%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP183-3 : 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 01:25:36 PM UTC 2026
% Result : Unsatisfiable 14.28s 7.50s
% Output : CNFRefutation 14.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 18
% Syntax : Number of clauses : 179 ( 179 unt; 0 nHn; 106 RR)
% Number of literals : 179 ( 178 equ; 11 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 122 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t49,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t39,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t48,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t24,t39]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t3174,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t48,t19]) ).
cnf(t980,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t3174]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t52,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t23,t49]) ).
cnf(t111,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t52]) ).
cnf(t9,axiom,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t53,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t7,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t18,axiom,
sFlat3 = greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),
introduced(definition) ).
cnf(t3103,plain,
sFlat3 = greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(inverse(a),identity)),
inference(step,[status(thm)],[t18,t49]) ).
cnf(t15,axiom,
sFlat0 = least_upper_bound(a,identity),
introduced(definition) ).
cnf(t3101,plain,
sFlat0 = least_upper_bound(identity,a),
inference(step,[status(thm)],[t15,t49]) ).
cnf(t63,plain,
least_upper_bound(identity,a) = sFlat0,
inference(orient,[status(thm)],[t3101]) ).
cnf(t3104,plain,
sFlat3 = greatest_lower_bound(sFlat0,least_upper_bound(inverse(a),identity)),
inference(step,[status(thm)],[t3103,t63]) ).
cnf(t3105,plain,
sFlat3 = greatest_lower_bound(sFlat0,least_upper_bound(identity,inverse(a))),
inference(step,[status(thm)],[t3104,t49]) ).
cnf(t17,axiom,
sFlat2 = least_upper_bound(inverse(a),identity),
introduced(definition) ).
cnf(t3102,plain,
sFlat2 = least_upper_bound(identity,inverse(a)),
inference(step,[status(thm)],[t17,t49]) ).
cnf(t66,plain,
least_upper_bound(identity,inverse(a)) = sFlat2,
inference(orient,[status(thm)],[t3102]) ).
cnf(t3106,plain,
sFlat3 = greatest_lower_bound(sFlat0,sFlat2),
inference(step,[status(thm)],[t3105,t66]) ).
cnf(t83,plain,
greatest_lower_bound(sFlat0,sFlat2) = sFlat3,
inference(orient,[status(thm)],[t3106]) ).
cnf(t84,plain,
sFlat0 = least_upper_bound(sFlat0,sFlat3),
inference(cp,[status(thm)],[t21,t83]) ).
cnf(t92,plain,
least_upper_bound(sFlat0,sFlat3) = sFlat0,
inference(orient,[status(thm)],[t84]) ).
cnf(t93,plain,
least_upper_bound(sFlat0,least_upper_bound(sFlat3,X1)) = least_upper_bound(sFlat0,X1),
inference(cp,[status(thm)],[t53,t92]) ).
cnf(t263,plain,
least_upper_bound(sFlat0,least_upper_bound(sFlat3,X1)) = least_upper_bound(sFlat0,X1),
inference(orient,[status(thm)],[t93]) ).
cnf(t14,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(t28,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t29,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t28,t19]) ).
cnf(t241,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t29]) ).
cnf(t11,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(t27,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t985,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t980,t39]) ).
cnf(t1187,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t985]) ).
cnf(t988,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t980,t980]) ).
cnf(t1264,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t988]) ).
cnf(t3181,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t1187,t1264]) ).
cnf(t1276,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t3181]) ).
cnf(t1277,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t1276]) ).
cnf(t1280,plain,
multiply(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t27,t1277]) ).
cnf(t2800,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(orient,[status(thm)],[t1280]) ).
cnf(t12,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(t34,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t16,axiom,
sFlat1 = inverse(a),
introduced(definition) ).
cnf(t86,plain,
inverse(a) = sFlat1,
inference(orient,[status(thm)],[t16]) ).
cnf(t87,plain,
identity = multiply(sFlat1,a),
inference(cp,[status(thm)],[t39,t86]) ).
cnf(t94,plain,
multiply(sFlat1,a) = identity,
inference(orient,[status(thm)],[t87]) ).
cnf(t244,plain,
multiply(least_upper_bound(identity,sFlat1),a) = least_upper_bound(a,identity),
inference(cp,[status(thm)],[t241,t94]) ).
cnf(t3140,plain,
multiply(least_upper_bound(sFlat1,identity),a) = least_upper_bound(a,identity),
inference(step,[status(thm)],[t244,t49]) ).
cnf(t3107,plain,
least_upper_bound(identity,sFlat1) = sFlat2,
inference(step,[status(thm)],[t66,t86]) ).
cnf(t88,plain,
least_upper_bound(identity,sFlat1) = sFlat2,
inference(rw,[status(thm)],[t3107]) ).
cnf(t3109,plain,
least_upper_bound(sFlat1,identity) = sFlat2,
inference(step,[status(thm)],[t88,t49]) ).
cnf(t104,plain,
least_upper_bound(sFlat1,identity) = sFlat2,
inference(orient,[status(thm)],[t3109]) ).
cnf(t3141,plain,
multiply(sFlat2,a) = least_upper_bound(a,identity),
inference(step,[status(thm)],[t3140,t104]) ).
cnf(t3142,plain,
multiply(sFlat2,a) = least_upper_bound(identity,a),
inference(step,[status(thm)],[t3141,t49]) ).
cnf(t3143,plain,
multiply(sFlat2,a) = sFlat0,
inference(step,[status(thm)],[t3142,t63]) ).
cnf(t544,plain,
multiply(sFlat2,a) = sFlat0,
inference(orient,[status(thm)],[t3143]) ).
cnf(t546,plain,
multiply(greatest_lower_bound(sFlat2,X1),a) = greatest_lower_bound(sFlat0,multiply(X1,a)),
inference(cp,[status(thm)],[t34,t544]) ).
cnf(t2177,plain,
greatest_lower_bound(sFlat0,multiply(X1,a)) = multiply(greatest_lower_bound(sFlat2,X1),a),
inference(orient,[status(thm)],[t546]) ).
cnf(t2805,plain,
multiply(sFlat0,greatest_lower_bound(identity,a)) = multiply(greatest_lower_bound(sFlat2,sFlat0),a),
inference(cp,[status(thm)],[t2800,t2177]) ).
cnf(t103,plain,
multiply(sFlat1,multiply(a,X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t24,t94]) ).
cnf(t3115,plain,
multiply(sFlat1,multiply(a,X1)) = X1,
inference(step,[status(thm)],[t103,t19]) ).
cnf(t148,plain,
multiply(sFlat1,multiply(a,X1)) = X1,
inference(orient,[status(thm)],[t3115]) ).
cnf(t984,plain,
multiply(a,X1) = multiply(inverse(sFlat1),X1),
inference(cp,[status(thm)],[t980,t148]) ).
cnf(t1037,plain,
multiply(inverse(sFlat1),X1) = multiply(a,X1),
inference(orient,[status(thm)],[t984]) ).
cnf(t1039,plain,
multiply(a,multiply(sFlat1,X1)) = X1,
inference(cp,[status(thm)],[t1037,t980]) ).
cnf(t1232,plain,
multiply(a,multiply(sFlat1,X1)) = X1,
inference(orient,[status(thm)],[t1039]) ).
cnf(t13,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t25,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t101,plain,
multiply(sFlat1,least_upper_bound(a,X1)) = least_upper_bound(identity,multiply(sFlat1,X1)),
inference(cp,[status(thm)],[t25,t94]) ).
cnf(t1503,plain,
least_upper_bound(identity,multiply(sFlat1,X1)) = multiply(sFlat1,least_upper_bound(a,X1)),
inference(orient,[status(thm)],[t101]) ).
cnf(t1504,plain,
multiply(sFlat1,least_upper_bound(a,identity)) = multiply(least_upper_bound(identity,sFlat1),identity),
inference(cp,[status(thm)],[t1503,t241]) ).
cnf(t3191,plain,
multiply(sFlat1,least_upper_bound(identity,a)) = multiply(least_upper_bound(identity,sFlat1),identity),
inference(step,[status(thm)],[t1504,t49]) ).
cnf(t3192,plain,
multiply(sFlat1,sFlat0) = multiply(least_upper_bound(identity,sFlat1),identity),
inference(step,[status(thm)],[t3191,t63]) ).
cnf(t3193,plain,
multiply(sFlat1,sFlat0) = least_upper_bound(identity,sFlat1),
inference(step,[status(thm)],[t3192,t1277]) ).
cnf(t3194,plain,
multiply(sFlat1,sFlat0) = least_upper_bound(sFlat1,identity),
inference(step,[status(thm)],[t3193,t49]) ).
cnf(t3195,plain,
multiply(sFlat1,sFlat0) = sFlat2,
inference(step,[status(thm)],[t3194,t104]) ).
cnf(t1514,plain,
multiply(sFlat1,sFlat0) = sFlat2,
inference(orient,[status(thm)],[t3195]) ).
cnf(t1519,plain,
sFlat0 = multiply(a,sFlat2),
inference(cp,[status(thm)],[t1232,t1514]) ).
cnf(t1535,plain,
multiply(a,sFlat2) = sFlat0,
inference(orient,[status(thm)],[t1519]) ).
cnf(t1547,plain,
multiply(a,multiply(sFlat2,X1)) = multiply(sFlat0,X1),
inference(cp,[status(thm)],[t24,t1535]) ).
cnf(t1712,plain,
multiply(a,multiply(sFlat2,X1)) = multiply(sFlat0,X1),
inference(orient,[status(thm)],[t1547]) ).
cnf(t550,plain,
multiply(sFlat2,greatest_lower_bound(a,X1)) = greatest_lower_bound(sFlat0,multiply(sFlat2,X1)),
inference(cp,[status(thm)],[t27,t544]) ).
cnf(t2199,plain,
greatest_lower_bound(sFlat0,multiply(sFlat2,X1)) = multiply(sFlat2,greatest_lower_bound(a,X1)),
inference(orient,[status(thm)],[t550]) ).
cnf(t2207,plain,
multiply(sFlat2,greatest_lower_bound(a,identity)) = greatest_lower_bound(sFlat0,sFlat2),
inference(cp,[status(thm)],[t2199,t1277]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t69,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t3238,plain,
multiply(sFlat2,greatest_lower_bound(identity,a)) = greatest_lower_bound(sFlat0,sFlat2),
inference(step,[status(thm)],[t2207,t69]) ).
cnf(t3239,plain,
multiply(sFlat2,greatest_lower_bound(identity,a)) = sFlat3,
inference(step,[status(thm)],[t3238,t83]) ).
cnf(t2216,plain,
multiply(sFlat2,greatest_lower_bound(identity,a)) = sFlat3,
inference(orient,[status(thm)],[t3239]) ).
cnf(t2218,plain,
multiply(sFlat0,greatest_lower_bound(identity,a)) = multiply(a,sFlat3),
inference(cp,[status(thm)],[t1712,t2216]) ).
cnf(t2255,plain,
multiply(sFlat0,greatest_lower_bound(identity,a)) = multiply(a,sFlat3),
inference(orient,[status(thm)],[t2218]) ).
cnf(t3273,plain,
multiply(a,sFlat3) = multiply(greatest_lower_bound(sFlat2,sFlat0),a),
inference(step,[status(thm)],[t2805,t2255]) ).
cnf(t3274,plain,
multiply(a,sFlat3) = multiply(greatest_lower_bound(sFlat0,sFlat2),a),
inference(step,[status(thm)],[t3273,t69]) ).
cnf(t3275,plain,
multiply(a,sFlat3) = multiply(sFlat3,a),
inference(step,[status(thm)],[t3274,t83]) ).
cnf(t2905,plain,
multiply(a,sFlat3) = multiply(sFlat3,a),
inference(orient,[status(thm)],[t3275]) ).
cnf(t2913,plain,
multiply(least_upper_bound(identity,a),sFlat3) = least_upper_bound(sFlat3,multiply(sFlat3,a)),
inference(cp,[status(thm)],[t241,t2905]) ).
cnf(t3281,plain,
multiply(sFlat0,sFlat3) = least_upper_bound(sFlat3,multiply(sFlat3,a)),
inference(step,[status(thm)],[t2913,t63]) ).
cnf(t2993,plain,
least_upper_bound(sFlat3,multiply(sFlat3,a)) = multiply(sFlat0,sFlat3),
inference(orient,[status(thm)],[t3281]) ).
cnf(t2998,plain,
least_upper_bound(sFlat0,multiply(sFlat3,a)) = least_upper_bound(sFlat0,multiply(sFlat0,sFlat3)),
inference(cp,[status(thm)],[t263,t2993]) ).
cnf(t548,plain,
multiply(least_upper_bound(sFlat2,X1),a) = least_upper_bound(sFlat0,multiply(X1,a)),
inference(cp,[status(thm)],[t28,t544]) ).
cnf(t2188,plain,
least_upper_bound(sFlat0,multiply(X1,a)) = multiply(least_upper_bound(sFlat2,X1),a),
inference(orient,[status(thm)],[t548]) ).
cnf(t3282,plain,
multiply(least_upper_bound(sFlat2,sFlat3),a) = least_upper_bound(sFlat0,multiply(sFlat0,sFlat3)),
inference(step,[status(thm)],[t2998,t2188]) ).
cnf(t72,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t21,t69]) ).
cnf(t134,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t72]) ).
cnf(t138,plain,
sFlat2 = least_upper_bound(sFlat2,sFlat3),
inference(cp,[status(thm)],[t134,t83]) ).
cnf(t143,plain,
least_upper_bound(sFlat2,sFlat3) = sFlat2,
inference(orient,[status(thm)],[t138]) ).
cnf(t3283,plain,
multiply(sFlat2,a) = least_upper_bound(sFlat0,multiply(sFlat0,sFlat3)),
inference(step,[status(thm)],[t3282,t143]) ).
cnf(t3284,plain,
sFlat0 = least_upper_bound(sFlat0,multiply(sFlat0,sFlat3)),
inference(step,[status(thm)],[t3283,t544]) ).
cnf(t3006,plain,
least_upper_bound(sFlat0,multiply(sFlat0,sFlat3)) = sFlat0,
inference(orient,[status(thm)],[t3284]) ).
cnf(t3013,plain,
multiply(sFlat0,sFlat3) = greatest_lower_bound(multiply(sFlat0,sFlat3),sFlat0),
inference(cp,[status(thm)],[t111,t3006]) ).
cnf(t3288,plain,
multiply(sFlat0,sFlat3) = greatest_lower_bound(sFlat0,multiply(sFlat0,sFlat3)),
inference(step,[status(thm)],[t3013,t69]) ).
cnf(t3289,plain,
multiply(sFlat0,sFlat3) = multiply(sFlat0,greatest_lower_bound(identity,sFlat3)),
inference(step,[status(thm)],[t3288,t2800]) ).
cnf(t3290,plain,
multiply(sFlat0,sFlat3) = multiply(sFlat0,greatest_lower_bound(sFlat3,identity)),
inference(step,[status(thm)],[t3289,t69]) ).
cnf(t8,axiom,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t73,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t85,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(sFlat2,X1)) = greatest_lower_bound(sFlat3,X1),
inference(cp,[status(thm)],[t73,t83]) ).
cnf(t198,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(sFlat2,X1)) = greatest_lower_bound(sFlat3,X1),
inference(orient,[status(thm)],[t85]) ).
cnf(t114,plain,
identity = greatest_lower_bound(identity,sFlat2),
inference(cp,[status(thm)],[t111,t104]) ).
cnf(t3110,plain,
identity = greatest_lower_bound(sFlat2,identity),
inference(step,[status(thm)],[t114,t69]) ).
cnf(t120,plain,
greatest_lower_bound(sFlat2,identity) = identity,
inference(orient,[status(thm)],[t3110]) ).
cnf(t199,plain,
greatest_lower_bound(sFlat3,identity) = greatest_lower_bound(sFlat0,identity),
inference(cp,[status(thm)],[t198,t120]) ).
cnf(t65,plain,
identity = greatest_lower_bound(identity,sFlat0),
inference(cp,[status(thm)],[t23,t63]) ).
cnf(t3108,plain,
identity = greatest_lower_bound(sFlat0,identity),
inference(step,[status(thm)],[t65,t69]) ).
cnf(t89,plain,
greatest_lower_bound(sFlat0,identity) = identity,
inference(orient,[status(thm)],[t3108]) ).
cnf(t3118,plain,
greatest_lower_bound(sFlat3,identity) = identity,
inference(step,[status(thm)],[t199,t89]) ).
cnf(t208,plain,
greatest_lower_bound(sFlat3,identity) = identity,
inference(orient,[status(thm)],[t3118]) ).
cnf(t3291,plain,
multiply(sFlat0,sFlat3) = multiply(sFlat0,identity),
inference(step,[status(thm)],[t3290,t208]) ).
cnf(t554,plain,
multiply(sFlat2,multiply(a,X1)) = multiply(sFlat0,X1),
inference(cp,[status(thm)],[t24,t544]) ).
cnf(t791,plain,
multiply(sFlat2,multiply(a,X1)) = multiply(sFlat0,X1),
inference(orient,[status(thm)],[t554]) ).
cnf(t983,plain,
a = multiply(inverse(sFlat1),identity),
inference(cp,[status(thm)],[t980,t94]) ).
cnf(t1014,plain,
multiply(inverse(sFlat1),identity) = a,
inference(orient,[status(thm)],[t983]) ).
cnf(t3175,plain,
multiply(a,identity) = a,
inference(step,[status(thm)],[t1014,t1037]) ).
cnf(t1048,plain,
multiply(a,identity) = a,
inference(rw,[status(thm)],[t3175]) ).
cnf(t1098,plain,
multiply(a,identity) = a,
inference(orient,[status(thm)],[t1048]) ).
cnf(t1099,plain,
multiply(sFlat0,identity) = multiply(sFlat2,a),
inference(cp,[status(thm)],[t791,t1098]) ).
cnf(t3179,plain,
multiply(sFlat0,identity) = sFlat0,
inference(step,[status(thm)],[t1099,t544]) ).
cnf(t1143,plain,
multiply(sFlat0,identity) = sFlat0,
inference(orient,[status(thm)],[t3179]) ).
cnf(t3292,plain,
multiply(sFlat0,sFlat3) = sFlat0,
inference(step,[status(thm)],[t3291,t1143]) ).
cnf(t3024,plain,
multiply(sFlat0,sFlat3) = sFlat0,
inference(orient,[status(thm)],[t3292]) ).
cnf(t3034,plain,
sFlat3 = multiply(inverse(sFlat0),sFlat0),
inference(cp,[status(thm)],[t980,t3024]) ).
cnf(t3300,plain,
sFlat3 = identity,
inference(step,[status(thm)],[t3034,t39]) ).
cnf(t3055,plain,
identity = sFlat3,
inference(orient,[status(thm)],[t3300]) ).
cnf(t209,plain,
sFlat3 = least_upper_bound(sFlat3,identity),
inference(cp,[status(thm)],[t21,t208]) ).
cnf(t211,plain,
least_upper_bound(sFlat3,identity) = sFlat3,
inference(orient,[status(thm)],[t209]) ).
cnf(t213,plain,
least_upper_bound(sFlat3,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(cp,[status(thm)],[t53,t211]) ).
cnf(t503,plain,
least_upper_bound(sFlat3,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t213]) ).
cnf(t504,plain,
least_upper_bound(sFlat3,a) = least_upper_bound(sFlat3,sFlat0),
inference(cp,[status(thm)],[t503,t63]) ).
cnf(t3136,plain,
least_upper_bound(sFlat3,a) = least_upper_bound(sFlat0,sFlat3),
inference(step,[status(thm)],[t504,t49]) ).
cnf(t3137,plain,
least_upper_bound(sFlat3,a) = sFlat0,
inference(step,[status(thm)],[t3136,t92]) ).
cnf(t511,plain,
least_upper_bound(sFlat3,a) = sFlat0,
inference(orient,[status(thm)],[t3137]) ).
cnf(t105,plain,
least_upper_bound(sFlat1,least_upper_bound(identity,X1)) = least_upper_bound(sFlat2,X1),
inference(cp,[status(thm)],[t53,t104]) ).
cnf(t267,plain,
least_upper_bound(sFlat1,least_upper_bound(identity,X1)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t105]) ).
cnf(t274,plain,
least_upper_bound(sFlat2,X1) = least_upper_bound(sFlat1,least_upper_bound(X1,identity)),
inference(cp,[status(thm)],[t267,t49]) ).
cnf(t566,plain,
least_upper_bound(sFlat1,least_upper_bound(X1,identity)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t274]) ).
cnf(t568,plain,
least_upper_bound(sFlat2,sFlat3) = least_upper_bound(sFlat1,sFlat3),
inference(cp,[status(thm)],[t566,t211]) ).
cnf(t3145,plain,
sFlat2 = least_upper_bound(sFlat1,sFlat3),
inference(step,[status(thm)],[t568,t143]) ).
cnf(t595,plain,
least_upper_bound(sFlat1,sFlat3) = sFlat2,
inference(orient,[status(thm)],[t3145]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(inverse(a),identity)) != identity,
inference(rw,[status(thm)],[goal_0,t49]) ).
cnf(g0_1,plain,
greatest_lower_bound(least_upper_bound(sFlat3,a),least_upper_bound(inverse(a),identity)) != identity,
inference(rw,[status(thm)],[g0_0,t3055]) ).
cnf(g0_2,plain,
greatest_lower_bound(sFlat0,least_upper_bound(inverse(a),identity)) != identity,
inference(rw,[status(thm)],[g0_1,t511]) ).
cnf(g0_3,plain,
greatest_lower_bound(sFlat0,least_upper_bound(identity,inverse(a))) != identity,
inference(rw,[status(thm)],[g0_2,t49]) ).
cnf(g0_4,plain,
greatest_lower_bound(sFlat0,least_upper_bound(sFlat3,inverse(a))) != identity,
inference(rw,[status(thm)],[g0_3,t3055]) ).
cnf(g0_5,plain,
greatest_lower_bound(sFlat0,least_upper_bound(sFlat3,sFlat1)) != identity,
inference(rw,[status(thm)],[g0_4,t86]) ).
cnf(g0_6,plain,
greatest_lower_bound(sFlat0,least_upper_bound(sFlat1,sFlat3)) != identity,
inference(rw,[status(thm)],[g0_5,t49]) ).
cnf(g0_7,plain,
greatest_lower_bound(sFlat0,sFlat2) != identity,
inference(rw,[status(thm)],[g0_6,t595]) ).
cnf(g0_8,plain,
sFlat3 != identity,
inference(rw,[status(thm)],[g0_7,t83]) ).
cnf(g0_9,plain,
sFlat3 != sFlat3,
inference(rw,[status(thm)],[g0_8,t3055]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP183-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.59 % Computer : n026.cluster.edu
% 0.09/5.59 % Model : x86_64 x86_64
% 0.09/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.59 % Memory : 8046.5625MB
% 0.09/5.59 % OS : Linux 6.8.0-71-generic
% 0.09/5.59 % CPULimit : 300
% 0.09/5.60 % WCLimit : 300
% 0.09/5.60 % DateTime : Wed Sep 23 14:05:15 UTC 2026
% 0.14/5.60 % CPUTime :
% 0.14/5.60 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.28/7.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.28/7.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------