%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP488-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 01:27:10 PM UTC 2026
% Result : Unsatisfiable 3.65s 0.91s
% Output : CNFRefutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 7
% Syntax : Number of clauses : 95 ( 95 unt; 0 nHn; 58 RR)
% Number of literals : 95 ( 94 equ; 7 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 : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
double_divide(X1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X2,X3))),X2),identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
double_divide(X1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X2,X3))),X2),identity)) = X3,
inference(orient,[status(thm)],[t1]) ).
cnf(u1,axiom,
identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d1,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/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,
double_divide(X1,identity) = double_divide(X2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X2,identity),identity)),X1),identity)),
inference(cp,[status(thm)],[t4,t7]) ).
cnf(t257,plain,
double_divide(X1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),identity)),X2),identity)) = double_divide(X2,identity),
inference(orient,[status(thm)],[t9]) ).
cnf(t2,axiom,
sFlat0 = double_divide(a2,identity),
introduced(definition) ).
cnf(t14,plain,
double_divide(a2,identity) = sFlat0,
inference(orient,[status(thm)],[t2]) ).
cnf(t16,plain,
X1 = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(sFlat0,double_divide(X2,X1))),X2),identity)),
inference(cp,[status(thm)],[t4,t14]) ).
cnf(t43,plain,
double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(sFlat0,double_divide(X1,X2))),X1),identity)) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t8,plain,
identity = double_divide(X1,double_divide(double_divide(double_divide(identity,identity),double_divide(X1,identity)),identity)),
inference(cp,[status(thm)],[t4,t7]) ).
cnf(t27,plain,
double_divide(X1,double_divide(double_divide(double_divide(identity,identity),double_divide(X1,identity)),identity)) = identity,
inference(orient,[status(thm)],[t8]) ).
cnf(t28,plain,
identity = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(cp,[status(thm)],[t27,t7]) ).
cnf(t34,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(orient,[status(thm)],[t28]) ).
cnf(t51,plain,
double_divide(identity,identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(sFlat0,identity)),double_divide(identity,identity)),identity)),
inference(cp,[status(thm)],[t43,t34]) ).
cnf(t3,axiom,
sFlat1 = double_divide(double_divide(a2,identity),identity),
introduced(definition) ).
cnf(t10,plain,
double_divide(double_divide(a2,identity),identity) = sFlat1,
inference(orient,[status(thm)],[t3]) ).
cnf(t360,plain,
double_divide(sFlat0,identity) = sFlat1,
inference(step,[status(thm)],[t10,t14]) ).
cnf(t18,plain,
double_divide(sFlat0,identity) = sFlat1,
inference(rw,[status(thm)],[t360]) ).
cnf(t21,plain,
double_divide(sFlat0,identity) = sFlat1,
inference(orient,[status(thm)],[t18]) ).
cnf(t373,plain,
double_divide(identity,identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,sFlat1),double_divide(identity,identity)),identity)),
inference(step,[status(thm)],[t51,t21]) ).
cnf(t49,plain,
double_divide(X1,identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(sFlat0,identity)),X1),identity)),
inference(cp,[status(thm)],[t43,t7]) ).
cnf(t363,plain,
double_divide(X1,identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,sFlat1),X1),identity)),
inference(step,[status(thm)],[t49,t21]) ).
cnf(t65,plain,
double_divide(a2,double_divide(double_divide(double_divide(identity,sFlat1),X1),identity)) = double_divide(X1,identity),
inference(orient,[status(thm)],[t363]) ).
cnf(t374,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,identity),identity),
inference(step,[status(thm)],[t373,t65]) ).
cnf(t117,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(orient,[status(thm)],[t374]) ).
cnf(t262,plain,
double_divide(X1,identity) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),X1),identity)),
inference(cp,[status(thm)],[t257,t117]) ).
cnf(t401,plain,
double_divide(X1,identity) = double_divide(identity,double_divide(double_divide(identity,X1),identity)),
inference(step,[status(thm)],[t262,t7]) ).
cnf(t281,plain,
double_divide(identity,double_divide(double_divide(identity,X1),identity)) = double_divide(X1,identity),
inference(orient,[status(thm)],[t401]) ).
cnf(t48,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(X1,identity)),identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(sFlat0,identity)),X1),identity)),
inference(cp,[status(thm)],[t43,t27]) ).
cnf(t376,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(X1,identity)),identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,sFlat1),X1),identity)),
inference(step,[status(thm)],[t48,t21]) ).
cnf(t377,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(step,[status(thm)],[t376,t65]) ).
cnf(t131,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(orient,[status(thm)],[t377]) ).
cnf(t282,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(identity,identity)),
inference(cp,[status(thm)],[t281,t117]) ).
cnf(t402,plain,
double_divide(identity,identity) = identity,
inference(step,[status(thm)],[t282,t7]) ).
cnf(t291,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t402]) ).
cnf(t408,plain,
double_divide(double_divide(identity,double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(step,[status(thm)],[t131,t291]) ).
cnf(t298,plain,
double_divide(double_divide(identity,double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(rw,[status(thm)],[t408]) ).
cnf(t321,plain,
double_divide(double_divide(identity,double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(orient,[status(thm)],[t298]) ).
cnf(t326,plain,
double_divide(double_divide(X1,identity),identity) = double_divide(identity,double_divide(X1,identity)),
inference(cp,[status(thm)],[t281,t321]) ).
cnf(t332,plain,
double_divide(double_divide(X1,identity),identity) = double_divide(identity,double_divide(X1,identity)),
inference(orient,[status(thm)],[t326]) ).
cnf(t15,plain,
identity = double_divide(a2,sFlat0),
inference(cp,[status(thm)],[t7,t14]) ).
cnf(t19,plain,
double_divide(a2,sFlat0) = identity,
inference(orient,[status(thm)],[t15]) ).
cnf(t20,plain,
sFlat0 = double_divide(X1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),identity)),a2),identity)),
inference(cp,[status(thm)],[t4,t19]) ).
cnf(t190,plain,
double_divide(X1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),identity)),a2),identity)) = sFlat0,
inference(orient,[status(thm)],[t20]) ).
cnf(t207,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),identity)),a2),identity) = double_divide(sFlat0,identity),
inference(cp,[status(thm)],[t131,t190]) ).
cnf(t35,plain,
identity = double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),identity)),
inference(cp,[status(thm)],[t4,t34]) ).
cnf(t41,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),identity)) = identity,
inference(orient,[status(thm)],[t35]) ).
cnf(t384,plain,
double_divide(double_divide(identity,a2),identity) = double_divide(sFlat0,identity),
inference(step,[status(thm)],[t207,t41]) ).
cnf(t385,plain,
double_divide(double_divide(identity,a2),identity) = sFlat1,
inference(step,[status(thm)],[t384,t21]) ).
cnf(t213,plain,
double_divide(double_divide(identity,a2),identity) = sFlat1,
inference(orient,[status(thm)],[t385]) ).
cnf(t340,plain,
X1 = double_divide(a2,double_divide(identity,double_divide(double_divide(identity,double_divide(sFlat0,double_divide(identity,X1))),identity))),
inference(cp,[status(thm)],[t43,t332]) ).
cnf(t417,plain,
X1 = double_divide(a2,double_divide(double_divide(sFlat0,double_divide(identity,X1)),identity)),
inference(step,[status(thm)],[t340,t281]) ).
cnf(t193,plain,
sFlat0 = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),a2),identity)),
inference(cp,[status(thm)],[t190,t117]) ).
cnf(t386,plain,
sFlat0 = double_divide(identity,double_divide(double_divide(identity,a2),identity)),
inference(step,[status(thm)],[t193,t7]) ).
cnf(t387,plain,
sFlat0 = double_divide(identity,sFlat1),
inference(step,[status(thm)],[t386,t213]) ).
cnf(t221,plain,
double_divide(identity,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t387]) ).
cnf(t393,plain,
double_divide(a2,double_divide(double_divide(sFlat0,X1),identity)) = double_divide(X1,identity),
inference(step,[status(thm)],[t65,t221]) ).
cnf(t227,plain,
double_divide(a2,double_divide(double_divide(sFlat0,X1),identity)) = double_divide(X1,identity),
inference(rw,[status(thm)],[t393]) ).
cnf(t237,plain,
double_divide(a2,double_divide(double_divide(sFlat0,X1),identity)) = double_divide(X1,identity),
inference(orient,[status(thm)],[t227]) ).
cnf(t418,plain,
X1 = double_divide(double_divide(identity,X1),identity),
inference(step,[status(thm)],[t417,t237]) ).
cnf(t343,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(orient,[status(thm)],[t418]) ).
cnf(t419,plain,
a2 = sFlat1,
inference(step,[status(thm)],[t213,t343]) ).
cnf(t352,plain,
a2 = sFlat1,
inference(rw,[status(thm)],[t419]) ).
cnf(t354,plain,
a2 = sFlat1,
inference(orient,[status(thm)],[t352]) ).
cnf(t283,plain,
double_divide(sFlat1,identity) = double_divide(identity,double_divide(sFlat0,identity)),
inference(cp,[status(thm)],[t281,t221]) ).
cnf(t412,plain,
double_divide(sFlat1,identity) = double_divide(identity,sFlat1),
inference(step,[status(thm)],[t283,t21]) ).
cnf(t413,plain,
double_divide(sFlat1,identity) = sFlat0,
inference(step,[status(thm)],[t412,t221]) ).
cnf(t302,plain,
double_divide(sFlat1,identity) = sFlat0,
inference(orient,[status(thm)],[t413]) ).
cnf(t31,plain,
identity = double_divide(a2,double_divide(double_divide(double_divide(identity,identity),sFlat0),identity)),
inference(cp,[status(thm)],[t27,t14]) ).
cnf(t39,plain,
double_divide(a2,double_divide(double_divide(double_divide(identity,identity),sFlat0),identity)) = identity,
inference(orient,[status(thm)],[t31]) ).
cnf(t54,plain,
double_divide(double_divide(double_divide(identity,identity),sFlat0),identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(sFlat0,identity)),a2),identity)),
inference(cp,[status(thm)],[t43,t39]) ).
cnf(t371,plain,
double_divide(double_divide(double_divide(identity,identity),sFlat0),identity) = double_divide(a2,double_divide(double_divide(double_divide(identity,sFlat1),a2),identity)),
inference(step,[status(thm)],[t54,t21]) ).
cnf(t56,plain,
sFlat0 = double_divide(a2,double_divide(double_divide(double_divide(identity,double_divide(sFlat0,identity)),a2),identity)),
inference(cp,[status(thm)],[t43,t19]) ).
cnf(t362,plain,
sFlat0 = double_divide(a2,double_divide(double_divide(double_divide(identity,sFlat1),a2),identity)),
inference(step,[status(thm)],[t56,t21]) ).
cnf(t62,plain,
double_divide(a2,double_divide(double_divide(double_divide(identity,sFlat1),a2),identity)) = sFlat0,
inference(orient,[status(thm)],[t362]) ).
cnf(t372,plain,
double_divide(double_divide(double_divide(identity,identity),sFlat0),identity) = sFlat0,
inference(step,[status(thm)],[t371,t62]) ).
cnf(t110,plain,
double_divide(double_divide(double_divide(identity,identity),sFlat0),identity) = sFlat0,
inference(orient,[status(thm)],[t372]) ).
cnf(t410,plain,
double_divide(double_divide(identity,sFlat0),identity) = sFlat0,
inference(step,[status(thm)],[t110,t291]) ).
cnf(t300,plain,
double_divide(double_divide(identity,sFlat0),identity) = sFlat0,
inference(rw,[status(thm)],[t410]) ).
cnf(t313,plain,
double_divide(double_divide(identity,sFlat0),identity) = sFlat0,
inference(orient,[status(thm)],[t300]) ).
cnf(t314,plain,
double_divide(sFlat0,identity) = double_divide(identity,sFlat0),
inference(cp,[status(thm)],[t281,t313]) ).
cnf(t415,plain,
sFlat1 = double_divide(identity,sFlat0),
inference(step,[status(thm)],[t314,t21]) ).
cnf(t319,plain,
double_divide(identity,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t415]) ).
cnf(u0,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox/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(identity,double_divide(a2,identity)) != a2,
inference(rw,[status(thm)],[goal_0,t332]) ).
cnf(g0_1,plain,
double_divide(identity,double_divide(sFlat1,identity)) != a2,
inference(rw,[status(thm)],[g0_0,t354]) ).
cnf(g0_2,plain,
double_divide(identity,sFlat0) != a2,
inference(rw,[status(thm)],[g0_1,t302]) ).
cnf(g0_3,plain,
sFlat1 != a2,
inference(rw,[status(thm)],[g0_2,t319]) ).
cnf(g0_4,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_3,t354]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP488-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 14:52:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.65/0.91 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.65/0.91 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------