%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP558-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:27:31 PM UTC 2026
% Result : Unsatisfiable 3.90s 1.06s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 26 RR)
% Number of literals : 51 ( 50 equ; 6 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
sF0 = inverse(b2),
introduced(definition) ).
cnf(t5,plain,
inverse(b2) = sF0,
inference(orient,[status(thm)],[t1]) ).
cnf(t2,axiom,
sF1 = divide(inverse(b2),inverse(b2)),
introduced(definition) ).
cnf(t250,plain,
sF1 = divide(sF0,inverse(b2)),
inference(step,[status(thm)],[t2,t5]) ).
cnf(t251,plain,
sF1 = divide(sF0,sF0),
inference(step,[status(thm)],[t250,t5]) ).
cnf(t7,plain,
divide(sF0,sF0) = sF1,
inference(orient,[status(thm)],[t251]) ).
cnf(t0,axiom,
divide(X1,inverse(divide(divide(X2,X3),divide(X1,X3)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
divide(X1,inverse(divide(divide(X2,X3),divide(X1,X3)))) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t4,axiom,
sF3 = divide(divide(inverse(b2),inverse(b2)),inverse(a2)),
introduced(definition) ).
cnf(t252,plain,
sF3 = divide(divide(sF0,inverse(b2)),inverse(a2)),
inference(step,[status(thm)],[t4,t5]) ).
cnf(t253,plain,
sF3 = divide(divide(sF0,sF0),inverse(a2)),
inference(step,[status(thm)],[t252,t5]) ).
cnf(t254,plain,
sF3 = divide(sF1,inverse(a2)),
inference(step,[status(thm)],[t253,t7]) ).
cnf(t3,axiom,
sF2 = inverse(a2),
introduced(definition) ).
cnf(t6,plain,
inverse(a2) = sF2,
inference(orient,[status(thm)],[t3]) ).
cnf(t255,plain,
sF3 = divide(sF1,sF2),
inference(step,[status(thm)],[t254,t6]) ).
cnf(t8,plain,
divide(sF1,sF2) = sF3,
inference(orient,[status(thm)],[t255]) ).
cnf(t12,plain,
sF1 = divide(X1,inverse(divide(sF3,divide(X1,sF2)))),
inference(cp,[status(thm)],[t9,t8]) ).
cnf(t26,plain,
divide(X1,inverse(divide(sF3,divide(X1,sF2)))) = sF1,
inference(orient,[status(thm)],[t12]) ).
cnf(t27,plain,
sF1 = divide(sF1,inverse(divide(sF3,sF3))),
inference(cp,[status(thm)],[t26,t8]) ).
cnf(t30,plain,
divide(sF1,inverse(divide(sF3,sF3))) = sF1,
inference(orient,[status(thm)],[t27]) ).
cnf(t32,plain,
X1 = divide(sF1,inverse(divide(divide(X1,inverse(divide(sF3,sF3))),sF1))),
inference(cp,[status(thm)],[t9,t30]) ).
cnf(t67,plain,
divide(sF1,inverse(divide(divide(X1,inverse(divide(sF3,sF3))),sF1))) = X1,
inference(orient,[status(thm)],[t32]) ).
cnf(t14,plain,
X1 = divide(X2,inverse(divide(X3,divide(X2,inverse(divide(divide(X3,Y3),divide(X1,Y3))))))),
inference(cp,[status(thm)],[t9,t9]) ).
cnf(t70,plain,
divide(X1,inverse(divide(X2,divide(X1,inverse(divide(divide(X2,X3),divide(Y3,X3))))))) = Y3,
inference(orient,[status(thm)],[t14]) ).
cnf(t71,plain,
X1 = divide(X1,inverse(divide(X2,X2))),
inference(cp,[status(thm)],[t70,t9]) ).
cnf(t103,plain,
divide(X1,inverse(divide(X2,X2))) = X1,
inference(orient,[status(thm)],[t71]) ).
cnf(t263,plain,
divide(sF1,inverse(divide(X1,sF1))) = X1,
inference(step,[status(thm)],[t67,t103]) ).
cnf(t110,plain,
divide(sF1,inverse(divide(X1,sF1))) = X1,
inference(rw,[status(thm)],[t263]) ).
cnf(t111,plain,
X1 = divide(X1,inverse(sF1)),
inference(cp,[status(thm)],[t103,t7]) ).
cnf(t115,plain,
divide(X1,inverse(sF1)) = X1,
inference(orient,[status(thm)],[t111]) ).
cnf(t31,plain,
sF1 = divide(X1,inverse(divide(sF1,divide(X1,inverse(divide(sF3,sF3)))))),
inference(cp,[status(thm)],[t9,t30]) ).
cnf(t52,plain,
divide(X1,inverse(divide(sF1,divide(X1,inverse(divide(sF3,sF3)))))) = sF1,
inference(orient,[status(thm)],[t31]) ).
cnf(t261,plain,
divide(X1,inverse(divide(sF1,X1))) = sF1,
inference(step,[status(thm)],[t52,t103]) ).
cnf(t108,plain,
divide(X1,inverse(divide(sF1,X1))) = sF1,
inference(rw,[status(thm)],[t261]) ).
cnf(t174,plain,
divide(X1,inverse(divide(sF1,X1))) = sF1,
inference(orient,[status(thm)],[t108]) ).
cnf(t182,plain,
sF1 = divide(inverse(sF1),inverse(sF1)),
inference(cp,[status(thm)],[t174,t115]) ).
cnf(t269,plain,
sF1 = inverse(sF1),
inference(step,[status(thm)],[t182,t115]) ).
cnf(t190,plain,
inverse(sF1) = sF1,
inference(orient,[status(thm)],[t269]) ).
cnf(t270,plain,
divide(X1,sF1) = X1,
inference(step,[status(thm)],[t115,t190]) ).
cnf(t191,plain,
divide(X1,sF1) = X1,
inference(rw,[status(thm)],[t270]) ).
cnf(t194,plain,
divide(X1,sF1) = X1,
inference(orient,[status(thm)],[t191]) ).
cnf(t280,plain,
divide(sF1,inverse(X1)) = X1,
inference(step,[status(thm)],[t110,t194]) ).
cnf(t231,plain,
divide(sF1,inverse(X1)) = X1,
inference(orient,[status(thm)],[t280]) ).
cnf(u0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
divide(divide(sF0,inverse(b2)),inverse(a2)) != a2,
inference(rw,[status(thm)],[goal_0,t5]) ).
cnf(g0_1,plain,
divide(divide(sF0,sF0),inverse(a2)) != a2,
inference(rw,[status(thm)],[g0_0,t5]) ).
cnf(g0_2,plain,
divide(sF1,inverse(a2)) != a2,
inference(rw,[status(thm)],[g0_1,t7]) ).
cnf(g0_3,plain,
a2 != a2,
inference(rw,[status(thm)],[g0_2,t231]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP558-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 15:06:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.90/1.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.90/1.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------