%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP551-1 : 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 01:27:30 PM UTC 2026
% Result : Unsatisfiable 5.49s 1.33s
% Output : CNFRefutation 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 5
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 6 RR)
% Number of literals : 81 ( 80 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 140 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t11,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t2]) ).
cnf(t1,axiom,
divide(identity,X1) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
divide(identity,X1) = inverse(X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t327,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t11,t19]) ).
cnf(t21,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[t327]) ).
cnf(t24,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t21]) ).
cnf(t3,axiom,
divide(divide(identity,X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
divide(divide(identity,X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(orient,[status(thm)],[t3]) ).
cnf(t328,plain,
divide(inverse(X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(step,[status(thm)],[t4,t19]) ).
cnf(t22,plain,
divide(inverse(X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(rw,[status(thm)],[t328]) ).
cnf(t46,plain,
divide(inverse(X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(orient,[status(thm)],[t22]) ).
cnf(t0,axiom,
divide(X1,X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
divide(X1,X1) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t57,plain,
X1 = divide(inverse(X2),divide(divide(identity,X1),X2)),
inference(cp,[status(thm)],[t46,t7]) ).
cnf(t355,plain,
X1 = divide(inverse(X2),divide(inverse(X1),X2)),
inference(step,[status(thm)],[t57,t19]) ).
cnf(t125,plain,
divide(inverse(X1),divide(inverse(X2),X1)) = X2,
inference(orient,[status(thm)],[t355]) ).
cnf(t26,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t24,t19]) ).
cnf(t28,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t26]) ).
cnf(t53,plain,
divide(X1,X2) = divide(inverse(X2),divide(identity,X1)),
inference(cp,[status(thm)],[t46,t7]) ).
cnf(t330,plain,
divide(X1,X2) = divide(inverse(X2),inverse(X1)),
inference(step,[status(thm)],[t53,t19]) ).
cnf(t331,plain,
divide(X1,X2) = multiply(inverse(X2),X1),
inference(step,[status(thm)],[t330,t24]) ).
cnf(t63,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(orient,[status(thm)],[t331]) ).
cnf(t66,plain,
divide(X1,inverse(X2)) = multiply(multiply(identity,X2),X1),
inference(cp,[status(thm)],[t63,t28]) ).
cnf(t341,plain,
multiply(X1,X2) = multiply(multiply(identity,X2),X1),
inference(step,[status(thm)],[t66,t24]) ).
cnf(t93,plain,
multiply(multiply(identity,X1),X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t341]) ).
cnf(t31,plain,
multiply(identity,inverse(X1)) = inverse(multiply(identity,X1)),
inference(cp,[status(thm)],[t28,t28]) ).
cnf(t36,plain,
inverse(multiply(identity,X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t31]) ).
cnf(t20,plain,
inverse(identity) = identity,
inference(cp,[status(thm)],[t19,t7]) ).
cnf(t23,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t20]) ).
cnf(t65,plain,
divide(X1,identity) = multiply(identity,X1),
inference(cp,[status(thm)],[t63,t23]) ).
cnf(t27,plain,
multiply(X1,identity) = divide(X1,identity),
inference(cp,[status(thm)],[t24,t23]) ).
cnf(t33,plain,
divide(X1,identity) = multiply(X1,identity),
inference(orient,[status(thm)],[t27]) ).
cnf(t332,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(step,[status(thm)],[t65,t33]) ).
cnf(t67,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(orient,[status(thm)],[t332]) ).
cnf(t71,plain,
multiply(identity,inverse(X1)) = inverse(multiply(X1,identity)),
inference(cp,[status(thm)],[t36,t67]) ).
cnf(t68,plain,
multiply(identity,inverse(X1)) = divide(identity,X1),
inference(cp,[status(thm)],[t67,t63]) ).
cnf(t333,plain,
multiply(identity,inverse(X1)) = inverse(X1),
inference(step,[status(thm)],[t68,t19]) ).
cnf(t73,plain,
multiply(identity,inverse(X1)) = inverse(X1),
inference(orient,[status(thm)],[t333]) ).
cnf(t340,plain,
inverse(X1) = inverse(multiply(X1,identity)),
inference(step,[status(thm)],[t71,t73]) ).
cnf(t87,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t340]) ).
cnf(t89,plain,
divide(X1,multiply(X2,identity)) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t63,t87]) ).
cnf(t346,plain,
divide(X1,multiply(X2,identity)) = divide(X1,X2),
inference(step,[status(thm)],[t89,t63]) ).
cnf(t111,plain,
divide(X1,multiply(X2,identity)) = divide(X1,X2),
inference(orient,[status(thm)],[t346]) ).
cnf(t114,plain,
multiply(X1,identity) = divide(inverse(X2),divide(divide(divide(X3,X2),X1),X3)),
inference(cp,[status(thm)],[t46,t111]) ).
cnf(t347,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t114,t46]) ).
cnf(t115,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t347]) ).
cnf(t118,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(cp,[status(thm)],[t93,t115]) ).
cnf(t351,plain,
X1 = multiply(identity,X1),
inference(step,[status(thm)],[t118,t115]) ).
cnf(t120,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t351]) ).
cnf(t352,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t28,t120]) ).
cnf(t121,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t352]) ).
cnf(t126,plain,
X1 = divide(X2,divide(inverse(X1),inverse(X2))),
inference(cp,[status(thm)],[t125,t121]) ).
cnf(t356,plain,
X1 = divide(X2,multiply(inverse(X1),X2)),
inference(step,[status(thm)],[t126,t24]) ).
cnf(t357,plain,
X1 = divide(X2,divide(X2,X1)),
inference(step,[status(thm)],[t356,t63]) ).
cnf(t132,plain,
divide(X1,divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t357]) ).
cnf(t137,plain,
divide(divide(X1,X2),X3) = divide(inverse(X2),divide(X3,X1)),
inference(cp,[status(thm)],[t46,t132]) ).
cnf(t159,plain,
divide(inverse(X1),divide(X2,X3)) = divide(divide(X3,X1),X2),
inference(orient,[status(thm)],[t137]) ).
cnf(t162,plain,
divide(divide(X1,identity),X2) = divide(identity,divide(X2,X1)),
inference(cp,[status(thm)],[t159,t23]) ).
cnf(t348,plain,
divide(X1,identity) = X1,
inference(step,[status(thm)],[t33,t115]) ).
cnf(t116,plain,
divide(X1,identity) = X1,
inference(orient,[status(thm)],[t348]) ).
cnf(t358,plain,
divide(X1,X2) = divide(identity,divide(X2,X1)),
inference(step,[status(thm)],[t162,t116]) ).
cnf(t359,plain,
divide(X1,X2) = inverse(divide(X2,X1)),
inference(step,[status(thm)],[t358,t19]) ).
cnf(t172,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(orient,[status(thm)],[t359]) ).
cnf(t179,plain,
multiply(X1,divide(X2,X3)) = divide(X1,divide(X3,X2)),
inference(cp,[status(thm)],[t24,t172]) ).
cnf(t177,plain,
divide(divide(X1,X2),inverse(X3)) = inverse(divide(divide(X2,X3),X1)),
inference(cp,[status(thm)],[t172,t159]) ).
cnf(t366,plain,
multiply(divide(X1,X2),X3) = inverse(divide(divide(X2,X3),X1)),
inference(step,[status(thm)],[t177,t24]) ).
cnf(t367,plain,
multiply(divide(X1,X2),X3) = divide(X1,divide(X2,X3)),
inference(step,[status(thm)],[t366,t172]) ).
cnf(t242,plain,
divide(X1,divide(X2,X3)) = multiply(divide(X1,X2),X3),
inference(orient,[status(thm)],[t367]) ).
cnf(t371,plain,
multiply(X1,divide(X2,X3)) = multiply(divide(X1,X3),X2),
inference(step,[status(thm)],[t179,t242]) ).
cnf(t261,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(orient,[status(thm)],[t371]) ).
cnf(t273,plain,
multiply(X1,divide(X2,inverse(X3))) = multiply(multiply(X1,X3),X2),
inference(cp,[status(thm)],[t261,t24]) ).
cnf(t379,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X3),X2),
inference(step,[status(thm)],[t273,t24]) ).
cnf(t312,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t379]) ).
cnf(t354,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(step,[status(thm)],[t93,t120]) ).
cnf(t123,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[t354]) ).
cnf(t124,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t123]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[goal_0,t312]) ).
cnf(g0_1,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(c3,b3)),
inference(rw,[status(thm)],[g0_0,t124]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP551-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.56 % Computer : n002.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Wed Sep 23 15:05:37 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.56 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.49/1.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.49/1.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------