%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP518-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:27:26 PM UTC 2026
% Result : Unsatisfiable 4.77s 1.14s
% Output : CNFRefutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 2
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 4 RR)
% Number of literals : 43 ( 42 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 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 : 119 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
multiply(X1,multiply(multiply(inverse(multiply(X1,X2)),X3),X2)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1,plain,
multiply(X1,multiply(multiply(inverse(multiply(X1,X2)),X3),X2)) = X3,
inference(orient,[status(thm)],[t0]) ).
cnf(t2,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),Y3),X3) = multiply(X1,multiply(Y3,X2)),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),Y3),X3) = multiply(X1,multiply(Y3,X2)),
inference(orient,[status(thm)],[t2]) ).
cnf(t5,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(inverse(Y3),X2),multiply(multiply(inverse(multiply(inverse(multiply(X1,X3)),Y4)),Y3),Y4)),
inference(cp,[status(thm)],[t4,t1]) ).
cnf(t211,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(inverse(Y3),X2),multiply(X1,multiply(Y3,X3))),
inference(step,[status(thm)],[t5,t4]) ).
cnf(t38,plain,
multiply(multiply(inverse(X1),X2),multiply(X3,multiply(X1,Y3))) = multiply(X3,multiply(X2,Y3)),
inference(orient,[status(thm)],[t211]) ).
cnf(t53,plain,
multiply(multiply(inverse(X1),X2),multiply(X3,multiply(X1,Y3))) = multiply(multiply(inverse(Y4),X3),multiply(Y4,multiply(X2,Y3))),
inference(cp,[status(thm)],[t38,t38]) ).
cnf(t212,plain,
multiply(X3,multiply(X2,Y3)) = multiply(multiply(inverse(Y4),X3),multiply(Y4,multiply(X2,Y3))),
inference(step,[status(thm)],[t53,t38]) ).
cnf(t59,plain,
multiply(multiply(inverse(X1),X2),multiply(X1,multiply(X3,Y3))) = multiply(X2,multiply(X3,Y3)),
inference(orient,[status(thm)],[t212]) ).
cnf(t69,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(multiply(X2,X3)),Y3),X3))) = multiply(multiply(inverse(Y4),X1),multiply(Y4,Y3)),
inference(cp,[status(thm)],[t59,t1]) ).
cnf(t213,plain,
multiply(X1,Y3) = multiply(multiply(inverse(Y4),X1),multiply(Y4,Y3)),
inference(step,[status(thm)],[t69,t1]) ).
cnf(t82,plain,
multiply(multiply(inverse(X1),X2),multiply(X1,X3)) = multiply(X2,X3),
inference(orient,[status(thm)],[t213]) ).
cnf(t7,plain,
X1 = multiply(inverse(multiply(X2,X3)),multiply(X2,multiply(X1,X3))),
inference(cp,[status(thm)],[t1,t4]) ).
cnf(t10,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,X2))) = X3,
inference(orient,[status(thm)],[t7]) ).
cnf(t84,plain,
multiply(multiply(X1,multiply(X2,X3)),Y3) = multiply(X2,multiply(multiply(X1,X3),Y3)),
inference(cp,[status(thm)],[t82,t10]) ).
cnf(t102,plain,
multiply(multiply(X1,multiply(X2,X3)),Y3) = multiply(X2,multiply(multiply(X1,X3),Y3)),
inference(orient,[status(thm)],[t84]) ).
cnf(t105,plain,
multiply(X1,multiply(multiply(inverse(X2),X3),multiply(X2,Y3))) = multiply(multiply(X1,X3),Y3),
inference(cp,[status(thm)],[t102,t82]) ).
cnf(t214,plain,
multiply(X1,multiply(X3,Y3)) = multiply(multiply(X1,X3),Y3),
inference(step,[status(thm)],[t105,t82]) ).
cnf(t128,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t214]) ).
cnf(t17,plain,
X1 = multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X3,X2))),X3),
inference(cp,[status(thm)],[t10,t10]) ).
cnf(t22,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X3,X2))),X3) = X1,
inference(orient,[status(thm)],[t17]) ).
cnf(t218,plain,
multiply(inverse(X1),multiply(X2,multiply(X1,X3))) = multiply(X2,X3),
inference(step,[status(thm)],[t82,t128]) ).
cnf(t137,plain,
multiply(inverse(X1),multiply(X2,multiply(X1,X3))) = multiply(X2,X3),
inference(rw,[status(thm)],[t218]) ).
cnf(t141,plain,
multiply(inverse(X1),multiply(X2,multiply(X1,X3))) = multiply(X2,X3),
inference(orient,[status(thm)],[t137]) ).
cnf(t143,plain,
multiply(inverse(multiply(X1,X2)),multiply(X3,X2)) = multiply(inverse(X1),X3),
inference(cp,[status(thm)],[t141,t10]) ).
cnf(t155,plain,
multiply(inverse(multiply(X1,X2)),multiply(X3,X2)) = multiply(inverse(X1),X3),
inference(orient,[status(thm)],[t143]) ).
cnf(t222,plain,
multiply(inverse(multiply(inverse(X1),X3)),X3) = X1,
inference(step,[status(thm)],[t22,t155]) ).
cnf(t170,plain,
multiply(inverse(multiply(inverse(X1),X3)),X3) = X1,
inference(rw,[status(thm)],[t222]) ).
cnf(t171,plain,
multiply(inverse(multiply(inverse(X1),X2)),X2) = X1,
inference(orient,[status(thm)],[t170]) ).
cnf(t174,plain,
X1 = multiply(inverse(X2),multiply(inverse(multiply(inverse(X2),X3)),multiply(X1,X3))),
inference(cp,[status(thm)],[t10,t171]) ).
cnf(t223,plain,
X1 = multiply(inverse(X2),multiply(inverse(inverse(X2)),X1)),
inference(step,[status(thm)],[t174,t155]) ).
cnf(t181,plain,
multiply(inverse(X1),multiply(inverse(inverse(X1)),X2)) = X2,
inference(orient,[status(thm)],[t223]) ).
cnf(t186,plain,
inverse(inverse(X1)) = multiply(inverse(multiply(inverse(X1),X2)),X2),
inference(cp,[status(thm)],[t10,t181]) ).
cnf(t224,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t186,t171]) ).
cnf(t194,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t224]) ).
cnf(t225,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t181,t194]) ).
cnf(t197,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[t225]) ).
cnf(t198,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t197]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(inverse(b2),multiply(b2,a2)) != a2,
inference(rw,[status(thm)],[goal_0,t128]) ).
cnf(g0_1,plain,
a2 != a2,
inference(rw,[status(thm)],[g0_0,t198]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP518-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 15:03:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.77/1.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.77/1.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------