%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP495-1 : 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 01:27:11 PM UTC 2026
% Result : Unsatisfiable 4.06s 1.00s
% Output : CNFRefutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 11
% Syntax : Number of clauses : 95 ( 95 unt; 0 nHn; 49 RR)
% Number of literals : 95 ( 94 equ; 8 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 : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
sF0 = double_divide(c3,b3),
introduced(definition) ).
cnf(t10,plain,
double_divide(c3,b3) = sF0,
inference(orient,[status(thm)],[t2]) ).
cnf(t3,axiom,
sF1 = double_divide(double_divide(c3,b3),identity),
introduced(definition) ).
cnf(t771,plain,
sF1 = double_divide(sF0,identity),
inference(step,[status(thm)],[t3,t10]) ).
cnf(t13,plain,
double_divide(sF0,identity) = sF1,
inference(orient,[status(thm)],[t771]) ).
cnf(t4,axiom,
sF2 = double_divide(double_divide(double_divide(c3,b3),identity),a3),
introduced(definition) ).
cnf(t773,plain,
sF2 = double_divide(double_divide(sF0,identity),a3),
inference(step,[status(thm)],[t4,t10]) ).
cnf(t774,plain,
sF2 = double_divide(sF1,a3),
inference(step,[status(thm)],[t773,t13]) ).
cnf(t19,plain,
double_divide(sF1,a3) = sF2,
inference(orient,[status(thm)],[t774]) ).
cnf(t6,axiom,
sF4 = double_divide(b3,a3),
introduced(definition) ).
cnf(t11,plain,
double_divide(b3,a3) = sF4,
inference(orient,[status(thm)],[t6]) ).
cnf(t7,axiom,
sF5 = double_divide(double_divide(b3,a3),identity),
introduced(definition) ).
cnf(t772,plain,
sF5 = double_divide(sF4,identity),
inference(step,[status(thm)],[t7,t11]) ).
cnf(t16,plain,
double_divide(sF4,identity) = sF5,
inference(orient,[status(thm)],[t772]) ).
cnf(t8,axiom,
sF6 = double_divide(c3,double_divide(double_divide(b3,a3),identity)),
introduced(definition) ).
cnf(t775,plain,
sF6 = double_divide(c3,double_divide(sF4,identity)),
inference(step,[status(thm)],[t8,t11]) ).
cnf(t776,plain,
sF6 = double_divide(c3,sF5),
inference(step,[status(thm)],[t775,t16]) ).
cnf(t20,plain,
double_divide(c3,sF5) = sF6,
inference(orient,[status(thm)],[t776]) ).
cnf(t1,axiom,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),double_divide(identity,identity)),double_divide(X1,X3))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),double_divide(identity,identity)),double_divide(X1,X3))) = X2,
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(t12,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t30,plain,
X1 = double_divide(double_divide(identity,X2),double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(X2,double_divide(X1,identity)))),
inference(cp,[status(thm)],[t23,t12]) ).
cnf(t792,plain,
X1 = double_divide(double_divide(identity,X2),double_divide(identity,double_divide(X2,double_divide(X1,identity)))),
inference(step,[status(thm)],[t30,t12]) ).
cnf(t354,plain,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,double_divide(X2,identity)))) = X2,
inference(orient,[status(thm)],[t792]) ).
cnf(t356,plain,
X1 = double_divide(double_divide(identity,X1),double_divide(identity,identity)),
inference(cp,[status(thm)],[t354,t12]) ).
cnf(t382,plain,
double_divide(double_divide(identity,X1),double_divide(identity,identity)) = X1,
inference(orient,[status(thm)],[t356]) ).
cnf(t388,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(identity,identity)),
inference(cp,[status(thm)],[t382,t12]) ).
cnf(t798,plain,
double_divide(identity,identity) = identity,
inference(step,[status(thm)],[t388,t12]) ).
cnf(t412,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t798]) ).
cnf(t799,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),identity),double_divide(X1,X3))) = X2,
inference(step,[status(thm)],[t23,t412]) ).
cnf(t413,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),identity),double_divide(X1,X3))) = X2,
inference(rw,[status(thm)],[t799]) ).
cnf(t581,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),identity),double_divide(X1,X3))) = X2,
inference(orient,[status(thm)],[t413]) ).
cnf(t813,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(step,[status(thm)],[t382,t412]) ).
cnf(t430,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(rw,[status(thm)],[t813]) ).
cnf(t434,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(orient,[status(thm)],[t430]) ).
cnf(t614,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,X2)),double_divide(double_divide(double_divide(X1,identity),identity),X2)),
inference(cp,[status(thm)],[t581,t434]) ).
cnf(t355,plain,
X1 = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,identity),double_divide(X1,identity)))),
inference(cp,[status(thm)],[t354,t12]) ).
cnf(t827,plain,
X1 = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X1,identity)))),
inference(step,[status(thm)],[t355,t412]) ).
cnf(t435,plain,
identity = double_divide(double_divide(identity,X1),X1),
inference(cp,[status(thm)],[t12,t434]) ).
cnf(t437,plain,
double_divide(double_divide(identity,X1),X1) = identity,
inference(orient,[status(thm)],[t435]) ).
cnf(t446,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t354,t437]) ).
cnf(t823,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity),
inference(step,[status(thm)],[t446,t412]) ).
cnf(t824,plain,
X1 = double_divide(identity,double_divide(X1,identity)),
inference(step,[status(thm)],[t823,t434]) ).
cnf(t491,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(orient,[status(thm)],[t824]) ).
cnf(t828,plain,
X1 = double_divide(identity,double_divide(identity,X1)),
inference(step,[status(thm)],[t827,t491]) ).
cnf(t556,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(orient,[status(thm)],[t828]) ).
cnf(t839,plain,
X1 = double_divide(X2,double_divide(double_divide(double_divide(X1,identity),identity),X2)),
inference(step,[status(thm)],[t614,t556]) ).
cnf(t29,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(identity,identity))),identity),
inference(cp,[status(thm)],[t23,t12]) ).
cnf(t226,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(identity,identity))),identity) = X1,
inference(orient,[status(thm)],[t29]) ).
cnf(t231,plain,
double_divide(identity,double_divide(double_divide(X1,identity),double_divide(identity,identity))) = double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),identity),
inference(cp,[status(thm)],[t226,t226]) ).
cnf(t255,plain,
double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),identity) = double_divide(identity,double_divide(double_divide(X1,identity),double_divide(identity,identity))),
inference(orient,[status(thm)],[t231]) ).
cnf(t787,plain,
double_divide(identity,double_divide(double_divide(double_divide(X1,identity),identity),double_divide(identity,identity))) = X1,
inference(step,[status(thm)],[t226,t255]) ).
cnf(t256,plain,
double_divide(identity,double_divide(double_divide(double_divide(X1,identity),identity),double_divide(identity,identity))) = X1,
inference(rw,[status(thm)],[t787]) ).
cnf(t825,plain,
double_divide(identity,double_divide(double_divide(double_divide(X1,identity),identity),identity)) = X1,
inference(step,[status(thm)],[t256,t412]) ).
cnf(t826,plain,
double_divide(double_divide(X1,identity),identity) = X1,
inference(step,[status(thm)],[t825,t491]) ).
cnf(t502,plain,
double_divide(double_divide(X1,identity),identity) = X1,
inference(orient,[status(thm)],[t826]) ).
cnf(t840,plain,
X1 = double_divide(X2,double_divide(X1,X2)),
inference(step,[status(thm)],[t839,t502]) ).
cnf(t676,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t840]) ).
cnf(t24,plain,
c3 = double_divide(double_divide(identity,X1),double_divide(double_divide(sF0,double_divide(identity,identity)),double_divide(X1,b3))),
inference(cp,[status(thm)],[t23,t10]) ).
cnf(t89,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(sF0,double_divide(identity,identity)),double_divide(X1,b3))) = c3,
inference(orient,[status(thm)],[t24]) ).
cnf(t414,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(sF0,identity),double_divide(X1,b3))) = c3,
inference(rw,[status(thm)],[t89]) ).
cnf(t847,plain,
double_divide(double_divide(identity,X1),double_divide(sF1,double_divide(X1,b3))) = c3,
inference(step,[status(thm)],[t414,t13]) ).
cnf(t707,plain,
double_divide(double_divide(identity,X1),double_divide(sF1,double_divide(X1,b3))) = c3,
inference(orient,[status(thm)],[t847]) ).
cnf(t688,plain,
b3 = double_divide(a3,sF4),
inference(cp,[status(thm)],[t676,t11]) ).
cnf(t726,plain,
double_divide(a3,sF4) = b3,
inference(orient,[status(thm)],[t688]) ).
cnf(t729,plain,
a3 = double_divide(sF4,b3),
inference(cp,[status(thm)],[t676,t726]) ).
cnf(t740,plain,
double_divide(sF4,b3) = a3,
inference(orient,[status(thm)],[t729]) ).
cnf(t743,plain,
c3 = double_divide(double_divide(identity,sF4),double_divide(sF1,a3)),
inference(cp,[status(thm)],[t707,t740]) ).
cnf(t504,plain,
sF4 = double_divide(sF5,identity),
inference(cp,[status(thm)],[t502,t16]) ).
cnf(t514,plain,
double_divide(sF5,identity) = sF4,
inference(orient,[status(thm)],[t504]) ).
cnf(t517,plain,
sF5 = double_divide(identity,sF4),
inference(cp,[status(thm)],[t491,t514]) ).
cnf(t537,plain,
double_divide(identity,sF4) = sF5,
inference(orient,[status(thm)],[t517]) ).
cnf(t848,plain,
c3 = double_divide(sF5,double_divide(sF1,a3)),
inference(step,[status(thm)],[t743,t537]) ).
cnf(t849,plain,
c3 = double_divide(sF5,sF2),
inference(step,[status(thm)],[t848,t19]) ).
cnf(t748,plain,
double_divide(sF5,sF2) = c3,
inference(orient,[status(thm)],[t849]) ).
cnf(t751,plain,
sF5 = double_divide(sF2,c3),
inference(cp,[status(thm)],[t676,t748]) ).
cnf(t752,plain,
double_divide(sF2,c3) = sF5,
inference(orient,[status(thm)],[t751]) ).
cnf(t755,plain,
sF2 = double_divide(c3,sF5),
inference(cp,[status(thm)],[t676,t752]) ).
cnf(t850,plain,
sF2 = sF6,
inference(step,[status(thm)],[t755,t20]) ).
cnf(t756,plain,
sF6 = sF2,
inference(orient,[status(thm)],[t850]) ).
cnf(t851,plain,
double_divide(c3,sF5) = sF2,
inference(step,[status(thm)],[t20,t756]) ).
cnf(t757,plain,
double_divide(c3,sF5) = sF2,
inference(orient,[status(thm)],[t851]) ).
cnf(u0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
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(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
double_divide(double_divide(double_divide(sF0,identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(rw,[status(thm)],[goal_0,t10]) ).
cnf(g0_1,plain,
double_divide(double_divide(sF1,a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(rw,[status(thm)],[g0_0,t13]) ).
cnf(g0_2,plain,
double_divide(sF2,identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(rw,[status(thm)],[g0_1,t19]) ).
cnf(g0_3,plain,
double_divide(sF2,identity) != double_divide(double_divide(c3,double_divide(sF4,identity)),identity),
inference(rw,[status(thm)],[g0_2,t11]) ).
cnf(g0_4,plain,
double_divide(sF2,identity) != double_divide(double_divide(c3,sF5),identity),
inference(rw,[status(thm)],[g0_3,t16]) ).
cnf(g0_5,plain,
double_divide(sF2,identity) != double_divide(sF2,identity),
inference(rw,[status(thm)],[g0_4,t757]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP495-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:54:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.06/1.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.06/1.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------