%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP574-1 : 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 01:27:34 PM UTC 2026
% Result : Unsatisfiable 5.03s 1.08s
% Output : CNFRefutation 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 7
% Syntax : Number of clauses : 78 ( 78 unt; 0 nHn; 58 RR)
% Number of literals : 78 ( 77 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 : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t11,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
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(X1,sF0),double_divide(a2,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t11,t4]) ).
cnf(t124,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(X1,sF0),sF0)),double_divide(identity,identity)),
inference(step,[status(thm)],[t12,t4]) ).
cnf(t22,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,sF0),sF0)),double_divide(identity,identity)) = X1,
inference(orient,[status(thm)],[t124]) ).
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(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(t23,plain,
a2 = double_divide(double_divide(identity,double_divide(identity,sF0)),double_divide(identity,identity)),
inference(cp,[status(thm)],[t22,t7]) ).
cnf(t26,plain,
double_divide(double_divide(identity,double_divide(identity,sF0)),double_divide(identity,identity)) = a2,
inference(orient,[status(thm)],[t23]) ).
cnf(t27,plain,
identity = double_divide(double_divide(sF0,a2),double_divide(identity,identity)),
inference(cp,[status(thm)],[t11,t26]) ).
cnf(t30,plain,
double_divide(double_divide(sF0,a2),double_divide(identity,identity)) = identity,
inference(orient,[status(thm)],[t27]) ).
cnf(t31,plain,
double_divide(sF0,a2) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t11,t30]) ).
cnf(t125,plain,
double_divide(sF0,a2) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(step,[status(thm)],[t31,t5]) ).
cnf(t33,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(sF0,a2),
inference(orient,[status(thm)],[t125]) ).
cnf(t34,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(double_divide(sF0,a2),double_divide(identity,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t11,t33]) ).
cnf(t126,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(step,[status(thm)],[t34,t30]) ).
cnf(t127,plain,
double_divide(identity,identity) = double_divide(sF0,a2),
inference(step,[status(thm)],[t126,t33]) ).
cnf(t39,plain,
double_divide(identity,identity) = double_divide(sF0,a2),
inference(orient,[status(thm)],[t127]) ).
cnf(t129,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,sF0),sF0)),double_divide(sF0,a2)) = X1,
inference(step,[status(thm)],[t22,t39]) ).
cnf(t41,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,sF0),sF0)),double_divide(sF0,a2)) = X1,
inference(rw,[status(thm)],[t129]) ).
cnf(t132,plain,
double_divide(double_divide(sF0,a2),double_divide(identity,identity)) = double_divide(sF0,a2),
inference(step,[status(thm)],[t33,t39]) ).
cnf(t133,plain,
double_divide(double_divide(sF0,a2),double_divide(sF0,a2)) = double_divide(sF0,a2),
inference(step,[status(thm)],[t132,t39]) ).
cnf(t44,plain,
double_divide(double_divide(sF0,a2),double_divide(sF0,a2)) = double_divide(sF0,a2),
inference(rw,[status(thm)],[t133]) ).
cnf(t131,plain,
double_divide(double_divide(sF0,a2),double_divide(sF0,a2)) = identity,
inference(step,[status(thm)],[t30,t39]) ).
cnf(t43,plain,
double_divide(double_divide(sF0,a2),double_divide(sF0,a2)) = identity,
inference(rw,[status(thm)],[t131]) ).
cnf(t48,plain,
double_divide(double_divide(sF0,a2),double_divide(sF0,a2)) = identity,
inference(orient,[status(thm)],[t43]) ).
cnf(t135,plain,
identity = double_divide(sF0,a2),
inference(step,[status(thm)],[t44,t48]) ).
cnf(t49,plain,
double_divide(sF0,a2) = identity,
inference(orient,[status(thm)],[t135]) ).
cnf(t139,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,sF0),sF0)),identity) = X1,
inference(step,[status(thm)],[t41,t49]) ).
cnf(t57,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,sF0),sF0)),identity) = X1,
inference(orient,[status(thm)],[t139]) ).
cnf(t128,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(sF0,a2)) = X2,
inference(step,[status(thm)],[t11,t39]) ).
cnf(t40,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(sF0,a2)) = X2,
inference(rw,[status(thm)],[t128]) ).
cnf(t140,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),identity) = X2,
inference(step,[status(thm)],[t40,t49]) ).
cnf(t62,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),identity) = X2,
inference(orient,[status(thm)],[t140]) ).
cnf(t64,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity),
inference(cp,[status(thm)],[t62,t5]) ).
cnf(t85,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity) = X1,
inference(orient,[status(thm)],[t64]) ).
cnf(t3,axiom,
sF1 = double_divide(double_divide(a2,identity),identity),
introduced(definition) ).
cnf(t123,plain,
sF1 = double_divide(sF0,identity),
inference(step,[status(thm)],[t3,t4]) ).
cnf(t8,plain,
double_divide(sF0,identity) = sF1,
inference(orient,[status(thm)],[t123]) ).
cnf(t86,plain,
sF0 = double_divide(double_divide(identity,double_divide(identity,sF1)),identity),
inference(cp,[status(thm)],[t85,t8]) ).
cnf(t94,plain,
double_divide(double_divide(identity,double_divide(identity,sF1)),identity) = sF0,
inference(orient,[status(thm)],[t86]) ).
cnf(t97,plain,
double_divide(identity,double_divide(identity,sF1)) = double_divide(double_divide(identity,double_divide(identity,sF0)),identity),
inference(cp,[status(thm)],[t85,t94]) ).
cnf(t130,plain,
double_divide(double_divide(identity,double_divide(identity,sF0)),double_divide(sF0,a2)) = a2,
inference(step,[status(thm)],[t26,t39]) ).
cnf(t42,plain,
double_divide(double_divide(identity,double_divide(identity,sF0)),double_divide(sF0,a2)) = a2,
inference(rw,[status(thm)],[t130]) ).
cnf(t138,plain,
double_divide(double_divide(identity,double_divide(identity,sF0)),identity) = a2,
inference(step,[status(thm)],[t42,t49]) ).
cnf(t54,plain,
double_divide(double_divide(identity,double_divide(identity,sF0)),identity) = a2,
inference(orient,[status(thm)],[t138]) ).
cnf(t142,plain,
double_divide(identity,double_divide(identity,sF1)) = a2,
inference(step,[status(thm)],[t97,t54]) ).
cnf(t98,plain,
double_divide(identity,double_divide(identity,sF1)) = a2,
inference(orient,[status(thm)],[t142]) ).
cnf(t100,plain,
identity = double_divide(double_divide(sF1,double_divide(a2,double_divide(identity,identity))),identity),
inference(cp,[status(thm)],[t62,t98]) ).
cnf(t136,plain,
double_divide(identity,identity) = identity,
inference(step,[status(thm)],[t39,t49]) ).
cnf(t50,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t136]) ).
cnf(t143,plain,
identity = double_divide(double_divide(sF1,double_divide(a2,identity)),identity),
inference(step,[status(thm)],[t100,t50]) ).
cnf(t144,plain,
identity = double_divide(double_divide(sF1,sF0),identity),
inference(step,[status(thm)],[t143,t4]) ).
cnf(t102,plain,
double_divide(double_divide(sF1,sF0),identity) = identity,
inference(orient,[status(thm)],[t144]) ).
cnf(t104,plain,
double_divide(sF1,sF0) = double_divide(double_divide(identity,double_divide(identity,identity)),identity),
inference(cp,[status(thm)],[t85,t102]) ).
cnf(t145,plain,
double_divide(sF1,sF0) = double_divide(identity,identity),
inference(step,[status(thm)],[t104,t5]) ).
cnf(t146,plain,
double_divide(sF1,sF0) = identity,
inference(step,[status(thm)],[t145,t50]) ).
cnf(t105,plain,
double_divide(sF1,sF0) = identity,
inference(orient,[status(thm)],[t146]) ).
cnf(t107,plain,
sF1 = double_divide(double_divide(identity,double_divide(identity,sF0)),identity),
inference(cp,[status(thm)],[t57,t105]) ).
cnf(t147,plain,
sF1 = a2,
inference(step,[status(thm)],[t107,t54]) ).
cnf(t110,plain,
a2 = sF1,
inference(orient,[status(thm)],[t147]) ).
cnf(t148,plain,
double_divide(sF1,identity) = sF0,
inference(step,[status(thm)],[t4,t110]) ).
cnf(t111,plain,
double_divide(sF1,identity) = sF0,
inference(rw,[status(thm)],[t148]) ).
cnf(t121,plain,
double_divide(sF1,identity) = sF0,
inference(orient,[status(thm)],[t111]) ).
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,t110]) ).
cnf(g0_1,plain,
double_divide(sF0,identity) != a2,
inference(rw,[status(thm)],[g0_0,t121]) ).
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,t110]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP574-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 15:09:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.03/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/1.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------