%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP581-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 01:27:35 PM UTC 2026
% Result : Unsatisfiable 1.68s 0.91s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 32 RR)
% Number of literals : 49 ( 48 equ; 8 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
sFlat1 = double_divide(a1,double_divide(a1,identity)),
introduced(definition) ).
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(t8,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t48,plain,
sFlat1 = identity,
inference(step,[status(thm)],[t3,t8]) ).
cnf(t15,plain,
identity = sFlat1,
inference(orient,[status(thm)],[t48]) ).
cnf(t2,axiom,
sFlat0 = double_divide(a1,identity),
introduced(definition) ).
cnf(t53,plain,
sFlat0 = double_divide(a1,sFlat1),
inference(step,[status(thm)],[t2,t15]) ).
cnf(t18,plain,
double_divide(a1,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t53]) ).
cnf(t51,plain,
double_divide(X1,double_divide(X1,sFlat1)) = identity,
inference(step,[status(thm)],[t8,t15]) ).
cnf(t52,plain,
double_divide(X1,double_divide(X1,sFlat1)) = sFlat1,
inference(step,[status(thm)],[t51,t15]) ).
cnf(t17,plain,
double_divide(X1,double_divide(X1,sFlat1)) = sFlat1,
inference(rw,[status(thm)],[t52]) ).
cnf(t20,plain,
double_divide(X1,double_divide(X1,sFlat1)) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t21,plain,
sFlat1 = double_divide(a1,sFlat0),
inference(cp,[status(thm)],[t20,t18]) ).
cnf(t23,plain,
double_divide(a1,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t21]) ).
cnf(t4,axiom,
sFlat2 = double_divide(double_divide(a1,double_divide(a1,identity)),identity),
introduced(definition) ).
cnf(t46,plain,
sFlat2 = double_divide(identity,identity),
inference(step,[status(thm)],[t4,t8]) ).
cnf(t12,plain,
double_divide(identity,identity) = sFlat2,
inference(orient,[status(thm)],[t46]) ).
cnf(t49,plain,
double_divide(sFlat1,identity) = sFlat2,
inference(step,[status(thm)],[t12,t15]) ).
cnf(t50,plain,
double_divide(sFlat1,sFlat1) = sFlat2,
inference(step,[status(thm)],[t49,t15]) ).
cnf(t16,plain,
double_divide(sFlat1,sFlat1) = sFlat2,
inference(rw,[status(thm)],[t50]) ).
cnf(t19,plain,
double_divide(sFlat1,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t16]) ).
cnf(t1,axiom,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),double_divide(identity,identity)) = X3,
inference(orient,[status(thm)],[t1]) ).
cnf(t47,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),sFlat2) = X3,
inference(step,[status(thm)],[t5,t12]) ).
cnf(t14,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),sFlat2) = X3,
inference(rw,[status(thm)],[t47]) ).
cnf(t54,plain,
double_divide(double_divide(X1,double_divide(double_divide(sFlat1,X2),double_divide(X3,double_divide(X2,X1)))),sFlat2) = X3,
inference(step,[status(thm)],[t14,t15]) ).
cnf(t25,plain,
double_divide(double_divide(X1,double_divide(double_divide(sFlat1,X2),double_divide(X3,double_divide(X2,X1)))),sFlat2) = X3,
inference(orient,[status(thm)],[t54]) ).
cnf(t29,plain,
X1 = double_divide(double_divide(sFlat1,double_divide(double_divide(sFlat1,X1),sFlat1)),sFlat2),
inference(cp,[status(thm)],[t25,t20]) ).
cnf(t36,plain,
double_divide(double_divide(sFlat1,double_divide(double_divide(sFlat1,X1),sFlat1)),sFlat2) = X1,
inference(orient,[status(thm)],[t29]) ).
cnf(t22,plain,
sFlat1 = double_divide(sFlat1,sFlat2),
inference(cp,[status(thm)],[t20,t19]) ).
cnf(t24,plain,
double_divide(sFlat1,sFlat2) = sFlat1,
inference(orient,[status(thm)],[t22]) ).
cnf(t38,plain,
sFlat2 = double_divide(double_divide(sFlat1,double_divide(sFlat1,sFlat1)),sFlat2),
inference(cp,[status(thm)],[t36,t24]) ).
cnf(t55,plain,
sFlat2 = double_divide(sFlat1,sFlat2),
inference(step,[status(thm)],[t38,t20]) ).
cnf(t56,plain,
sFlat2 = sFlat1,
inference(step,[status(thm)],[t55,t24]) ).
cnf(t41,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t56]) ).
cnf(t57,plain,
double_divide(sFlat1,sFlat1) = sFlat1,
inference(step,[status(thm)],[t19,t41]) ).
cnf(t42,plain,
double_divide(sFlat1,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t57]) ).
cnf(u0,negated_conjecture,
multiply(inverse(a1),a1) != identity,
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(a1,double_divide(a1,identity)),identity) != identity,
inference(definition_unfolding,[status(thm)],[u0,d0,d1]) ).
cnf(g0_0,plain,
double_divide(double_divide(a1,double_divide(a1,sFlat1)),identity) != identity,
inference(rw,[status(thm)],[goal_0,t15]) ).
cnf(g0_1,plain,
double_divide(double_divide(a1,sFlat0),identity) != identity,
inference(rw,[status(thm)],[g0_0,t18]) ).
cnf(g0_2,plain,
double_divide(sFlat1,identity) != identity,
inference(rw,[status(thm)],[g0_1,t23]) ).
cnf(g0_3,plain,
double_divide(sFlat1,sFlat1) != identity,
inference(rw,[status(thm)],[g0_2,t15]) ).
cnf(g0_4,plain,
sFlat1 != identity,
inference(rw,[status(thm)],[g0_3,t42]) ).
cnf(g0_5,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_4,t15]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP581-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 15:10:48 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.68/0.91 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.68/0.91 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------