%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP451-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 5.84s 1.18s
% Output : CNFRefutation 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 20 RR)
% Number of literals : 69 ( 68 equ; 5 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 : 76 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
sFlat0 = inverse(b1),
introduced(definition) ).
cnf(t24,plain,
inverse(b1) = sFlat0,
inference(orient,[status(thm)],[t3]) ).
cnf(t4,axiom,
sFlat1 = multiply(inverse(b1),b1),
introduced(definition) ).
cnf(t273,plain,
sFlat1 = multiply(sFlat0,b1),
inference(step,[status(thm)],[t4,t24]) ).
cnf(t26,plain,
multiply(sFlat0,b1) = sFlat1,
inference(orient,[status(thm)],[t273]) ).
cnf(t5,axiom,
sFlat2 = inverse(a1),
introduced(definition) ).
cnf(t23,plain,
inverse(a1) = sFlat2,
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
sFlat3 = multiply(inverse(a1),a1),
introduced(definition) ).
cnf(t272,plain,
sFlat3 = multiply(sFlat2,a1),
inference(step,[status(thm)],[t6,t23]) ).
cnf(t25,plain,
multiply(sFlat2,a1) = sFlat3,
inference(orient,[status(thm)],[t272]) ).
cnf(t2,axiom,
divide(divide(divide(X1,X1),divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
divide(divide(divide(X1,X1),divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t0,axiom,
divide(divide(X1,X1),X2) = inverse(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(orient,[status(thm)],[t0]) ).
cnf(t270,plain,
divide(inverse(divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),X3) = X2,
inference(step,[status(thm)],[t7,t19]) ).
cnf(t271,plain,
divide(inverse(divide(X1,divide(X2,divide(inverse(X1),X3)))),X3) = X2,
inference(step,[status(thm)],[t270,t19]) ).
cnf(t22,plain,
divide(inverse(divide(X1,divide(X2,divide(inverse(X1),X3)))),X3) = X2,
inference(rw,[status(thm)],[t271]) ).
cnf(t191,plain,
divide(inverse(divide(X1,divide(X2,divide(inverse(X1),X3)))),X3) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t1,axiom,
divide(X1,divide(divide(X2,X2),X3)) = multiply(X1,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
divide(X1,divide(divide(X2,X2),X3)) = multiply(X1,X3),
inference(orient,[status(thm)],[t1]) ).
cnf(t269,plain,
divide(X1,inverse(X3)) = multiply(X1,X3),
inference(step,[status(thm)],[t9,t19]) ).
cnf(t21,plain,
divide(X1,inverse(X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[t269]) ).
cnf(t27,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t21]) ).
cnf(t29,plain,
multiply(X1,a1) = divide(X1,sFlat2),
inference(cp,[status(thm)],[t27,t23]) ).
cnf(t32,plain,
divide(X1,sFlat2) = multiply(X1,a1),
inference(orient,[status(thm)],[t29]) ).
cnf(t34,plain,
inverse(X1) = divide(multiply(sFlat2,a1),X1),
inference(cp,[status(thm)],[t19,t32]) ).
cnf(t274,plain,
inverse(X1) = divide(sFlat3,X1),
inference(step,[status(thm)],[t34,t25]) ).
cnf(t35,plain,
divide(sFlat3,X1) = inverse(X1),
inference(orient,[status(thm)],[t274]) ).
cnf(t38,plain,
inverse(X1) = divide(inverse(sFlat3),X1),
inference(cp,[status(thm)],[t19,t35]) ).
cnf(t58,plain,
divide(inverse(sFlat3),X1) = inverse(X1),
inference(orient,[status(thm)],[t38]) ).
cnf(t62,plain,
inverse(X1) = divide(inverse(inverse(sFlat3)),X1),
inference(cp,[status(thm)],[t19,t58]) ).
cnf(t36,plain,
inverse(inverse(X1)) = multiply(sFlat3,X1),
inference(cp,[status(thm)],[t35,t27]) ).
cnf(t52,plain,
inverse(inverse(X1)) = multiply(sFlat3,X1),
inference(orient,[status(thm)],[t36]) ).
cnf(t30,plain,
multiply(X1,b1) = divide(X1,sFlat0),
inference(cp,[status(thm)],[t27,t24]) ).
cnf(t40,plain,
divide(X1,sFlat0) = multiply(X1,b1),
inference(orient,[status(thm)],[t30]) ).
cnf(t43,plain,
inverse(X1) = divide(multiply(sFlat0,b1),X1),
inference(cp,[status(thm)],[t19,t40]) ).
cnf(t275,plain,
inverse(X1) = divide(sFlat1,X1),
inference(step,[status(thm)],[t43,t26]) ).
cnf(t45,plain,
divide(sFlat1,X1) = inverse(X1),
inference(orient,[status(thm)],[t275]) ).
cnf(t47,plain,
inverse(inverse(X1)) = multiply(sFlat1,X1),
inference(cp,[status(thm)],[t45,t27]) ).
cnf(t276,plain,
multiply(sFlat3,X1) = multiply(sFlat1,X1),
inference(step,[status(thm)],[t47,t52]) ).
cnf(t55,plain,
multiply(sFlat3,X1) = multiply(sFlat1,X1),
inference(orient,[status(thm)],[t276]) ).
cnf(t277,plain,
inverse(inverse(X1)) = multiply(sFlat1,X1),
inference(step,[status(thm)],[t52,t55]) ).
cnf(t56,plain,
inverse(inverse(X1)) = multiply(sFlat1,X1),
inference(orient,[status(thm)],[t277]) ).
cnf(t283,plain,
inverse(X1) = divide(multiply(sFlat1,sFlat3),X1),
inference(step,[status(thm)],[t62,t56]) ).
cnf(t86,plain,
divide(multiply(sFlat1,sFlat3),X1) = inverse(X1),
inference(orient,[status(thm)],[t283]) ).
cnf(t200,plain,
X1 = divide(inverse(inverse(divide(X1,divide(inverse(multiply(sFlat1,sFlat3)),X2)))),X2),
inference(cp,[status(thm)],[t191,t86]) ).
cnf(t297,plain,
X1 = divide(multiply(sFlat1,divide(X1,divide(inverse(multiply(sFlat1,sFlat3)),X2))),X2),
inference(step,[status(thm)],[t200,t56]) ).
cnf(t53,plain,
multiply(sFlat3,inverse(X1)) = inverse(multiply(sFlat3,X1)),
inference(cp,[status(thm)],[t52,t52]) ).
cnf(t281,plain,
multiply(sFlat1,inverse(X1)) = inverse(multiply(sFlat3,X1)),
inference(step,[status(thm)],[t53,t55]) ).
cnf(t282,plain,
multiply(sFlat1,inverse(X1)) = inverse(multiply(sFlat1,X1)),
inference(step,[status(thm)],[t281,t55]) ).
cnf(t74,plain,
inverse(multiply(sFlat1,X1)) = multiply(sFlat1,inverse(X1)),
inference(orient,[status(thm)],[t282]) ).
cnf(t298,plain,
X1 = divide(multiply(sFlat1,divide(X1,divide(multiply(sFlat1,inverse(sFlat3)),X2))),X2),
inference(step,[status(thm)],[t297,t74]) ).
cnf(t90,plain,
inverse(X1) = divide(inverse(multiply(sFlat1,sFlat3)),X1),
inference(cp,[status(thm)],[t19,t86]) ).
cnf(t293,plain,
inverse(X1) = divide(multiply(sFlat1,inverse(sFlat3)),X1),
inference(step,[status(thm)],[t90,t74]) ).
cnf(t141,plain,
divide(multiply(sFlat1,inverse(sFlat3)),X1) = inverse(X1),
inference(orient,[status(thm)],[t293]) ).
cnf(t299,plain,
X1 = divide(multiply(sFlat1,divide(X1,inverse(X2))),X2),
inference(step,[status(thm)],[t298,t141]) ).
cnf(t300,plain,
X1 = divide(multiply(sFlat1,multiply(X1,X2)),X2),
inference(step,[status(thm)],[t299,t27]) ).
cnf(t248,plain,
divide(multiply(sFlat1,multiply(X1,X2)),X2) = X1,
inference(orient,[status(thm)],[t300]) ).
cnf(t262,plain,
sFlat3 = divide(multiply(sFlat1,multiply(sFlat1,X1)),X1),
inference(cp,[status(thm)],[t248,t55]) ).
cnf(t301,plain,
sFlat3 = sFlat1,
inference(step,[status(thm)],[t262,t248]) ).
cnf(t266,plain,
sFlat3 = sFlat1,
inference(orient,[status(thm)],[t301]) ).
cnf(t302,plain,
multiply(sFlat2,a1) = sFlat1,
inference(step,[status(thm)],[t25,t266]) ).
cnf(t267,plain,
multiply(sFlat2,a1) = sFlat1,
inference(orient,[status(thm)],[t302]) ).
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(sFlat0,b1) != multiply(inverse(a1),a1),
inference(rw,[status(thm)],[goal_0,t24]) ).
cnf(g0_1,plain,
sFlat1 != multiply(inverse(a1),a1),
inference(rw,[status(thm)],[g0_0,t26]) ).
cnf(g0_2,plain,
sFlat1 != multiply(sFlat2,a1),
inference(rw,[status(thm)],[g0_1,t23]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t267]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP451-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:52:50 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.84/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.84/1.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------