%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP613-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 01:27:40 PM UTC 2026
% Result : Unsatisfiable 7.57s 1.52s
% Output : CNFRefutation 7.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 3
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 5 RR)
% Number of literals : 60 ( 59 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 136 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t1,axiom,
double_divide(inverse(double_divide(inverse(double_divide(X1,inverse(X2))),X3)),double_divide(X1,X3)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t2,plain,
double_divide(inverse(double_divide(inverse(double_divide(X1,inverse(X2))),X3)),double_divide(X1,X3)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t722,plain,
double_divide(multiply(X3,inverse(double_divide(X1,inverse(X2)))),double_divide(X1,X3)) = X2,
inference(step,[status(thm)],[t2,t5]) ).
cnf(t723,plain,
double_divide(multiply(X3,multiply(inverse(X2),X1)),double_divide(X1,X3)) = X2,
inference(step,[status(thm)],[t722,t5]) ).
cnf(t6,plain,
double_divide(multiply(X3,multiply(inverse(X2),X1)),double_divide(X1,X3)) = X2,
inference(rw,[status(thm)],[t723]) ).
cnf(t7,plain,
double_divide(multiply(X1,multiply(inverse(X2),X3)),double_divide(X3,X1)) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t9,plain,
multiply(double_divide(X1,X2),multiply(X2,multiply(inverse(X3),X1))) = inverse(X3),
inference(cp,[status(thm)],[t5,t7]) ).
cnf(t11,plain,
multiply(double_divide(X1,X2),multiply(X2,multiply(inverse(X3),X1))) = inverse(X3),
inference(orient,[status(thm)],[t9]) ).
cnf(t15,plain,
inverse(X1) = multiply(double_divide(multiply(inverse(X2),X3),double_divide(X3,inverse(X1))),inverse(X2)),
inference(cp,[status(thm)],[t11,t11]) ).
cnf(t40,plain,
multiply(double_divide(multiply(inverse(X1),X2),double_divide(X2,inverse(X3))),inverse(X1)) = inverse(X3),
inference(orient,[status(thm)],[t15]) ).
cnf(t12,plain,
inverse(X1) = multiply(X2,multiply(double_divide(X3,Y3),multiply(inverse(X1),multiply(Y3,multiply(inverse(X2),X3))))),
inference(cp,[status(thm)],[t11,t7]) ).
cnf(t91,plain,
multiply(X1,multiply(double_divide(X2,X3),multiply(inverse(Y3),multiply(X3,multiply(inverse(X1),X2))))) = inverse(Y3),
inference(orient,[status(thm)],[t12]) ).
cnf(t115,plain,
inverse(X1) = multiply(X2,multiply(double_divide(multiply(X3,multiply(inverse(inverse(X1)),Y3)),double_divide(Y3,X3)),inverse(X2))),
inference(cp,[status(thm)],[t91,t91]) ).
cnf(t726,plain,
inverse(X1) = multiply(X2,multiply(inverse(X1),inverse(X2))),
inference(step,[status(thm)],[t115,t7]) ).
cnf(t133,plain,
multiply(X1,multiply(inverse(X2),inverse(X1))) = inverse(X2),
inference(orient,[status(thm)],[t726]) ).
cnf(t136,plain,
X1 = double_divide(inverse(X1),double_divide(inverse(X2),X2)),
inference(cp,[status(thm)],[t7,t133]) ).
cnf(t152,plain,
double_divide(inverse(X1),double_divide(inverse(X2),X2)) = X1,
inference(orient,[status(thm)],[t136]) ).
cnf(t153,plain,
double_divide(X1,X2) = double_divide(multiply(X2,X1),double_divide(inverse(X3),X3)),
inference(cp,[status(thm)],[t152,t5]) ).
cnf(t196,plain,
double_divide(multiply(X1,X2),double_divide(inverse(X3),X3)) = double_divide(X2,X1),
inference(orient,[status(thm)],[t153]) ).
cnf(t10,plain,
X1 = double_divide(multiply(double_divide(X2,X3),multiply(inverse(X1),multiply(X3,multiply(inverse(Y3),X2)))),Y3),
inference(cp,[status(thm)],[t7,t7]) ).
cnf(t68,plain,
double_divide(multiply(double_divide(X1,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(Y3),X1)))),Y3) = X3,
inference(orient,[status(thm)],[t10]) ).
cnf(t113,plain,
X1 = double_divide(multiply(double_divide(multiply(X2,multiply(inverse(inverse(X1)),X3)),double_divide(X3,X2)),inverse(Y3)),Y3),
inference(cp,[status(thm)],[t68,t91]) ).
cnf(t725,plain,
X1 = double_divide(multiply(inverse(X1),inverse(Y3)),Y3),
inference(step,[status(thm)],[t113,t7]) ).
cnf(t117,plain,
double_divide(multiply(inverse(X1),inverse(X2)),X2) = X1,
inference(orient,[status(thm)],[t725]) ).
cnf(t198,plain,
double_divide(inverse(double_divide(inverse(X1),X1)),inverse(X2)) = X2,
inference(cp,[status(thm)],[t196,t117]) ).
cnf(t728,plain,
double_divide(multiply(X1,inverse(X1)),inverse(X2)) = X2,
inference(step,[status(thm)],[t198,t5]) ).
cnf(t214,plain,
double_divide(multiply(X1,inverse(X1)),inverse(X2)) = X2,
inference(orient,[status(thm)],[t728]) ).
cnf(t217,plain,
multiply(inverse(X1),multiply(X2,inverse(X2))) = inverse(X1),
inference(cp,[status(thm)],[t5,t214]) ).
cnf(t228,plain,
multiply(inverse(X1),multiply(X2,inverse(X2))) = inverse(X1),
inference(orient,[status(thm)],[t217]) ).
cnf(t235,plain,
inverse(X1) = multiply(double_divide(inverse(X2),double_divide(multiply(X3,inverse(X3)),inverse(X1))),inverse(X2)),
inference(cp,[status(thm)],[t40,t228]) ).
cnf(t730,plain,
inverse(X1) = multiply(double_divide(inverse(X2),X1),inverse(X2)),
inference(step,[status(thm)],[t235,t214]) ).
cnf(t258,plain,
multiply(double_divide(inverse(X1),X2),inverse(X1)) = inverse(X2),
inference(orient,[status(thm)],[t730]) ).
cnf(t14,plain,
X1 = double_divide(inverse(X2),double_divide(multiply(inverse(X2),X3),double_divide(X3,inverse(X1)))),
inference(cp,[status(thm)],[t7,t11]) ).
cnf(t31,plain,
double_divide(inverse(X1),double_divide(multiply(inverse(X1),X2),double_divide(X2,inverse(X3)))) = X3,
inference(orient,[status(thm)],[t14]) ).
cnf(t208,plain,
X1 = double_divide(inverse(X2),double_divide(inverse(inverse(X1)),inverse(X2))),
inference(cp,[status(thm)],[t31,t196]) ).
cnf(t341,plain,
double_divide(inverse(X1),double_divide(inverse(inverse(X2)),inverse(X1))) = X2,
inference(orient,[status(thm)],[t208]) ).
cnf(t236,plain,
X1 = double_divide(inverse(X2),double_divide(inverse(X2),double_divide(multiply(X3,inverse(X3)),inverse(X1)))),
inference(cp,[status(thm)],[t31,t228]) ).
cnf(t729,plain,
X1 = double_divide(inverse(X2),double_divide(inverse(X2),X1)),
inference(step,[status(thm)],[t236,t214]) ).
cnf(t245,plain,
double_divide(inverse(X1),double_divide(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t729]) ).
cnf(t342,plain,
X1 = inverse(inverse(X1)),
inference(cp,[status(thm)],[t341,t245]) ).
cnf(t355,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t342]) ).
cnf(t362,plain,
inverse(X1) = multiply(double_divide(X2,X1),inverse(inverse(X2))),
inference(cp,[status(thm)],[t258,t355]) ).
cnf(t737,plain,
inverse(X1) = multiply(double_divide(X2,X1),X2),
inference(step,[status(thm)],[t362,t355]) ).
cnf(t464,plain,
multiply(double_divide(X1,X2),X1) = inverse(X2),
inference(orient,[status(thm)],[t737]) ).
cnf(t366,plain,
inverse(inverse(X1)) = multiply(X1,multiply(X2,inverse(X2))),
inference(cp,[status(thm)],[t228,t355]) ).
cnf(t738,plain,
X1 = multiply(X1,multiply(X2,inverse(X2))),
inference(step,[status(thm)],[t366,t355]) ).
cnf(t483,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(orient,[status(thm)],[t738]) ).
cnf(t496,plain,
X1 = double_divide(X2,double_divide(inverse(inverse(X1)),X2)),
inference(cp,[status(thm)],[t7,t483]) ).
cnf(t739,plain,
X1 = double_divide(X2,double_divide(X1,X2)),
inference(step,[status(thm)],[t496,t355]) ).
cnf(t516,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t739]) ).
cnf(t533,plain,
inverse(double_divide(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t464,t516]) ).
cnf(t741,plain,
multiply(X2,X1) = multiply(X1,X2),
inference(step,[status(thm)],[t533,t5]) ).
cnf(t681,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t741]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(rw,[status(thm)],[goal_0,t681]) ).
cnf(g0_1,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[g0_0,t681]) ).
cnf(g0_2,plain,
multiply(b1,inverse(b1)) != multiply(b1,inverse(b1)),
inference(rw,[status(thm)],[g0_1]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP613-1 : 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 : n015.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 15:15:55 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.57/1.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.57/1.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------