain,
multiply(X1,multiply(X2,inverse(multiply(X3,X1,X4)),X4),X3) = multiply(X1,inverse(multiply(X3,X1,inverse(X2))),X3),
inference(orient,[status(thm)],[t798]) ).
cnf(t825,plain,
multiply(X1,inverse(multiply(X2,X1,inverse(multiply(X2,X1,X3)))),X2) = multiply(X1,X3,X2),
inference(cp,[status(thm)],[t824,t776]) ).
cnf(t827,plain,
multiply(X1,inverse(multiply(X2,X1,inverse(X3))),X2) = multiply(X1,multiply(X3,inverse(X1),inverse(X2)),X2),
inference(cp,[status(thm)],[t824,t795]) ).
cnf(t833,plain,
multiply(X1,inverse(multiply(X2,X1,inverse(X3))),X2) = multiply(X1,multiply(X3,inverse(X1),inverse(X2)),X2),
inference(orient,[status(thm)],[t827]) ).
cnf(t1447,plain,
multiply(X1,multiply(multiply(X2,X1,X3),inverse(X1),inverse(X2)),X2) = multiply(X1,X3,X2),
inference(step,[status(thm)],[t825,t833]) ).
cnf(t871,plain,
multiply(X1,multiply(multiply(X2,X1,X3),inverse(X1),inverse(X2)),X2) = multiply(X1,X3,X2),
inference(orient,[status(thm)],[t1447]) ).
cnf(t794,plain,
X1 = multiply(X1,X2,inverse(X2)),
inference(cp,[status(thm)],[t702,t791]) ).
cnf(t816,plain,
multiply(X1,X2,inverse(X2)) = X1,
inference(orient,[status(thm)],[t794]) ).
cnf(t828,plain,
multiply(X1,inverse(multiply(X2,X1,inverse(X3))),X2) = multiply(X1,multiply(X3,inverse(X2),inverse(X1)),X2),
inference(cp,[status(thm)],[t824,t816]) ).
cnf(t1442,plain,
multiply(X1,multiply(X3,inverse(X1),inverse(X2)),X2) = multiply(X1,multiply(X3,inverse(X2),inverse(X1)),X2),
inference(step,[status(thm)],[t828,t833]) ).
cnf(t841,plain,
multiply(X1,multiply(X2,inverse(X1),inverse(X3)),X3) = multiply(X1,multiply(X2,inverse(X3),inverse(X1)),X3),
inference(orient,[status(thm)],[t1442]) ).
cnf(t872,plain,
multiply(X1,X2,X3) = multiply(X1,multiply(multiply(X3,X1,X2),inverse(X3),inverse(X1)),X3),
inference(cp,[status(thm)],[t871,t841]) ).
cnf(t909,plain,
multiply(X1,multiply(multiply(X2,X1,X3),inverse(X2),inverse(X1)),X2) = multiply(X1,X3,X2),
inference(orient,[status(thm)],[t872]) ).
cnf(t1422,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(X3),multiply(X5,inverse(multiply(multiply(X5,X4,X6),multiply(inverse(X4),inverse(multiply(X6,inverse(X6),X7)),X7),multiply(X5,X4,inverse(X6)))),X3)) = X2,
inference(step,[status(thm)],[t443,t587]) ).
cnf(t639,plain,
multiply(multiply(X1,inverse(X1),X2),inverse(X3),multiply(X5,inverse(multiply(multiply(X5,X4,X6),multiply(inverse(X4),inverse(multiply(X6,inverse(X6),X7)),X7),multiply(X5,X4,inverse(X6)))),X3)) = X2,
inference(rw,[status(thm)],[t1422]) ).
cnf(t1467,plain,
multiply(X2,inverse(X3),multiply(X5,inverse(multiply(multiply(X5,X4,X6),multiply(inverse(X4),inverse(multiply(X6,inverse(X6),X7)),X7),multiply(X5,X4,inverse(X6)))),X3)) = X2,
inference(step,[status(thm)],[t639,t776]) ).
cnf(t1468,plain,
multiply(X2,inverse(X3),multiply(X5,inverse(multiply(multiply(X5,X4,X6),multiply(inverse(X4),inverse(X7),X7),multiply(X5,X4,inverse(X6)))),X3)) = X2,
inference(step,[status(thm)],[t1467,t681]) ).
cnf(t1469,plain,
multiply(X2,inverse(X3),multiply(X5,inverse(multiply(multiply(X5,X4,X6),inverse(X4),multiply(X5,X4,inverse(X6)))),X3)) = X2,
inference(step,[status(thm)],[t1468,t702]) ).
cnf(t1241,plain,
multiply(X1,inverse(X2),multiply(X3,inverse(multiply(multiply(X3,X4,X5),inverse(X4),multiply(X3,X4,inverse(X5)))),X2)) = X1,
inference(orient,[status(thm)],[t1469]) ).
cnf(t1253,plain,
X1 = multiply(X1,inverse(X2),multiply(X3,inverse(multiply(X4,inverse(X4),multiply(X3,X4,inverse(inverse(X3))))),X2)),
inference(cp,[status(thm)],[t1241,t795]) ).
cnf(t1470,plain,
X1 = multiply(X1,inverse(X2),multiply(X3,inverse(multiply(X3,X4,inverse(inverse(X3)))),X2)),
inference(step,[status(thm)],[t1253,t681]) ).
cnf(t1471,plain,
X1 = multiply(X1,inverse(X2),multiply(X3,inverse(multiply(X3,X4,X3)),X2)),
inference(step,[status(thm)],[t1470,t791]) ).
cnf(t1332,plain,
multiply(X1,inverse(X2),multiply(X3,inverse(multiply(X3,X4,X3)),X2)) = X1,
inference(orient,[status(thm)],[t1471]) ).
cnf(t1333,plain,
X1 = multiply(X2,inverse(multiply(X2,X3,X2)),X1),
inference(cp,[status(thm)],[t1332,t776]) ).
cnf(t1365,plain,
multiply(X1,inverse(multiply(X1,X2,X1)),X3) = X3,
inference(orient,[status(thm)],[t1333]) ).
cnf(t1368,plain,
multiply(X1,X2,X1) = X1,
inference(cp,[status(thm)],[t1365,t702]) ).
cnf(t1397,plain,
multiply(X1,X2,X1) = X1,
inference(orient,[status(thm)],[t1368]) ).
cnf(t1398,plain,
multiply(X1,X2,X2) = multiply(X1,multiply(X2,inverse(X2),inverse(X1)),X2),
inference(cp,[status(thm)],[t909,t1397]) ).
cnf(t1478,plain,
multiply(X1,X2,X2) = multiply(X1,inverse(X1),X2),
inference(step,[status(thm)],[t1398,t776]) ).
cnf(t1479,plain,
multiply(X1,X2,X2) = X2,
inference(step,[status(thm)],[t1478,t776]) ).
cnf(t1410,plain,
multiply(X1,X2,X2) = X2,
inference(orient,[status(thm)],[t1479]) ).
cnf(t1411,plain,
multiply(X1,X1,X2) = multiply(X1,multiply(X1,inverse(X2),inverse(X1)),X2),
inference(cp,[status(thm)],[t909,t1410]) ).
cnf(t1480,plain,
multiply(X1,X1,X2) = multiply(X1,inverse(X2),X2),
inference(step,[status(thm)],[t1411,t795]) ).
cnf(t1481,plain,
multiply(X1,X1,X2) = X1,
inference(step,[status(thm)],[t1480,t702]) ).
cnf(t1417,plain,
multiply(X1,X1,X2) = X1,
inference(orient,[status(thm)],[t1481]) ).
cnf(goal_0,negated_conjecture,
multiply(a,a,b) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a != a,
inference(rw,[status(thm)],[goal_0,t1417]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 06:43:03 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.69/1.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.69/1.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------