%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 01:25:12 PM UTC 2026
% Result : Unsatisfiable 7.04s 6.49s
% Output : CNFRefutation 7.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of clauses : 132 ( 132 unt; 0 nHn; 5 RR)
% Number of literals : 132 ( 131 equ; 2 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 207 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t26,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t6,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t41,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t6]) ).
cnf(t51,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t26,t41]) ).
cnf(t3,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t3664,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t51,t20]) ).
cnf(t314,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t3664]) ).
cnf(t17,axiom,
intersection(multiply(X1,X2),multiply(X3,X2)) = multiply(intersection(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t36,plain,
intersection(multiply(X1,X2),multiply(X3,X2)) = multiply(intersection(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
cnf(t37,plain,
multiply(intersection(identity,X1),X2) = intersection(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t36,t20]) ).
cnf(t5,axiom,
intersection(X1,identity) = negative_part(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t95,plain,
intersection(X1,identity) = negative_part(X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t8,axiom,
intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t84,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t98,plain,
negative_part(X1) = intersection(identity,X1),
inference(cp,[status(thm)],[t95,t84]) ).
cnf(t107,plain,
intersection(identity,X1) = negative_part(X1),
inference(orient,[status(thm)],[t98]) ).
cnf(t3678,plain,
multiply(negative_part(X1),X2) = intersection(X2,multiply(X1,X2)),
inference(step,[status(thm)],[t37,t107]) ).
cnf(t718,plain,
intersection(X1,multiply(X2,X1)) = multiply(negative_part(X2),X1),
inference(orient,[status(thm)],[t3678]) ).
cnf(t732,plain,
multiply(negative_part(inverse(X1)),X1) = intersection(X1,identity),
inference(cp,[status(thm)],[t718,t41]) ).
cnf(t3679,plain,
multiply(negative_part(inverse(X1)),X1) = negative_part(X1),
inference(step,[status(thm)],[t732,t95]) ).
cnf(t761,plain,
multiply(negative_part(inverse(X1)),X1) = negative_part(X1),
inference(orient,[status(thm)],[t3679]) ).
cnf(t767,plain,
X1 = multiply(inverse(negative_part(inverse(X1))),negative_part(X1)),
inference(cp,[status(thm)],[t314,t761]) ).
cnf(t1275,plain,
multiply(inverse(negative_part(inverse(X1))),negative_part(X1)) = X1,
inference(orient,[status(thm)],[t767]) ).
cnf(t12,axiom,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t52,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t12]) ).
cnf(t2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t55,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t52,t25]) ).
cnf(t409,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t55]) ).
cnf(t410,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(cp,[status(thm)],[t409,t314]) ).
cnf(t689,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(orient,[status(thm)],[t410]) ).
cnf(t11,axiom,
union(intersection(X1,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
union(intersection(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t69,plain,
union(intersection(X1,X2),X2) = X2,
inference(rw,[status(thm)],[t22]) ).
cnf(t10,axiom,
union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t65,plain,
union(X1,X2) = union(X2,X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t3640,plain,
union(X2,intersection(X1,X2)) = X2,
inference(step,[status(thm)],[t69,t65]) ).
cnf(t130,plain,
union(X1,intersection(X2,X1)) = X1,
inference(orient,[status(thm)],[t3640]) ).
cnf(t134,plain,
X1 = union(X1,negative_part(X1)),
inference(cp,[status(thm)],[t130,t107]) ).
cnf(t139,plain,
union(X1,negative_part(X1)) = X1,
inference(orient,[status(thm)],[t134]) ).
cnf(t13,axiom,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t88,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t97,plain,
negative_part(intersection(X1,X2)) = intersection(X1,intersection(X2,identity)),
inference(cp,[status(thm)],[t95,t88]) ).
cnf(t3649,plain,
negative_part(intersection(X1,X2)) = intersection(X1,negative_part(X2)),
inference(step,[status(thm)],[t97,t95]) ).
cnf(t192,plain,
negative_part(intersection(X1,X2)) = intersection(X1,negative_part(X2)),
inference(orient,[status(thm)],[t3649]) ).
cnf(t16,axiom,
intersection(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,intersection(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t29,plain,
intersection(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,intersection(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t0,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t100,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t101,plain,
inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)),
inference(cp,[status(thm)],[t52,t100]) ).
cnf(t3638,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(step,[status(thm)],[t101,t20]) ).
cnf(t120,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t3638]) ).
cnf(t124,plain,
multiply(X1,identity) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t25,t120]) ).
cnf(t3639,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t124,t25]) ).
cnf(t125,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t3639]) ).
cnf(t126,plain,
multiply(X1,intersection(identity,X2)) = intersection(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t29,t125]) ).
cnf(t3666,plain,
multiply(X1,negative_part(X2)) = intersection(X1,multiply(X1,X2)),
inference(step,[status(thm)],[t126,t107]) ).
cnf(t419,plain,
intersection(X1,multiply(X1,X2)) = multiply(X1,negative_part(X2)),
inference(orient,[status(thm)],[t3666]) ).
cnf(t431,plain,
intersection(X1,negative_part(multiply(X1,X2))) = negative_part(multiply(X1,negative_part(X2))),
inference(cp,[status(thm)],[t192,t419]) ).
cnf(t3272,plain,
intersection(X1,negative_part(multiply(X1,X2))) = negative_part(multiply(X1,negative_part(X2))),
inference(orient,[status(thm)],[t431]) ).
cnf(t19,axiom,
union(multiply(X1,X2),multiply(X3,X2)) = multiply(union(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t30,plain,
union(multiply(X1,X2),multiply(X3,X2)) = multiply(union(X1,X3),X2),
inference(orient,[status(thm)],[t19]) ).
cnf(t31,plain,
multiply(union(identity,X1),X2) = union(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t30,t20]) ).
cnf(t7,axiom,
union(X1,identity) = positive_part(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t78,plain,
union(X1,identity) = positive_part(X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t81,plain,
positive_part(X1) = union(identity,X1),
inference(cp,[status(thm)],[t78,t65]) ).
cnf(t105,plain,
union(identity,X1) = positive_part(X1),
inference(orient,[status(thm)],[t81]) ).
cnf(t3656,plain,
multiply(positive_part(X1),X2) = union(X2,multiply(X1,X2)),
inference(step,[status(thm)],[t31,t105]) ).
cnf(t241,plain,
union(X1,multiply(X2,X1)) = multiply(positive_part(X2),X1),
inference(orient,[status(thm)],[t3656]) ).
cnf(t246,plain,
multiply(positive_part(inverse(X1)),X1) = union(X1,identity),
inference(cp,[status(thm)],[t241,t41]) ).
cnf(t3657,plain,
multiply(positive_part(inverse(X1)),X1) = positive_part(X1),
inference(step,[status(thm)],[t246,t78]) ).
cnf(t252,plain,
multiply(positive_part(inverse(X1)),X1) = positive_part(X1),
inference(orient,[status(thm)],[t3657]) ).
cnf(t3306,plain,
negative_part(multiply(positive_part(inverse(X1)),negative_part(X1))) = intersection(positive_part(inverse(X1)),negative_part(positive_part(X1))),
inference(cp,[status(thm)],[t3272,t252]) ).
cnf(t108,plain,
intersection(identity,intersection(X1,X2)) = intersection(negative_part(X1),X2),
inference(cp,[status(thm)],[t88,t107]) ).
cnf(t3652,plain,
negative_part(intersection(X1,X2)) = intersection(negative_part(X1),X2),
inference(step,[status(thm)],[t108,t107]) ).
cnf(t3653,plain,
intersection(X1,negative_part(X2)) = intersection(negative_part(X1),X2),
inference(step,[status(thm)],[t3652,t192]) ).
cnf(t217,plain,
intersection(negative_part(X1),X2) = intersection(X1,negative_part(X2)),
inference(orient,[status(thm)],[t3653]) ).
cnf(t9,axiom,
intersection(union(X1,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
intersection(union(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t87,plain,
intersection(union(X1,X2),X2) = X2,
inference(rw,[status(thm)],[t24]) ).
cnf(t3642,plain,
intersection(X2,union(X1,X2)) = X2,
inference(step,[status(thm)],[t87,t84]) ).
cnf(t142,plain,
intersection(X1,union(X2,X1)) = X1,
inference(orient,[status(thm)],[t3642]) ).
cnf(t143,plain,
identity = negative_part(union(X1,identity)),
inference(cp,[status(thm)],[t142,t107]) ).
cnf(t3643,plain,
identity = negative_part(positive_part(X1)),
inference(step,[status(thm)],[t143,t78]) ).
cnf(t151,plain,
negative_part(positive_part(X1)) = identity,
inference(orient,[status(thm)],[t3643]) ).
cnf(t222,plain,
intersection(positive_part(X1),negative_part(X2)) = intersection(identity,X2),
inference(cp,[status(thm)],[t217,t151]) ).
cnf(t3655,plain,
intersection(positive_part(X1),negative_part(X2)) = negative_part(X2),
inference(step,[status(thm)],[t222,t107]) ).
cnf(t229,plain,
intersection(positive_part(X1),negative_part(X2)) = negative_part(X2),
inference(orient,[status(thm)],[t3655]) ).
cnf(t3803,plain,
negative_part(multiply(positive_part(inverse(X1)),negative_part(X1))) = negative_part(positive_part(X1)),
inference(step,[status(thm)],[t3306,t229]) ).
cnf(t3804,plain,
negative_part(multiply(positive_part(inverse(X1)),negative_part(X1))) = identity,
inference(step,[status(thm)],[t3803,t151]) ).
cnf(t3332,plain,
negative_part(multiply(positive_part(inverse(X1)),negative_part(X1))) = identity,
inference(orient,[status(thm)],[t3804]) ).
cnf(t3340,plain,
multiply(positive_part(inverse(X1)),negative_part(X1)) = union(multiply(positive_part(inverse(X1)),negative_part(X1)),identity),
inference(cp,[status(thm)],[t139,t3332]) ).
cnf(t3805,plain,
multiply(positive_part(inverse(X1)),negative_part(X1)) = positive_part(multiply(positive_part(inverse(X1)),negative_part(X1))),
inference(step,[status(thm)],[t3340,t78]) ).
cnf(t15,axiom,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t70,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
cnf(t80,plain,
positive_part(union(X1,X2)) = union(X1,union(X2,identity)),
inference(cp,[status(thm)],[t78,t70]) ).
cnf(t3648,plain,
positive_part(union(X1,X2)) = union(X1,positive_part(X2)),
inference(step,[status(thm)],[t80,t78]) ).
cnf(t176,plain,
positive_part(union(X1,X2)) = union(X1,positive_part(X2)),
inference(orient,[status(thm)],[t3648]) ).
cnf(t249,plain,
union(X1,positive_part(multiply(X2,X1))) = positive_part(multiply(positive_part(X2),X1)),
inference(cp,[status(thm)],[t176,t241]) ).
cnf(t2970,plain,
union(X1,positive_part(multiply(X2,X1))) = positive_part(multiply(positive_part(X2),X1)),
inference(orient,[status(thm)],[t249]) ).
cnf(t427,plain,
multiply(inverse(X1),negative_part(X1)) = intersection(inverse(X1),identity),
inference(cp,[status(thm)],[t419,t41]) ).
cnf(t3668,plain,
multiply(inverse(X1),negative_part(X1)) = negative_part(inverse(X1)),
inference(step,[status(thm)],[t427,t95]) ).
cnf(t452,plain,
multiply(inverse(X1),negative_part(X1)) = negative_part(inverse(X1)),
inference(orient,[status(thm)],[t3668]) ).
cnf(t3003,plain,
positive_part(multiply(positive_part(inverse(X1)),negative_part(X1))) = union(negative_part(X1),positive_part(negative_part(inverse(X1)))),
inference(cp,[status(thm)],[t2970,t452]) ).
cnf(t106,plain,
union(identity,union(X1,X2)) = union(positive_part(X1),X2),
inference(cp,[status(thm)],[t70,t105]) ).
cnf(t3650,plain,
positive_part(union(X1,X2)) = union(positive_part(X1),X2),
inference(step,[status(thm)],[t106,t105]) ).
cnf(t3651,plain,
union(X1,positive_part(X2)) = union(positive_part(X1),X2),
inference(step,[status(thm)],[t3650,t176]) ).
cnf(t208,plain,
union(positive_part(X1),X2) = union(X1,positive_part(X2)),
inference(orient,[status(thm)],[t3651]) ).
cnf(t131,plain,
identity = positive_part(intersection(X1,identity)),
inference(cp,[status(thm)],[t130,t105]) ).
cnf(t3641,plain,
identity = positive_part(negative_part(X1)),
inference(step,[status(thm)],[t131,t95]) ).
cnf(t138,plain,
positive_part(negative_part(X1)) = identity,
inference(orient,[status(thm)],[t3641]) ).
cnf(t214,plain,
union(negative_part(X1),positive_part(X2)) = union(identity,X2),
inference(cp,[status(thm)],[t208,t138]) ).
cnf(t3654,plain,
union(negative_part(X1),positive_part(X2)) = positive_part(X2),
inference(step,[status(thm)],[t214,t105]) ).
cnf(t225,plain,
union(negative_part(X1),positive_part(X2)) = positive_part(X2),
inference(orient,[status(thm)],[t3654]) ).
cnf(t3799,plain,
positive_part(multiply(positive_part(inverse(X1)),negative_part(X1))) = positive_part(negative_part(inverse(X1))),
inference(step,[status(thm)],[t3003,t225]) ).
cnf(t3800,plain,
positive_part(multiply(positive_part(inverse(X1)),negative_part(X1))) = identity,
inference(step,[status(thm)],[t3799,t138]) ).
cnf(t3048,plain,
positive_part(multiply(positive_part(inverse(X1)),negative_part(X1))) = identity,
inference(orient,[status(thm)],[t3800]) ).
cnf(t3806,plain,
multiply(positive_part(inverse(X1)),negative_part(X1)) = identity,
inference(step,[status(thm)],[t3805,t3048]) ).
cnf(t3468,plain,
multiply(positive_part(inverse(X1)),negative_part(X1)) = identity,
inference(orient,[status(thm)],[t3806]) ).
cnf(t3490,plain,
inverse(negative_part(X1)) = multiply(inverse(identity),positive_part(inverse(X1))),
inference(cp,[status(thm)],[t689,t3468]) ).
cnf(t3807,plain,
inverse(negative_part(X1)) = multiply(identity,positive_part(inverse(X1))),
inference(step,[status(thm)],[t3490,t100]) ).
cnf(t3808,plain,
inverse(negative_part(X1)) = positive_part(inverse(X1)),
inference(step,[status(thm)],[t3807,t20]) ).
cnf(t3492,plain,
inverse(negative_part(X1)) = positive_part(inverse(X1)),
inference(orient,[status(thm)],[t3808]) ).
cnf(t3812,plain,
multiply(positive_part(inverse(inverse(X1))),negative_part(X1)) = X1,
inference(step,[status(thm)],[t1275,t3492]) ).
cnf(t3813,plain,
multiply(positive_part(X1),negative_part(X1)) = X1,
inference(step,[status(thm)],[t3812,t25]) ).
cnf(t3526,plain,
multiply(positive_part(X1),negative_part(X1)) = X1,
inference(rw,[status(thm)],[t3813]) ).
cnf(t3599,plain,
multiply(positive_part(X1),negative_part(X1)) = X1,
inference(orient,[status(thm)],[t3526]) ).
cnf(goal_0,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a != a,
inference(rw,[status(thm)],[goal_0,t3599]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n014.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 13:34:09 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.04/6.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.04/6.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------