%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 6.36s 1.64s
% Output : CNFRefutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 18
% Syntax : Number of clauses : 185 ( 185 unt; 0 nHn; 96 RR)
% Number of literals : 185 ( 184 equ; 15 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 : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 135 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
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(t76,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(t15,axiom,
sFlat0 = multiply(a,b),
introduced(definition) ).
cnf(t51,plain,
multiply(a,b) = sFlat0,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sFlat1 = least_upper_bound(multiply(a,b),identity),
introduced(definition) ).
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t71,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t3426,plain,
sFlat1 = least_upper_bound(identity,multiply(a,b)),
inference(step,[status(thm)],[t16,t71]) ).
cnf(t3427,plain,
sFlat1 = least_upper_bound(identity,sFlat0),
inference(step,[status(thm)],[t3426,t51]) ).
cnf(t3428,plain,
sFlat1 = least_upper_bound(sFlat0,identity),
inference(step,[status(thm)],[t3427,t71]) ).
cnf(t86,plain,
least_upper_bound(sFlat0,identity) = sFlat1,
inference(orient,[status(thm)],[t3428]) ).
cnf(t87,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(cp,[status(thm)],[t76,t86]) ).
cnf(t176,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t87]) ).
cnf(t17,axiom,
sFlat2 = least_upper_bound(a,identity),
introduced(definition) ).
cnf(t3433,plain,
sFlat2 = least_upper_bound(identity,a),
inference(step,[status(thm)],[t17,t71]) ).
cnf(t92,plain,
least_upper_bound(identity,a) = sFlat2,
inference(orient,[status(thm)],[t3433]) ).
cnf(t18,axiom,
sFlat3 = least_upper_bound(b,identity),
introduced(definition) ).
cnf(t3435,plain,
sFlat3 = least_upper_bound(identity,b),
inference(step,[status(thm)],[t18,t71]) ).
cnf(t96,plain,
least_upper_bound(identity,b) = sFlat3,
inference(orient,[status(thm)],[t3435]) ).
cnf(t19,axiom,
sFlat4 = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
introduced(definition) ).
cnf(t36,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = sFlat4,
inference(orient,[status(thm)],[t19]) ).
cnf(t75,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = sFlat4,
inference(rw,[status(thm)],[t36]) ).
cnf(t3576,plain,
multiply(least_upper_bound(identity,a),least_upper_bound(b,identity)) = sFlat4,
inference(step,[status(thm)],[t75,t71]) ).
cnf(t3577,plain,
multiply(sFlat2,least_upper_bound(b,identity)) = sFlat4,
inference(step,[status(thm)],[t3576,t92]) ).
cnf(t3578,plain,
multiply(sFlat2,least_upper_bound(identity,b)) = sFlat4,
inference(step,[status(thm)],[t3577,t71]) ).
cnf(t3579,plain,
multiply(sFlat2,sFlat3) = sFlat4,
inference(step,[status(thm)],[t3578,t96]) ).
cnf(t2585,plain,
multiply(sFlat2,sFlat3) = sFlat4,
inference(orient,[status(thm)],[t3579]) ).
cnf(t1,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22,plain,
least_upper_bound(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t80,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(cp,[status(thm)],[t76,t22]) ).
cnf(t170,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t80]) ).
cnf(t97,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(sFlat3,X1),
inference(cp,[status(thm)],[t76,t96]) ).
cnf(t278,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t97]) ).
cnf(t285,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(identity,least_upper_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t170,t278]) ).
cnf(t3463,plain,
least_upper_bound(sFlat3,X1) = least_upper_bound(identity,least_upper_bound(sFlat3,X1)),
inference(step,[status(thm)],[t285,t278]) ).
cnf(t539,plain,
least_upper_bound(identity,least_upper_bound(sFlat3,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t3463]) ).
cnf(t7,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)],[t7]) ).
cnf(t5,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)],[t5]) ).
cnf(t98,plain,
identity = greatest_lower_bound(identity,sFlat3),
inference(cp,[status(thm)],[t25,t96]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t99,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t3437,plain,
identity = greatest_lower_bound(sFlat3,identity),
inference(step,[status(thm)],[t98,t99]) ).
cnf(t118,plain,
greatest_lower_bound(sFlat3,identity) = identity,
inference(orient,[status(thm)],[t3437]) ).
cnf(t119,plain,
sFlat3 = least_upper_bound(sFlat3,identity),
inference(cp,[status(thm)],[t23,t118]) ).
cnf(t123,plain,
least_upper_bound(sFlat3,identity) = sFlat3,
inference(orient,[status(thm)],[t119]) ).
cnf(t124,plain,
least_upper_bound(sFlat3,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(cp,[status(thm)],[t76,t123]) ).
cnf(t357,plain,
least_upper_bound(sFlat3,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t124]) ).
cnf(t93,plain,
least_upper_bound(identity,least_upper_bound(a,X1)) = least_upper_bound(sFlat2,X1),
inference(cp,[status(thm)],[t76,t92]) ).
cnf(t222,plain,
least_upper_bound(identity,least_upper_bound(a,X1)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t93]) ).
cnf(t226,plain,
least_upper_bound(sFlat2,X1) = least_upper_bound(identity,least_upper_bound(X1,a)),
inference(cp,[status(thm)],[t222,t71]) ).
cnf(t479,plain,
least_upper_bound(identity,least_upper_bound(X1,a)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t226]) ).
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(t27,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t58,plain,
multiply(a,least_upper_bound(b,X1)) = least_upper_bound(sFlat0,multiply(a,X1)),
inference(cp,[status(thm)],[t27,t51]) ).
cnf(t1133,plain,
least_upper_bound(sFlat0,multiply(a,X1)) = multiply(a,least_upper_bound(b,X1)),
inference(orient,[status(thm)],[t58]) ).
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(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t61,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t70,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t26,t61]) ).
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(t3493,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t70,t21]) ).
cnf(t841,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t3493]) ).
cnf(t842,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t841,t61]) ).
cnf(t882,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t842]) ).
cnf(t847,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t841,t841]) ).
cnf(t921,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t847]) ).
cnf(t3494,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t882,t921]) ).
cnf(t931,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t3494]) ).
cnf(t932,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t931]) ).
cnf(t1137,plain,
multiply(a,least_upper_bound(b,identity)) = least_upper_bound(sFlat0,a),
inference(cp,[status(thm)],[t1133,t932]) ).
cnf(t3506,plain,
multiply(a,least_upper_bound(identity,b)) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t1137,t71]) ).
cnf(t3507,plain,
multiply(a,sFlat3) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t3506,t96]) ).
cnf(t1163,plain,
least_upper_bound(sFlat0,a) = multiply(a,sFlat3),
inference(orient,[status(thm)],[t3507]) ).
cnf(t1166,plain,
least_upper_bound(sFlat2,sFlat0) = least_upper_bound(identity,multiply(a,sFlat3)),
inference(cp,[status(thm)],[t479,t1163]) ).
cnf(t3510,plain,
least_upper_bound(sFlat0,sFlat2) = least_upper_bound(identity,multiply(a,sFlat3)),
inference(step,[status(thm)],[t1166,t71]) ).
cnf(t1185,plain,
least_upper_bound(identity,multiply(a,sFlat3)) = least_upper_bound(sFlat0,sFlat2),
inference(orient,[status(thm)],[t3510]) ).
cnf(t1187,plain,
least_upper_bound(sFlat3,multiply(a,sFlat3)) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(cp,[status(thm)],[t357,t1185]) ).
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(t30,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t31,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t30,t21]) ).
cnf(t239,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t3513,plain,
multiply(least_upper_bound(identity,a),sFlat3) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(step,[status(thm)],[t1187,t239]) ).
cnf(t3514,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(step,[status(thm)],[t3513,t92]) ).
cnf(t1195,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t3514]) ).
cnf(t1197,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = least_upper_bound(identity,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t539,t1195]) ).
cnf(t3515,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(identity,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1197,t1195]) ).
cnf(t1210,plain,
least_upper_bound(identity,multiply(sFlat2,sFlat3)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t3515]) ).
cnf(t1212,plain,
least_upper_bound(sFlat1,multiply(sFlat2,sFlat3)) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t176,t1210]) ).
cnf(t1555,plain,
least_upper_bound(sFlat1,multiply(sFlat2,sFlat3)) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(orient,[status(thm)],[t1212]) ).
cnf(t3586,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1555,t2585]) ).
cnf(t3587,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(step,[status(thm)],[t3586,t2585]) ).
cnf(t2613,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(rw,[status(thm)],[t3587]) ).
cnf(t2641,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(orient,[status(thm)],[t2613]) ).
cnf(t3590,plain,
least_upper_bound(identity,sFlat4) = multiply(sFlat2,sFlat3),
inference(step,[status(thm)],[t1210,t2585]) ).
cnf(t3591,plain,
least_upper_bound(identity,sFlat4) = sFlat4,
inference(step,[status(thm)],[t3590,t2585]) ).
cnf(t2615,plain,
least_upper_bound(identity,sFlat4) = sFlat4,
inference(rw,[status(thm)],[t3591]) ).
cnf(t3595,plain,
least_upper_bound(sFlat4,identity) = sFlat4,
inference(step,[status(thm)],[t2615,t71]) ).
cnf(t2623,plain,
least_upper_bound(sFlat4,identity) = sFlat4,
inference(orient,[status(thm)],[t3595]) ).
cnf(t2629,plain,
least_upper_bound(sFlat4,least_upper_bound(identity,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t76,t2623]) ).
cnf(t2962,plain,
least_upper_bound(sFlat4,least_upper_bound(identity,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t2629]) ).
cnf(t2971,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t2962,t278]) ).
cnf(t102,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t23,t99]) ).
cnf(t153,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t102]) ).
cnf(t74,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t25,t71]) ).
cnf(t125,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t74]) ).
cnf(t281,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = least_upper_bound(identity,b),
inference(cp,[status(thm)],[t278,t23]) ).
cnf(t3448,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = sFlat3,
inference(step,[status(thm)],[t281,t96]) ).
cnf(t288,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = sFlat3,
inference(orient,[status(thm)],[t3448]) ).
cnf(t290,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(greatest_lower_bound(b,X1),sFlat3),
inference(cp,[status(thm)],[t125,t288]) ).
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(t103,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(t3464,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(b,greatest_lower_bound(X1,sFlat3)),
inference(step,[status(thm)],[t290,t103]) ).
cnf(t554,plain,
greatest_lower_bound(b,greatest_lower_bound(X1,sFlat3)) = greatest_lower_bound(b,X1),
inference(orient,[status(thm)],[t3464]) ).
cnf(t557,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(b,greatest_lower_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t554,t99]) ).
cnf(t744,plain,
greatest_lower_bound(b,greatest_lower_bound(sFlat3,X1)) = greatest_lower_bound(b,X1),
inference(orient,[status(thm)],[t557]) ).
cnf(t747,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = greatest_lower_bound(b,sFlat3),
inference(cp,[status(thm)],[t744,t25]) ).
cnf(t3491,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = greatest_lower_bound(sFlat3,b),
inference(step,[status(thm)],[t747,t99]) ).
cnf(t131,plain,
b = greatest_lower_bound(b,sFlat3),
inference(cp,[status(thm)],[t125,t96]) ).
cnf(t3439,plain,
b = greatest_lower_bound(sFlat3,b),
inference(step,[status(thm)],[t131,t99]) ).
cnf(t138,plain,
greatest_lower_bound(sFlat3,b) = b,
inference(orient,[status(thm)],[t3439]) ).
cnf(t3492,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = b,
inference(step,[status(thm)],[t3491,t138]) ).
cnf(t824,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = b,
inference(orient,[status(thm)],[t3492]) ).
cnf(t1196,plain,
b = greatest_lower_bound(b,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t824,t1195]) ).
cnf(t1204,plain,
greatest_lower_bound(b,multiply(sFlat2,sFlat3)) = b,
inference(orient,[status(thm)],[t1196]) ).
cnf(t1205,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(multiply(sFlat2,sFlat3),b),
inference(cp,[status(thm)],[t153,t1204]) ).
cnf(t3516,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(b,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1205,t71]) ).
cnf(t1214,plain,
least_upper_bound(b,multiply(sFlat2,sFlat3)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t3516]) ).
cnf(t3588,plain,
least_upper_bound(b,sFlat4) = multiply(sFlat2,sFlat3),
inference(step,[status(thm)],[t1214,t2585]) ).
cnf(t3589,plain,
least_upper_bound(b,sFlat4) = sFlat4,
inference(step,[status(thm)],[t3588,t2585]) ).
cnf(t2614,plain,
least_upper_bound(b,sFlat4) = sFlat4,
inference(rw,[status(thm)],[t3589]) ).
cnf(t3594,plain,
least_upper_bound(sFlat4,b) = sFlat4,
inference(step,[status(thm)],[t2614,t71]) ).
cnf(t2618,plain,
least_upper_bound(sFlat4,b) = sFlat4,
inference(orient,[status(thm)],[t3594]) ).
cnf(t2622,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t76,t2618]) ).
cnf(t2942,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t2622]) ).
cnf(t3611,plain,
least_upper_bound(sFlat4,X1) = least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)),
inference(step,[status(thm)],[t2971,t2942]) ).
cnf(t3192,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t3611]) ).
cnf(t3580,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(step,[status(thm)],[t1195,t2585]) ).
cnf(t2586,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(orient,[status(thm)],[t3580]) ).
cnf(t3197,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = least_upper_bound(sFlat4,sFlat4),
inference(cp,[status(thm)],[t3192,t2586]) ).
cnf(t3612,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(step,[status(thm)],[t3197,t22]) ).
cnf(t3214,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(orient,[status(thm)],[t3612]) ).
cnf(t155,plain,
least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1),
inference(cp,[status(thm)],[t153,t25]) ).
cnf(t3454,plain,
least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t155,t76]) ).
cnf(t419,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t3454]) ).
cnf(t936,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t27,t932]) ).
cnf(t1433,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t936]) ).
cnf(t2593,plain,
multiply(sFlat2,least_upper_bound(identity,sFlat3)) = least_upper_bound(sFlat2,sFlat4),
inference(cp,[status(thm)],[t1433,t2585]) ).
cnf(t3600,plain,
multiply(sFlat2,least_upper_bound(sFlat3,identity)) = least_upper_bound(sFlat2,sFlat4),
inference(step,[status(thm)],[t2593,t71]) ).
cnf(t3601,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(sFlat2,sFlat4),
inference(step,[status(thm)],[t3600,t123]) ).
cnf(t3602,plain,
sFlat4 = least_upper_bound(sFlat2,sFlat4),
inference(step,[status(thm)],[t3601,t2585]) ).
cnf(t2848,plain,
least_upper_bound(sFlat2,sFlat4) = sFlat4,
inference(orient,[status(thm)],[t3602]) ).
cnf(t2853,plain,
least_upper_bound(sFlat2,least_upper_bound(sFlat4,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t76,t2848]) ).
cnf(t3083,plain,
least_upper_bound(sFlat2,least_upper_bound(sFlat4,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t2853]) ).
cnf(t3092,plain,
least_upper_bound(least_upper_bound(sFlat4,X1),sFlat2) = least_upper_bound(least_upper_bound(sFlat4,X1),least_upper_bound(sFlat4,X1)),
inference(cp,[status(thm)],[t419,t3083]) ).
cnf(t3628,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(least_upper_bound(sFlat4,X1),least_upper_bound(sFlat4,X1)),
inference(step,[status(thm)],[t3092,t76]) ).
cnf(t3629,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,least_upper_bound(X1,least_upper_bound(sFlat4,X1))),
inference(step,[status(thm)],[t3628,t76]) ).
cnf(t3630,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,least_upper_bound(X1,sFlat4)),
inference(step,[status(thm)],[t3629,t419]) ).
cnf(t3631,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,X1),
inference(step,[status(thm)],[t3630,t419]) ).
cnf(t3398,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t3631]) ).
cnf(t3632,plain,
least_upper_bound(sFlat4,sFlat0) = sFlat4,
inference(step,[status(thm)],[t3214,t3398]) ).
cnf(t3411,plain,
least_upper_bound(sFlat4,sFlat0) = sFlat4,
inference(rw,[status(thm)],[t3632]) ).
cnf(t3633,plain,
least_upper_bound(sFlat0,sFlat4) = sFlat4,
inference(step,[status(thm)],[t3411,t71]) ).
cnf(t3412,plain,
least_upper_bound(sFlat0,sFlat4) = sFlat4,
inference(orient,[status(thm)],[t3633]) ).
cnf(t3636,plain,
least_upper_bound(sFlat1,sFlat4) = sFlat4,
inference(step,[status(thm)],[t2641,t3412]) ).
cnf(t3415,plain,
least_upper_bound(sFlat1,sFlat4) = sFlat4,
inference(orient,[status(thm)],[t3636]) ).
cnf(goal_0,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[goal_0,t76]) ).
cnf(g0_1,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_0,t51]) ).
cnf(g0_2,plain,
least_upper_bound(sFlat1,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_1,t176]) ).
cnf(g0_3,plain,
least_upper_bound(sFlat1,multiply(least_upper_bound(identity,a),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_2,t71]) ).
cnf(g0_4,plain,
least_upper_bound(sFlat1,multiply(sFlat2,least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_3,t92]) ).
cnf(g0_5,plain,
least_upper_bound(sFlat1,multiply(sFlat2,least_upper_bound(identity,b))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_4,t71]) ).
cnf(g0_6,plain,
least_upper_bound(sFlat1,multiply(sFlat2,sFlat3)) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_5,t96]) ).
cnf(g0_7,plain,
least_upper_bound(sFlat1,sFlat4) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_6,t2585]) ).
cnf(g0_8,plain,
sFlat4 != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_7,t3415]) ).
cnf(g0_9,plain,
sFlat4 != multiply(least_upper_bound(identity,a),least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_8,t71]) ).
cnf(g0_10,plain,
sFlat4 != multiply(sFlat2,least_upper_bound(b,identity)),
inference(rw,[status(thm)],[g0_9,t92]) ).
cnf(g0_11,plain,
sFlat4 != multiply(sFlat2,least_upper_bound(identity,b)),
inference(rw,[status(thm)],[g0_10,t71]) ).
cnf(g0_12,plain,
sFlat4 != multiply(sFlat2,sFlat3),
inference(rw,[status(thm)],[g0_11,t96]) ).
cnf(g0_13,plain,
sFlat4 != sFlat4,
inference(rw,[status(thm)],[g0_12,t2585]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.57 % Computer : n016.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Wed Sep 23 14:07:57 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.36/1.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.36/1.64 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------