%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP601-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 01:27:38 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.83s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 3
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 5 RR)
% Number of literals : 67 ( 66 equ; 4 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 169 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
inverse(double_divide(inverse(double_divide(X1,inverse(double_divide(X2,double_divide(X1,X3))))),X3)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t2,plain,
inverse(double_divide(inverse(double_divide(X1,inverse(double_divide(X2,double_divide(X1,X3))))),X3)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t0,axiom,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t4,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t672,plain,
multiply(X3,inverse(double_divide(X1,inverse(double_divide(X2,double_divide(X1,X3)))))) = X2,
inference(step,[status(thm)],[t2,t4]) ).
cnf(t673,plain,
multiply(X3,multiply(inverse(double_divide(X2,double_divide(X1,X3))),X1)) = X2,
inference(step,[status(thm)],[t672,t4]) ).
cnf(t674,plain,
multiply(X3,multiply(multiply(double_divide(X1,X3),X2),X1)) = X2,
inference(step,[status(thm)],[t673,t4]) ).
cnf(t5,plain,
multiply(X3,multiply(multiply(double_divide(X1,X3),X2),X1)) = X2,
inference(rw,[status(thm)],[t674]) ).
cnf(t6,plain,
multiply(X1,multiply(multiply(double_divide(X2,X1),X3),X2)) = X3,
inference(orient,[status(thm)],[t5]) ).
cnf(t7,plain,
multiply(multiply(double_divide(X1,double_divide(X2,X3)),Y3),X1) = multiply(X3,multiply(Y3,X2)),
inference(cp,[status(thm)],[t6,t6]) ).
cnf(t8,plain,
multiply(multiply(double_divide(X1,double_divide(X2,X3)),Y3),X1) = multiply(X3,multiply(Y3,X2)),
inference(orient,[status(thm)],[t7]) ).
cnf(t9,plain,
X1 = multiply(double_divide(X2,X3),multiply(X3,multiply(X1,X2))),
inference(cp,[status(thm)],[t6,t8]) ).
cnf(t10,plain,
multiply(double_divide(X1,X2),multiply(X2,multiply(X3,X1))) = X3,
inference(orient,[status(thm)],[t9]) ).
cnf(t15,plain,
double_divide(X1,X2) = multiply(double_divide(multiply(X2,multiply(X3,X1)),Y3),multiply(Y3,X3)),
inference(cp,[status(thm)],[t10,t10]) ).
cnf(t23,plain,
multiply(double_divide(multiply(X1,multiply(X2,X3)),Y3),multiply(Y3,X2)) = double_divide(X3,X1),
inference(orient,[status(thm)],[t15]) ).
cnf(t14,plain,
X1 = multiply(double_divide(multiply(X2,X3),double_divide(X3,X1)),X2),
inference(cp,[status(thm)],[t10,t10]) ).
cnf(t16,plain,
multiply(double_divide(multiply(X1,X2),double_divide(X2,X3)),X1) = X3,
inference(orient,[status(thm)],[t14]) ).
cnf(t24,plain,
double_divide(X1,multiply(double_divide(multiply(X2,X1),X3),X2)) = X3,
inference(cp,[status(thm)],[t23,t16]) ).
cnf(t42,plain,
double_divide(X1,multiply(double_divide(multiply(X2,X1),X3),X2)) = X3,
inference(orient,[status(thm)],[t24]) ).
cnf(t43,plain,
X1 = double_divide(multiply(X2,X3),double_divide(X3,multiply(X1,X2))),
inference(cp,[status(thm)],[t42,t23]) ).
cnf(t56,plain,
double_divide(multiply(X1,X2),double_divide(X2,multiply(X3,X1))) = X3,
inference(orient,[status(thm)],[t43]) ).
cnf(t67,plain,
multiply(double_divide(X1,multiply(X2,X3)),multiply(X3,X1)) = inverse(X2),
inference(cp,[status(thm)],[t4,t56]) ).
cnf(t92,plain,
multiply(double_divide(X1,multiply(X2,X3)),multiply(X3,X1)) = inverse(X2),
inference(orient,[status(thm)],[t67]) ).
cnf(t112,plain,
multiply(X1,X2) = multiply(multiply(X3,X1),multiply(inverse(X3),X2)),
inference(cp,[status(thm)],[t6,t92]) ).
cnf(t118,plain,
multiply(multiply(X1,X2),multiply(inverse(X1),X3)) = multiply(X2,X3),
inference(orient,[status(thm)],[t112]) ).
cnf(t120,plain,
multiply(multiply(X1,multiply(X2,X3)),Y3) = multiply(X2,multiply(inverse(double_divide(X3,X1)),Y3)),
inference(cp,[status(thm)],[t118,t10]) ).
cnf(t675,plain,
multiply(multiply(X1,multiply(X2,X3)),Y3) = multiply(X2,multiply(multiply(X1,X3),Y3)),
inference(step,[status(thm)],[t120,t4]) ).
cnf(t140,plain,
multiply(multiply(X1,multiply(X2,X3)),Y3) = multiply(X2,multiply(multiply(X1,X3),Y3)),
inference(orient,[status(thm)],[t675]) ).
cnf(t141,plain,
multiply(X1,multiply(multiply(X2,X3),multiply(inverse(X2),Y3))) = multiply(multiply(X1,X3),Y3),
inference(cp,[status(thm)],[t140,t118]) ).
cnf(t676,plain,
multiply(X1,multiply(X3,Y3)) = multiply(multiply(X1,X3),Y3),
inference(step,[status(thm)],[t141,t118]) ).
cnf(t175,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t676]) ).
cnf(t681,plain,
multiply(X1,multiply(double_divide(X2,X1),multiply(X3,X2))) = X3,
inference(step,[status(thm)],[t6,t175]) ).
cnf(t193,plain,
multiply(X1,multiply(double_divide(X2,X1),multiply(X3,X2))) = X3,
inference(rw,[status(thm)],[t681]) ).
cnf(t239,plain,
multiply(X1,multiply(double_divide(X2,X1),multiply(X3,X2))) = X3,
inference(orient,[status(thm)],[t193]) ).
cnf(t680,plain,
multiply(X1,multiply(X2,multiply(inverse(X1),X3))) = multiply(X2,X3),
inference(step,[status(thm)],[t118,t175]) ).
cnf(t192,plain,
multiply(X1,multiply(X2,multiply(inverse(X1),X3))) = multiply(X2,X3),
inference(rw,[status(thm)],[t680]) ).
cnf(t196,plain,
multiply(X1,multiply(X2,multiply(inverse(X1),X3))) = multiply(X2,X3),
inference(orient,[status(thm)],[t192]) ).
cnf(t199,plain,
multiply(double_divide(X1,inverse(X2)),multiply(X3,X1)) = multiply(X2,X3),
inference(cp,[status(thm)],[t196,t10]) ).
cnf(t217,plain,
multiply(double_divide(X1,inverse(X2)),multiply(X3,X1)) = multiply(X2,X3),
inference(orient,[status(thm)],[t199]) ).
cnf(t243,plain,
X1 = multiply(inverse(X2),multiply(X2,X1)),
inference(cp,[status(thm)],[t239,t217]) ).
cnf(t293,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t243]) ).
cnf(t244,plain,
X1 = multiply(multiply(X2,X1),inverse(X2)),
inference(cp,[status(thm)],[t239,t92]) ).
cnf(t686,plain,
X1 = multiply(X2,multiply(X1,inverse(X2))),
inference(step,[status(thm)],[t244,t175]) ).
cnf(t338,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(orient,[status(thm)],[t686]) ).
cnf(t240,plain,
inverse(X1) = multiply(double_divide(X2,X1),X2),
inference(cp,[status(thm)],[t239,t196]) ).
cnf(t277,plain,
multiply(double_divide(X1,X2),X1) = inverse(X2),
inference(orient,[status(thm)],[t240]) ).
cnf(t341,plain,
double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)),
inference(cp,[status(thm)],[t338,t277]) ).
cnf(t362,plain,
double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)),
inference(orient,[status(thm)],[t341]) ).
cnf(t306,plain,
X1 = multiply(double_divide(X2,inverse(X1)),X2),
inference(cp,[status(thm)],[t10,t293]) ).
cnf(t685,plain,
X1 = inverse(inverse(X1)),
inference(step,[status(thm)],[t306,t277]) ).
cnf(t321,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t685]) ).
cnf(t366,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(cp,[status(thm)],[t362,t321]) ).
cnf(t371,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(orient,[status(thm)],[t366]) ).
cnf(t377,plain,
inverse(X1) = multiply(inverse(inverse(X2)),double_divide(X2,X1)),
inference(cp,[status(thm)],[t293,t371]) ).
cnf(t689,plain,
inverse(X1) = multiply(X2,double_divide(X2,X1)),
inference(step,[status(thm)],[t377,t321]) ).
cnf(t403,plain,
multiply(X1,double_divide(X1,X2)) = inverse(X2),
inference(orient,[status(thm)],[t689]) ).
cnf(t256,plain,
X1 = multiply(double_divide(multiply(double_divide(X2,X1),multiply(X3,X2)),Y3),multiply(Y3,X3)),
inference(cp,[status(thm)],[t10,t239]) ).
cnf(t684,plain,
X1 = double_divide(X2,double_divide(X2,X1)),
inference(step,[status(thm)],[t256,t23]) ).
cnf(t270,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t684]) ).
cnf(t407,plain,
inverse(double_divide(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t403,t270]) ).
cnf(t694,plain,
multiply(X2,X1) = multiply(X1,X2),
inference(step,[status(thm)],[t407,t4]) ).
cnf(t506,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t694]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(rw,[status(thm)],[goal_0,t506]) ).
cnf(g0_1,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[g0_0,t506]) ).
cnf(g0_2,plain,
multiply(b1,inverse(b1)) != multiply(b1,inverse(b1)),
inference(rw,[status(thm)],[g0_1]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP601-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Wed Sep 23 15:11:14 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/5.83 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------