%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 01:25:37 PM UTC 2026
% Result : Unsatisfiable 15.14s 2.81s
% Output : CNFRefutation 15.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 21
% Syntax : Number of clauses : 260 ( 260 unt; 0 nHn; 145 RR)
% Number of literals : 260 ( 259 equ; 12 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 : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 178 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t15,axiom,
sFlat0 = inverse(b),
introduced(definition) ).
cnf(t108,plain,
inverse(b) = sFlat0,
inference(orient,[status(thm)],[t15]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t71,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t16,axiom,
sFlat1 = greatest_lower_bound(a,inverse(b)),
introduced(definition) ).
cnf(t85,plain,
greatest_lower_bound(a,inverse(b)) = sFlat1,
inference(orient,[status(thm)],[t16]) ).
cnf(t19162,plain,
greatest_lower_bound(a,sFlat0) = sFlat1,
inference(step,[status(thm)],[t85,t108]) ).
cnf(t110,plain,
greatest_lower_bound(a,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t19162]) ).
cnf(t19163,plain,
greatest_lower_bound(sFlat0,a) = sFlat1,
inference(step,[status(thm)],[t110,t71]) ).
cnf(t133,plain,
greatest_lower_bound(sFlat0,a) = sFlat1,
inference(orient,[status(thm)],[t19163]) ).
cnf(t17,axiom,
sFlat2 = inverse(greatest_lower_bound(a,inverse(b))),
introduced(definition) ).
cnf(t19161,plain,
sFlat2 = inverse(sFlat1),
inference(step,[status(thm)],[t17,t85]) ).
cnf(t106,plain,
inverse(sFlat1) = sFlat2,
inference(orient,[status(thm)],[t19161]) ).
cnf(t18,axiom,
sFlat3 = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
introduced(definition) ).
cnf(t51,plain,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) = sFlat3,
inference(orient,[status(thm)],[t18]) ).
cnf(t19157,plain,
multiply(a,inverse(sFlat1)) = sFlat3,
inference(step,[status(thm)],[t51,t85]) ).
cnf(t88,plain,
multiply(a,inverse(sFlat1)) = sFlat3,
inference(rw,[status(thm)],[t19157]) ).
cnf(t19164,plain,
multiply(a,sFlat2) = sFlat3,
inference(step,[status(thm)],[t88,t106]) ).
cnf(t138,plain,
multiply(a,sFlat2) = sFlat3,
inference(orient,[status(thm)],[t19164]) ).
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t89,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
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(t36,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t41,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t109,plain,
identity = multiply(sFlat0,b),
inference(cp,[status(thm)],[t41,t108]) ).
cnf(t123,plain,
multiply(sFlat0,b) = identity,
inference(orient,[status(thm)],[t109]) ).
cnf(t124,plain,
multiply(least_upper_bound(sFlat0,X1),b) = least_upper_bound(identity,multiply(X1,b)),
inference(cp,[status(thm)],[t36,t123]) ).
cnf(t1694,plain,
least_upper_bound(identity,multiply(X1,b)) = multiply(least_upper_bound(sFlat0,X1),b),
inference(orient,[status(thm)],[t124]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t37,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t36,t21]) ).
cnf(t1108,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t37]) ).
cnf(t10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t26,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t19,axiom,
sFlat4 = multiply(a,b),
introduced(definition) ).
cnf(t61,plain,
multiply(a,b) = sFlat4,
inference(orient,[status(thm)],[t19]) ).
cnf(t70,plain,
multiply(a,multiply(b,X1)) = multiply(sFlat4,X1),
inference(cp,[status(thm)],[t26,t61]) ).
cnf(t196,plain,
multiply(a,multiply(b,X1)) = multiply(sFlat4,X1),
inference(orient,[status(thm)],[t70]) ).
cnf(t50,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t26,t41]) ).
cnf(t19194,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t50,t21]) ).
cnf(t589,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t19194]) ).
cnf(t132,plain,
multiply(sFlat0,multiply(b,X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t26,t123]) ).
cnf(t19170,plain,
multiply(sFlat0,multiply(b,X1)) = X1,
inference(step,[status(thm)],[t132,t21]) ).
cnf(t187,plain,
multiply(sFlat0,multiply(b,X1)) = X1,
inference(orient,[status(thm)],[t19170]) ).
cnf(t596,plain,
multiply(b,X1) = multiply(inverse(sFlat0),X1),
inference(cp,[status(thm)],[t589,t187]) ).
cnf(t672,plain,
multiply(inverse(sFlat0),X1) = multiply(b,X1),
inference(orient,[status(thm)],[t596]) ).
cnf(t673,plain,
multiply(b,sFlat0) = identity,
inference(cp,[status(thm)],[t672,t41]) ).
cnf(t682,plain,
multiply(b,sFlat0) = identity,
inference(orient,[status(thm)],[t673]) ).
cnf(t685,plain,
multiply(sFlat4,sFlat0) = multiply(a,identity),
inference(cp,[status(thm)],[t196,t682]) ).
cnf(t147,plain,
multiply(a,multiply(sFlat2,X1)) = multiply(sFlat3,X1),
inference(cp,[status(thm)],[t26,t138]) ).
cnf(t285,plain,
multiply(a,multiply(sFlat2,X1)) = multiply(sFlat3,X1),
inference(orient,[status(thm)],[t147]) ).
cnf(t107,plain,
identity = multiply(sFlat2,sFlat1),
inference(cp,[status(thm)],[t41,t106]) ).
cnf(t113,plain,
multiply(sFlat2,sFlat1) = identity,
inference(orient,[status(thm)],[t107]) ).
cnf(t286,plain,
multiply(sFlat3,sFlat1) = multiply(a,identity),
inference(cp,[status(thm)],[t285,t113]) ).
cnf(t297,plain,
multiply(a,identity) = multiply(sFlat3,sFlat1),
inference(orient,[status(thm)],[t286]) ).
cnf(t19198,plain,
multiply(sFlat4,sFlat0) = multiply(sFlat3,sFlat1),
inference(step,[status(thm)],[t685,t297]) ).
cnf(t790,plain,
multiply(sFlat4,sFlat0) = multiply(sFlat3,sFlat1),
inference(orient,[status(thm)],[t19198]) ).
cnf(t122,plain,
multiply(sFlat2,multiply(sFlat1,X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t26,t113]) ).
cnf(t19169,plain,
multiply(sFlat2,multiply(sFlat1,X1)) = X1,
inference(step,[status(thm)],[t122,t21]) ).
cnf(t178,plain,
multiply(sFlat2,multiply(sFlat1,X1)) = X1,
inference(orient,[status(thm)],[t19169]) ).
cnf(t287,plain,
multiply(sFlat3,multiply(sFlat1,X1)) = multiply(a,X1),
inference(cp,[status(thm)],[t285,t178]) ).
cnf(t453,plain,
multiply(sFlat3,multiply(sFlat1,X1)) = multiply(a,X1),
inference(orient,[status(thm)],[t287]) ).
cnf(t604,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t589,t41]) ).
cnf(t869,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t604]) ).
cnf(t607,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t589,t589]) ).
cnf(t947,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t607]) ).
cnf(t19202,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t869,t947]) ).
cnf(t957,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t19202]) ).
cnf(t958,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t957]) ).
cnf(t962,plain,
multiply(a,identity) = multiply(sFlat3,sFlat1),
inference(cp,[status(thm)],[t453,t958]) ).
cnf(t19207,plain,
a = multiply(sFlat3,sFlat1),
inference(step,[status(thm)],[t962,t958]) ).
cnf(t973,plain,
multiply(sFlat3,sFlat1) = a,
inference(orient,[status(thm)],[t19207]) ).
cnf(t19208,plain,
multiply(sFlat4,sFlat0) = a,
inference(step,[status(thm)],[t790,t973]) ).
cnf(t974,plain,
multiply(sFlat4,sFlat0) = a,
inference(orient,[status(thm)],[t19208]) ).
cnf(t1118,plain,
multiply(least_upper_bound(identity,sFlat4),sFlat0) = least_upper_bound(sFlat0,a),
inference(cp,[status(thm)],[t1108,t974]) ).
cnf(t19219,plain,
multiply(least_upper_bound(sFlat4,identity),sFlat0) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t1118,t89]) ).
cnf(t20,axiom,
sFlat5 = least_upper_bound(multiply(a,b),identity),
introduced(definition) ).
cnf(t19158,plain,
sFlat5 = least_upper_bound(identity,multiply(a,b)),
inference(step,[status(thm)],[t20,t89]) ).
cnf(t19159,plain,
sFlat5 = least_upper_bound(identity,sFlat4),
inference(step,[status(thm)],[t19158,t61]) ).
cnf(t19160,plain,
sFlat5 = least_upper_bound(sFlat4,identity),
inference(step,[status(thm)],[t19159,t89]) ).
cnf(t103,plain,
least_upper_bound(sFlat4,identity) = sFlat5,
inference(orient,[status(thm)],[t19160]) ).
cnf(t19220,plain,
multiply(sFlat5,sFlat0) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t19219,t103]) ).
cnf(t1176,plain,
least_upper_bound(sFlat0,a) = multiply(sFlat5,sFlat0),
inference(orient,[status(thm)],[t19220]) ).
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(t30,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t45,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(multiply(X1,X2),identity),
inference(cp,[status(thm)],[t30,t41]) ).
cnf(t19428,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(step,[status(thm)],[t45,t71]) ).
cnf(t6445,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t19428]) ).
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(t75,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(t31,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t30,t21]) ).
cnf(t264,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t959,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t958,t947]) ).
cnf(t19206,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t959,t958]) ).
cnf(t970,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t19206]) ).
cnf(t972,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t41,t970]) ).
cnf(t988,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t972]) ).
cnf(t990,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t264,t988]) ).
cnf(t19612,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t990,t71]) ).
cnf(t13327,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t19612]) ).
cnf(t13404,plain,
greatest_lower_bound(identity,inverse(X1)) = multiply(greatest_lower_bound(X1,identity),inverse(X1)),
inference(cp,[status(thm)],[t13327,t71]) ).
cnf(t17753,plain,
multiply(greatest_lower_bound(X1,identity),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t13404]) ).
cnf(t64,plain,
multiply(greatest_lower_bound(a,X1),b) = greatest_lower_bound(sFlat4,multiply(X1,b)),
inference(cp,[status(thm)],[t30,t61]) ).
cnf(t1292,plain,
greatest_lower_bound(sFlat4,multiply(X1,b)) = multiply(greatest_lower_bound(a,X1),b),
inference(orient,[status(thm)],[t64]) ).
cnf(t1296,plain,
multiply(greatest_lower_bound(a,sFlat0),b) = greatest_lower_bound(sFlat4,identity),
inference(cp,[status(thm)],[t1292,t123]) ).
cnf(t19229,plain,
multiply(greatest_lower_bound(sFlat0,a),b) = greatest_lower_bound(sFlat4,identity),
inference(step,[status(thm)],[t1296,t71]) ).
cnf(t19230,plain,
multiply(sFlat1,b) = greatest_lower_bound(sFlat4,identity),
inference(step,[status(thm)],[t19229,t133]) ).
cnf(t1303,plain,
greatest_lower_bound(sFlat4,identity) = multiply(sFlat1,b),
inference(orient,[status(thm)],[t19230]) ).
cnf(t17755,plain,
greatest_lower_bound(identity,inverse(sFlat4)) = multiply(multiply(sFlat1,b),inverse(sFlat4)),
inference(cp,[status(thm)],[t17753,t1303]) ).
cnf(t19706,plain,
greatest_lower_bound(identity,inverse(sFlat4)) = multiply(sFlat1,multiply(b,inverse(sFlat4))),
inference(step,[status(thm)],[t17755,t26]) ).
cnf(t600,plain,
multiply(b,X1) = multiply(inverse(a),multiply(sFlat4,X1)),
inference(cp,[status(thm)],[t589,t196]) ).
cnf(t4394,plain,
multiply(inverse(a),multiply(sFlat4,X1)) = multiply(b,X1),
inference(orient,[status(thm)],[t600]) ).
cnf(t4401,plain,
multiply(b,inverse(sFlat4)) = multiply(inverse(a),identity),
inference(cp,[status(thm)],[t4394,t988]) ).
cnf(t19385,plain,
multiply(b,inverse(sFlat4)) = inverse(a),
inference(step,[status(thm)],[t4401,t958]) ).
cnf(t4422,plain,
multiply(b,inverse(sFlat4)) = inverse(a),
inference(orient,[status(thm)],[t19385]) ).
cnf(t19707,plain,
greatest_lower_bound(identity,inverse(sFlat4)) = multiply(sFlat1,inverse(a)),
inference(step,[status(thm)],[t19706,t4422]) ).
cnf(t590,plain,
multiply(sFlat1,X1) = multiply(inverse(sFlat3),multiply(a,X1)),
inference(cp,[status(thm)],[t589,t453]) ).
cnf(t4268,plain,
multiply(inverse(sFlat3),multiply(a,X1)) = multiply(sFlat1,X1),
inference(orient,[status(thm)],[t590]) ).
cnf(t4276,plain,
multiply(sFlat1,inverse(a)) = multiply(inverse(sFlat3),identity),
inference(cp,[status(thm)],[t4268,t988]) ).
cnf(t19375,plain,
multiply(sFlat1,inverse(a)) = inverse(sFlat3),
inference(step,[status(thm)],[t4276,t958]) ).
cnf(t4297,plain,
multiply(sFlat1,inverse(a)) = inverse(sFlat3),
inference(orient,[status(thm)],[t19375]) ).
cnf(t19708,plain,
greatest_lower_bound(identity,inverse(sFlat4)) = inverse(sFlat3),
inference(step,[status(thm)],[t19707,t4297]) ).
cnf(t17785,plain,
greatest_lower_bound(identity,inverse(sFlat4)) = inverse(sFlat3),
inference(orient,[status(thm)],[t19708]) ).
cnf(t17793,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(sFlat4),X1)) = greatest_lower_bound(inverse(sFlat3),X1),
inference(cp,[status(thm)],[t75,t17785]) ).
cnf(t19003,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(sFlat4),X1)) = greatest_lower_bound(inverse(sFlat3),X1),
inference(orient,[status(thm)],[t17793]) ).
cnf(t83,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X2,X1),X3),
inference(cp,[status(thm)],[t75,t71]) ).
cnf(t19646,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)),
inference(step,[status(thm)],[t83,t75]) ).
cnf(t15221,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)),
inference(orient,[status(thm)],[t19646]) ).
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(t92,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t23,t89]) ).
cnf(t163,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t92]) ).
cnf(t1112,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t1108,t988]) ).
cnf(t19616,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t1112,t89]) ).
cnf(t13484,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t19616]) ).
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(t93,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(t1,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
least_upper_bound(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t97,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(cp,[status(thm)],[t93,t24]) ).
cnf(t209,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t97]) ).
cnf(t13504,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) = multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,X1))),
inference(cp,[status(thm)],[t13484,t209]) ).
cnf(t19617,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) = identity,
inference(step,[status(thm)],[t13504,t988]) ).
cnf(t13540,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X1))) = identity,
inference(orient,[status(thm)],[t19617]) ).
cnf(t13551,plain,
identity = least_upper_bound(identity,inverse(least_upper_bound(X1,identity))),
inference(cp,[status(thm)],[t13540,t89]) ).
cnf(t13571,plain,
least_upper_bound(identity,inverse(least_upper_bound(X1,identity))) = identity,
inference(orient,[status(thm)],[t13551]) ).
cnf(t7,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t25,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t167,plain,
identity = greatest_lower_bound(identity,sFlat5),
inference(cp,[status(thm)],[t163,t103]) ).
cnf(t19168,plain,
identity = greatest_lower_bound(sFlat5,identity),
inference(step,[status(thm)],[t167,t71]) ).
cnf(t172,plain,
greatest_lower_bound(sFlat5,identity) = identity,
inference(orient,[status(thm)],[t19168]) ).
cnf(t174,plain,
sFlat5 = least_upper_bound(sFlat5,identity),
inference(cp,[status(thm)],[t25,t172]) ).
cnf(t175,plain,
least_upper_bound(sFlat5,identity) = sFlat5,
inference(orient,[status(thm)],[t174]) ).
cnf(t13573,plain,
identity = least_upper_bound(identity,inverse(sFlat5)),
inference(cp,[status(thm)],[t13571,t175]) ).
cnf(t13598,plain,
least_upper_bound(identity,inverse(sFlat5)) = identity,
inference(orient,[status(thm)],[t13573]) ).
cnf(t13604,plain,
inverse(sFlat5) = greatest_lower_bound(inverse(sFlat5),identity),
inference(cp,[status(thm)],[t163,t13598]) ).
cnf(t19620,plain,
inverse(sFlat5) = greatest_lower_bound(identity,inverse(sFlat5)),
inference(step,[status(thm)],[t13604,t71]) ).
cnf(t13635,plain,
greatest_lower_bound(identity,inverse(sFlat5)) = inverse(sFlat5),
inference(orient,[status(thm)],[t19620]) ).
cnf(t15355,plain,
greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(sFlat5))) = greatest_lower_bound(X1,inverse(sFlat5)),
inference(cp,[status(thm)],[t15221,t13635]) ).
cnf(t18801,plain,
greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(sFlat5))) = greatest_lower_bound(X1,inverse(sFlat5)),
inference(orient,[status(thm)],[t15355]) ).
cnf(t19004,plain,
greatest_lower_bound(inverse(sFlat3),inverse(sFlat5)) = greatest_lower_bound(inverse(sFlat4),inverse(sFlat5)),
inference(cp,[status(thm)],[t19003,t18801]) ).
cnf(t19048,plain,
greatest_lower_bound(inverse(sFlat4),inverse(sFlat5)) = greatest_lower_bound(inverse(sFlat3),inverse(sFlat5)),
inference(orient,[status(thm)],[t19004]) ).
cnf(t19056,plain,
greatest_lower_bound(identity,multiply(inverse(sFlat4),sFlat5)) = multiply(greatest_lower_bound(inverse(sFlat3),inverse(sFlat5)),sFlat5),
inference(cp,[status(thm)],[t6445,t19048]) ).
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(t49,plain,
multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity),
inference(cp,[status(thm)],[t27,t41]) ).
cnf(t19542,plain,
multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)),
inference(step,[status(thm)],[t49,t71]) ).
cnf(t9026,plain,
multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t19542]) ).
cnf(t19750,plain,
multiply(inverse(sFlat4),greatest_lower_bound(sFlat5,sFlat4)) = multiply(greatest_lower_bound(inverse(sFlat3),inverse(sFlat5)),sFlat5),
inference(step,[status(thm)],[t19056,t9026]) ).
cnf(t19751,plain,
multiply(inverse(sFlat4),greatest_lower_bound(sFlat4,sFlat5)) = multiply(greatest_lower_bound(inverse(sFlat3),inverse(sFlat5)),sFlat5),
inference(step,[status(thm)],[t19750,t71]) ).
cnf(t104,plain,
sFlat4 = greatest_lower_bound(sFlat4,sFlat5),
inference(cp,[status(thm)],[t23,t103]) ).
cnf(t111,plain,
greatest_lower_bound(sFlat4,sFlat5) = sFlat4,
inference(orient,[status(thm)],[t104]) ).
cnf(t19752,plain,
multiply(inverse(sFlat4),sFlat4) = multiply(greatest_lower_bound(inverse(sFlat3),inverse(sFlat5)),sFlat5),
inference(step,[status(thm)],[t19751,t111]) ).
cnf(t19753,plain,
identity = multiply(greatest_lower_bound(inverse(sFlat3),inverse(sFlat5)),sFlat5),
inference(step,[status(thm)],[t19752,t41]) ).
cnf(t19754,plain,
identity = greatest_lower_bound(identity,multiply(inverse(sFlat3),sFlat5)),
inference(step,[status(thm)],[t19753,t6445]) ).
cnf(t19755,plain,
identity = multiply(inverse(sFlat3),greatest_lower_bound(sFlat5,sFlat3)),
inference(step,[status(thm)],[t19754,t9026]) ).
cnf(t19756,plain,
identity = multiply(inverse(sFlat3),greatest_lower_bound(sFlat3,sFlat5)),
inference(step,[status(thm)],[t19755,t71]) ).
cnf(t105,plain,
least_upper_bound(sFlat4,least_upper_bound(identity,X1)) = least_upper_bound(sFlat5,X1),
inference(cp,[status(thm)],[t93,t103]) ).
cnf(t213,plain,
least_upper_bound(sFlat4,least_upper_bound(identity,X1)) = least_upper_bound(sFlat5,X1),
inference(orient,[status(thm)],[t105]) ).
cnf(t217,plain,
least_upper_bound(sFlat5,X1) = least_upper_bound(sFlat4,least_upper_bound(X1,identity)),
inference(cp,[status(thm)],[t213,t89]) ).
cnf(t360,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,identity)) = least_upper_bound(sFlat5,X1),
inference(orient,[status(thm)],[t217]) ).
cnf(t139,plain,
multiply(least_upper_bound(a,X1),sFlat2) = least_upper_bound(sFlat3,multiply(X1,sFlat2)),
inference(cp,[status(thm)],[t36,t138]) ).
cnf(t1842,plain,
least_upper_bound(sFlat3,multiply(X1,sFlat2)) = multiply(least_upper_bound(a,X1),sFlat2),
inference(orient,[status(thm)],[t139]) ).
cnf(t598,plain,
multiply(sFlat1,X1) = multiply(inverse(sFlat2),X1),
inference(cp,[status(thm)],[t589,t178]) ).
cnf(t804,plain,
multiply(inverse(sFlat2),X1) = multiply(sFlat1,X1),
inference(orient,[status(thm)],[t598]) ).
cnf(t805,plain,
multiply(sFlat1,sFlat2) = identity,
inference(cp,[status(thm)],[t804,t41]) ).
cnf(t816,plain,
multiply(sFlat1,sFlat2) = identity,
inference(orient,[status(thm)],[t805]) ).
cnf(t1846,plain,
multiply(least_upper_bound(a,sFlat1),sFlat2) = least_upper_bound(sFlat3,identity),
inference(cp,[status(thm)],[t1842,t816]) ).
cnf(t19256,plain,
multiply(least_upper_bound(sFlat1,a),sFlat2) = least_upper_bound(sFlat3,identity),
inference(step,[status(thm)],[t1846,t89]) ).
cnf(t74,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t25,t71]) ).
cnf(t148,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t74]) ).
cnf(t151,plain,
a = least_upper_bound(a,sFlat1),
inference(cp,[status(thm)],[t148,t133]) ).
cnf(t19165,plain,
a = least_upper_bound(sFlat1,a),
inference(step,[status(thm)],[t151,t89]) ).
cnf(t155,plain,
least_upper_bound(sFlat1,a) = a,
inference(orient,[status(thm)],[t19165]) ).
cnf(t19257,plain,
multiply(a,sFlat2) = least_upper_bound(sFlat3,identity),
inference(step,[status(thm)],[t19256,t155]) ).
cnf(t19258,plain,
sFlat3 = least_upper_bound(sFlat3,identity),
inference(step,[status(thm)],[t19257,t138]) ).
cnf(t1856,plain,
least_upper_bound(sFlat3,identity) = sFlat3,
inference(orient,[status(thm)],[t19258]) ).
cnf(t1857,plain,
least_upper_bound(sFlat5,sFlat3) = least_upper_bound(sFlat4,sFlat3),
inference(cp,[status(thm)],[t360,t1856]) ).
cnf(t19260,plain,
least_upper_bound(sFlat3,sFlat5) = least_upper_bound(sFlat4,sFlat3),
inference(step,[status(thm)],[t1857,t89]) ).
cnf(t19261,plain,
least_upper_bound(sFlat3,sFlat5) = least_upper_bound(sFlat3,sFlat4),
inference(step,[status(thm)],[t19260,t89]) ).
cnf(t1864,plain,
least_upper_bound(sFlat3,sFlat5) = least_upper_bound(sFlat3,sFlat4),
inference(orient,[status(thm)],[t19261]) ).
cnf(t1867,plain,
sFlat5 = greatest_lower_bound(sFlat5,least_upper_bound(sFlat3,sFlat4)),
inference(cp,[status(thm)],[t163,t1864]) ).
cnf(t1871,plain,
greatest_lower_bound(sFlat5,least_upper_bound(sFlat3,sFlat4)) = sFlat5,
inference(orient,[status(thm)],[t1867]) ).
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(t29,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t66,plain,
multiply(a,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,multiply(a,X1)),
inference(cp,[status(thm)],[t29,t61]) ).
cnf(t1421,plain,
least_upper_bound(sFlat4,multiply(a,X1)) = multiply(a,least_upper_bound(b,X1)),
inference(orient,[status(thm)],[t66]) ).
cnf(t1425,plain,
multiply(a,least_upper_bound(b,sFlat2)) = least_upper_bound(sFlat4,sFlat3),
inference(cp,[status(thm)],[t1421,t138]) ).
cnf(t19235,plain,
multiply(a,least_upper_bound(sFlat2,b)) = least_upper_bound(sFlat4,sFlat3),
inference(step,[status(thm)],[t1425,t89]) ).
cnf(t19236,plain,
multiply(a,least_upper_bound(sFlat2,b)) = least_upper_bound(sFlat3,sFlat4),
inference(step,[status(thm)],[t19235,t89]) ).
cnf(t1433,plain,
multiply(a,least_upper_bound(sFlat2,b)) = least_upper_bound(sFlat3,sFlat4),
inference(orient,[status(thm)],[t19236]) ).
cnf(t691,plain,
multiply(b,least_upper_bound(sFlat0,X1)) = least_upper_bound(identity,multiply(b,X1)),
inference(cp,[status(thm)],[t29,t682]) ).
cnf(t2256,plain,
least_upper_bound(identity,multiply(b,X1)) = multiply(b,least_upper_bound(sFlat0,X1)),
inference(orient,[status(thm)],[t691]) ).
cnf(t114,plain,
multiply(least_upper_bound(sFlat2,X1),sFlat1) = least_upper_bound(identity,multiply(X1,sFlat1)),
inference(cp,[status(thm)],[t36,t113]) ).
cnf(t1542,plain,
least_upper_bound(identity,multiply(X1,sFlat1)) = multiply(least_upper_bound(sFlat2,X1),sFlat1),
inference(orient,[status(thm)],[t114]) ).
cnf(t2257,plain,
multiply(b,least_upper_bound(sFlat0,sFlat1)) = multiply(least_upper_bound(sFlat2,b),sFlat1),
inference(cp,[status(thm)],[t2256,t1542]) ).
cnf(t135,plain,
sFlat0 = least_upper_bound(sFlat0,sFlat1),
inference(cp,[status(thm)],[t25,t133]) ).
cnf(t136,plain,
least_upper_bound(sFlat0,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t135]) ).
cnf(t19280,plain,
multiply(b,sFlat0) = multiply(least_upper_bound(sFlat2,b),sFlat1),
inference(step,[status(thm)],[t2257,t136]) ).
cnf(t19281,plain,
identity = multiply(least_upper_bound(sFlat2,b),sFlat1),
inference(step,[status(thm)],[t19280,t682]) ).
cnf(t2267,plain,
multiply(least_upper_bound(sFlat2,b),sFlat1) = identity,
inference(orient,[status(thm)],[t19281]) ).
cnf(t2269,plain,
sFlat1 = multiply(inverse(least_upper_bound(sFlat2,b)),identity),
inference(cp,[status(thm)],[t589,t2267]) ).
cnf(t19282,plain,
sFlat1 = inverse(least_upper_bound(sFlat2,b)),
inference(step,[status(thm)],[t2269,t958]) ).
cnf(t2286,plain,
inverse(least_upper_bound(sFlat2,b)) = sFlat1,
inference(orient,[status(thm)],[t19282]) ).
cnf(t2287,plain,
least_upper_bound(sFlat2,b) = inverse(sFlat1),
inference(cp,[status(thm)],[t970,t2286]) ).
cnf(t19283,plain,
least_upper_bound(sFlat2,b) = sFlat2,
inference(step,[status(thm)],[t2287,t106]) ).
cnf(t2291,plain,
least_upper_bound(sFlat2,b) = sFlat2,
inference(orient,[status(thm)],[t19283]) ).
cnf(t19284,plain,
multiply(a,sFlat2) = least_upper_bound(sFlat3,sFlat4),
inference(step,[status(thm)],[t1433,t2291]) ).
cnf(t19285,plain,
sFlat3 = least_upper_bound(sFlat3,sFlat4),
inference(step,[status(thm)],[t19284,t138]) ).
cnf(t2294,plain,
sFlat3 = least_upper_bound(sFlat3,sFlat4),
inference(rw,[status(thm)],[t19285]) ).
cnf(t2299,plain,
least_upper_bound(sFlat3,sFlat4) = sFlat3,
inference(orient,[status(thm)],[t2294]) ).
cnf(t19291,plain,
greatest_lower_bound(sFlat5,sFlat3) = sFlat5,
inference(step,[status(thm)],[t1871,t2299]) ).
cnf(t2305,plain,
greatest_lower_bound(sFlat5,sFlat3) = sFlat5,
inference(rw,[status(thm)],[t19291]) ).
cnf(t19292,plain,
greatest_lower_bound(sFlat3,sFlat5) = sFlat5,
inference(step,[status(thm)],[t2305,t71]) ).
cnf(t2310,plain,
greatest_lower_bound(sFlat3,sFlat5) = sFlat5,
inference(orient,[status(thm)],[t19292]) ).
cnf(t19757,plain,
identity = multiply(inverse(sFlat3),sFlat5),
inference(step,[status(thm)],[t19756,t2310]) ).
cnf(t19064,plain,
multiply(inverse(sFlat3),sFlat5) = identity,
inference(orient,[status(thm)],[t19757]) ).
cnf(t19067,plain,
sFlat5 = multiply(inverse(inverse(sFlat3)),identity),
inference(cp,[status(thm)],[t589,t19064]) ).
cnf(t19758,plain,
sFlat5 = multiply(sFlat3,identity),
inference(step,[status(thm)],[t19067,t947]) ).
cnf(t818,plain,
multiply(a,sFlat2) = multiply(sFlat3,identity),
inference(cp,[status(thm)],[t453,t816]) ).
cnf(t19201,plain,
sFlat3 = multiply(sFlat3,identity),
inference(step,[status(thm)],[t818,t138]) ).
cnf(t857,plain,
multiply(sFlat3,identity) = sFlat3,
inference(orient,[status(thm)],[t19201]) ).
cnf(t19759,plain,
sFlat5 = sFlat3,
inference(step,[status(thm)],[t19758,t857]) ).
cnf(t19093,plain,
sFlat5 = sFlat3,
inference(orient,[status(thm)],[t19759]) ).
cnf(t19766,plain,
least_upper_bound(sFlat0,a) = multiply(sFlat3,sFlat0),
inference(step,[status(thm)],[t1176,t19093]) ).
cnf(t19100,plain,
least_upper_bound(sFlat0,a) = multiply(sFlat3,sFlat0),
inference(orient,[status(thm)],[t19766]) ).
cnf(goal_0,negated_conjecture,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != least_upper_bound(multiply(a,b),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a,inverse(greatest_lower_bound(a,sFlat0))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[goal_0,t108]) ).
cnf(g0_1,plain,
multiply(a,inverse(greatest_lower_bound(sFlat0,a))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_0,t71]) ).
cnf(g0_2,plain,
multiply(a,inverse(sFlat1)) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_1,t133]) ).
cnf(g0_3,plain,
multiply(a,sFlat2) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_2,t106]) ).
cnf(g0_4,plain,
sFlat3 != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_3,t138]) ).
cnf(g0_5,plain,
sFlat3 != least_upper_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[g0_4,t89]) ).
cnf(g0_6,plain,
sFlat3 != multiply(least_upper_bound(sFlat0,a),b),
inference(rw,[status(thm)],[g0_5,t1694]) ).
cnf(g0_7,plain,
sFlat3 != multiply(multiply(sFlat3,sFlat0),b),
inference(rw,[status(thm)],[g0_6,t19100]) ).
cnf(g0_8,plain,
sFlat3 != multiply(sFlat3,multiply(sFlat0,b)),
inference(rw,[status(thm)],[g0_7,t26]) ).
cnf(g0_9,plain,
sFlat3 != multiply(sFlat3,identity),
inference(rw,[status(thm)],[g0_8,t123]) ).
cnf(g0_10,plain,
sFlat3 != sFlat3,
inference(rw,[status(thm)],[g0_9,t958]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:03:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.14/2.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.14/2.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------