%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP497-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:27:11 PM UTC 2026
% Result : Unsatisfiable 5.44s 1.07s
% Output : CNFRefutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 7
% Syntax : Number of clauses : 73 ( 73 unt; 0 nHn; 58 RR)
% Number of literals : 73 ( 72 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
double_divide(double_divide(identity,double_divide(X1,double_divide(X2,identity))),double_divide(double_divide(X2,double_divide(X3,X1)),identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t11,plain,
double_divide(double_divide(identity,double_divide(X1,double_divide(X2,identity))),double_divide(double_divide(X2,double_divide(X3,X1)),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(t5,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t15,plain,
X1 = double_divide(double_divide(identity,identity),double_divide(double_divide(X2,double_divide(X1,X2)),identity)),
inference(cp,[status(thm)],[t11,t5]) ).
cnf(t14,plain,
double_divide(identity,identity) = identity,
inference(cp,[status(thm)],[t11,t5]) ).
cnf(t25,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t14]) ).
cnf(t126,plain,
X1 = double_divide(identity,double_divide(double_divide(X2,double_divide(X1,X2)),identity)),
inference(step,[status(thm)],[t15,t25]) ).
cnf(t28,plain,
double_divide(identity,double_divide(double_divide(X1,double_divide(X2,X1)),identity)) = X2,
inference(orient,[status(thm)],[t126]) ).
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(X2,sF0)),double_divide(double_divide(a2,double_divide(X1,X2)),identity)),
inference(cp,[status(thm)],[t11,t4]) ).
cnf(t46,plain,
double_divide(double_divide(identity,double_divide(X1,sF0)),double_divide(double_divide(a2,double_divide(X2,X1)),identity)) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t53,plain,
identity = double_divide(double_divide(identity,double_divide(identity,sF0)),double_divide(double_divide(a2,identity),identity)),
inference(cp,[status(thm)],[t46,t25]) ).
cnf(t6,plain,
identity = double_divide(a2,sF0),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t7,plain,
double_divide(a2,sF0) = identity,
inference(orient,[status(thm)],[t6]) ).
cnf(t31,plain,
a2 = double_divide(identity,double_divide(double_divide(sF0,identity),identity)),
inference(cp,[status(thm)],[t28,t7]) ).
cnf(t3,axiom,
sF1 = double_divide(double_divide(a2,identity),identity),
introduced(definition) ).
cnf(t125,plain,
sF1 = double_divide(sF0,identity),
inference(step,[status(thm)],[t3,t4]) ).
cnf(t8,plain,
double_divide(sF0,identity) = sF1,
inference(orient,[status(thm)],[t125]) ).
cnf(t127,plain,
a2 = double_divide(identity,double_divide(sF1,identity)),
inference(step,[status(thm)],[t31,t8]) ).
cnf(t39,plain,
double_divide(identity,double_divide(sF1,identity)) = a2,
inference(orient,[status(thm)],[t127]) ).
cnf(t41,plain,
sF1 = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(a2,identity)),
inference(cp,[status(thm)],[t11,t39]) ).
cnf(t128,plain,
sF1 = double_divide(double_divide(identity,identity),double_divide(a2,identity)),
inference(step,[status(thm)],[t41,t5]) ).
cnf(t129,plain,
sF1 = double_divide(identity,double_divide(a2,identity)),
inference(step,[status(thm)],[t128,t25]) ).
cnf(t130,plain,
sF1 = double_divide(identity,sF0),
inference(step,[status(thm)],[t129,t4]) ).
cnf(t44,plain,
double_divide(identity,sF0) = sF1,
inference(orient,[status(thm)],[t130]) ).
cnf(t134,plain,
identity = double_divide(double_divide(identity,sF1),double_divide(double_divide(a2,identity),identity)),
inference(step,[status(thm)],[t53,t44]) ).
cnf(t135,plain,
identity = double_divide(double_divide(identity,sF1),double_divide(sF0,identity)),
inference(step,[status(thm)],[t134,t4]) ).
cnf(t136,plain,
identity = double_divide(double_divide(identity,sF1),sF1),
inference(step,[status(thm)],[t135,t8]) ).
cnf(t69,plain,
double_divide(double_divide(identity,sF1),sF1) = identity,
inference(orient,[status(thm)],[t136]) ).
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(t33,plain,
sF0 = double_divide(identity,double_divide(double_divide(sF1,identity),identity)),
inference(cp,[status(thm)],[t28,t10]) ).
cnf(t77,plain,
double_divide(identity,double_divide(double_divide(sF1,identity),identity)) = sF0,
inference(orient,[status(thm)],[t33]) ).
cnf(t79,plain,
double_divide(sF1,identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(sF0,identity)),
inference(cp,[status(thm)],[t11,t77]) ).
cnf(t138,plain,
double_divide(sF1,identity) = double_divide(double_divide(identity,identity),double_divide(sF0,identity)),
inference(step,[status(thm)],[t79,t5]) ).
cnf(t139,plain,
double_divide(sF1,identity) = double_divide(identity,double_divide(sF0,identity)),
inference(step,[status(thm)],[t138,t25]) ).
cnf(t140,plain,
double_divide(sF1,identity) = double_divide(identity,sF1),
inference(step,[status(thm)],[t139,t8]) ).
cnf(t83,plain,
double_divide(identity,sF1) = double_divide(sF1,identity),
inference(orient,[status(thm)],[t140]) ).
cnf(t142,plain,
double_divide(double_divide(sF1,identity),sF1) = identity,
inference(step,[status(thm)],[t69,t83]) ).
cnf(t85,plain,
double_divide(double_divide(sF1,identity),sF1) = identity,
inference(rw,[status(thm)],[t142]) ).
cnf(t94,plain,
double_divide(double_divide(sF1,identity),sF1) = identity,
inference(orient,[status(thm)],[t85]) ).
cnf(t96,plain,
double_divide(sF1,identity) = double_divide(identity,double_divide(double_divide(sF1,identity),identity)),
inference(cp,[status(thm)],[t28,t94]) ).
cnf(t47,plain,
a2 = double_divide(double_divide(identity,double_divide(identity,sF0)),double_divide(double_divide(a2,sF0),identity)),
inference(cp,[status(thm)],[t46,t4]) ).
cnf(t131,plain,
a2 = double_divide(double_divide(identity,sF1),double_divide(double_divide(a2,sF0),identity)),
inference(step,[status(thm)],[t47,t44]) ).
cnf(t132,plain,
a2 = double_divide(double_divide(identity,sF1),double_divide(identity,identity)),
inference(step,[status(thm)],[t131,t7]) ).
cnf(t133,plain,
a2 = double_divide(double_divide(identity,sF1),identity),
inference(step,[status(thm)],[t132,t25]) ).
cnf(t63,plain,
double_divide(double_divide(identity,sF1),identity) = a2,
inference(orient,[status(thm)],[t133]) ).
cnf(t141,plain,
double_divide(double_divide(sF1,identity),identity) = a2,
inference(step,[status(thm)],[t63,t83]) ).
cnf(t84,plain,
double_divide(double_divide(sF1,identity),identity) = a2,
inference(rw,[status(thm)],[t141]) ).
cnf(t89,plain,
double_divide(double_divide(sF1,identity),identity) = a2,
inference(orient,[status(thm)],[t84]) ).
cnf(t144,plain,
double_divide(sF1,identity) = double_divide(identity,a2),
inference(step,[status(thm)],[t96,t89]) ).
cnf(t32,plain,
sF0 = double_divide(identity,double_divide(double_divide(identity,sF1),identity)),
inference(cp,[status(thm)],[t28,t8]) ).
cnf(t137,plain,
sF0 = double_divide(identity,a2),
inference(step,[status(thm)],[t32,t63]) ).
cnf(t75,plain,
double_divide(identity,a2) = sF0,
inference(orient,[status(thm)],[t137]) ).
cnf(t145,plain,
double_divide(sF1,identity) = sF0,
inference(step,[status(thm)],[t144,t75]) ).
cnf(t108,plain,
double_divide(sF1,identity) = sF0,
inference(orient,[status(thm)],[t145]) ).
cnf(t116,plain,
sF1 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(double_divide(X1,sF0),identity)),
inference(cp,[status(thm)],[t11,t108]) ).
cnf(t13,plain,
a2 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(double_divide(X1,sF0),identity)),
inference(cp,[status(thm)],[t11,t4]) ).
cnf(t98,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(double_divide(X1,sF0),identity)) = a2,
inference(orient,[status(thm)],[t13]) ).
cnf(t148,plain,
sF1 = a2,
inference(step,[status(thm)],[t116,t98]) ).
cnf(t118,plain,
a2 = sF1,
inference(orient,[status(thm)],[t148]) ).
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,t118]) ).
cnf(g0_1,plain,
double_divide(sF0,identity) != a2,
inference(rw,[status(thm)],[g0_0,t108]) ).
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,t118]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP497-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n026.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % 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 14:57:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.44/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/1.07 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------