%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP167-4 : 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 01:25:30 PM UTC 2026
% Result : Unsatisfiable 13.01s 7.21s
% Output : CNFRefutation 13.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 20
% Syntax : Number of clauses : 170 ( 170 unt; 0 nHn; 71 RR)
% Number of literals : 170 ( 169 equ; 3 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 149 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t27,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t16,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(t28,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t26,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t10,axiom,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t63,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t10]) ).
cnf(t0,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t111,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t112,plain,
inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)),
inference(cp,[status(thm)],[t63,t111]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t18261,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(step,[status(thm)],[t112,t21]) ).
cnf(t135,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t18261]) ).
cnf(t139,plain,
multiply(X1,identity) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t26,t135]) ).
cnf(t18262,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t139,t26]) ).
cnf(t140,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t18262]) ).
cnf(t143,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t28,t140]) ).
cnf(t823,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t143]) ).
cnf(t17,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(t31,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
cnf(t32,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t31,t21]) ).
cnf(t269,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t32]) ).
cnf(t824,plain,
multiply(X1,least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),X1),
inference(cp,[status(thm)],[t823,t269]) ).
cnf(t1184,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(orient,[status(thm)],[t824]) ).
cnf(t18,axiom,
sFlat0 = least_upper_bound(a,identity),
introduced(definition) ).
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t76,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t18257,plain,
sFlat0 = least_upper_bound(identity,a),
inference(step,[status(thm)],[t18,t76]) ).
cnf(t91,plain,
least_upper_bound(identity,a) = sFlat0,
inference(orient,[status(thm)],[t18257]) ).
cnf(t1187,plain,
multiply(a,least_upper_bound(identity,a)) = multiply(sFlat0,a),
inference(cp,[status(thm)],[t1184,t91]) ).
cnf(t18312,plain,
multiply(a,sFlat0) = multiply(sFlat0,a),
inference(step,[status(thm)],[t1187,t91]) ).
cnf(t1211,plain,
multiply(a,sFlat0) = multiply(sFlat0,a),
inference(orient,[status(thm)],[t18312]) ).
cnf(t1223,plain,
multiply(a,multiply(sFlat0,X1)) = multiply(multiply(sFlat0,a),X1),
inference(cp,[status(thm)],[t27,t1211]) ).
cnf(t18320,plain,
multiply(a,multiply(sFlat0,X1)) = multiply(sFlat0,multiply(a,X1)),
inference(step,[status(thm)],[t1223,t27]) ).
cnf(t1442,plain,
multiply(a,multiply(sFlat0,X1)) = multiply(sFlat0,multiply(a,X1)),
inference(orient,[status(thm)],[t18320]) ).
cnf(t20,axiom,
sFlat2 = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
introduced(definition) ).
cnf(t37,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) = sFlat2,
inference(orient,[status(thm)],[t20]) ).
cnf(t80,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) = sFlat2,
inference(rw,[status(thm)],[t37]) ).
cnf(t18321,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(a,identity)) = sFlat2,
inference(step,[status(thm)],[t80,t76]) ).
cnf(t18322,plain,
multiply(sFlat0,greatest_lower_bound(a,identity)) = sFlat2,
inference(step,[status(thm)],[t18321,t91]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t94,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t18323,plain,
multiply(sFlat0,greatest_lower_bound(identity,a)) = sFlat2,
inference(step,[status(thm)],[t18322,t94]) ).
cnf(t19,axiom,
sFlat1 = greatest_lower_bound(a,identity),
introduced(definition) ).
cnf(t18258,plain,
sFlat1 = greatest_lower_bound(identity,a),
inference(step,[status(thm)],[t19,t94]) ).
cnf(t108,plain,
greatest_lower_bound(identity,a) = sFlat1,
inference(orient,[status(thm)],[t18258]) ).
cnf(t18324,plain,
multiply(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t18323,t108]) ).
cnf(t1559,plain,
multiply(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t18324]) ).
cnf(t1577,plain,
multiply(sFlat0,multiply(sFlat1,X1)) = multiply(sFlat2,X1),
inference(cp,[status(thm)],[t27,t1559]) ).
cnf(t1909,plain,
multiply(sFlat0,multiply(sFlat1,X1)) = multiply(sFlat2,X1),
inference(orient,[status(thm)],[t1577]) ).
cnf(t1920,plain,
multiply(sFlat0,multiply(a,multiply(sFlat1,X1))) = multiply(a,multiply(sFlat2,X1)),
inference(cp,[status(thm)],[t1442,t1909]) ).
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(t30,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t141,plain,
multiply(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t30,t140]) ).
cnf(t797,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(orient,[status(thm)],[t141]) ).
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(t45,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t15]) ).
cnf(t47,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t45,t21]) ).
cnf(t772,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t47]) ).
cnf(t798,plain,
multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),X1),
inference(cp,[status(thm)],[t797,t772]) ).
cnf(t867,plain,
multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)),
inference(orient,[status(thm)],[t798]) ).
cnf(t873,plain,
multiply(a,greatest_lower_bound(identity,a)) = multiply(sFlat1,a),
inference(cp,[status(thm)],[t867,t108]) ).
cnf(t18296,plain,
multiply(a,sFlat1) = multiply(sFlat1,a),
inference(step,[status(thm)],[t873,t108]) ).
cnf(t894,plain,
multiply(a,sFlat1) = multiply(sFlat1,a),
inference(orient,[status(thm)],[t18296]) ).
cnf(t907,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(multiply(sFlat1,a),X1),
inference(cp,[status(thm)],[t27,t894]) ).
cnf(t18318,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(sFlat1,multiply(a,X1)),
inference(step,[status(thm)],[t907,t27]) ).
cnf(t1374,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(sFlat1,multiply(a,X1)),
inference(orient,[status(thm)],[t18318]) ).
cnf(t18369,plain,
multiply(sFlat0,multiply(sFlat1,multiply(a,X1))) = multiply(a,multiply(sFlat2,X1)),
inference(step,[status(thm)],[t1920,t1374]) ).
cnf(t18370,plain,
multiply(sFlat2,multiply(a,X1)) = multiply(a,multiply(sFlat2,X1)),
inference(step,[status(thm)],[t18369,t1909]) ).
cnf(t2763,plain,
multiply(a,multiply(sFlat2,X1)) = multiply(sFlat2,multiply(a,X1)),
inference(orient,[status(thm)],[t18370]) ).
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t25,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t79,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t25,t76]) ).
cnf(t145,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t79]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t97,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t23,t94]) ).
cnf(t158,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t97]) ).
cnf(t12,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(t81,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t109,plain,
identity = least_upper_bound(identity,sFlat1),
inference(cp,[status(thm)],[t23,t108]) ).
cnf(t18260,plain,
identity = least_upper_bound(sFlat1,identity),
inference(step,[status(thm)],[t109,t76]) ).
cnf(t117,plain,
least_upper_bound(sFlat1,identity) = identity,
inference(orient,[status(thm)],[t18260]) ).
cnf(t118,plain,
least_upper_bound(sFlat1,least_upper_bound(identity,X1)) = least_upper_bound(identity,X1),
inference(cp,[status(thm)],[t81,t117]) ).
cnf(t291,plain,
least_upper_bound(sFlat1,least_upper_bound(identity,X1)) = least_upper_bound(identity,X1),
inference(orient,[status(thm)],[t118]) ).
cnf(t295,plain,
sFlat1 = greatest_lower_bound(sFlat1,least_upper_bound(identity,X1)),
inference(cp,[status(thm)],[t25,t291]) ).
cnf(t296,plain,
greatest_lower_bound(sFlat1,least_upper_bound(identity,X1)) = sFlat1,
inference(orient,[status(thm)],[t295]) ).
cnf(t301,plain,
least_upper_bound(identity,X1) = least_upper_bound(least_upper_bound(identity,X1),sFlat1),
inference(cp,[status(thm)],[t158,t296]) ).
cnf(t18281,plain,
least_upper_bound(identity,X1) = least_upper_bound(identity,least_upper_bound(X1,sFlat1)),
inference(step,[status(thm)],[t301,t81]) ).
cnf(t529,plain,
least_upper_bound(identity,least_upper_bound(X1,sFlat1)) = least_upper_bound(identity,X1),
inference(orient,[status(thm)],[t18281]) ).
cnf(t533,plain,
least_upper_bound(identity,X1) = least_upper_bound(identity,least_upper_bound(sFlat1,X1)),
inference(cp,[status(thm)],[t529,t76]) ).
cnf(t637,plain,
least_upper_bound(identity,least_upper_bound(sFlat1,X1)) = least_upper_bound(identity,X1),
inference(orient,[status(thm)],[t533]) ).
cnf(t643,plain,
least_upper_bound(sFlat1,X1) = greatest_lower_bound(least_upper_bound(sFlat1,X1),least_upper_bound(identity,X1)),
inference(cp,[status(thm)],[t145,t637]) ).
cnf(t18087,plain,
greatest_lower_bound(least_upper_bound(sFlat1,X1),least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t643]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t52,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t53,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t52,t26]) ).
cnf(t124,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t53]) ).
cnf(t776,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t772,t124]) ).
cnf(t18496,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t776,t94]) ).
cnf(t6889,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t18496]) ).
cnf(t6918,plain,
greatest_lower_bound(identity,inverse(a)) = multiply(sFlat1,inverse(a)),
inference(cp,[status(thm)],[t6889,t108]) ).
cnf(t6954,plain,
greatest_lower_bound(identity,inverse(a)) = multiply(sFlat1,inverse(a)),
inference(orient,[status(thm)],[t6918]) ).
cnf(t6955,plain,
identity = least_upper_bound(identity,multiply(sFlat1,inverse(a))),
inference(cp,[status(thm)],[t23,t6954]) ).
cnf(t7018,plain,
least_upper_bound(identity,multiply(sFlat1,inverse(a))) = identity,
inference(orient,[status(thm)],[t6955]) ).
cnf(t18111,plain,
least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))) = greatest_lower_bound(least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))),identity),
inference(cp,[status(thm)],[t18087,t7018]) ).
cnf(t18749,plain,
multiply(sFlat1,least_upper_bound(identity,inverse(a))) = greatest_lower_bound(least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))),identity),
inference(step,[status(thm)],[t18111,t823]) ).
cnf(t272,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t269,t124]) ).
cnf(t18484,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t272,t76]) ).
cnf(t6618,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t18484]) ).
cnf(t6646,plain,
least_upper_bound(identity,inverse(a)) = multiply(sFlat0,inverse(a)),
inference(cp,[status(thm)],[t6618,t91]) ).
cnf(t6682,plain,
least_upper_bound(identity,inverse(a)) = multiply(sFlat0,inverse(a)),
inference(orient,[status(thm)],[t6646]) ).
cnf(t18750,plain,
multiply(sFlat1,multiply(sFlat0,inverse(a))) = greatest_lower_bound(least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))),identity),
inference(step,[status(thm)],[t18749,t6682]) ).
cnf(t898,plain,
multiply(least_upper_bound(identity,a),sFlat1) = least_upper_bound(sFlat1,multiply(sFlat1,a)),
inference(cp,[status(thm)],[t269,t894]) ).
cnf(t18297,plain,
multiply(sFlat0,sFlat1) = least_upper_bound(sFlat1,multiply(sFlat1,a)),
inference(step,[status(thm)],[t898,t91]) ).
cnf(t18298,plain,
multiply(sFlat0,sFlat1) = multiply(sFlat1,least_upper_bound(identity,a)),
inference(step,[status(thm)],[t18297,t823]) ).
cnf(t18299,plain,
multiply(sFlat0,sFlat1) = multiply(sFlat1,sFlat0),
inference(step,[status(thm)],[t18298,t91]) ).
cnf(t912,plain,
multiply(sFlat1,sFlat0) = multiply(sFlat0,sFlat1),
inference(orient,[status(thm)],[t18299]) ).
cnf(t926,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(multiply(sFlat0,sFlat1),X1),
inference(cp,[status(thm)],[t27,t912]) ).
cnf(t18319,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(sFlat0,multiply(sFlat1,X1)),
inference(step,[status(thm)],[t926,t27]) ).
cnf(t1396,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(sFlat0,multiply(sFlat1,X1)),
inference(orient,[status(thm)],[t18319]) ).
cnf(t18341,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(sFlat2,X1),
inference(step,[status(thm)],[t1396,t1909]) ).
cnf(t1910,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(sFlat2,X1),
inference(orient,[status(thm)],[t18341]) ).
cnf(t18751,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))),identity),
inference(step,[status(thm)],[t18750,t1910]) ).
cnf(t18752,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(identity,least_upper_bound(sFlat1,multiply(sFlat1,inverse(a)))),
inference(step,[status(thm)],[t18751,t94]) ).
cnf(t18753,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(identity,multiply(sFlat1,least_upper_bound(identity,inverse(a)))),
inference(step,[status(thm)],[t18752,t823]) ).
cnf(t18754,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(identity,multiply(sFlat1,multiply(sFlat0,inverse(a)))),
inference(step,[status(thm)],[t18753,t6682]) ).
cnf(t18755,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(identity,multiply(sFlat2,inverse(a))),
inference(step,[status(thm)],[t18754,t1910]) ).
cnf(t11,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(t98,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t93,plain,
identity = greatest_lower_bound(identity,sFlat0),
inference(cp,[status(thm)],[t25,t91]) ).
cnf(t18259,plain,
identity = greatest_lower_bound(sFlat0,identity),
inference(step,[status(thm)],[t93,t94]) ).
cnf(t114,plain,
greatest_lower_bound(sFlat0,identity) = identity,
inference(orient,[status(thm)],[t18259]) ).
cnf(t116,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,X1),
inference(cp,[status(thm)],[t98,t114]) ).
cnf(t254,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t116]) ).
cnf(t257,plain,
sFlat0 = least_upper_bound(sFlat0,greatest_lower_bound(identity,X1)),
inference(cp,[status(thm)],[t23,t254]) ).
cnf(t258,plain,
least_upper_bound(sFlat0,greatest_lower_bound(identity,X1)) = sFlat0,
inference(orient,[status(thm)],[t257]) ).
cnf(t262,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(greatest_lower_bound(identity,X1),sFlat0),
inference(cp,[status(thm)],[t145,t258]) ).
cnf(t18278,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(X1,sFlat0)),
inference(step,[status(thm)],[t262,t98]) ).
cnf(t485,plain,
greatest_lower_bound(identity,greatest_lower_bound(X1,sFlat0)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t18278]) ).
cnf(t490,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(sFlat0,X1)),
inference(cp,[status(thm)],[t485,t94]) ).
cnf(t613,plain,
greatest_lower_bound(identity,greatest_lower_bound(sFlat0,X1)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t490]) ).
cnf(t620,plain,
greatest_lower_bound(sFlat0,X1) = least_upper_bound(greatest_lower_bound(sFlat0,X1),greatest_lower_bound(identity,X1)),
inference(cp,[status(thm)],[t158,t613]) ).
cnf(t17769,plain,
least_upper_bound(greatest_lower_bound(sFlat0,X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(sFlat0,X1),
inference(orient,[status(thm)],[t620]) ).
cnf(t6692,plain,
identity = greatest_lower_bound(identity,multiply(sFlat0,inverse(a))),
inference(cp,[status(thm)],[t25,t6682]) ).
cnf(t6763,plain,
greatest_lower_bound(identity,multiply(sFlat0,inverse(a))) = identity,
inference(orient,[status(thm)],[t6692]) ).
cnf(t17792,plain,
greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))) = least_upper_bound(greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))),identity),
inference(cp,[status(thm)],[t17769,t6763]) ).
cnf(t18730,plain,
multiply(sFlat0,greatest_lower_bound(identity,inverse(a))) = least_upper_bound(greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))),identity),
inference(step,[status(thm)],[t17792,t797]) ).
cnf(t18731,plain,
multiply(sFlat0,multiply(sFlat1,inverse(a))) = least_upper_bound(greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))),identity),
inference(step,[status(thm)],[t18730,t6954]) ).
cnf(t18732,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))),identity),
inference(step,[status(thm)],[t18731,t1909]) ).
cnf(t18733,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(identity,greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a)))),
inference(step,[status(thm)],[t18732,t76]) ).
cnf(t18734,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(identity,multiply(sFlat0,greatest_lower_bound(identity,inverse(a)))),
inference(step,[status(thm)],[t18733,t797]) ).
cnf(t18735,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(identity,multiply(sFlat0,multiply(sFlat1,inverse(a)))),
inference(step,[status(thm)],[t18734,t6954]) ).
cnf(t18736,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(identity,multiply(sFlat2,inverse(a))),
inference(step,[status(thm)],[t18735,t1909]) ).
cnf(t17819,plain,
least_upper_bound(identity,multiply(sFlat2,inverse(a))) = multiply(sFlat2,inverse(a)),
inference(orient,[status(thm)],[t18736]) ).
cnf(t17827,plain,
identity = greatest_lower_bound(identity,multiply(sFlat2,inverse(a))),
inference(cp,[status(thm)],[t25,t17819]) ).
cnf(t17868,plain,
greatest_lower_bound(identity,multiply(sFlat2,inverse(a))) = identity,
inference(orient,[status(thm)],[t17827]) ).
cnf(t18756,plain,
multiply(sFlat2,inverse(a)) = identity,
inference(step,[status(thm)],[t18755,t17868]) ).
cnf(t18138,plain,
multiply(sFlat2,inverse(a)) = identity,
inference(orient,[status(thm)],[t18756]) ).
cnf(t18143,plain,
multiply(sFlat2,multiply(a,inverse(a))) = multiply(a,identity),
inference(cp,[status(thm)],[t2763,t18138]) ).
cnf(t18760,plain,
multiply(sFlat2,identity) = multiply(a,identity),
inference(step,[status(thm)],[t18143,t124]) ).
cnf(t18761,plain,
sFlat2 = multiply(a,identity),
inference(step,[status(thm)],[t18760,t140]) ).
cnf(t18762,plain,
sFlat2 = a,
inference(step,[status(thm)],[t18761,t140]) ).
cnf(t18178,plain,
a = sFlat2,
inference(orient,[status(thm)],[t18762]) ).
cnf(goal_0,negated_conjecture,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != sFlat2,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_0,t18178]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n026.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Wed Sep 23 13:59:01 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.01/7.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.01/7.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------