%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP568-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 01:27:33 PM UTC 2026
% Result : Unsatisfiable 5.17s 1.08s
% Output : CNFRefutation 5.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 9
% Syntax : Number of clauses : 82 ( 82 unt; 0 nHn; 34 RR)
% Number of literals : 82 ( 81 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
sF0 = double_divide(b,a),
introduced(definition) ).
cnf(t6,plain,
double_divide(b,a) = sF0,
inference(orient,[status(thm)],[t2]) ).
cnf(t3,axiom,
sF1 = double_divide(double_divide(b,a),identity),
introduced(definition) ).
cnf(t315,plain,
sF1 = double_divide(sF0,identity),
inference(step,[status(thm)],[t3,t6]) ).
cnf(t9,plain,
double_divide(sF0,identity) = sF1,
inference(orient,[status(thm)],[t315]) ).
cnf(t4,axiom,
sF2 = double_divide(a,b),
introduced(definition) ).
cnf(t7,plain,
double_divide(a,b) = sF2,
inference(orient,[status(thm)],[t4]) ).
cnf(t5,axiom,
sF3 = double_divide(double_divide(a,b),identity),
introduced(definition) ).
cnf(t316,plain,
sF3 = double_divide(sF2,identity),
inference(step,[status(thm)],[t5,t7]) ).
cnf(t12,plain,
double_divide(sF2,identity) = sF3,
inference(orient,[status(thm)],[t316]) ).
cnf(t1,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t15,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),double_divide(identity,identity)) = 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(t8,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t18,plain,
X1 = double_divide(double_divide(X1,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t15,t8]) ).
cnf(t317,plain,
X1 = double_divide(double_divide(X1,identity),double_divide(identity,identity)),
inference(step,[status(thm)],[t18,t8]) ).
cnf(t27,plain,
double_divide(double_divide(X1,identity),double_divide(identity,identity)) = X1,
inference(orient,[status(thm)],[t317]) ).
cnf(t30,plain,
double_divide(X1,identity) = double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t15,t27]) ).
cnf(t41,plain,
double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(X1,identity),
inference(orient,[status(thm)],[t30]) ).
cnf(t42,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(cp,[status(thm)],[t41,t8]) ).
cnf(t318,plain,
double_divide(identity,identity) = identity,
inference(step,[status(thm)],[t42,t27]) ).
cnf(t52,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t318]) ).
cnf(t319,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),identity) = X2,
inference(step,[status(thm)],[t15,t52]) ).
cnf(t53,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),identity) = X2,
inference(rw,[status(thm)],[t319]) ).
cnf(t77,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),identity) = X2,
inference(orient,[status(thm)],[t53]) ).
cnf(t320,plain,
double_divide(double_divide(X1,identity),identity) = X1,
inference(step,[status(thm)],[t27,t52]) ).
cnf(t54,plain,
double_divide(double_divide(X1,identity),identity) = X1,
inference(rw,[status(thm)],[t320]) ).
cnf(t65,plain,
double_divide(double_divide(X1,identity),identity) = X1,
inference(orient,[status(thm)],[t54]) ).
cnf(t66,plain,
identity = double_divide(double_divide(X1,identity),X1),
inference(cp,[status(thm)],[t8,t65]) ).
cnf(t67,plain,
double_divide(double_divide(X1,identity),X1) = identity,
inference(orient,[status(thm)],[t66]) ).
cnf(t324,plain,
double_divide(double_divide(identity,double_divide(X1,identity)),double_divide(identity,identity)) = double_divide(X1,identity),
inference(step,[status(thm)],[t41,t52]) ).
cnf(t325,plain,
double_divide(double_divide(identity,double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(step,[status(thm)],[t324,t52]) ).
cnf(t58,plain,
double_divide(double_divide(identity,double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(rw,[status(thm)],[t325]) ).
cnf(t68,plain,
double_divide(double_divide(identity,double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(orient,[status(thm)],[t58]) ).
cnf(t73,plain,
double_divide(double_divide(X1,identity),identity) = double_divide(double_divide(identity,X1),identity),
inference(cp,[status(thm)],[t68,t65]) ).
cnf(t334,plain,
X1 = double_divide(double_divide(identity,X1),identity),
inference(step,[status(thm)],[t73,t65]) ).
cnf(t140,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(orient,[status(thm)],[t334]) ).
cnf(t145,plain,
identity = double_divide(X1,double_divide(identity,X1)),
inference(cp,[status(thm)],[t67,t140]) ).
cnf(t150,plain,
double_divide(X1,double_divide(identity,X1)) = identity,
inference(orient,[status(thm)],[t145]) ).
cnf(t151,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,X1))),identity),
inference(cp,[status(thm)],[t77,t150]) ).
cnf(t336,plain,
X1 = double_divide(identity,double_divide(identity,X1)),
inference(step,[status(thm)],[t151,t140]) ).
cnf(t153,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(orient,[status(thm)],[t336]) ).
cnf(t154,plain,
X1 = double_divide(double_divide(identity,double_divide(double_divide(X1,X2),double_divide(identity,double_divide(identity,X2)))),identity),
inference(cp,[status(thm)],[t77,t153]) ).
cnf(t337,plain,
X1 = double_divide(double_divide(X1,X2),double_divide(identity,double_divide(identity,X2))),
inference(step,[status(thm)],[t154,t140]) ).
cnf(t338,plain,
X1 = double_divide(double_divide(X1,X2),X2),
inference(step,[status(thm)],[t337,t153]) ).
cnf(t156,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t338]) ).
cnf(t162,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(cp,[status(thm)],[t156,t67]) ).
cnf(t184,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(orient,[status(thm)],[t162]) ).
cnf(t341,plain,
double_divide(identity,double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3)))) = X2,
inference(step,[status(thm)],[t77,t184]) ).
cnf(t185,plain,
double_divide(identity,double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3)))) = X2,
inference(rw,[status(thm)],[t341]) ).
cnf(t198,plain,
double_divide(identity,double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3)))) = X2,
inference(orient,[status(thm)],[t185]) ).
cnf(t199,plain,
X1 = double_divide(identity,double_divide(X2,double_divide(double_divide(X1,identity),double_divide(identity,double_divide(X2,identity))))),
inference(cp,[status(thm)],[t198,t8]) ).
cnf(t161,plain,
X1 = double_divide(identity,double_divide(X1,identity)),
inference(cp,[status(thm)],[t156,t8]) ).
cnf(t179,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(orient,[status(thm)],[t161]) ).
cnf(t344,plain,
X1 = double_divide(identity,double_divide(X2,double_divide(double_divide(X1,identity),X2))),
inference(step,[status(thm)],[t199,t179]) ).
cnf(t223,plain,
double_divide(identity,double_divide(X1,double_divide(double_divide(X2,identity),X1))) = X2,
inference(orient,[status(thm)],[t344]) ).
cnf(t28,plain,
sF0 = double_divide(sF1,double_divide(identity,identity)),
inference(cp,[status(thm)],[t27,t9]) ).
cnf(t32,plain,
double_divide(sF1,double_divide(identity,identity)) = sF0,
inference(orient,[status(thm)],[t28]) ).
cnf(t321,plain,
double_divide(sF1,identity) = sF0,
inference(step,[status(thm)],[t32,t52]) ).
cnf(t55,plain,
double_divide(sF1,identity) = sF0,
inference(rw,[status(thm)],[t321]) ).
cnf(t59,plain,
double_divide(sF1,identity) = sF0,
inference(orient,[status(thm)],[t55]) ).
cnf(t226,plain,
sF1 = double_divide(identity,double_divide(X1,double_divide(sF0,X1))),
inference(cp,[status(thm)],[t223,t59]) ).
cnf(t296,plain,
double_divide(identity,double_divide(X1,double_divide(sF0,X1))) = sF1,
inference(orient,[status(thm)],[t226]) ).
cnf(t159,plain,
b = double_divide(sF0,a),
inference(cp,[status(thm)],[t156,t6]) ).
cnf(t168,plain,
double_divide(sF0,a) = b,
inference(orient,[status(thm)],[t159]) ).
cnf(t298,plain,
sF1 = double_divide(identity,double_divide(a,b)),
inference(cp,[status(thm)],[t296,t168]) ).
cnf(t351,plain,
sF1 = double_divide(identity,sF2),
inference(step,[status(thm)],[t298,t7]) ).
cnf(t352,plain,
sF1 = double_divide(sF2,identity),
inference(step,[status(thm)],[t351,t184]) ).
cnf(t353,plain,
sF1 = sF3,
inference(step,[status(thm)],[t352,t12]) ).
cnf(t305,plain,
sF3 = sF1,
inference(orient,[status(thm)],[t353]) ).
cnf(t354,plain,
double_divide(sF2,identity) = sF1,
inference(step,[status(thm)],[t12,t305]) ).
cnf(t306,plain,
double_divide(sF2,identity) = sF1,
inference(orient,[status(thm)],[t354]) ).
cnf(u0,negated_conjecture,
multiply(a,b) != multiply(b,a),
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(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
double_divide(sF0,identity) != double_divide(double_divide(a,b),identity),
inference(rw,[status(thm)],[goal_0,t6]) ).
cnf(g0_1,plain,
sF1 != double_divide(double_divide(a,b),identity),
inference(rw,[status(thm)],[g0_0,t9]) ).
cnf(g0_2,plain,
sF1 != double_divide(sF2,identity),
inference(rw,[status(thm)],[g0_1,t7]) ).
cnf(g0_3,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_2,t306]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP568-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n007.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 15:03:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.17/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.17/1.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------