%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP456-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 01:26:54 PM UTC 2026
% Result : Unsatisfiable 2.57s 0.79s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 5
% Syntax : Number of clauses : 88 ( 88 unt; 0 nHn; 5 RR)
% Number of literals : 88 ( 87 equ; 2 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 165 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
divide(divide(identity,divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t4,plain,
divide(divide(identity,divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t0,axiom,
divide(X1,X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t6,plain,
divide(X1,X1) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t346,plain,
divide(divide(identity,divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
inference(step,[status(thm)],[t4,t6]) ).
cnf(t7,plain,
divide(divide(identity,divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
inference(rw,[status(thm)],[t346]) ).
cnf(t1,axiom,
divide(identity,X1) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t12,plain,
divide(identity,X1) = inverse(X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t349,plain,
divide(inverse(divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
inference(step,[status(thm)],[t7,t12]) ).
cnf(t350,plain,
divide(inverse(divide(X1,divide(X2,divide(inverse(X1),X3)))),X3) = X2,
inference(step,[status(thm)],[t349,t12]) ).
cnf(t44,plain,
divide(inverse(divide(X1,divide(X2,divide(inverse(X1),X3)))),X3) = X2,
inference(orient,[status(thm)],[t350]) ).
cnf(t48,plain,
X1 = divide(inverse(inverse(divide(X1,divide(inverse(identity),X2)))),X2),
inference(cp,[status(thm)],[t44,t12]) ).
cnf(t2,axiom,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t8,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t2]) ).
cnf(t347,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t8,t12]) ).
cnf(t14,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[t347]) ).
cnf(t16,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t18,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t16,t12]) ).
cnf(t20,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t18]) ).
cnf(t351,plain,
X1 = divide(multiply(identity,divide(X1,divide(inverse(identity),X2))),X2),
inference(step,[status(thm)],[t48,t20]) ).
cnf(t13,plain,
inverse(identity) = identity,
inference(cp,[status(thm)],[t12,t6]) ).
cnf(t15,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t13]) ).
cnf(t352,plain,
X1 = divide(multiply(identity,divide(X1,divide(identity,X2))),X2),
inference(step,[status(thm)],[t351,t15]) ).
cnf(t353,plain,
X1 = divide(multiply(identity,divide(X1,inverse(X2))),X2),
inference(step,[status(thm)],[t352,t12]) ).
cnf(t354,plain,
X1 = divide(multiply(identity,multiply(X1,X2)),X2),
inference(step,[status(thm)],[t353,t16]) ).
cnf(t60,plain,
divide(multiply(identity,multiply(X1,X2)),X2) = X1,
inference(orient,[status(thm)],[t354]) ).
cnf(t49,plain,
divide(inverse(X1),X2) = divide(inverse(divide(X1,identity)),X2),
inference(cp,[status(thm)],[t44,t6]) ).
cnf(t19,plain,
multiply(X1,identity) = divide(X1,identity),
inference(cp,[status(thm)],[t16,t15]) ).
cnf(t25,plain,
divide(X1,identity) = multiply(X1,identity),
inference(orient,[status(thm)],[t19]) ).
cnf(t356,plain,
divide(inverse(X1),X2) = divide(inverse(multiply(X1,identity)),X2),
inference(step,[status(thm)],[t49,t25]) ).
cnf(t79,plain,
divide(inverse(multiply(X1,identity)),X2) = divide(inverse(X1),X2),
inference(orient,[status(thm)],[t356]) ).
cnf(t86,plain,
inverse(multiply(X1,identity)) = divide(inverse(divide(X2,divide(inverse(X1),divide(inverse(X2),X3)))),X3),
inference(cp,[status(thm)],[t44,t79]) ).
cnf(t357,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(step,[status(thm)],[t86,t44]) ).
cnf(t88,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t357]) ).
cnf(t89,plain,
multiply(X1,multiply(X2,identity)) = divide(X1,inverse(X2)),
inference(cp,[status(thm)],[t16,t88]) ).
cnf(t358,plain,
multiply(X1,multiply(X2,identity)) = multiply(X1,X2),
inference(step,[status(thm)],[t89,t16]) ).
cnf(t97,plain,
multiply(X1,multiply(X2,identity)) = multiply(X1,X2),
inference(orient,[status(thm)],[t358]) ).
cnf(t100,plain,
X1 = divide(multiply(identity,X1),identity),
inference(cp,[status(thm)],[t60,t97]) ).
cnf(t363,plain,
X1 = multiply(multiply(identity,X1),identity),
inference(step,[status(thm)],[t100,t25]) ).
cnf(t62,plain,
X1 = multiply(multiply(identity,multiply(X1,identity)),identity),
inference(cp,[status(thm)],[t60,t25]) ).
cnf(t65,plain,
multiply(multiply(identity,multiply(X1,identity)),identity) = X1,
inference(orient,[status(thm)],[t62]) ).
cnf(t66,plain,
multiply(identity,multiply(X1,identity)) = multiply(multiply(identity,X1),identity),
inference(cp,[status(thm)],[t65,t65]) ).
cnf(t68,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,multiply(X1,identity)),
inference(orient,[status(thm)],[t66]) ).
cnf(t359,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,X1),
inference(step,[status(thm)],[t68,t97]) ).
cnf(t98,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,X1),
inference(orient,[status(thm)],[t359]) ).
cnf(t364,plain,
X1 = multiply(identity,X1),
inference(step,[status(thm)],[t363,t98]) ).
cnf(t103,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t364]) ).
cnf(t371,plain,
divide(multiply(X1,X2),X2) = X1,
inference(step,[status(thm)],[t60,t103]) ).
cnf(t110,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[t371]) ).
cnf(t117,plain,
divide(multiply(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t110]) ).
cnf(t51,plain,
X1 = divide(inverse(divide(X2,divide(X1,identity))),inverse(X2)),
inference(cp,[status(thm)],[t44,t6]) ).
cnf(t379,plain,
X1 = multiply(inverse(divide(X2,divide(X1,identity))),X2),
inference(step,[status(thm)],[t51,t16]) ).
cnf(t106,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(cp,[status(thm)],[t103,t97]) ).
cnf(t375,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t106,t103]) ).
cnf(t112,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t375]) ).
cnf(t376,plain,
divide(X1,identity) = X1,
inference(step,[status(thm)],[t25,t112]) ).
cnf(t113,plain,
divide(X1,identity) = X1,
inference(orient,[status(thm)],[t376]) ).
cnf(t380,plain,
X1 = multiply(inverse(divide(X2,X1)),X2),
inference(step,[status(thm)],[t379,t113]) ).
cnf(t123,plain,
multiply(inverse(divide(X1,X2)),X1) = X2,
inference(orient,[status(thm)],[t380]) ).
cnf(t128,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(cp,[status(thm)],[t117,t123]) ).
cnf(t129,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(orient,[status(thm)],[t128]) ).
cnf(t381,plain,
divide(divide(divide(X2,divide(inverse(X1),X3)),X1),X3) = X2,
inference(step,[status(thm)],[t44,t129]) ).
cnf(t135,plain,
divide(divide(divide(X2,divide(inverse(X1),X3)),X1),X3) = X2,
inference(rw,[status(thm)],[t381]) ).
cnf(t132,plain,
multiply(X1,divide(X2,X3)) = divide(X1,divide(X3,X2)),
inference(cp,[status(thm)],[t16,t129]) ).
cnf(t164,plain,
divide(X1,divide(X2,X3)) = multiply(X1,divide(X3,X2)),
inference(orient,[status(thm)],[t132]) ).
cnf(t382,plain,
divide(divide(multiply(X2,divide(X3,inverse(X1))),X1),X3) = X2,
inference(step,[status(thm)],[t135,t164]) ).
cnf(t383,plain,
divide(divide(multiply(X2,multiply(X3,X1)),X1),X3) = X2,
inference(step,[status(thm)],[t382,t16]) ).
cnf(t243,plain,
divide(divide(multiply(X1,multiply(X2,X3)),X3),X2) = X1,
inference(orient,[status(thm)],[t383]) ).
cnf(t118,plain,
X1 = multiply(multiply(X1,inverse(X2)),X2),
inference(cp,[status(thm)],[t117,t16]) ).
cnf(t22,plain,
multiply(X1,inverse(X2)) = divide(X1,multiply(identity,X2)),
inference(cp,[status(thm)],[t16,t20]) ).
cnf(t34,plain,
divide(X1,multiply(identity,X2)) = multiply(X1,inverse(X2)),
inference(orient,[status(thm)],[t22]) ).
cnf(t369,plain,
divide(X1,X2) = multiply(X1,inverse(X2)),
inference(step,[status(thm)],[t34,t103]) ).
cnf(t108,plain,
divide(X1,X2) = multiply(X1,inverse(X2)),
inference(rw,[status(thm)],[t369]) ).
cnf(t116,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(orient,[status(thm)],[t108]) ).
cnf(t378,plain,
X1 = multiply(divide(X1,X2),X2),
inference(step,[status(thm)],[t118,t116]) ).
cnf(t121,plain,
multiply(divide(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t378]) ).
cnf(t252,plain,
divide(X1,multiply(X2,X3)) = divide(divide(X1,X3),X2),
inference(cp,[status(thm)],[t243,t121]) ).
cnf(t276,plain,
divide(divide(X1,X2),X3) = divide(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t252]) ).
cnf(t288,plain,
divide(X1,multiply(X2,inverse(X3))) = divide(multiply(X1,X3),X2),
inference(cp,[status(thm)],[t276,t16]) ).
cnf(t387,plain,
divide(X1,divide(X2,X3)) = divide(multiply(X1,X3),X2),
inference(step,[status(thm)],[t288,t116]) ).
cnf(t388,plain,
multiply(X1,divide(X3,X2)) = divide(multiply(X1,X3),X2),
inference(step,[status(thm)],[t387,t164]) ).
cnf(t313,plain,
divide(multiply(X1,X2),X3) = multiply(X1,divide(X2,X3)),
inference(orient,[status(thm)],[t388]) ).
cnf(t318,plain,
multiply(X1,divide(X2,inverse(X3))) = multiply(multiply(X1,X2),X3),
inference(cp,[status(thm)],[t313,t16]) ).
cnf(t389,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t318,t16]) ).
cnf(t334,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t389]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[goal_0,t334]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP456-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n020.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Wed Sep 23 14:49:02 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.57/0.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.57/0.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------