%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP181-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 27.34s 3.98s
% Output : CNFRefutation 27.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 15
% Syntax : Number of clauses : 200 ( 200 unt; 0 nHn; 41 RR)
% Number of literals : 200 ( 199 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 307 ( 55 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t12,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t37,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t46,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t22,t37]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t100166,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t46,t17]) ).
cnf(t129,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t100166]) ).
cnf(t130,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t129,t37]) ).
cnf(t148,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t130]) ).
cnf(t133,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t129,t129]) ).
cnf(t167,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t133]) ).
cnf(t100167,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t148,t167]) ).
cnf(t174,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t100167]) ).
cnf(t175,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t174]) ).
cnf(t176,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t175,t167]) ).
cnf(t100168,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t176,t175]) ).
cnf(t181,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t100168]) ).
cnf(t183,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t37,t181]) ).
cnf(t184,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t183]) ).
cnf(t185,plain,
identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))),
inference(cp,[status(thm)],[t184,t22]) ).
cnf(t1481,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(orient,[status(thm)],[t185]) ).
cnf(t1509,plain,
multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity),
inference(cp,[status(thm)],[t129,t1481]) ).
cnf(t100211,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(step,[status(thm)],[t1509,t175]) ).
cnf(t1526,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(orient,[status(thm)],[t100211]) ).
cnf(t16,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t32,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t16]) ).
cnf(t38,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(cp,[status(thm)],[t32,t37]) ).
cnf(t748,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(orient,[status(thm)],[t38]) ).
cnf(t15,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
cnf(t177,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t25,t175]) ).
cnf(t244,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t177]) ).
cnf(t182,plain,
X1 = multiply(X2,multiply(inverse(X2),X1)),
inference(cp,[status(thm)],[t129,t181]) ).
cnf(t195,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t182]) ).
cnf(t248,plain,
multiply(X1,least_upper_bound(identity,multiply(inverse(X1),X2))) = least_upper_bound(X1,X2),
inference(cp,[status(thm)],[t244,t195]) ).
cnf(t3376,plain,
multiply(X1,least_upper_bound(identity,multiply(inverse(X1),X2))) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t248]) ).
cnf(t42,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(cp,[status(thm)],[t25,t37]) ).
cnf(t6384,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t42]) ).
cnf(t8,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t21,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t47,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t50,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t21,t47]) ).
cnf(t79,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t50]) ).
cnf(t6408,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = multiply(inverse(X1),X1),
inference(cp,[status(thm)],[t6384,t79]) ).
cnf(t100309,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = identity,
inference(step,[status(thm)],[t6408,t37]) ).
cnf(t6535,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = identity,
inference(orient,[status(thm)],[t100309]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t251,plain,
multiply(inverse(X1),least_upper_bound(identity,multiply(X1,X2))) = least_upper_bound(inverse(X1),X2),
inference(cp,[status(thm)],[t244,t129]) ).
cnf(t10421,plain,
multiply(inverse(X1),least_upper_bound(identity,multiply(X1,X2))) = least_upper_bound(inverse(X1),X2),
inference(orient,[status(thm)],[t251]) ).
cnf(t14,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t26,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t41,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(multiply(X1,X2),identity),
inference(cp,[status(thm)],[t26,t37]) ).
cnf(t100187,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(step,[status(thm)],[t41,t47]) ).
cnf(t820,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t100187]) ).
cnf(t10447,plain,
least_upper_bound(inverse(greatest_lower_bound(X1,inverse(X2))),X2) = multiply(inverse(greatest_lower_bound(X1,inverse(X2))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X1,X2)))),
inference(cp,[status(thm)],[t10421,t820]) ).
cnf(t7,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t63,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t100333,plain,
least_upper_bound(X2,inverse(greatest_lower_bound(X1,inverse(X2)))) = multiply(inverse(greatest_lower_bound(X1,inverse(X2))),least_upper_bound(identity,greatest_lower_bound(identity,multiply(X1,X2)))),
inference(step,[status(thm)],[t10447,t63]) ).
cnf(t100334,plain,
least_upper_bound(X2,inverse(greatest_lower_bound(X1,inverse(X2)))) = multiply(inverse(greatest_lower_bound(X1,inverse(X2))),identity),
inference(step,[status(thm)],[t100333,t21]) ).
cnf(t100335,plain,
least_upper_bound(X2,inverse(greatest_lower_bound(X1,inverse(X2)))) = inverse(greatest_lower_bound(X1,inverse(X2))),
inference(step,[status(thm)],[t100334,t175]) ).
cnf(t10501,plain,
least_upper_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = inverse(greatest_lower_bound(X2,inverse(X1))),
inference(orient,[status(thm)],[t100335]) ).
cnf(t10523,plain,
X1 = greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))),
inference(cp,[status(thm)],[t19,t10501]) ).
cnf(t10570,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = X1,
inference(orient,[status(thm)],[t10523]) ).
cnf(t10584,plain,
inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))),
inference(cp,[status(thm)],[t10570,t181]) ).
cnf(t10658,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(X1),
inference(orient,[status(thm)],[t10584]) ).
cnf(t10772,plain,
identity = least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X1,X2))),inverse(X2))),
inference(cp,[status(thm)],[t6535,t10658]) ).
cnf(t100340,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X1,X2),inverse(X2))),
inference(step,[status(thm)],[t10772,t167]) ).
cnf(t11002,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X1,X2),inverse(X2))) = identity,
inference(orient,[status(thm)],[t100340]) ).
cnf(t11031,plain,
identity = least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))),
inference(cp,[status(thm)],[t11002,t19]) ).
cnf(t11416,plain,
least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = identity,
inference(orient,[status(thm)],[t11031]) ).
cnf(t11458,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = multiply(X1,identity),
inference(cp,[status(thm)],[t3376,t11416]) ).
cnf(t100345,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1,
inference(step,[status(thm)],[t11458,t175]) ).
cnf(t11461,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1,
inference(orient,[status(thm)],[t100345]) ).
cnf(t11463,plain,
X1 = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))),
inference(cp,[status(thm)],[t11461,t63]) ).
cnf(t11496,plain,
least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = X1,
inference(orient,[status(thm)],[t11463]) ).
cnf(t11509,plain,
inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))),
inference(cp,[status(thm)],[t11496,t181]) ).
cnf(t11581,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1),
inference(orient,[status(thm)],[t11509]) ).
cnf(t10,axiom,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t51,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t83,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))),
inference(cp,[status(thm)],[t79,t51]) ).
cnf(t426,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(orient,[status(thm)],[t83]) ).
cnf(t429,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(greatest_lower_bound(X2,X1),X3)),
inference(cp,[status(thm)],[t426,t47]) ).
cnf(t100171,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))),
inference(step,[status(thm)],[t429,t51]) ).
cnf(t463,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1,
inference(orient,[status(thm)],[t100171]) ).
cnf(t6,axiom,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t100154,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(a,c),
inference(step,[status(thm)],[t6,t47]) ).
cnf(t100155,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,a),
inference(step,[status(thm)],[t100154,t47]) ).
cnf(t61,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(orient,[status(thm)],[t100155]) ).
cnf(t62,plain,
greatest_lower_bound(c,greatest_lower_bound(a,X1)) = greatest_lower_bound(greatest_lower_bound(c,b),X1),
inference(cp,[status(thm)],[t51,t61]) ).
cnf(t100169,plain,
greatest_lower_bound(c,greatest_lower_bound(a,X1)) = greatest_lower_bound(c,greatest_lower_bound(b,X1)),
inference(step,[status(thm)],[t62,t51]) ).
cnf(t226,plain,
greatest_lower_bound(c,greatest_lower_bound(a,X1)) = greatest_lower_bound(c,greatest_lower_bound(b,X1)),
inference(orient,[status(thm)],[t100169]) ).
cnf(t27,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t26,t17]) ).
cnf(t205,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t27]) ).
cnf(t227,plain,
greatest_lower_bound(c,greatest_lower_bound(b,multiply(X1,a))) = greatest_lower_bound(c,multiply(greatest_lower_bound(identity,X1),a)),
inference(cp,[status(thm)],[t226,t205]) ).
cnf(t19430,plain,
greatest_lower_bound(c,greatest_lower_bound(b,multiply(X1,a))) = greatest_lower_bound(c,multiply(greatest_lower_bound(identity,X1),a)),
inference(orient,[status(thm)],[t227]) ).
cnf(t19467,plain,
b = least_upper_bound(b,greatest_lower_bound(c,multiply(greatest_lower_bound(identity,X1),a))),
inference(cp,[status(thm)],[t463,t19430]) ).
cnf(t19479,plain,
least_upper_bound(b,greatest_lower_bound(c,multiply(greatest_lower_bound(identity,X1),a))) = b,
inference(orient,[status(thm)],[t19467]) ).
cnf(t209,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t205,t184]) ).
cnf(t100173,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t209,t47]) ).
cnf(t526,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t100173]) ).
cnf(t529,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = multiply(identity,inverse(least_upper_bound(identity,X1))),
inference(cp,[status(thm)],[t526,t19]) ).
cnf(t100179,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(step,[status(thm)],[t529,t17]) ).
cnf(t680,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(orient,[status(thm)],[t100179]) ).
cnf(t19481,plain,
b = least_upper_bound(b,greatest_lower_bound(c,multiply(inverse(least_upper_bound(identity,X1)),a))),
inference(cp,[status(thm)],[t19479,t680]) ).
cnf(t98855,plain,
least_upper_bound(b,greatest_lower_bound(c,multiply(inverse(least_upper_bound(identity,X1)),a))) = b,
inference(orient,[status(thm)],[t19481]) ).
cnf(t1564,plain,
inverse(X1) = multiply(inverse(multiply(X2,X1)),inverse(inverse(X2))),
inference(cp,[status(thm)],[t1526,t1526]) ).
cnf(t1553,plain,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
inference(cp,[status(thm)],[t129,t1526]) ).
cnf(t1569,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t1553]) ).
cnf(t100212,plain,
inverse(X1) = inverse(multiply(inverse(X2),multiply(X2,X1))),
inference(step,[status(thm)],[t1564,t1569]) ).
cnf(t1571,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t1569,t181]) ).
cnf(t1623,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t1571]) ).
cnf(t100213,plain,
inverse(X1) = multiply(inverse(multiply(X2,X1)),X2),
inference(step,[status(thm)],[t100212,t1623]) ).
cnf(t1655,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(orient,[status(thm)],[t100213]) ).
cnf(t190,plain,
multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)),
inference(cp,[status(thm)],[t25,t184]) ).
cnf(t844,plain,
multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t190]) ).
cnf(t1658,plain,
inverse(least_upper_bound(inverse(X1),X2)) = multiply(inverse(least_upper_bound(identity,multiply(X1,X2))),X1),
inference(cp,[status(thm)],[t1655,t844]) ).
cnf(t31437,plain,
multiply(inverse(least_upper_bound(identity,multiply(X1,X2))),X1) = inverse(least_upper_bound(inverse(X1),X2)),
inference(orient,[status(thm)],[t1658]) ).
cnf(t98857,plain,
b = least_upper_bound(b,greatest_lower_bound(c,inverse(least_upper_bound(inverse(a),X1)))),
inference(cp,[status(thm)],[t98855,t31437]) ).
cnf(t98995,plain,
least_upper_bound(b,greatest_lower_bound(c,inverse(least_upper_bound(inverse(a),X1)))) = b,
inference(orient,[status(thm)],[t98857]) ).
cnf(t66,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t19,t63]) ).
cnf(t85,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t66]) ).
cnf(t11515,plain,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(inverse(least_upper_bound(X1,inverse(X2))),X2),
inference(cp,[status(thm)],[t85,t11496]) ).
cnf(t100357,plain,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(X2,inverse(least_upper_bound(X1,inverse(X2)))),
inference(step,[status(thm)],[t11515,t47]) ).
cnf(t12382,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_bound(X2,inverse(X1))),
inference(orient,[status(thm)],[t100357]) ).
cnf(t98996,plain,
b = least_upper_bound(b,inverse(least_upper_bound(inverse(a),inverse(c)))),
inference(cp,[status(thm)],[t98995,t12382]) ).
cnf(t100841,plain,
b = least_upper_bound(b,inverse(least_upper_bound(inverse(c),inverse(a)))),
inference(step,[status(thm)],[t98996,t63]) ).
cnf(t99073,plain,
least_upper_bound(b,inverse(least_upper_bound(inverse(c),inverse(a)))) = b,
inference(orient,[status(thm)],[t100841]) ).
cnf(t99087,plain,
inverse(inverse(least_upper_bound(inverse(c),inverse(a)))) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(c),inverse(a)))),inverse(b)),
inference(cp,[status(thm)],[t11581,t99073]) ).
cnf(t100850,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(c),inverse(a)))),inverse(b)),
inference(step,[status(thm)],[t99087,t181]) ).
cnf(t100851,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(b),inverse(inverse(least_upper_bound(inverse(c),inverse(a))))),
inference(step,[status(thm)],[t100850,t63]) ).
cnf(t100852,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(b),least_upper_bound(inverse(c),inverse(a))),
inference(step,[status(thm)],[t100851,t181]) ).
cnf(t11,axiom,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t67,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t75,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X2,X1),X3),
inference(cp,[status(thm)],[t67,t63]) ).
cnf(t100494,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(step,[status(thm)],[t75,t67]) ).
cnf(t28618,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(orient,[status(thm)],[t100494]) ).
cnf(t100853,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(c),least_upper_bound(inverse(b),inverse(a))),
inference(step,[status(thm)],[t100852,t28618]) ).
cnf(t436,plain,
a = least_upper_bound(a,greatest_lower_bound(X1,greatest_lower_bound(c,b))),
inference(cp,[status(thm)],[t426,t61]) ).
cnf(t477,plain,
least_upper_bound(a,greatest_lower_bound(X1,greatest_lower_bound(c,b))) = a,
inference(orient,[status(thm)],[t436]) ).
cnf(t479,plain,
a = least_upper_bound(a,greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(c,b)))),
inference(cp,[status(thm)],[t477,t51]) ).
cnf(t4028,plain,
least_upper_bound(a,greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(c,b)))) = a,
inference(orient,[status(thm)],[t479]) ).
cnf(t87,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(greatest_lower_bound(X1,X2),X1),
inference(cp,[status(thm)],[t85,t21]) ).
cnf(t100159,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)),
inference(step,[status(thm)],[t87,t51]) ).
cnf(t111,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
inference(orient,[status(thm)],[t100159]) ).
cnf(t114,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))),
inference(cp,[status(thm)],[t111,t51]) ).
cnf(t2874,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t114]) ).
cnf(t4029,plain,
a = least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(X1,c))),
inference(cp,[status(thm)],[t4028,t2874]) ).
cnf(t4040,plain,
least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(X1,c))) = a,
inference(orient,[status(thm)],[t4029]) ).
cnf(t4046,plain,
a = least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))),
inference(cp,[status(thm)],[t4040,t47]) ).
cnf(t4055,plain,
least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))) = a,
inference(orient,[status(thm)],[t4046]) ).
cnf(t11471,plain,
inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(least_upper_bound(inverse(X1),X2)),X1),
inference(cp,[status(thm)],[t85,t11461]) ).
cnf(t100356,plain,
inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))),
inference(step,[status(thm)],[t11471,t47]) ).
cnf(t12329,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)),
inference(orient,[status(thm)],[t100356]) ).
cnf(t12352,plain,
a = least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))),
inference(cp,[status(thm)],[t4055,t12329]) ).
cnf(t14410,plain,
least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))) = a,
inference(orient,[status(thm)],[t12352]) ).
cnf(t14411,plain,
a = least_upper_bound(a,inverse(least_upper_bound(inverse(c),inverse(b)))),
inference(cp,[status(thm)],[t14410,t12382]) ).
cnf(t14474,plain,
least_upper_bound(a,inverse(least_upper_bound(inverse(c),inverse(b)))) = a,
inference(orient,[status(thm)],[t14411]) ).
cnf(t14479,plain,
inverse(inverse(least_upper_bound(inverse(c),inverse(b)))) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(c),inverse(b)))),inverse(a)),
inference(cp,[status(thm)],[t11581,t14474]) ).
cnf(t100508,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(c),inverse(b)))),inverse(a)),
inference(step,[status(thm)],[t14479,t181]) ).
cnf(t100509,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(a),inverse(inverse(least_upper_bound(inverse(c),inverse(b))))),
inference(step,[status(thm)],[t100508,t63]) ).
cnf(t100510,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(a),least_upper_bound(inverse(c),inverse(b))),
inference(step,[status(thm)],[t100509,t181]) ).
cnf(t70,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)),
inference(cp,[status(thm)],[t67,t63]) ).
cnf(t27934,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)),
inference(orient,[status(thm)],[t70]) ).
cnf(t81,plain,
least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1),
inference(cp,[status(thm)],[t79,t19]) ).
cnf(t100158,plain,
least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t81,t67]) ).
cnf(t105,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t100158]) ).
cnf(t27988,plain,
least_upper_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t27934,t105]) ).
cnf(t100497,plain,
least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X2))) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t27988,t67]) ).
cnf(t100498,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t100497,t105]) ).
cnf(t29297,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(orient,[status(thm)],[t100498]) ).
cnf(t100511,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(b),least_upper_bound(inverse(c),inverse(a))),
inference(step,[status(thm)],[t100510,t29297]) ).
cnf(t100512,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(c),least_upper_bound(inverse(b),inverse(a))),
inference(step,[status(thm)],[t100511,t28618]) ).
cnf(t31977,plain,
least_upper_bound(inverse(c),least_upper_bound(inverse(b),inverse(a))) = least_upper_bound(inverse(c),inverse(b)),
inference(orient,[status(thm)],[t100512]) ).
cnf(t100854,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(c),inverse(b)),
inference(step,[status(thm)],[t100853,t31977]) ).
cnf(t99879,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(c),inverse(b)),
inference(orient,[status(thm)],[t100854]) ).
cnf(t99914,plain,
least_upper_bound(identity,multiply(inverse(a),c)) = multiply(least_upper_bound(inverse(c),inverse(b)),c),
inference(cp,[status(thm)],[t748,t99879]) ).
cnf(t43,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity),
inference(cp,[status(thm)],[t25,t37]) ).
cnf(t100330,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(step,[status(thm)],[t43,t63]) ).
cnf(t9101,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t100330]) ).
cnf(t100858,plain,
multiply(inverse(a),least_upper_bound(c,a)) = multiply(least_upper_bound(inverse(c),inverse(b)),c),
inference(step,[status(thm)],[t99914,t9101]) ).
cnf(t9,axiom,
least_upper_bound(b,c) = least_upper_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t100156,plain,
least_upper_bound(c,b) = least_upper_bound(a,c),
inference(step,[status(thm)],[t9,t63]) ).
cnf(t100157,plain,
least_upper_bound(c,b) = least_upper_bound(c,a),
inference(step,[status(thm)],[t100156,t63]) ).
cnf(t77,plain,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(orient,[status(thm)],[t100157]) ).
cnf(t100859,plain,
multiply(inverse(a),least_upper_bound(c,b)) = multiply(least_upper_bound(inverse(c),inverse(b)),c),
inference(step,[status(thm)],[t100858,t77]) ).
cnf(t100860,plain,
multiply(inverse(a),least_upper_bound(c,b)) = least_upper_bound(identity,multiply(inverse(b),c)),
inference(step,[status(thm)],[t100859,t748]) ).
cnf(t100861,plain,
multiply(inverse(a),least_upper_bound(c,b)) = multiply(inverse(b),least_upper_bound(c,b)),
inference(step,[status(thm)],[t100860,t9101]) ).
cnf(t100067,plain,
multiply(inverse(a),least_upper_bound(c,b)) = multiply(inverse(b),least_upper_bound(c,b)),
inference(orient,[status(thm)],[t100861]) ).
cnf(t100119,plain,
inverse(inverse(a)) = multiply(least_upper_bound(c,b),inverse(multiply(inverse(b),least_upper_bound(c,b)))),
inference(cp,[status(thm)],[t1526,t100067]) ).
cnf(t100862,plain,
a = multiply(least_upper_bound(c,b),inverse(multiply(inverse(b),least_upper_bound(c,b)))),
inference(step,[status(thm)],[t100119,t181]) ).
cnf(t100863,plain,
a = inverse(inverse(b)),
inference(step,[status(thm)],[t100862,t1526]) ).
cnf(t100864,plain,
a = b,
inference(step,[status(thm)],[t100863,t181]) ).
cnf(t100138,plain,
a = b,
inference(orient,[status(thm)],[t100864]) ).
cnf(goal_0,negated_conjecture,
b != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
b != b,
inference(rw,[status(thm)],[goal_0,t100138]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP181-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 14:00:56 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.34/3.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.34/3.98 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------