%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP582-1 : 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 01:27:35 PM UTC 2026
% Result : Unsatisfiable 3.71s 1.02s
% Output : CNFRefutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 7
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 40 RR)
% Number of literals : 81 ( 80 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t4,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),double_divide(identity,identity)) = X3,
inference(orient,[status(thm)],[t1]) ).
cnf(u1,axiom,
identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(d1,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t0,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(definition_unfolding,[status(thm)],[u1,d1]) ).
cnf(t7,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t9,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),double_divide(identity,identity)),
inference(cp,[status(thm)],[t4,t7]) ).
cnf(t25,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),double_divide(identity,identity)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t26,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,identity)),
inference(cp,[status(thm)],[t25,t7]) ).
cnf(t170,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(identity,identity)),
inference(step,[status(thm)],[t26,t7]) ).
cnf(t171,plain,
double_divide(identity,identity) = identity,
inference(step,[status(thm)],[t170,t7]) ).
cnf(t29,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t171]) ).
cnf(t173,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),identity) = X3,
inference(step,[status(thm)],[t4,t29]) ).
cnf(t31,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),identity) = X3,
inference(rw,[status(thm)],[t173]) ).
cnf(t35,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),identity) = X3,
inference(orient,[status(thm)],[t31]) ).
cnf(t172,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),identity) = X1,
inference(step,[status(thm)],[t25,t29]) ).
cnf(t30,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),identity) = X1,
inference(rw,[status(thm)],[t172]) ).
cnf(t32,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),identity) = X1,
inference(orient,[status(thm)],[t30]) ).
cnf(t42,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(X1,identity))),identity),
inference(cp,[status(thm)],[t35,t29]) ).
cnf(t174,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity),
inference(step,[status(thm)],[t42,t29]) ).
cnf(t51,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity) = X1,
inference(orient,[status(thm)],[t174]) ).
cnf(t57,plain,
double_divide(identity,double_divide(X1,identity)) = double_divide(double_divide(identity,X1),identity),
inference(cp,[status(thm)],[t32,t51]) ).
cnf(t61,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(identity,double_divide(X1,identity)),
inference(orient,[status(thm)],[t57]) ).
cnf(t175,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,X1),identity),identity)) = X1,
inference(step,[status(thm)],[t32,t61]) ).
cnf(t176,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(X1,identity)),identity)) = X1,
inference(step,[status(thm)],[t175,t61]) ).
cnf(t177,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity))) = X1,
inference(step,[status(thm)],[t176,t61]) ).
cnf(t65,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity))) = X1,
inference(rw,[status(thm)],[t177]) ).
cnf(t97,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity))) = X1,
inference(orient,[status(thm)],[t65]) ).
cnf(t33,plain,
identity = double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),X1),
inference(cp,[status(thm)],[t7,t32]) ).
cnf(t34,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),X1) = identity,
inference(orient,[status(thm)],[t33]) ).
cnf(t180,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),X1) = identity,
inference(step,[status(thm)],[t34,t61]) ).
cnf(t67,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),X1) = identity,
inference(rw,[status(thm)],[t180]) ).
cnf(t122,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),X1) = identity,
inference(orient,[status(thm)],[t67]) ).
cnf(t2,axiom,
sFlat0 = double_divide(a2,identity),
introduced(definition) ).
cnf(t14,plain,
double_divide(a2,identity) = sFlat0,
inference(orient,[status(thm)],[t2]) ).
cnf(t125,plain,
identity = double_divide(double_divide(identity,double_divide(identity,sFlat0)),a2),
inference(cp,[status(thm)],[t122,t14]) ).
cnf(t128,plain,
double_divide(double_divide(identity,double_divide(identity,sFlat0)),a2) = identity,
inference(orient,[status(thm)],[t125]) ).
cnf(t129,plain,
X1 = double_divide(double_divide(a2,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,sFlat0))),double_divide(X1,identity))),identity),
inference(cp,[status(thm)],[t35,t128]) ).
cnf(t63,plain,
identity = double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,identity))),
inference(cp,[status(thm)],[t7,t61]) ).
cnf(t68,plain,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,identity))) = identity,
inference(orient,[status(thm)],[t63]) ).
cnf(t3,axiom,
sFlat1 = double_divide(double_divide(a2,identity),identity),
introduced(definition) ).
cnf(t11,plain,
double_divide(double_divide(a2,identity),identity) = sFlat1,
inference(orient,[status(thm)],[t3]) ).
cnf(t169,plain,
double_divide(sFlat0,identity) = sFlat1,
inference(step,[status(thm)],[t11,t14]) ).
cnf(t17,plain,
double_divide(sFlat0,identity) = sFlat1,
inference(rw,[status(thm)],[t169]) ).
cnf(t20,plain,
double_divide(sFlat0,identity) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t71,plain,
identity = double_divide(double_divide(identity,sFlat0),double_divide(identity,sFlat1)),
inference(cp,[status(thm)],[t68,t20]) ).
cnf(t75,plain,
double_divide(double_divide(identity,sFlat0),double_divide(identity,sFlat1)) = identity,
inference(orient,[status(thm)],[t71]) ).
cnf(t76,plain,
double_divide(identity,sFlat0) = double_divide(double_divide(sFlat1,double_divide(double_divide(identity,identity),identity)),identity),
inference(cp,[status(thm)],[t35,t75]) ).
cnf(t181,plain,
double_divide(identity,sFlat0) = double_divide(double_divide(sFlat1,double_divide(identity,double_divide(identity,identity))),identity),
inference(step,[status(thm)],[t76,t61]) ).
cnf(t182,plain,
double_divide(identity,sFlat0) = double_divide(double_divide(sFlat1,identity),identity),
inference(step,[status(thm)],[t181,t7]) ).
cnf(t78,plain,
double_divide(double_divide(sFlat1,identity),identity) = double_divide(identity,sFlat0),
inference(orient,[status(thm)],[t182]) ).
cnf(t99,plain,
sFlat1 = double_divide(identity,double_divide(identity,double_divide(identity,sFlat0))),
inference(cp,[status(thm)],[t97,t78]) ).
cnf(t113,plain,
double_divide(identity,double_divide(identity,double_divide(identity,sFlat0))) = sFlat1,
inference(orient,[status(thm)],[t99]) ).
cnf(t190,plain,
X1 = double_divide(double_divide(a2,double_divide(sFlat1,double_divide(X1,identity))),identity),
inference(step,[status(thm)],[t129,t113]) ).
cnf(t134,plain,
double_divide(double_divide(a2,double_divide(sFlat1,double_divide(X1,identity))),identity) = X1,
inference(orient,[status(thm)],[t190]) ).
cnf(t135,plain,
double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(double_divide(a2,double_divide(sFlat1,identity)),identity),
inference(cp,[status(thm)],[t134,t122]) ).
cnf(t73,plain,
double_divide(identity,X1) = double_divide(double_divide(double_divide(X1,identity),double_divide(double_divide(identity,identity),identity)),identity),
inference(cp,[status(thm)],[t35,t68]) ).
cnf(t187,plain,
double_divide(identity,X1) = double_divide(double_divide(double_divide(X1,identity),double_divide(identity,double_divide(identity,identity))),identity),
inference(step,[status(thm)],[t73,t61]) ).
cnf(t188,plain,
double_divide(identity,X1) = double_divide(double_divide(double_divide(X1,identity),identity),identity),
inference(step,[status(thm)],[t187,t7]) ).
cnf(t92,plain,
double_divide(double_divide(double_divide(X1,identity),identity),identity) = double_divide(identity,X1),
inference(orient,[status(thm)],[t188]) ).
cnf(t98,plain,
double_divide(X1,identity) = double_divide(identity,double_divide(identity,double_divide(identity,X1))),
inference(cp,[status(thm)],[t97,t92]) ).
cnf(t119,plain,
double_divide(identity,double_divide(identity,double_divide(identity,X1))) = double_divide(X1,identity),
inference(orient,[status(thm)],[t98]) ).
cnf(t191,plain,
double_divide(identity,identity) = double_divide(double_divide(a2,double_divide(sFlat1,identity)),identity),
inference(step,[status(thm)],[t135,t119]) ).
cnf(t192,plain,
identity = double_divide(double_divide(a2,double_divide(sFlat1,identity)),identity),
inference(step,[status(thm)],[t191,t29]) ).
cnf(t151,plain,
double_divide(double_divide(a2,double_divide(sFlat1,identity)),identity) = identity,
inference(orient,[status(thm)],[t192]) ).
cnf(t154,plain,
double_divide(a2,double_divide(sFlat1,identity)) = double_divide(identity,double_divide(identity,double_divide(identity,identity))),
inference(cp,[status(thm)],[t97,t151]) ).
cnf(t193,plain,
double_divide(a2,double_divide(sFlat1,identity)) = double_divide(identity,identity),
inference(step,[status(thm)],[t154,t119]) ).
cnf(t194,plain,
double_divide(a2,double_divide(sFlat1,identity)) = identity,
inference(step,[status(thm)],[t193,t29]) ).
cnf(t158,plain,
double_divide(a2,double_divide(sFlat1,identity)) = identity,
inference(orient,[status(thm)],[t194]) ).
cnf(t159,plain,
a2 = double_divide(double_divide(identity,double_divide(double_divide(identity,sFlat1),identity)),identity),
inference(cp,[status(thm)],[t35,t158]) ).
cnf(t195,plain,
a2 = double_divide(identity,double_divide(double_divide(double_divide(identity,sFlat1),identity),identity)),
inference(step,[status(thm)],[t159,t61]) ).
cnf(t196,plain,
a2 = double_divide(identity,double_divide(double_divide(identity,double_divide(sFlat1,identity)),identity)),
inference(step,[status(thm)],[t195,t61]) ).
cnf(t197,plain,
a2 = double_divide(identity,double_divide(identity,double_divide(double_divide(sFlat1,identity),identity))),
inference(step,[status(thm)],[t196,t61]) ).
cnf(t198,plain,
a2 = sFlat1,
inference(step,[status(thm)],[t197,t97]) ).
cnf(t161,plain,
a2 = sFlat1,
inference(orient,[status(thm)],[t198]) ).
cnf(u0,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
double_divide(double_divide(a2,identity),identity) != a2,
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
double_divide(double_divide(a2,identity),identity) != sFlat1,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_0,t161]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP582-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 15:08:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.71/1.02 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.71/1.02 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------