%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP167-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:25:29 PM UTC 2026
% Result : Unsatisfiable 3.37s 1.50s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 14
% Syntax : Number of clauses : 151 ( 151 unt; 0 nHn; 3 RR)
% Number of literals : 151 ( 150 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 213 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t12,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t106,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t111,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t112,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t106,t111]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t3207,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t112,t23]) ).
cnf(t276,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t3207]) ).
cnf(t15,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t94,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t15]) ).
cnf(t97,plain,
multiply(greatest_lower_bound(X1,identity),X2) = greatest_lower_bound(multiply(X1,X2),X2),
inference(cp,[status(thm)],[t94,t23]) ).
cnf(t3,axiom,
greatest_lower_bound(X1,identity) = negative_part(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t86,plain,
greatest_lower_bound(X1,identity) = negative_part(X1),
inference(orient,[status(thm)],[t3]) ).
cnf(t3217,plain,
multiply(negative_part(X1),X2) = greatest_lower_bound(multiply(X1,X2),X2),
inference(step,[status(thm)],[t97,t86]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t73,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t3218,plain,
multiply(negative_part(X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(step,[status(thm)],[t3217,t73]) ).
cnf(t511,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(negative_part(X2),X1),
inference(orient,[status(thm)],[t3218]) ).
cnf(t517,plain,
multiply(negative_part(inverse(X1)),X1) = greatest_lower_bound(X1,identity),
inference(cp,[status(thm)],[t511,t111]) ).
cnf(t3219,plain,
multiply(negative_part(inverse(X1)),X1) = negative_part(X1),
inference(step,[status(thm)],[t517,t86]) ).
cnf(t527,plain,
multiply(negative_part(inverse(X1)),X1) = negative_part(X1),
inference(orient,[status(thm)],[t3219]) ).
cnf(t529,plain,
X1 = multiply(inverse(negative_part(inverse(X1))),negative_part(X1)),
inference(cp,[status(thm)],[t276,t527]) ).
cnf(t1398,plain,
multiply(inverse(negative_part(inverse(X1))),negative_part(X1)) = X1,
inference(orient,[status(thm)],[t529]) ).
cnf(t14,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t101,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t277,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t276,t111]) ).
cnf(t295,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t277]) ).
cnf(t280,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t276,t276]) ).
cnf(t343,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t280]) ).
cnf(t3208,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t295,t343]) ).
cnf(t350,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t3208]) ).
cnf(t351,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t350]) ).
cnf(t352,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t351,t343]) ).
cnf(t3209,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t352,t351]) ).
cnf(t357,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t3209]) ).
cnf(t359,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t111,t357]) ).
cnf(t360,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t359]) ).
cnf(t364,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(multiply(X1,X2),identity),
inference(cp,[status(thm)],[t101,t360]) ).
cnf(t3296,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = negative_part(multiply(X1,X2)),
inference(step,[status(thm)],[t364,t86]) ).
cnf(t2003,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = negative_part(multiply(X1,X2)),
inference(orient,[status(thm)],[t3296]) ).
cnf(t16,axiom,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)) = greatest_lower_bound(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t49,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)) = greatest_lower_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t93,plain,
greatest_lower_bound(X1,least_upper_bound(X2,identity)) = least_upper_bound(greatest_lower_bound(X1,X2),negative_part(X1)),
inference(cp,[status(thm)],[t49,t86]) ).
cnf(t4,axiom,
least_upper_bound(X1,identity) = positive_part(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t41,plain,
least_upper_bound(X1,identity) = positive_part(X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t3272,plain,
greatest_lower_bound(X1,positive_part(X2)) = least_upper_bound(greatest_lower_bound(X1,X2),negative_part(X1)),
inference(step,[status(thm)],[t93,t41]) ).
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t3273,plain,
greatest_lower_bound(X1,positive_part(X2)) = least_upper_bound(negative_part(X1),greatest_lower_bound(X1,X2)),
inference(step,[status(thm)],[t3272,t24]) ).
cnf(t1586,plain,
least_upper_bound(negative_part(X1),greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,positive_part(X2)),
inference(orient,[status(thm)],[t3273]) ).
cnf(t1620,plain,
greatest_lower_bound(X1,positive_part(X2)) = least_upper_bound(negative_part(X1),greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t1586,t73]) ).
cnf(t2299,plain,
least_upper_bound(negative_part(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,positive_part(X2)),
inference(orient,[status(thm)],[t1620]) ).
cnf(t353,plain,
multiply(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t101,t351]) ).
cnf(t89,plain,
negative_part(X1) = greatest_lower_bound(identity,X1),
inference(cp,[status(thm)],[t86,t73]) ).
cnf(t129,plain,
greatest_lower_bound(identity,X1) = negative_part(X1),
inference(orient,[status(thm)],[t89]) ).
cnf(t3225,plain,
multiply(X1,negative_part(X2)) = greatest_lower_bound(X1,multiply(X1,X2)),
inference(step,[status(thm)],[t353,t129]) ).
cnf(t595,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,negative_part(X2)),
inference(orient,[status(thm)],[t3225]) ).
cnf(t1410,plain,
multiply(inverse(negative_part(inverse(X1))),negative_part(negative_part(X1))) = greatest_lower_bound(inverse(negative_part(inverse(X1))),X1),
inference(cp,[status(thm)],[t595,t1398]) ).
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t48,plain,
X1 = greatest_lower_bound(X1,positive_part(X1)),
inference(cp,[status(thm)],[t22,t41]) ).
cnf(t137,plain,
greatest_lower_bound(X1,positive_part(X1)) = X1,
inference(orient,[status(thm)],[t48]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t20,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t131,plain,
identity = least_upper_bound(identity,negative_part(X1)),
inference(cp,[status(thm)],[t20,t129]) ).
cnf(t44,plain,
positive_part(X1) = least_upper_bound(identity,X1),
inference(cp,[status(thm)],[t41,t24]) ).
cnf(t123,plain,
least_upper_bound(identity,X1) = positive_part(X1),
inference(orient,[status(thm)],[t44]) ).
cnf(t3192,plain,
identity = positive_part(negative_part(X1)),
inference(step,[status(thm)],[t131,t123]) ).
cnf(t136,plain,
positive_part(negative_part(X1)) = identity,
inference(orient,[status(thm)],[t3192]) ).
cnf(t139,plain,
negative_part(X1) = greatest_lower_bound(negative_part(X1),identity),
inference(cp,[status(thm)],[t137,t136]) ).
cnf(t3193,plain,
negative_part(X1) = negative_part(negative_part(X1)),
inference(step,[status(thm)],[t139,t86]) ).
cnf(t143,plain,
negative_part(negative_part(X1)) = negative_part(X1),
inference(orient,[status(thm)],[t3193]) ).
cnf(t3253,plain,
multiply(inverse(negative_part(inverse(X1))),negative_part(X1)) = greatest_lower_bound(inverse(negative_part(inverse(X1))),X1),
inference(step,[status(thm)],[t1410,t143]) ).
cnf(t3254,plain,
X1 = greatest_lower_bound(inverse(negative_part(inverse(X1))),X1),
inference(step,[status(thm)],[t3253,t1398]) ).
cnf(t3255,plain,
X1 = greatest_lower_bound(X1,inverse(negative_part(inverse(X1)))),
inference(step,[status(thm)],[t3254,t73]) ).
cnf(t1421,plain,
greatest_lower_bound(X1,inverse(negative_part(inverse(X1)))) = X1,
inference(orient,[status(thm)],[t3255]) ).
cnf(t2325,plain,
greatest_lower_bound(inverse(negative_part(inverse(X1))),positive_part(X1)) = least_upper_bound(negative_part(inverse(negative_part(inverse(X1)))),X1),
inference(cp,[status(thm)],[t2299,t1421]) ).
cnf(t3336,plain,
greatest_lower_bound(positive_part(X1),inverse(negative_part(inverse(X1)))) = least_upper_bound(negative_part(inverse(negative_part(inverse(X1)))),X1),
inference(step,[status(thm)],[t2325,t73]) ).
cnf(t3337,plain,
greatest_lower_bound(positive_part(X1),inverse(negative_part(inverse(X1)))) = least_upper_bound(X1,negative_part(inverse(negative_part(inverse(X1))))),
inference(step,[status(thm)],[t3336,t24]) ).
cnf(t130,plain,
negative_part(least_upper_bound(identity,X1)) = identity,
inference(cp,[status(thm)],[t129,t22]) ).
cnf(t3191,plain,
negative_part(positive_part(X1)) = identity,
inference(step,[status(thm)],[t130,t123]) ).
cnf(t135,plain,
negative_part(positive_part(X1)) = identity,
inference(orient,[status(thm)],[t3191]) ).
cnf(t18,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t59,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t18]) ).
cnf(t62,plain,
multiply(least_upper_bound(X1,identity),X2) = least_upper_bound(multiply(X1,X2),X2),
inference(cp,[status(thm)],[t59,t23]) ).
cnf(t3210,plain,
multiply(positive_part(X1),X2) = least_upper_bound(multiply(X1,X2),X2),
inference(step,[status(thm)],[t62,t41]) ).
cnf(t3211,plain,
multiply(positive_part(X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(step,[status(thm)],[t3210,t24]) ).
cnf(t396,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(positive_part(X2),X1),
inference(orient,[status(thm)],[t3211]) ).
cnf(t401,plain,
multiply(positive_part(X1),inverse(X1)) = least_upper_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t396,t360]) ).
cnf(t3213,plain,
multiply(positive_part(X1),inverse(X1)) = positive_part(inverse(X1)),
inference(step,[status(thm)],[t401,t41]) ).
cnf(t424,plain,
multiply(positive_part(X1),inverse(X1)) = positive_part(inverse(X1)),
inference(orient,[status(thm)],[t3213]) ).
cnf(t428,plain,
positive_part(inverse(negative_part(X1))) = multiply(identity,inverse(negative_part(X1))),
inference(cp,[status(thm)],[t424,t136]) ).
cnf(t3215,plain,
positive_part(inverse(negative_part(X1))) = inverse(negative_part(X1)),
inference(step,[status(thm)],[t428,t23]) ).
cnf(t444,plain,
positive_part(inverse(negative_part(X1))) = inverse(negative_part(X1)),
inference(orient,[status(thm)],[t3215]) ).
cnf(t449,plain,
identity = negative_part(inverse(negative_part(X1))),
inference(cp,[status(thm)],[t135,t444]) ).
cnf(t451,plain,
negative_part(inverse(negative_part(X1))) = identity,
inference(orient,[status(thm)],[t449]) ).
cnf(t3338,plain,
greatest_lower_bound(positive_part(X1),inverse(negative_part(inverse(X1)))) = least_upper_bound(X1,identity),
inference(step,[status(thm)],[t3337,t451]) ).
cnf(t3339,plain,
greatest_lower_bound(positive_part(X1),inverse(negative_part(inverse(X1)))) = positive_part(X1),
inference(step,[status(thm)],[t3338,t41]) ).
cnf(t3008,plain,
greatest_lower_bound(positive_part(X1),inverse(negative_part(inverse(X1)))) = positive_part(X1),
inference(orient,[status(thm)],[t3339]) ).
cnf(t3018,plain,
negative_part(multiply(negative_part(inverse(X1)),positive_part(X1))) = multiply(negative_part(inverse(X1)),positive_part(X1)),
inference(cp,[status(thm)],[t2003,t3008]) ).
cnf(t116,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(multiply(X1,X2),identity),
inference(cp,[status(thm)],[t94,t111]) ).
cnf(t3274,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = negative_part(multiply(X1,X2)),
inference(step,[status(thm)],[t116,t86]) ).
cnf(t1630,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = negative_part(multiply(X1,X2)),
inference(orient,[status(thm)],[t3274]) ).
cnf(t1633,plain,
negative_part(multiply(X1,X2)) = multiply(greatest_lower_bound(inverse(X2),X1),X2),
inference(cp,[status(thm)],[t1630,t73]) ).
cnf(t2356,plain,
multiply(greatest_lower_bound(inverse(X1),X2),X1) = negative_part(multiply(X2,X1)),
inference(orient,[status(thm)],[t1633]) ).
cnf(t2370,plain,
negative_part(multiply(least_upper_bound(inverse(X1),X2),X1)) = multiply(inverse(X1),X1),
inference(cp,[status(thm)],[t2356,t22]) ).
cnf(t3320,plain,
negative_part(multiply(least_upper_bound(inverse(X1),X2),X1)) = identity,
inference(step,[status(thm)],[t2370,t111]) ).
cnf(t2387,plain,
negative_part(multiply(least_upper_bound(inverse(X1),X2),X1)) = identity,
inference(orient,[status(thm)],[t3320]) ).
cnf(t2392,plain,
identity = negative_part(multiply(least_upper_bound(X1,X2),inverse(X1))),
inference(cp,[status(thm)],[t2387,t357]) ).
cnf(t2411,plain,
negative_part(multiply(least_upper_bound(X1,X2),inverse(X1))) = identity,
inference(orient,[status(thm)],[t2392]) ).
cnf(t2422,plain,
identity = negative_part(multiply(least_upper_bound(X1,X2),inverse(X2))),
inference(cp,[status(thm)],[t2411,t24]) ).
cnf(t2444,plain,
negative_part(multiply(least_upper_bound(X1,X2),inverse(X2))) = identity,
inference(orient,[status(thm)],[t2422]) ).
cnf(t402,plain,
multiply(positive_part(inverse(X1)),X1) = least_upper_bound(X1,identity),
inference(cp,[status(thm)],[t396,t111]) ).
cnf(t3212,plain,
multiply(positive_part(inverse(X1)),X1) = positive_part(X1),
inference(step,[status(thm)],[t402,t41]) ).
cnf(t412,plain,
multiply(positive_part(inverse(X1)),X1) = positive_part(X1),
inference(orient,[status(thm)],[t3212]) ).
cnf(t414,plain,
X1 = multiply(inverse(positive_part(inverse(X1))),positive_part(X1)),
inference(cp,[status(thm)],[t276,t412]) ).
cnf(t1239,plain,
multiply(inverse(positive_part(inverse(X1))),positive_part(X1)) = X1,
inference(orient,[status(thm)],[t414]) ).
cnf(t1249,plain,
multiply(inverse(positive_part(inverse(X1))),negative_part(positive_part(X1))) = greatest_lower_bound(inverse(positive_part(inverse(X1))),X1),
inference(cp,[status(thm)],[t595,t1239]) ).
cnf(t3314,plain,
multiply(inverse(positive_part(inverse(X1))),identity) = greatest_lower_bound(inverse(positive_part(inverse(X1))),X1),
inference(step,[status(thm)],[t1249,t135]) ).
cnf(t3315,plain,
inverse(positive_part(inverse(X1))) = greatest_lower_bound(inverse(positive_part(inverse(X1))),X1),
inference(step,[status(thm)],[t3314,t351]) ).
cnf(t3316,plain,
inverse(positive_part(inverse(X1))) = greatest_lower_bound(X1,inverse(positive_part(inverse(X1)))),
inference(step,[status(thm)],[t3315,t73]) ).
cnf(t2278,plain,
greatest_lower_bound(X1,inverse(positive_part(inverse(X1)))) = inverse(positive_part(inverse(X1))),
inference(orient,[status(thm)],[t3316]) ).
cnf(t2280,plain,
greatest_lower_bound(X1,positive_part(inverse(positive_part(inverse(X1))))) = least_upper_bound(negative_part(X1),inverse(positive_part(inverse(X1)))),
inference(cp,[status(thm)],[t1586,t2278]) ).
cnf(t90,plain,
X1 = least_upper_bound(X1,negative_part(X1)),
inference(cp,[status(thm)],[t20,t86]) ).
cnf(t144,plain,
least_upper_bound(X1,negative_part(X1)) = X1,
inference(orient,[status(thm)],[t90]) ).
cnf(t146,plain,
positive_part(X1) = least_upper_bound(positive_part(X1),identity),
inference(cp,[status(thm)],[t144,t135]) ).
cnf(t3194,plain,
positive_part(X1) = positive_part(positive_part(X1)),
inference(step,[status(thm)],[t146,t41]) ).
cnf(t150,plain,
positive_part(positive_part(X1)) = positive_part(X1),
inference(orient,[status(thm)],[t3194]) ).
cnf(t427,plain,
positive_part(inverse(positive_part(X1))) = multiply(positive_part(X1),inverse(positive_part(X1))),
inference(cp,[status(thm)],[t424,t150]) ).
cnf(t3214,plain,
positive_part(inverse(positive_part(X1))) = identity,
inference(step,[status(thm)],[t427,t360]) ).
cnf(t439,plain,
positive_part(inverse(positive_part(X1))) = identity,
inference(orient,[status(thm)],[t3214]) ).
cnf(t3332,plain,
greatest_lower_bound(X1,identity) = least_upper_bound(negative_part(X1),inverse(positive_part(inverse(X1)))),
inference(step,[status(thm)],[t2280,t439]) ).
cnf(t3333,plain,
negative_part(X1) = least_upper_bound(negative_part(X1),inverse(positive_part(inverse(X1)))),
inference(step,[status(thm)],[t3332,t86]) ).
cnf(t2890,plain,
least_upper_bound(negative_part(X1),inverse(positive_part(inverse(X1)))) = negative_part(X1),
inference(orient,[status(thm)],[t3333]) ).
cnf(t2899,plain,
identity = negative_part(multiply(negative_part(X1),inverse(inverse(positive_part(inverse(X1)))))),
inference(cp,[status(thm)],[t2444,t2890]) ).
cnf(t3334,plain,
identity = negative_part(multiply(negative_part(X1),positive_part(inverse(X1)))),
inference(step,[status(thm)],[t2899,t357]) ).
cnf(t2908,plain,
negative_part(multiply(negative_part(X1),positive_part(inverse(X1)))) = identity,
inference(orient,[status(thm)],[t3334]) ).
cnf(t2912,plain,
identity = negative_part(multiply(negative_part(inverse(X1)),positive_part(X1))),
inference(cp,[status(thm)],[t2908,t357]) ).
cnf(t2956,plain,
negative_part(multiply(negative_part(inverse(X1)),positive_part(X1))) = identity,
inference(orient,[status(thm)],[t2912]) ).
cnf(t3340,plain,
identity = multiply(negative_part(inverse(X1)),positive_part(X1)),
inference(step,[status(thm)],[t3018,t2956]) ).
cnf(t3024,plain,
multiply(negative_part(inverse(X1)),positive_part(X1)) = identity,
inference(orient,[status(thm)],[t3340]) ).
cnf(t3032,plain,
positive_part(X1) = multiply(inverse(negative_part(inverse(X1))),identity),
inference(cp,[status(thm)],[t276,t3024]) ).
cnf(t3341,plain,
positive_part(X1) = inverse(negative_part(inverse(X1))),
inference(step,[status(thm)],[t3032,t351]) ).
cnf(t3042,plain,
inverse(negative_part(inverse(X1))) = positive_part(X1),
inference(orient,[status(thm)],[t3341]) ).
cnf(t3342,plain,
multiply(positive_part(X1),negative_part(X1)) = X1,
inference(step,[status(thm)],[t1398,t3042]) ).
cnf(t3066,plain,
multiply(positive_part(X1),negative_part(X1)) = X1,
inference(rw,[status(thm)],[t3342]) ).
cnf(t3154,plain,
multiply(positive_part(X1),negative_part(X1)) = X1,
inference(orient,[status(thm)],[t3066]) ).
cnf(goal_0,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a != a,
inference(rw,[status(thm)],[goal_0,t3154]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.39 % Computer : n026.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Wed Sep 23 13:58:38 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.37/1.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.37/1.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------