%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP484-1 : 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 01:27:09 PM UTC 2026
% Result : Unsatisfiable 3.16s 1.00s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 10 RR)
% Number of literals : 54 ( 53 equ; 2 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
double_divide(double_divide(X1,X2),identity) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t0,axiom,
double_divide(X1,identity) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
double_divide(X1,identity) = inverse(X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t186,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(step,[status(thm)],[t2,t8]) ).
cnf(t11,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t186]) ).
cnf(t1,axiom,
double_divide(X1,inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
double_divide(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t1]) ).
cnf(t13,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(cp,[status(thm)],[t11,t10]) ).
cnf(t19,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(orient,[status(thm)],[t13]) ).
cnf(t14,plain,
identity = double_divide(double_divide(X1,X2),multiply(X2,X1)),
inference(cp,[status(thm)],[t10,t11]) ).
cnf(t35,plain,
double_divide(double_divide(X1,X2),multiply(X2,X1)) = identity,
inference(orient,[status(thm)],[t14]) ).
cnf(t3,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
inference(orient,[status(thm)],[t3]) ).
cnf(t184,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),double_divide(identity,identity)) = X3,
inference(step,[status(thm)],[t4,t8]) ).
cnf(t185,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),inverse(identity)) = X3,
inference(step,[status(thm)],[t184,t8]) ).
cnf(t9,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),inverse(identity)) = X3,
inference(rw,[status(thm)],[t185]) ).
cnf(t70,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),inverse(identity)) = X3,
inference(orient,[status(thm)],[t9]) ).
cnf(t71,plain,
multiply(X1,X2) = double_divide(double_divide(X2,double_divide(identity,inverse(X1))),inverse(identity)),
inference(cp,[status(thm)],[t70,t35]) ).
cnf(t91,plain,
double_divide(double_divide(X1,double_divide(identity,inverse(X2))),inverse(identity)) = multiply(X2,X1),
inference(orient,[status(thm)],[t71]) ).
cnf(t100,plain,
double_divide(identity,inverse(X1)) = double_divide(double_divide(X2,multiply(X1,double_divide(X2,identity))),inverse(identity)),
inference(cp,[status(thm)],[t70,t91]) ).
cnf(t191,plain,
double_divide(identity,inverse(X1)) = double_divide(double_divide(X2,multiply(X1,inverse(X2))),inverse(identity)),
inference(step,[status(thm)],[t100,t8]) ).
cnf(t127,plain,
double_divide(double_divide(X1,multiply(X2,inverse(X1))),inverse(identity)) = double_divide(identity,inverse(X2)),
inference(orient,[status(thm)],[t191]) ).
cnf(t138,plain,
multiply(X1,inverse(double_divide(X2,identity))) = double_divide(double_divide(X2,double_divide(identity,inverse(X1))),inverse(identity)),
inference(cp,[status(thm)],[t70,t127]) ).
cnf(t195,plain,
multiply(X1,multiply(identity,X2)) = double_divide(double_divide(X2,double_divide(identity,inverse(X1))),inverse(identity)),
inference(step,[status(thm)],[t138,t11]) ).
cnf(t196,plain,
multiply(X1,multiply(identity,X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t195,t91]) ).
cnf(t148,plain,
multiply(X1,multiply(identity,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t196]) ).
cnf(t92,plain,
multiply(identity,X1) = double_divide(double_divide(X1,identity),inverse(identity)),
inference(cp,[status(thm)],[t91,t10]) ).
cnf(t187,plain,
multiply(identity,X1) = double_divide(inverse(X1),inverse(identity)),
inference(step,[status(thm)],[t92,t8]) ).
cnf(t103,plain,
double_divide(inverse(X1),inverse(identity)) = multiply(identity,X1),
inference(orient,[status(thm)],[t187]) ).
cnf(t110,plain,
multiply(inverse(identity),inverse(X1)) = inverse(multiply(identity,X1)),
inference(cp,[status(thm)],[t11,t103]) ).
cnf(t12,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t11,t8]) ).
cnf(t15,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t18,plain,
multiply(identity,inverse(X1)) = inverse(multiply(identity,X1)),
inference(cp,[status(thm)],[t15,t15]) ).
cnf(t22,plain,
inverse(multiply(identity,X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t18]) ).
cnf(t188,plain,
multiply(inverse(identity),inverse(X1)) = multiply(identity,inverse(X1)),
inference(step,[status(thm)],[t110,t22]) ).
cnf(t112,plain,
multiply(inverse(identity),inverse(X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t188]) ).
cnf(t114,plain,
multiply(identity,inverse(double_divide(X1,X2))) = multiply(inverse(identity),multiply(X2,X1)),
inference(cp,[status(thm)],[t112,t11]) ).
cnf(t190,plain,
multiply(identity,multiply(X2,X1)) = multiply(inverse(identity),multiply(X2,X1)),
inference(step,[status(thm)],[t114,t11]) ).
cnf(t122,plain,
multiply(inverse(identity),multiply(X1,X2)) = multiply(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t190]) ).
cnf(t150,plain,
multiply(inverse(identity),X1) = multiply(identity,multiply(identity,X1)),
inference(cp,[status(thm)],[t148,t122]) ).
cnf(t202,plain,
multiply(inverse(identity),X1) = multiply(identity,X1),
inference(step,[status(thm)],[t150,t148]) ).
cnf(t158,plain,
multiply(inverse(identity),X1) = multiply(identity,X1),
inference(orient,[status(thm)],[t202]) ).
cnf(t159,plain,
multiply(identity,identity) = inverse(identity),
inference(cp,[status(thm)],[t158,t19]) ).
cnf(t163,plain,
multiply(identity,identity) = inverse(identity),
inference(orient,[status(thm)],[t159]) ).
cnf(t167,plain,
identity = double_divide(double_divide(identity,identity),inverse(identity)),
inference(cp,[status(thm)],[t35,t163]) ).
cnf(t205,plain,
identity = double_divide(inverse(identity),inverse(identity)),
inference(step,[status(thm)],[t167,t8]) ).
cnf(t206,plain,
identity = multiply(identity,identity),
inference(step,[status(thm)],[t205,t103]) ).
cnf(t207,plain,
identity = inverse(identity),
inference(step,[status(thm)],[t206,t163]) ).
cnf(t172,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t207]) ).
cnf(t208,plain,
multiply(inverse(X1),X1) = identity,
inference(step,[status(thm)],[t19,t172]) ).
cnf(t173,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t208]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
identity != identity,
inference(rw,[status(thm)],[goal_0,t173]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP484-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 14:55:34 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.16/1.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.16/1.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------