%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP179-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:25:34 PM UTC 2026
% Result : Unsatisfiable 6.78s 1.63s
% Output : CNFRefutation 6.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 20
% Syntax : Number of clauses : 176 ( 176 unt; 0 nHn; 104 RR)
% Number of literals : 176 ( 175 equ; 8 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 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t84,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t18,axiom,
sFlat0 = inverse(a),
introduced(definition) ).
cnf(t109,plain,
inverse(a) = sFlat0,
inference(orient,[status(thm)],[t18]) ).
cnf(t19,axiom,
sFlat1 = least_upper_bound(inverse(a),identity),
introduced(definition) ).
cnf(t2176,plain,
sFlat1 = least_upper_bound(identity,inverse(a)),
inference(step,[status(thm)],[t19,t84]) ).
cnf(t98,plain,
least_upper_bound(identity,inverse(a)) = sFlat1,
inference(orient,[status(thm)],[t2176]) ).
cnf(t2179,plain,
least_upper_bound(identity,sFlat0) = sFlat1,
inference(step,[status(thm)],[t98,t109]) ).
cnf(t114,plain,
least_upper_bound(identity,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t2179]) ).
cnf(t2181,plain,
least_upper_bound(sFlat0,identity) = sFlat1,
inference(step,[status(thm)],[t114,t84]) ).
cnf(t146,plain,
least_upper_bound(sFlat0,identity) = sFlat1,
inference(orient,[status(thm)],[t2181]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t67,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t20,axiom,
sFlat2 = greatest_lower_bound(a,identity),
introduced(definition) ).
cnf(t2175,plain,
sFlat2 = greatest_lower_bound(identity,a),
inference(step,[status(thm)],[t20,t67]) ).
cnf(t81,plain,
greatest_lower_bound(identity,a) = sFlat2,
inference(orient,[status(thm)],[t2175]) ).
cnf(t21,axiom,
sFlat3 = inverse(greatest_lower_bound(a,identity)),
introduced(definition) ).
cnf(t2177,plain,
sFlat3 = inverse(greatest_lower_bound(identity,a)),
inference(step,[status(thm)],[t21,t67]) ).
cnf(t2178,plain,
sFlat3 = inverse(sFlat2),
inference(step,[status(thm)],[t2177,t81]) ).
cnf(t101,plain,
inverse(sFlat2) = sFlat3,
inference(orient,[status(thm)],[t2178]) ).
cnf(t13,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t28,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t43,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t53,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t28,t43]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t2255,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t53,t22]) ).
cnf(t1149,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t2255]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t26,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t70,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t26,t67]) ).
cnf(t194,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t70]) ).
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t87,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t24,t84]) ).
cnf(t210,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t87]) ).
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(t88,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(t148,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(cp,[status(thm)],[t88,t146]) ).
cnf(t404,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t148]) ).
cnf(t409,plain,
least_upper_bound(sFlat1,greatest_lower_bound(identity,X1)) = least_upper_bound(sFlat0,identity),
inference(cp,[status(thm)],[t404,t26]) ).
cnf(t2200,plain,
least_upper_bound(sFlat1,greatest_lower_bound(identity,X1)) = sFlat1,
inference(step,[status(thm)],[t409,t146]) ).
cnf(t427,plain,
least_upper_bound(sFlat1,greatest_lower_bound(identity,X1)) = sFlat1,
inference(orient,[status(thm)],[t2200]) ).
cnf(t429,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(greatest_lower_bound(identity,X1),sFlat1),
inference(cp,[status(thm)],[t210,t427]) ).
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(t71,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(t2217,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(X1,sFlat1)),
inference(step,[status(thm)],[t429,t71]) ).
cnf(t649,plain,
greatest_lower_bound(identity,greatest_lower_bound(X1,sFlat1)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t2217]) ).
cnf(t654,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(sFlat1,X1)),
inference(cp,[status(thm)],[t649,t67]) ).
cnf(t869,plain,
greatest_lower_bound(identity,greatest_lower_bound(sFlat1,X1)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t654]) ).
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(t32,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t15]) ).
cnf(t33,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t32,t22]) ).
cnf(t287,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t33]) ).
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(t31,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t112,plain,
identity = multiply(sFlat0,a),
inference(cp,[status(thm)],[t43,t109]) ).
cnf(t136,plain,
multiply(sFlat0,a) = identity,
inference(orient,[status(thm)],[t112]) ).
cnf(t141,plain,
multiply(sFlat0,least_upper_bound(a,X1)) = least_upper_bound(identity,multiply(sFlat0,X1)),
inference(cp,[status(thm)],[t31,t136]) ).
cnf(t1534,plain,
least_upper_bound(identity,multiply(sFlat0,X1)) = multiply(sFlat0,least_upper_bound(a,X1)),
inference(orient,[status(thm)],[t141]) ).
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(t38,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
cnf(t39,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t38,t22]) ).
cnf(t596,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t39]) ).
cnf(t1536,plain,
multiply(sFlat0,least_upper_bound(a,identity)) = multiply(least_upper_bound(identity,sFlat0),identity),
inference(cp,[status(thm)],[t1534,t596]) ).
cnf(t2278,plain,
multiply(sFlat0,least_upper_bound(identity,a)) = multiply(least_upper_bound(identity,sFlat0),identity),
inference(step,[status(thm)],[t1536,t84]) ).
cnf(t604,plain,
multiply(least_upper_bound(identity,sFlat0),a) = least_upper_bound(a,identity),
inference(cp,[status(thm)],[t596,t136]) ).
cnf(t2224,plain,
multiply(least_upper_bound(sFlat0,identity),a) = least_upper_bound(a,identity),
inference(step,[status(thm)],[t604,t84]) ).
cnf(t2225,plain,
multiply(sFlat1,a) = least_upper_bound(a,identity),
inference(step,[status(thm)],[t2224,t146]) ).
cnf(t2226,plain,
multiply(sFlat1,a) = least_upper_bound(identity,a),
inference(step,[status(thm)],[t2225,t84]) ).
cnf(t835,plain,
least_upper_bound(identity,a) = multiply(sFlat1,a),
inference(orient,[status(thm)],[t2226]) ).
cnf(t2279,plain,
multiply(sFlat0,multiply(sFlat1,a)) = multiply(least_upper_bound(identity,sFlat0),identity),
inference(step,[status(thm)],[t2278,t835]) ).
cnf(t2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t27,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(t54,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(t106,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t107,plain,
inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)),
inference(cp,[status(thm)],[t54,t106]) ).
cnf(t2182,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(step,[status(thm)],[t107,t22]) ).
cnf(t184,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t2182]) ).
cnf(t188,plain,
multiply(X1,identity) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t27,t184]) ).
cnf(t2183,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t188,t27]) ).
cnf(t189,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t2183]) ).
cnf(t2280,plain,
multiply(sFlat0,multiply(sFlat1,a)) = least_upper_bound(identity,sFlat0),
inference(step,[status(thm)],[t2279,t189]) ).
cnf(t2281,plain,
multiply(sFlat0,multiply(sFlat1,a)) = least_upper_bound(sFlat0,identity),
inference(step,[status(thm)],[t2280,t84]) ).
cnf(t2282,plain,
multiply(sFlat0,multiply(sFlat1,a)) = sFlat1,
inference(step,[status(thm)],[t2281,t146]) ).
cnf(t1549,plain,
multiply(sFlat0,multiply(sFlat1,a)) = sFlat1,
inference(orient,[status(thm)],[t2282]) ).
cnf(t1551,plain,
multiply(sFlat1,a) = multiply(inverse(sFlat0),sFlat1),
inference(cp,[status(thm)],[t1149,t1549]) ).
cnf(t113,plain,
a = inverse(sFlat0),
inference(cp,[status(thm)],[t27,t109]) ).
cnf(t119,plain,
inverse(sFlat0) = a,
inference(orient,[status(thm)],[t113]) ).
cnf(t2283,plain,
multiply(sFlat1,a) = multiply(a,sFlat1),
inference(step,[status(thm)],[t1551,t119]) ).
cnf(t1567,plain,
multiply(a,sFlat1) = multiply(sFlat1,a),
inference(orient,[status(thm)],[t2283]) ).
cnf(t1569,plain,
multiply(greatest_lower_bound(identity,a),sFlat1) = greatest_lower_bound(sFlat1,multiply(sFlat1,a)),
inference(cp,[status(thm)],[t287,t1567]) ).
cnf(t2289,plain,
multiply(sFlat2,sFlat1) = greatest_lower_bound(sFlat1,multiply(sFlat1,a)),
inference(step,[status(thm)],[t1569,t81]) ).
cnf(t1612,plain,
greatest_lower_bound(sFlat1,multiply(sFlat1,a)) = multiply(sFlat2,sFlat1),
inference(orient,[status(thm)],[t2289]) ).
cnf(t1614,plain,
greatest_lower_bound(identity,multiply(sFlat1,a)) = greatest_lower_bound(identity,multiply(sFlat2,sFlat1)),
inference(cp,[status(thm)],[t869,t1612]) ).
cnf(t836,plain,
identity = greatest_lower_bound(identity,multiply(sFlat1,a)),
inference(cp,[status(thm)],[t24,t835]) ).
cnf(t848,plain,
greatest_lower_bound(identity,multiply(sFlat1,a)) = identity,
inference(orient,[status(thm)],[t836]) ).
cnf(t2290,plain,
identity = greatest_lower_bound(identity,multiply(sFlat2,sFlat1)),
inference(step,[status(thm)],[t1614,t848]) ).
cnf(t1626,plain,
greatest_lower_bound(identity,multiply(sFlat2,sFlat1)) = identity,
inference(orient,[status(thm)],[t2290]) ).
cnf(t1628,plain,
multiply(sFlat2,sFlat1) = least_upper_bound(multiply(sFlat2,sFlat1),identity),
inference(cp,[status(thm)],[t194,t1626]) ).
cnf(t2293,plain,
multiply(sFlat2,sFlat1) = least_upper_bound(identity,multiply(sFlat2,sFlat1)),
inference(step,[status(thm)],[t1628,t84]) ).
cnf(t1641,plain,
least_upper_bound(identity,multiply(sFlat2,sFlat1)) = multiply(sFlat2,sFlat1),
inference(orient,[status(thm)],[t2293]) ).
cnf(t105,plain,
sFlat2 = inverse(sFlat3),
inference(cp,[status(thm)],[t27,t101]) ).
cnf(t115,plain,
inverse(sFlat3) = sFlat2,
inference(orient,[status(thm)],[t105]) ).
cnf(t118,plain,
identity = multiply(sFlat2,sFlat3),
inference(cp,[status(thm)],[t43,t115]) ).
cnf(t149,plain,
multiply(sFlat2,sFlat3) = identity,
inference(orient,[status(thm)],[t118]) ).
cnf(t154,plain,
multiply(sFlat2,least_upper_bound(sFlat3,X1)) = least_upper_bound(identity,multiply(sFlat2,X1)),
inference(cp,[status(thm)],[t31,t149]) ).
cnf(t2104,plain,
least_upper_bound(identity,multiply(sFlat2,X1)) = multiply(sFlat2,least_upper_bound(sFlat3,X1)),
inference(orient,[status(thm)],[t154]) ).
cnf(t2368,plain,
multiply(sFlat2,least_upper_bound(sFlat3,sFlat1)) = multiply(sFlat2,sFlat1),
inference(step,[status(thm)],[t1641,t2104]) ).
cnf(t2122,plain,
multiply(sFlat2,least_upper_bound(sFlat3,sFlat1)) = multiply(sFlat2,sFlat1),
inference(rw,[status(thm)],[t2368]) ).
cnf(t2369,plain,
multiply(sFlat2,least_upper_bound(sFlat1,sFlat3)) = multiply(sFlat2,sFlat1),
inference(step,[status(thm)],[t2122,t84]) ).
cnf(t411,plain,
least_upper_bound(sFlat1,X1) = least_upper_bound(sFlat0,least_upper_bound(X1,identity)),
inference(cp,[status(thm)],[t404,t84]) ).
cnf(t588,plain,
least_upper_bound(sFlat0,least_upper_bound(X1,identity)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t411]) ).
cnf(t293,plain,
multiply(greatest_lower_bound(identity,sFlat2),sFlat3) = greatest_lower_bound(sFlat3,identity),
inference(cp,[status(thm)],[t287,t149]) ).
cnf(t2204,plain,
multiply(greatest_lower_bound(sFlat2,identity),sFlat3) = greatest_lower_bound(sFlat3,identity),
inference(step,[status(thm)],[t293,t67]) ).
cnf(t83,plain,
identity = least_upper_bound(identity,sFlat2),
inference(cp,[status(thm)],[t26,t81]) ).
cnf(t2180,plain,
identity = least_upper_bound(sFlat2,identity),
inference(step,[status(thm)],[t83,t84]) ).
cnf(t123,plain,
least_upper_bound(sFlat2,identity) = identity,
inference(orient,[status(thm)],[t2180]) ).
cnf(t124,plain,
sFlat2 = greatest_lower_bound(sFlat2,identity),
inference(cp,[status(thm)],[t24,t123]) ).
cnf(t169,plain,
greatest_lower_bound(sFlat2,identity) = sFlat2,
inference(orient,[status(thm)],[t124]) ).
cnf(t2205,plain,
multiply(sFlat2,sFlat3) = greatest_lower_bound(sFlat3,identity),
inference(step,[status(thm)],[t2204,t169]) ).
cnf(t2206,plain,
identity = greatest_lower_bound(sFlat3,identity),
inference(step,[status(thm)],[t2205,t149]) ).
cnf(t501,plain,
greatest_lower_bound(sFlat3,identity) = identity,
inference(orient,[status(thm)],[t2206]) ).
cnf(t504,plain,
sFlat3 = least_upper_bound(sFlat3,identity),
inference(cp,[status(thm)],[t26,t501]) ).
cnf(t505,plain,
least_upper_bound(sFlat3,identity) = sFlat3,
inference(orient,[status(thm)],[t504]) ).
cnf(t590,plain,
least_upper_bound(sFlat1,sFlat3) = least_upper_bound(sFlat0,sFlat3),
inference(cp,[status(thm)],[t588,t505]) ).
cnf(t619,plain,
least_upper_bound(sFlat1,sFlat3) = least_upper_bound(sFlat0,sFlat3),
inference(orient,[status(thm)],[t590]) ).
cnf(t44,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t43,t27]) ).
cnf(t173,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t44]) ).
cnf(t183,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t28,t173]) ).
cnf(t2256,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t183,t22]) ).
cnf(t1163,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t2256]) ).
cnf(t1165,plain,
inverse(X1) = multiply(X2,inverse(multiply(X1,X2))),
inference(cp,[status(thm)],[t1163,t54]) ).
cnf(t1200,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(orient,[status(thm)],[t1165]) ).
cnf(t137,plain,
multiply(least_upper_bound(sFlat0,X1),a) = least_upper_bound(identity,multiply(X1,a)),
inference(cp,[status(thm)],[t38,t136]) ).
cnf(t1276,plain,
least_upper_bound(identity,multiply(X1,a)) = multiply(least_upper_bound(sFlat0,X1),a),
inference(orient,[status(thm)],[t137]) ).
cnf(t104,plain,
identity = multiply(sFlat3,sFlat2),
inference(cp,[status(thm)],[t43,t101]) ).
cnf(t126,plain,
multiply(sFlat3,sFlat2) = identity,
inference(orient,[status(thm)],[t104]) ).
cnf(t131,plain,
multiply(sFlat3,least_upper_bound(sFlat2,X1)) = least_upper_bound(identity,multiply(sFlat3,X1)),
inference(cp,[status(thm)],[t31,t126]) ).
cnf(t1249,plain,
least_upper_bound(identity,multiply(sFlat3,X1)) = multiply(sFlat3,least_upper_bound(sFlat2,X1)),
inference(orient,[status(thm)],[t131]) ).
cnf(t1277,plain,
multiply(least_upper_bound(sFlat0,sFlat3),a) = multiply(sFlat3,least_upper_bound(sFlat2,a)),
inference(cp,[status(thm)],[t1276,t1249]) ).
cnf(t199,plain,
a = least_upper_bound(a,sFlat2),
inference(cp,[status(thm)],[t194,t81]) ).
cnf(t2185,plain,
a = least_upper_bound(sFlat2,a),
inference(step,[status(thm)],[t199,t84]) ).
cnf(t204,plain,
least_upper_bound(sFlat2,a) = a,
inference(orient,[status(thm)],[t2185]) ).
cnf(t2257,plain,
multiply(least_upper_bound(sFlat0,sFlat3),a) = multiply(sFlat3,a),
inference(step,[status(thm)],[t1277,t204]) ).
cnf(t1287,plain,
multiply(least_upper_bound(sFlat0,sFlat3),a) = multiply(sFlat3,a),
inference(orient,[status(thm)],[t2257]) ).
cnf(t1302,plain,
inverse(least_upper_bound(sFlat0,sFlat3)) = multiply(a,inverse(multiply(sFlat3,a))),
inference(cp,[status(thm)],[t1200,t1287]) ).
cnf(t2258,plain,
inverse(least_upper_bound(sFlat0,sFlat3)) = inverse(sFlat3),
inference(step,[status(thm)],[t1302,t1200]) ).
cnf(t2259,plain,
inverse(least_upper_bound(sFlat0,sFlat3)) = sFlat2,
inference(step,[status(thm)],[t2258,t115]) ).
cnf(t1303,plain,
inverse(least_upper_bound(sFlat0,sFlat3)) = sFlat2,
inference(orient,[status(thm)],[t2259]) ).
cnf(t1309,plain,
least_upper_bound(sFlat0,sFlat3) = inverse(sFlat2),
inference(cp,[status(thm)],[t27,t1303]) ).
cnf(t2260,plain,
least_upper_bound(sFlat0,sFlat3) = sFlat3,
inference(step,[status(thm)],[t1309,t101]) ).
cnf(t1314,plain,
least_upper_bound(sFlat0,sFlat3) = sFlat3,
inference(orient,[status(thm)],[t2260]) ).
cnf(t2261,plain,
least_upper_bound(sFlat1,sFlat3) = sFlat3,
inference(step,[status(thm)],[t619,t1314]) ).
cnf(t1315,plain,
least_upper_bound(sFlat1,sFlat3) = sFlat3,
inference(orient,[status(thm)],[t2261]) ).
cnf(t2370,plain,
multiply(sFlat2,sFlat3) = multiply(sFlat2,sFlat1),
inference(step,[status(thm)],[t2369,t1315]) ).
cnf(t2371,plain,
identity = multiply(sFlat2,sFlat1),
inference(step,[status(thm)],[t2370,t149]) ).
cnf(t2123,plain,
multiply(sFlat2,sFlat1) = identity,
inference(orient,[status(thm)],[t2371]) ).
cnf(t2127,plain,
sFlat1 = multiply(inverse(sFlat2),identity),
inference(cp,[status(thm)],[t1149,t2123]) ).
cnf(t2374,plain,
sFlat1 = inverse(sFlat2),
inference(step,[status(thm)],[t2127,t189]) ).
cnf(t2375,plain,
sFlat1 = sFlat3,
inference(step,[status(thm)],[t2374,t101]) ).
cnf(t2143,plain,
sFlat3 = sFlat1,
inference(orient,[status(thm)],[t2375]) ).
cnf(t2376,plain,
inverse(sFlat2) = sFlat1,
inference(step,[status(thm)],[t101,t2143]) ).
cnf(t2144,plain,
inverse(sFlat2) = sFlat1,
inference(orient,[status(thm)],[t2376]) ).
cnf(goal_0,negated_conjecture,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[goal_0,t84]) ).
cnf(g0_1,plain,
least_upper_bound(identity,sFlat0) != inverse(greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[g0_0,t109]) ).
cnf(g0_2,plain,
least_upper_bound(sFlat0,identity) != inverse(greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[g0_1,t84]) ).
cnf(g0_3,plain,
sFlat1 != inverse(greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[g0_2,t146]) ).
cnf(g0_4,plain,
sFlat1 != inverse(greatest_lower_bound(identity,a)),
inference(rw,[status(thm)],[g0_3,t67]) ).
cnf(g0_5,plain,
sFlat1 != inverse(sFlat2),
inference(rw,[status(thm)],[g0_4,t81]) ).
cnf(g0_6,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_5,t2144]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP179-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 14:00:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.78/1.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.78/1.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------