%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP578-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 01:27:34 PM UTC 2026
% Result : Unsatisfiable 3.22s 1.60s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 7
% Syntax : Number of clauses : 114 ( 114 unt; 0 nHn; 62 RR)
% Number of literals : 114 ( 113 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t11,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
inference(orient,[status(thm)],[t1]) ).
cnf(t2,axiom,
sF0 = double_divide(a2,identity),
introduced(definition) ).
cnf(t4,plain,
double_divide(a2,identity) = sF0,
inference(orient,[status(thm)],[t2]) ).
cnf(t12,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(sF0,X1),double_divide(a2,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t11,t4]) ).
cnf(t286,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(sF0,X1),sF0)),double_divide(identity,identity)),
inference(step,[status(thm)],[t12,t4]) ).
cnf(t23,plain,
double_divide(double_divide(identity,double_divide(double_divide(sF0,X1),sF0)),double_divide(identity,identity)) = X1,
inference(orient,[status(thm)],[t286]) ).
cnf(t13,plain,
X1 = double_divide(double_divide(X2,double_divide(double_divide(double_divide(a2,X2),X1),sF0)),double_divide(identity,identity)),
inference(cp,[status(thm)],[t11,t4]) ).
cnf(t37,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(a2,X1),X2),sF0)),double_divide(identity,identity)) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t41,plain,
double_divide(double_divide(double_divide(a2,double_divide(identity,X1)),X2),sF0) = double_divide(double_divide(X1,X2),double_divide(identity,identity)),
inference(cp,[status(thm)],[t11,t37]) ).
cnf(t50,plain,
double_divide(double_divide(double_divide(a2,double_divide(identity,X1)),X2),sF0) = double_divide(double_divide(X1,X2),double_divide(identity,identity)),
inference(orient,[status(thm)],[t41]) ).
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(t5,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t51,plain,
double_divide(double_divide(double_divide(identity,identity),X1),double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),X1),sF0),
inference(cp,[status(thm)],[t50,t5]) ).
cnf(t289,plain,
double_divide(double_divide(double_divide(identity,identity),X1),double_divide(identity,identity)) = double_divide(double_divide(sF0,X1),sF0),
inference(step,[status(thm)],[t51,t4]) ).
cnf(t56,plain,
double_divide(double_divide(double_divide(identity,identity),X1),double_divide(identity,identity)) = double_divide(double_divide(sF0,X1),sF0),
inference(orient,[status(thm)],[t289]) ).
cnf(t57,plain,
double_divide(double_divide(sF0,double_divide(double_divide(identity,identity),identity)),sF0) = double_divide(identity,double_divide(identity,identity)),
inference(cp,[status(thm)],[t56,t5]) ).
cnf(t290,plain,
double_divide(double_divide(sF0,double_divide(double_divide(identity,identity),identity)),sF0) = identity,
inference(step,[status(thm)],[t57,t5]) ).
cnf(t72,plain,
double_divide(double_divide(sF0,double_divide(double_divide(identity,identity),identity)),sF0) = identity,
inference(orient,[status(thm)],[t290]) ).
cnf(t75,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(cp,[status(thm)],[t23,t72]) ).
cnf(t76,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),identity),
inference(orient,[status(thm)],[t75]) ).
cnf(t77,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t11,t76]) ).
cnf(t291,plain,
double_divide(identity,identity) = identity,
inference(step,[status(thm)],[t77,t11]) ).
cnf(t80,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t291]) ).
cnf(t293,plain,
double_divide(double_divide(identity,double_divide(double_divide(sF0,X1),sF0)),identity) = X1,
inference(step,[status(thm)],[t23,t80]) ).
cnf(t82,plain,
double_divide(double_divide(identity,double_divide(double_divide(sF0,X1),sF0)),identity) = X1,
inference(rw,[status(thm)],[t293]) ).
cnf(t299,plain,
double_divide(double_divide(identity,X1),double_divide(identity,identity)) = double_divide(double_divide(sF0,X1),sF0),
inference(step,[status(thm)],[t56,t80]) ).
cnf(t300,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(double_divide(sF0,X1),sF0),
inference(step,[status(thm)],[t299,t80]) ).
cnf(t89,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(double_divide(sF0,X1),sF0),
inference(rw,[status(thm)],[t300]) ).
cnf(t94,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(double_divide(sF0,X1),sF0),
inference(orient,[status(thm)],[t89]) ).
cnf(t307,plain,
double_divide(double_divide(sF0,double_divide(double_divide(sF0,X1),sF0)),sF0) = X1,
inference(step,[status(thm)],[t82,t94]) ).
cnf(t130,plain,
double_divide(double_divide(sF0,double_divide(double_divide(sF0,X1),sF0)),sF0) = X1,
inference(orient,[status(thm)],[t307]) ).
cnf(t292,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),identity) = X3,
inference(step,[status(thm)],[t11,t80]) ).
cnf(t81,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),identity) = X3,
inference(rw,[status(thm)],[t292]) ).
cnf(t97,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X1),X3),double_divide(X2,identity))),identity) = X3,
inference(orient,[status(thm)],[t81]) ).
cnf(t99,plain,
double_divide(double_divide(X1,X2),identity) = double_divide(double_divide(X2,double_divide(identity,double_divide(X1,identity))),identity),
inference(cp,[status(thm)],[t97,t5]) ).
cnf(t170,plain,
double_divide(double_divide(X1,double_divide(identity,double_divide(X2,identity))),identity) = double_divide(double_divide(X2,X1),identity),
inference(orient,[status(thm)],[t99]) ).
cnf(t297,plain,
double_divide(double_divide(double_divide(a2,double_divide(identity,X1)),X2),sF0) = double_divide(double_divide(X1,X2),identity),
inference(step,[status(thm)],[t50,t80]) ).
cnf(t87,plain,
double_divide(double_divide(double_divide(a2,double_divide(identity,X1)),X2),sF0) = double_divide(double_divide(X1,X2),identity),
inference(orient,[status(thm)],[t297]) ).
cnf(t183,plain,
double_divide(double_divide(double_divide(X1,identity),identity),identity) = double_divide(double_divide(double_divide(X1,a2),identity),sF0),
inference(cp,[status(thm)],[t87,t170]) ).
cnf(t199,plain,
double_divide(double_divide(double_divide(X1,a2),identity),sF0) = double_divide(double_divide(double_divide(X1,identity),identity),identity),
inference(orient,[status(thm)],[t183]) ).
cnf(t201,plain,
double_divide(double_divide(double_divide(identity,identity),identity),identity) = double_divide(double_divide(double_divide(sF0,a2),sF0),sF0),
inference(cp,[status(thm)],[t199,t94]) ).
cnf(t317,plain,
double_divide(double_divide(double_divide(sF0,identity),sF0),identity) = double_divide(double_divide(double_divide(sF0,a2),sF0),sF0),
inference(step,[status(thm)],[t201,t94]) ).
cnf(t3,axiom,
sF1 = double_divide(double_divide(a2,identity),identity),
introduced(definition) ).
cnf(t285,plain,
sF1 = double_divide(sF0,identity),
inference(step,[status(thm)],[t3,t4]) ).
cnf(t8,plain,
double_divide(sF0,identity) = sF1,
inference(orient,[status(thm)],[t285]) ).
cnf(t318,plain,
double_divide(double_divide(sF1,sF0),identity) = double_divide(double_divide(double_divide(sF0,a2),sF0),sF0),
inference(step,[status(thm)],[t317,t8]) ).
cnf(t95,plain,
double_divide(double_divide(sF0,double_divide(identity,identity)),sF0) = double_divide(identity,identity),
inference(cp,[status(thm)],[t94,t5]) ).
cnf(t301,plain,
double_divide(double_divide(sF0,identity),sF0) = double_divide(identity,identity),
inference(step,[status(thm)],[t95,t80]) ).
cnf(t302,plain,
double_divide(sF1,sF0) = double_divide(identity,identity),
inference(step,[status(thm)],[t301,t8]) ).
cnf(t303,plain,
double_divide(sF1,sF0) = identity,
inference(step,[status(thm)],[t302,t80]) ).
cnf(t116,plain,
double_divide(sF1,sF0) = identity,
inference(orient,[status(thm)],[t303]) ).
cnf(t319,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(sF0,a2),sF0),sF0),
inference(step,[status(thm)],[t318,t116]) ).
cnf(t320,plain,
identity = double_divide(double_divide(double_divide(sF0,a2),sF0),sF0),
inference(step,[status(thm)],[t319,t80]) ).
cnf(t219,plain,
double_divide(double_divide(double_divide(sF0,a2),sF0),sF0) = identity,
inference(orient,[status(thm)],[t320]) ).
cnf(t220,plain,
sF0 = double_divide(double_divide(sF0,double_divide(identity,double_divide(double_divide(sF0,a2),identity))),identity),
inference(cp,[status(thm)],[t97,t219]) ).
cnf(t321,plain,
sF0 = double_divide(double_divide(double_divide(sF0,a2),sF0),identity),
inference(step,[status(thm)],[t220,t170]) ).
cnf(t38,plain,
double_divide(double_divide(a2,X1),identity) = double_divide(double_divide(X1,double_divide(identity,sF0)),double_divide(identity,identity)),
inference(cp,[status(thm)],[t37,t5]) ).
cnf(t44,plain,
double_divide(double_divide(X1,double_divide(identity,sF0)),double_divide(identity,identity)) = double_divide(double_divide(a2,X1),identity),
inference(orient,[status(thm)],[t38]) ).
cnf(t296,plain,
double_divide(double_divide(X1,double_divide(identity,sF0)),identity) = double_divide(double_divide(a2,X1),identity),
inference(step,[status(thm)],[t44,t80]) ).
cnf(t86,plain,
double_divide(double_divide(X1,double_divide(identity,sF0)),identity) = double_divide(double_divide(a2,X1),identity),
inference(rw,[status(thm)],[t296]) ).
cnf(t118,plain,
double_divide(double_divide(X1,double_divide(identity,sF0)),identity) = double_divide(double_divide(a2,X1),identity),
inference(orient,[status(thm)],[t86]) ).
cnf(t96,plain,
identity = double_divide(double_divide(identity,X1),double_divide(double_divide(sF0,X1),sF0)),
inference(cp,[status(thm)],[t5,t94]) ).
cnf(t133,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(sF0,X1),sF0)) = identity,
inference(orient,[status(thm)],[t96]) ).
cnf(t134,plain,
identity = double_divide(double_divide(identity,double_divide(sF0,identity)),double_divide(identity,sF0)),
inference(cp,[status(thm)],[t133,t5]) ).
cnf(t308,plain,
identity = double_divide(double_divide(identity,sF1),double_divide(identity,sF0)),
inference(step,[status(thm)],[t134,t8]) ).
cnf(t139,plain,
double_divide(double_divide(identity,sF1),double_divide(identity,sF0)) = identity,
inference(orient,[status(thm)],[t308]) ).
cnf(t142,plain,
double_divide(double_divide(a2,double_divide(identity,sF1)),identity) = double_divide(identity,identity),
inference(cp,[status(thm)],[t118,t139]) ).
cnf(t310,plain,
double_divide(double_divide(a2,double_divide(identity,sF1)),identity) = identity,
inference(step,[status(thm)],[t142,t80]) ).
cnf(t149,plain,
double_divide(double_divide(a2,double_divide(identity,sF1)),identity) = identity,
inference(orient,[status(thm)],[t310]) ).
cnf(t171,plain,
double_divide(double_divide(sF0,X1),identity) = double_divide(double_divide(X1,double_divide(identity,sF1)),identity),
inference(cp,[status(thm)],[t170,t8]) ).
cnf(t187,plain,
double_divide(double_divide(X1,double_divide(identity,sF1)),identity) = double_divide(double_divide(sF0,X1),identity),
inference(orient,[status(thm)],[t171]) ).
cnf(t314,plain,
double_divide(double_divide(sF0,a2),identity) = identity,
inference(step,[status(thm)],[t149,t187]) ).
cnf(t188,plain,
double_divide(double_divide(sF0,a2),identity) = identity,
inference(rw,[status(thm)],[t314]) ).
cnf(t196,plain,
double_divide(double_divide(sF0,a2),identity) = identity,
inference(orient,[status(thm)],[t188]) ).
cnf(t198,plain,
double_divide(double_divide(double_divide(sF0,a2),X1),identity) = double_divide(double_divide(X1,double_divide(identity,identity)),identity),
inference(cp,[status(thm)],[t170,t196]) ).
cnf(t316,plain,
double_divide(double_divide(double_divide(sF0,a2),X1),identity) = double_divide(double_divide(X1,identity),identity),
inference(step,[status(thm)],[t198,t80]) ).
cnf(t209,plain,
double_divide(double_divide(double_divide(sF0,a2),X1),identity) = double_divide(double_divide(X1,identity),identity),
inference(orient,[status(thm)],[t316]) ).
cnf(t322,plain,
sF0 = double_divide(double_divide(sF0,identity),identity),
inference(step,[status(thm)],[t321,t209]) ).
cnf(t323,plain,
sF0 = double_divide(sF1,identity),
inference(step,[status(thm)],[t322,t8]) ).
cnf(t221,plain,
double_divide(sF1,identity) = sF0,
inference(orient,[status(thm)],[t323]) ).
cnf(t228,plain,
double_divide(double_divide(sF1,X1),identity) = double_divide(double_divide(X1,double_divide(identity,sF0)),identity),
inference(cp,[status(thm)],[t170,t221]) ).
cnf(t331,plain,
double_divide(double_divide(sF1,X1),identity) = double_divide(double_divide(a2,X1),identity),
inference(step,[status(thm)],[t228,t118]) ).
cnf(t246,plain,
double_divide(double_divide(a2,X1),identity) = double_divide(double_divide(sF1,X1),identity),
inference(orient,[status(thm)],[t331]) ).
cnf(t249,plain,
double_divide(double_divide(sF1,double_divide(identity,double_divide(X1,identity))),identity) = double_divide(double_divide(X1,a2),identity),
inference(cp,[status(thm)],[t246,t170]) ).
cnf(t334,plain,
double_divide(double_divide(X1,sF1),identity) = double_divide(double_divide(X1,a2),identity),
inference(step,[status(thm)],[t249,t170]) ).
cnf(t264,plain,
double_divide(double_divide(X1,a2),identity) = double_divide(double_divide(X1,sF1),identity),
inference(orient,[status(thm)],[t334]) ).
cnf(t267,plain,
double_divide(double_divide(identity,sF1),identity) = double_divide(double_divide(sF0,a2),sF0),
inference(cp,[status(thm)],[t264,t94]) ).
cnf(t336,plain,
double_divide(double_divide(sF0,sF1),sF0) = double_divide(double_divide(sF0,a2),sF0),
inference(step,[status(thm)],[t267,t94]) ).
cnf(t9,plain,
identity = double_divide(sF0,sF1),
inference(cp,[status(thm)],[t5,t8]) ).
cnf(t10,plain,
double_divide(sF0,sF1) = identity,
inference(orient,[status(thm)],[t9]) ).
cnf(t337,plain,
double_divide(identity,sF0) = double_divide(double_divide(sF0,a2),sF0),
inference(step,[status(thm)],[t336,t10]) ).
cnf(t140,plain,
double_divide(identity,sF0) = double_divide(double_divide(sF1,double_divide(identity,double_divide(identity,identity))),identity),
inference(cp,[status(thm)],[t97,t139]) ).
cnf(t309,plain,
double_divide(identity,sF0) = double_divide(double_divide(sF1,identity),identity),
inference(step,[status(thm)],[t140,t5]) ).
cnf(t143,plain,
double_divide(double_divide(sF1,identity),identity) = double_divide(identity,sF0),
inference(orient,[status(thm)],[t309]) ).
cnf(t222,plain,
double_divide(sF0,identity) = double_divide(identity,sF0),
inference(rw,[status(thm)],[t143]) ).
cnf(t327,plain,
sF1 = double_divide(identity,sF0),
inference(step,[status(thm)],[t222,t8]) ).
cnf(t236,plain,
double_divide(identity,sF0) = sF1,
inference(orient,[status(thm)],[t327]) ).
cnf(t338,plain,
sF1 = double_divide(double_divide(sF0,a2),sF0),
inference(step,[status(thm)],[t337,t236]) ).
cnf(t271,plain,
double_divide(double_divide(sF0,a2),sF0) = sF1,
inference(orient,[status(thm)],[t338]) ).
cnf(t274,plain,
a2 = double_divide(double_divide(sF0,sF1),sF0),
inference(cp,[status(thm)],[t130,t271]) ).
cnf(t339,plain,
a2 = double_divide(identity,sF0),
inference(step,[status(thm)],[t274,t10]) ).
cnf(t340,plain,
a2 = sF1,
inference(step,[status(thm)],[t339,t236]) ).
cnf(t276,plain,
a2 = sF1,
inference(orient,[status(thm)],[t340]) ).
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(double_divide(sF1,identity),identity) != a2,
inference(rw,[status(thm)],[goal_0,t276]) ).
cnf(g0_1,plain,
double_divide(sF0,identity) != a2,
inference(rw,[status(thm)],[g0_0,t221]) ).
cnf(g0_2,plain,
sF1 != a2,
inference(rw,[status(thm)],[g0_1,t8]) ).
cnf(g0_3,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_2,t276]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP578-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 15:07:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.22/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.22/1.60 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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