%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP179-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 01:25:33 PM UTC 2026
% Result : Unsatisfiable 5.80s 2.16s
% Output : CNFRefutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 18
% Syntax : Number of clauses : 177 ( 177 unt; 0 nHn; 98 RR)
% Number of literals : 177 ( 176 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 : 128 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t66,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t15,axiom,
sFlat0 = inverse(a),
introduced(definition) ).
cnf(t85,plain,
inverse(a) = sFlat0,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sFlat1 = least_upper_bound(inverse(a),identity),
introduced(definition) ).
cnf(t2076,plain,
sFlat1 = least_upper_bound(identity,inverse(a)),
inference(step,[status(thm)],[t16,t66]) ).
cnf(t80,plain,
least_upper_bound(identity,inverse(a)) = sFlat1,
inference(orient,[status(thm)],[t2076]) ).
cnf(t2079,plain,
least_upper_bound(identity,sFlat0) = sFlat1,
inference(step,[status(thm)],[t80,t85]) ).
cnf(t87,plain,
least_upper_bound(identity,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t2079]) ).
cnf(t2081,plain,
least_upper_bound(sFlat0,identity) = sFlat1,
inference(step,[status(thm)],[t87,t66]) ).
cnf(t111,plain,
least_upper_bound(sFlat0,identity) = sFlat1,
inference(orient,[status(thm)],[t2081]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t49,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t17,axiom,
sFlat2 = greatest_lower_bound(a,identity),
introduced(definition) ).
cnf(t2075,plain,
sFlat2 = greatest_lower_bound(identity,a),
inference(step,[status(thm)],[t17,t49]) ).
cnf(t63,plain,
greatest_lower_bound(identity,a) = sFlat2,
inference(orient,[status(thm)],[t2075]) ).
cnf(t18,axiom,
sFlat3 = inverse(greatest_lower_bound(a,identity)),
introduced(definition) ).
cnf(t2077,plain,
sFlat3 = inverse(greatest_lower_bound(identity,a)),
inference(step,[status(thm)],[t18,t49]) ).
cnf(t2078,plain,
sFlat3 = inverse(sFlat2),
inference(step,[status(thm)],[t2077,t63]) ).
cnf(t83,plain,
inverse(sFlat2) = sFlat3,
inference(orient,[status(thm)],[t2078]) ).
cnf(t10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t39,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t48,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t24,t39]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t2118,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t48,t19]) ).
cnf(t626,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t2118]) ).
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(t52,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t23,t49]) ).
cnf(t118,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t52]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t69,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t21,t66]) ).
cnf(t134,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t69]) ).
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(t70,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(t113,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(cp,[status(thm)],[t70,t111]) ).
cnf(t226,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t113]) ).
cnf(t230,plain,
least_upper_bound(sFlat1,greatest_lower_bound(identity,X1)) = least_upper_bound(sFlat0,identity),
inference(cp,[status(thm)],[t226,t23]) ).
cnf(t2092,plain,
least_upper_bound(sFlat1,greatest_lower_bound(identity,X1)) = sFlat1,
inference(step,[status(thm)],[t230,t111]) ).
cnf(t244,plain,
least_upper_bound(sFlat1,greatest_lower_bound(identity,X1)) = sFlat1,
inference(orient,[status(thm)],[t2092]) ).
cnf(t246,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(greatest_lower_bound(identity,X1),sFlat1),
inference(cp,[status(thm)],[t134,t244]) ).
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(t53,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(t2103,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(X1,sFlat1)),
inference(step,[status(thm)],[t246,t53]) ).
cnf(t425,plain,
greatest_lower_bound(identity,greatest_lower_bound(X1,sFlat1)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t2103]) ).
cnf(t430,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(sFlat1,X1)),
inference(cp,[status(thm)],[t425,t49]) ).
cnf(t535,plain,
greatest_lower_bound(identity,greatest_lower_bound(sFlat1,X1)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t430]) ).
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(t28,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t29,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t28,t19]) ).
cnf(t252,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t29]) ).
cnf(t86,plain,
identity = multiply(sFlat0,a),
inference(cp,[status(thm)],[t39,t85]) ).
cnf(t101,plain,
multiply(sFlat0,a) = identity,
inference(orient,[status(thm)],[t86]) ).
cnf(t110,plain,
multiply(sFlat0,multiply(a,X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t24,t101]) ).
cnf(t2086,plain,
multiply(sFlat0,multiply(a,X1)) = X1,
inference(step,[status(thm)],[t110,t19]) ).
cnf(t155,plain,
multiply(sFlat0,multiply(a,X1)) = X1,
inference(orient,[status(thm)],[t2086]) ).
cnf(t630,plain,
multiply(a,X1) = multiply(inverse(sFlat0),X1),
inference(cp,[status(thm)],[t626,t155]) ).
cnf(t707,plain,
multiply(inverse(sFlat0),X1) = multiply(a,X1),
inference(orient,[status(thm)],[t630]) ).
cnf(t709,plain,
multiply(a,multiply(sFlat0,X1)) = X1,
inference(cp,[status(thm)],[t707,t626]) ).
cnf(t845,plain,
multiply(a,multiply(sFlat0,X1)) = X1,
inference(orient,[status(thm)],[t709]) ).
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(t106,plain,
multiply(sFlat0,least_upper_bound(a,X1)) = least_upper_bound(identity,multiply(sFlat0,X1)),
inference(cp,[status(thm)],[t27,t101]) ).
cnf(t1550,plain,
least_upper_bound(identity,multiply(sFlat0,X1)) = multiply(sFlat0,least_upper_bound(a,X1)),
inference(orient,[status(thm)],[t106]) ).
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(t34,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t35,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t34,t19]) ).
cnf(t670,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t35]) ).
cnf(t1552,plain,
multiply(sFlat0,least_upper_bound(a,identity)) = multiply(least_upper_bound(identity,sFlat0),identity),
inference(cp,[status(thm)],[t1550,t670]) ).
cnf(t2188,plain,
multiply(sFlat0,least_upper_bound(identity,a)) = multiply(least_upper_bound(identity,sFlat0),identity),
inference(step,[status(thm)],[t1552,t66]) ).
cnf(t676,plain,
multiply(least_upper_bound(identity,sFlat0),a) = least_upper_bound(a,identity),
inference(cp,[status(thm)],[t670,t101]) ).
cnf(t2132,plain,
multiply(least_upper_bound(sFlat0,identity),a) = least_upper_bound(a,identity),
inference(step,[status(thm)],[t676,t66]) ).
cnf(t2133,plain,
multiply(sFlat1,a) = least_upper_bound(a,identity),
inference(step,[status(thm)],[t2132,t111]) ).
cnf(t2134,plain,
multiply(sFlat1,a) = least_upper_bound(identity,a),
inference(step,[status(thm)],[t2133,t66]) ).
cnf(t922,plain,
least_upper_bound(identity,a) = multiply(sFlat1,a),
inference(orient,[status(thm)],[t2134]) ).
cnf(t2189,plain,
multiply(sFlat0,multiply(sFlat1,a)) = multiply(least_upper_bound(identity,sFlat0),identity),
inference(step,[status(thm)],[t2188,t922]) ).
cnf(t633,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t626,t39]) ).
cnf(t810,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t633]) ).
cnf(t636,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t626,t626]) ).
cnf(t886,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t636]) ).
cnf(t2128,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t810,t886]) ).
cnf(t895,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t2128]) ).
cnf(t896,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t895]) ).
cnf(t2190,plain,
multiply(sFlat0,multiply(sFlat1,a)) = least_upper_bound(identity,sFlat0),
inference(step,[status(thm)],[t2189,t896]) ).
cnf(t2191,plain,
multiply(sFlat0,multiply(sFlat1,a)) = least_upper_bound(sFlat0,identity),
inference(step,[status(thm)],[t2190,t66]) ).
cnf(t2192,plain,
multiply(sFlat0,multiply(sFlat1,a)) = sFlat1,
inference(step,[status(thm)],[t2191,t111]) ).
cnf(t1564,plain,
multiply(sFlat0,multiply(sFlat1,a)) = sFlat1,
inference(orient,[status(thm)],[t2192]) ).
cnf(t1566,plain,
multiply(sFlat1,a) = multiply(a,sFlat1),
inference(cp,[status(thm)],[t845,t1564]) ).
cnf(t1579,plain,
multiply(a,sFlat1) = multiply(sFlat1,a),
inference(orient,[status(thm)],[t1566]) ).
cnf(t1581,plain,
multiply(greatest_lower_bound(identity,a),sFlat1) = greatest_lower_bound(sFlat1,multiply(sFlat1,a)),
inference(cp,[status(thm)],[t252,t1579]) ).
cnf(t2197,plain,
multiply(sFlat2,sFlat1) = greatest_lower_bound(sFlat1,multiply(sFlat1,a)),
inference(step,[status(thm)],[t1581,t63]) ).
cnf(t1604,plain,
greatest_lower_bound(sFlat1,multiply(sFlat1,a)) = multiply(sFlat2,sFlat1),
inference(orient,[status(thm)],[t2197]) ).
cnf(t1606,plain,
greatest_lower_bound(identity,multiply(sFlat1,a)) = greatest_lower_bound(identity,multiply(sFlat2,sFlat1)),
inference(cp,[status(thm)],[t535,t1604]) ).
cnf(t923,plain,
identity = greatest_lower_bound(identity,multiply(sFlat1,a)),
inference(cp,[status(thm)],[t21,t922]) ).
cnf(t934,plain,
greatest_lower_bound(identity,multiply(sFlat1,a)) = identity,
inference(orient,[status(thm)],[t923]) ).
cnf(t2198,plain,
identity = greatest_lower_bound(identity,multiply(sFlat2,sFlat1)),
inference(step,[status(thm)],[t1606,t934]) ).
cnf(t1618,plain,
greatest_lower_bound(identity,multiply(sFlat2,sFlat1)) = identity,
inference(orient,[status(thm)],[t2198]) ).
cnf(t1620,plain,
multiply(sFlat2,sFlat1) = least_upper_bound(multiply(sFlat2,sFlat1),identity),
inference(cp,[status(thm)],[t118,t1618]) ).
cnf(t2201,plain,
multiply(sFlat2,sFlat1) = least_upper_bound(identity,multiply(sFlat2,sFlat1)),
inference(step,[status(thm)],[t1620,t66]) ).
cnf(t1633,plain,
least_upper_bound(identity,multiply(sFlat2,sFlat1)) = multiply(sFlat2,sFlat1),
inference(orient,[status(thm)],[t2201]) ).
cnf(t84,plain,
identity = multiply(sFlat3,sFlat2),
inference(cp,[status(thm)],[t39,t83]) ).
cnf(t91,plain,
multiply(sFlat3,sFlat2) = identity,
inference(orient,[status(thm)],[t84]) ).
cnf(t100,plain,
multiply(sFlat3,multiply(sFlat2,X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t24,t91]) ).
cnf(t2085,plain,
multiply(sFlat3,multiply(sFlat2,X1)) = X1,
inference(step,[status(thm)],[t100,t19]) ).
cnf(t146,plain,
multiply(sFlat3,multiply(sFlat2,X1)) = X1,
inference(orient,[status(thm)],[t2085]) ).
cnf(t632,plain,
multiply(sFlat2,X1) = multiply(inverse(sFlat3),X1),
inference(cp,[status(thm)],[t626,t146]) ).
cnf(t775,plain,
multiply(inverse(sFlat3),X1) = multiply(sFlat2,X1),
inference(orient,[status(thm)],[t632]) ).
cnf(t776,plain,
multiply(sFlat2,sFlat3) = identity,
inference(cp,[status(thm)],[t775,t39]) ).
cnf(t785,plain,
multiply(sFlat2,sFlat3) = identity,
inference(orient,[status(thm)],[t776]) ).
cnf(t794,plain,
multiply(sFlat2,least_upper_bound(sFlat3,X1)) = least_upper_bound(identity,multiply(sFlat2,X1)),
inference(cp,[status(thm)],[t27,t785]) ).
cnf(t2016,plain,
least_upper_bound(identity,multiply(sFlat2,X1)) = multiply(sFlat2,least_upper_bound(sFlat3,X1)),
inference(orient,[status(thm)],[t794]) ).
cnf(t2248,plain,
multiply(sFlat2,least_upper_bound(sFlat3,sFlat1)) = multiply(sFlat2,sFlat1),
inference(step,[status(thm)],[t1633,t2016]) ).
cnf(t2032,plain,
multiply(sFlat2,least_upper_bound(sFlat3,sFlat1)) = multiply(sFlat2,sFlat1),
inference(rw,[status(thm)],[t2248]) ).
cnf(t2249,plain,
multiply(sFlat2,least_upper_bound(sFlat1,sFlat3)) = multiply(sFlat2,sFlat1),
inference(step,[status(thm)],[t2032,t66]) ).
cnf(t232,plain,
least_upper_bound(sFlat1,X1) = least_upper_bound(sFlat0,least_upper_bound(X1,identity)),
inference(cp,[status(thm)],[t226,t66]) ).
cnf(t410,plain,
least_upper_bound(sFlat0,least_upper_bound(X1,identity)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t232]) ).
cnf(t786,plain,
multiply(least_upper_bound(identity,sFlat2),sFlat3) = least_upper_bound(sFlat3,identity),
inference(cp,[status(thm)],[t670,t785]) ).
cnf(t2140,plain,
multiply(least_upper_bound(sFlat2,identity),sFlat3) = least_upper_bound(sFlat3,identity),
inference(step,[status(thm)],[t786,t66]) ).
cnf(t65,plain,
identity = least_upper_bound(identity,sFlat2),
inference(cp,[status(thm)],[t23,t63]) ).
cnf(t2080,plain,
identity = least_upper_bound(sFlat2,identity),
inference(step,[status(thm)],[t65,t66]) ).
cnf(t88,plain,
least_upper_bound(sFlat2,identity) = identity,
inference(orient,[status(thm)],[t2080]) ).
cnf(t2141,plain,
multiply(identity,sFlat3) = least_upper_bound(sFlat3,identity),
inference(step,[status(thm)],[t2140,t88]) ).
cnf(t2142,plain,
sFlat3 = least_upper_bound(sFlat3,identity),
inference(step,[status(thm)],[t2141,t19]) ).
cnf(t957,plain,
least_upper_bound(sFlat3,identity) = sFlat3,
inference(orient,[status(thm)],[t2142]) ).
cnf(t958,plain,
least_upper_bound(sFlat1,sFlat3) = least_upper_bound(sFlat0,sFlat3),
inference(cp,[status(thm)],[t410,t957]) ).
cnf(t976,plain,
least_upper_bound(sFlat1,sFlat3) = least_upper_bound(sFlat0,sFlat3),
inference(orient,[status(thm)],[t958]) ).
cnf(t897,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t896,t886]) ).
cnf(t2131,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t897,t896]) ).
cnf(t906,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t2131]) ).
cnf(t104,plain,
multiply(greatest_lower_bound(sFlat0,X1),a) = greatest_lower_bound(identity,multiply(X1,a)),
inference(cp,[status(thm)],[t28,t101]) ).
cnf(t1327,plain,
greatest_lower_bound(identity,multiply(X1,a)) = multiply(greatest_lower_bound(sFlat0,X1),a),
inference(orient,[status(thm)],[t104]) ).
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(t25,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t98,plain,
multiply(sFlat3,greatest_lower_bound(sFlat2,X1)) = greatest_lower_bound(identity,multiply(sFlat3,X1)),
inference(cp,[status(thm)],[t25,t91]) ).
cnf(t1291,plain,
greatest_lower_bound(identity,multiply(sFlat3,X1)) = multiply(sFlat3,greatest_lower_bound(sFlat2,X1)),
inference(orient,[status(thm)],[t98]) ).
cnf(t1328,plain,
multiply(greatest_lower_bound(sFlat0,sFlat3),a) = multiply(sFlat3,greatest_lower_bound(sFlat2,a)),
inference(cp,[status(thm)],[t1327,t1291]) ).
cnf(t123,plain,
a = least_upper_bound(a,sFlat2),
inference(cp,[status(thm)],[t118,t63]) ).
cnf(t2083,plain,
a = least_upper_bound(sFlat2,a),
inference(step,[status(thm)],[t123,t66]) ).
cnf(t128,plain,
least_upper_bound(sFlat2,a) = a,
inference(orient,[status(thm)],[t2083]) ).
cnf(t129,plain,
sFlat2 = greatest_lower_bound(sFlat2,a),
inference(cp,[status(thm)],[t21,t128]) ).
cnf(t131,plain,
greatest_lower_bound(sFlat2,a) = sFlat2,
inference(orient,[status(thm)],[t129]) ).
cnf(t2167,plain,
multiply(greatest_lower_bound(sFlat0,sFlat3),a) = multiply(sFlat3,sFlat2),
inference(step,[status(thm)],[t1328,t131]) ).
cnf(t2168,plain,
multiply(greatest_lower_bound(sFlat0,sFlat3),a) = identity,
inference(step,[status(thm)],[t2167,t91]) ).
cnf(t1337,plain,
multiply(greatest_lower_bound(sFlat0,sFlat3),a) = identity,
inference(orient,[status(thm)],[t2168]) ).
cnf(t1339,plain,
a = multiply(inverse(greatest_lower_bound(sFlat0,sFlat3)),identity),
inference(cp,[status(thm)],[t626,t1337]) ).
cnf(t2169,plain,
a = inverse(greatest_lower_bound(sFlat0,sFlat3)),
inference(step,[status(thm)],[t1339,t896]) ).
cnf(t1350,plain,
inverse(greatest_lower_bound(sFlat0,sFlat3)) = a,
inference(orient,[status(thm)],[t2169]) ).
cnf(t1351,plain,
greatest_lower_bound(sFlat0,sFlat3) = inverse(a),
inference(cp,[status(thm)],[t906,t1350]) ).
cnf(t2170,plain,
greatest_lower_bound(sFlat0,sFlat3) = sFlat0,
inference(step,[status(thm)],[t1351,t85]) ).
cnf(t1356,plain,
greatest_lower_bound(sFlat0,sFlat3) = sFlat0,
inference(orient,[status(thm)],[t2170]) ).
cnf(t1358,plain,
sFlat3 = least_upper_bound(sFlat3,sFlat0),
inference(cp,[status(thm)],[t118,t1356]) ).
cnf(t2171,plain,
sFlat3 = least_upper_bound(sFlat0,sFlat3),
inference(step,[status(thm)],[t1358,t66]) ).
cnf(t1360,plain,
least_upper_bound(sFlat0,sFlat3) = sFlat3,
inference(orient,[status(thm)],[t2171]) ).
cnf(t2172,plain,
least_upper_bound(sFlat1,sFlat3) = sFlat3,
inference(step,[status(thm)],[t976,t1360]) ).
cnf(t1361,plain,
least_upper_bound(sFlat1,sFlat3) = sFlat3,
inference(orient,[status(thm)],[t2172]) ).
cnf(t2250,plain,
multiply(sFlat2,sFlat3) = multiply(sFlat2,sFlat1),
inference(step,[status(thm)],[t2249,t1361]) ).
cnf(t2251,plain,
identity = multiply(sFlat2,sFlat1),
inference(step,[status(thm)],[t2250,t785]) ).
cnf(t2033,plain,
multiply(sFlat2,sFlat1) = identity,
inference(orient,[status(thm)],[t2251]) ).
cnf(t2040,plain,
sFlat1 = multiply(inverse(sFlat2),identity),
inference(cp,[status(thm)],[t626,t2033]) ).
cnf(t2254,plain,
sFlat1 = inverse(sFlat2),
inference(step,[status(thm)],[t2040,t896]) ).
cnf(t2255,plain,
sFlat1 = sFlat3,
inference(step,[status(thm)],[t2254,t83]) ).
cnf(t2052,plain,
sFlat3 = sFlat1,
inference(orient,[status(thm)],[t2255]) ).
cnf(t2256,plain,
inverse(sFlat2) = sFlat1,
inference(step,[status(thm)],[t83,t2052]) ).
cnf(t2053,plain,
inverse(sFlat2) = sFlat1,
inference(orient,[status(thm)],[t2256]) ).
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,t66]) ).
cnf(g0_1,plain,
least_upper_bound(identity,sFlat0) != inverse(greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[g0_0,t85]) ).
cnf(g0_2,plain,
least_upper_bound(sFlat0,identity) != inverse(greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[g0_1,t66]) ).
cnf(g0_3,plain,
sFlat1 != inverse(greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[g0_2,t111]) ).
cnf(g0_4,plain,
sFlat1 != inverse(greatest_lower_bound(identity,a)),
inference(rw,[status(thm)],[g0_3,t49]) ).
cnf(g0_5,plain,
sFlat1 != inverse(sFlat2),
inference(rw,[status(thm)],[g0_4,t63]) ).
cnf(g0_6,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_5,t2053]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP179-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.39 % Computer : n019.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Wed Sep 23 14:00:35 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.80/2.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.80/2.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------