%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP185-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:25:37 PM UTC 2026
% Result : Unsatisfiable 7.50s 1.57s
% Output : CNFRefutation 7.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 20
% Syntax : Number of clauses : 247 ( 247 unt; 0 nHn; 141 RR)
% Number of literals : 247 ( 246 equ; 15 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 : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 145 ( 24 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t89,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t18,axiom,
sFlat0 = multiply(a,b),
introduced(definition) ).
cnf(t79,plain,
multiply(a,b) = sFlat0,
inference(orient,[status(thm)],[t18]) ).
cnf(t19,axiom,
sFlat1 = least_upper_bound(multiply(a,b),identity),
introduced(definition) ).
cnf(t4661,plain,
sFlat1 = least_upper_bound(identity,multiply(a,b)),
inference(step,[status(thm)],[t19,t89]) ).
cnf(t4662,plain,
sFlat1 = least_upper_bound(identity,sFlat0),
inference(step,[status(thm)],[t4661,t79]) ).
cnf(t4663,plain,
sFlat1 = least_upper_bound(sFlat0,identity),
inference(step,[status(thm)],[t4662,t89]) ).
cnf(t104,plain,
least_upper_bound(sFlat0,identity) = sFlat1,
inference(orient,[status(thm)],[t4663]) ).
cnf(t20,axiom,
sFlat2 = least_upper_bound(a,identity),
introduced(definition) ).
cnf(t4664,plain,
sFlat2 = least_upper_bound(identity,a),
inference(step,[status(thm)],[t20,t89]) ).
cnf(t107,plain,
least_upper_bound(identity,a) = sFlat2,
inference(orient,[status(thm)],[t4664]) ).
cnf(t21,axiom,
sFlat3 = least_upper_bound(b,identity),
introduced(definition) ).
cnf(t4665,plain,
sFlat3 = least_upper_bound(identity,b),
inference(step,[status(thm)],[t21,t89]) ).
cnf(t110,plain,
least_upper_bound(identity,b) = sFlat3,
inference(orient,[status(thm)],[t4665]) ).
cnf(t22,axiom,
sFlat4 = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
introduced(definition) ).
cnf(t40,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = sFlat4,
inference(orient,[status(thm)],[t22]) ).
cnf(t93,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = sFlat4,
inference(rw,[status(thm)],[t40]) ).
cnf(t4861,plain,
multiply(least_upper_bound(identity,a),least_upper_bound(b,identity)) = sFlat4,
inference(step,[status(thm)],[t93,t89]) ).
cnf(t4862,plain,
multiply(sFlat2,least_upper_bound(b,identity)) = sFlat4,
inference(step,[status(thm)],[t4861,t107]) ).
cnf(t4863,plain,
multiply(sFlat2,least_upper_bound(identity,b)) = sFlat4,
inference(step,[status(thm)],[t4862,t89]) ).
cnf(t4864,plain,
multiply(sFlat2,sFlat3) = sFlat4,
inference(step,[status(thm)],[t4863,t110]) ).
cnf(t3533,plain,
multiply(sFlat2,sFlat3) = sFlat4,
inference(orient,[status(thm)],[t4864]) ).
cnf(t23,axiom,
sFlat5 = greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
introduced(definition) ).
cnf(t4666,plain,
sFlat5 = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t23,t89]) ).
cnf(t4667,plain,
sFlat5 = greatest_lower_bound(least_upper_bound(identity,sFlat0),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t4666,t79]) ).
cnf(t4668,plain,
sFlat5 = greatest_lower_bound(least_upper_bound(sFlat0,identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t4667,t89]) ).
cnf(t4669,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t4668,t104]) ).
cnf(t4670,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(least_upper_bound(identity,a),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t4669,t89]) ).
cnf(t4671,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(sFlat2,least_upper_bound(b,identity))),
inference(step,[status(thm)],[t4670,t107]) ).
cnf(t4672,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(sFlat2,least_upper_bound(identity,b))),
inference(step,[status(thm)],[t4671,t89]) ).
cnf(t4673,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t4672,t110]) ).
cnf(t127,plain,
greatest_lower_bound(sFlat1,multiply(sFlat2,sFlat3)) = sFlat5,
inference(orient,[status(thm)],[t4673]) ).
cnf(t4886,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat5,
inference(step,[status(thm)],[t127,t3533]) ).
cnf(t3575,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat5,
inference(rw,[status(thm)],[t4886]) ).
cnf(t3620,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat5,
inference(orient,[status(thm)],[t3575]) ).
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t12,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(t94,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(t105,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(cp,[status(thm)],[t94,t104]) ).
cnf(t234,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t105]) ).
cnf(t3,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
least_upper_bound(X1,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t98,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(cp,[status(thm)],[t94,t25]) ).
cnf(t228,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t98]) ).
cnf(t111,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(sFlat3,X1),
inference(cp,[status(thm)],[t94,t110]) ).
cnf(t338,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t111]) ).
cnf(t345,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(identity,least_upper_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t228,t338]) ).
cnf(t4708,plain,
least_upper_bound(sFlat3,X1) = least_upper_bound(identity,least_upper_bound(sFlat3,X1)),
inference(step,[status(thm)],[t345,t338]) ).
cnf(t649,plain,
least_upper_bound(identity,least_upper_bound(sFlat3,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t4708]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t26,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t112,plain,
identity = greatest_lower_bound(identity,sFlat3),
inference(cp,[status(thm)],[t28,t110]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t113,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t4675,plain,
identity = greatest_lower_bound(sFlat3,identity),
inference(step,[status(thm)],[t112,t113]) ).
cnf(t138,plain,
greatest_lower_bound(sFlat3,identity) = identity,
inference(orient,[status(thm)],[t4675]) ).
cnf(t139,plain,
sFlat3 = least_upper_bound(sFlat3,identity),
inference(cp,[status(thm)],[t26,t138]) ).
cnf(t145,plain,
least_upper_bound(sFlat3,identity) = sFlat3,
inference(orient,[status(thm)],[t139]) ).
cnf(t146,plain,
least_upper_bound(sFlat3,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(cp,[status(thm)],[t94,t145]) ).
cnf(t431,plain,
least_upper_bound(sFlat3,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t146]) ).
cnf(t108,plain,
least_upper_bound(identity,least_upper_bound(a,X1)) = least_upper_bound(sFlat2,X1),
inference(cp,[status(thm)],[t94,t107]) ).
cnf(t304,plain,
least_upper_bound(identity,least_upper_bound(a,X1)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t108]) ).
cnf(t309,plain,
least_upper_bound(sFlat2,X1) = least_upper_bound(identity,least_upper_bound(X1,a)),
inference(cp,[status(thm)],[t304,t89]) ).
cnf(t592,plain,
least_upper_bound(identity,least_upper_bound(X1,a)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t309]) ).
cnf(t16,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(t31,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t86,plain,
multiply(a,least_upper_bound(b,X1)) = least_upper_bound(sFlat0,multiply(a,X1)),
inference(cp,[status(thm)],[t31,t79]) ).
cnf(t1324,plain,
least_upper_bound(sFlat0,multiply(a,X1)) = multiply(a,least_upper_bound(b,X1)),
inference(orient,[status(thm)],[t86]) ).
cnf(t2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t29,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/sandbox/benchmark/theBenchmark.p') ).
cnf(t66,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t10]) ).
cnf(t0,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t130,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t131,plain,
inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)),
inference(cp,[status(thm)],[t66,t130]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t4676,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(step,[status(thm)],[t131,t24]) ).
cnf(t158,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t4676]) ).
cnf(t162,plain,
multiply(X1,identity) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t29,t158]) ).
cnf(t4677,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t162,t29]) ).
cnf(t163,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t4677]) ).
cnf(t1330,plain,
multiply(a,least_upper_bound(b,identity)) = least_upper_bound(sFlat0,a),
inference(cp,[status(thm)],[t1324,t163]) ).
cnf(t4762,plain,
multiply(a,least_upper_bound(identity,b)) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t1330,t89]) ).
cnf(t4763,plain,
multiply(a,sFlat3) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t4762,t110]) ).
cnf(t1357,plain,
least_upper_bound(sFlat0,a) = multiply(a,sFlat3),
inference(orient,[status(thm)],[t4763]) ).
cnf(t1360,plain,
least_upper_bound(sFlat2,sFlat0) = least_upper_bound(identity,multiply(a,sFlat3)),
inference(cp,[status(thm)],[t592,t1357]) ).
cnf(t4766,plain,
least_upper_bound(sFlat0,sFlat2) = least_upper_bound(identity,multiply(a,sFlat3)),
inference(step,[status(thm)],[t1360,t89]) ).
cnf(t1379,plain,
least_upper_bound(identity,multiply(a,sFlat3)) = least_upper_bound(sFlat0,sFlat2),
inference(orient,[status(thm)],[t4766]) ).
cnf(t1381,plain,
least_upper_bound(sFlat3,multiply(a,sFlat3)) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(cp,[status(thm)],[t431,t1379]) ).
cnf(t17,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(t34,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
cnf(t35,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t34,t24]) ).
cnf(t262,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t35]) ).
cnf(t4769,plain,
multiply(least_upper_bound(identity,a),sFlat3) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(step,[status(thm)],[t1381,t262]) ).
cnf(t4770,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(step,[status(thm)],[t4769,t107]) ).
cnf(t1389,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t4770]) ).
cnf(t1391,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = least_upper_bound(identity,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t649,t1389]) ).
cnf(t4775,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(identity,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1391,t1389]) ).
cnf(t1419,plain,
least_upper_bound(identity,multiply(sFlat2,sFlat3)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t4775]) ).
cnf(t1421,plain,
least_upper_bound(sFlat1,multiply(sFlat2,sFlat3)) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t234,t1419]) ).
cnf(t1973,plain,
least_upper_bound(sFlat1,multiply(sFlat2,sFlat3)) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(orient,[status(thm)],[t1421]) ).
cnf(t4871,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1973,t3533]) ).
cnf(t4872,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(step,[status(thm)],[t4871,t3533]) ).
cnf(t3565,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(rw,[status(thm)],[t4872]) ).
cnf(t3626,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(orient,[status(thm)],[t3565]) ).
cnf(t3631,plain,
sFlat1 = greatest_lower_bound(sFlat1,least_upper_bound(sFlat0,sFlat4)),
inference(cp,[status(thm)],[t28,t3626]) ).
cnf(t3761,plain,
greatest_lower_bound(sFlat1,least_upper_bound(sFlat0,sFlat4)) = sFlat1,
inference(orient,[status(thm)],[t3631]) ).
cnf(t4878,plain,
least_upper_bound(identity,sFlat4) = multiply(sFlat2,sFlat3),
inference(step,[status(thm)],[t1419,t3533]) ).
cnf(t4879,plain,
least_upper_bound(identity,sFlat4) = sFlat4,
inference(step,[status(thm)],[t4878,t3533]) ).
cnf(t3569,plain,
least_upper_bound(identity,sFlat4) = sFlat4,
inference(rw,[status(thm)],[t4879]) ).
cnf(t4890,plain,
least_upper_bound(sFlat4,identity) = sFlat4,
inference(step,[status(thm)],[t3569,t89]) ).
cnf(t3590,plain,
least_upper_bound(sFlat4,identity) = sFlat4,
inference(orient,[status(thm)],[t4890]) ).
cnf(t3596,plain,
least_upper_bound(sFlat4,least_upper_bound(identity,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t94,t3590]) ).
cnf(t3875,plain,
least_upper_bound(sFlat4,least_upper_bound(identity,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t3596]) ).
cnf(t3884,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t3875,t338]) ).
cnf(t116,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t26,t113]) ).
cnf(t199,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t116]) ).
cnf(t92,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t28,t89]) ).
cnf(t168,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t92]) ).
cnf(t341,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = least_upper_bound(identity,b),
inference(cp,[status(thm)],[t338,t26]) ).
cnf(t4690,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = sFlat3,
inference(step,[status(thm)],[t341,t110]) ).
cnf(t348,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = sFlat3,
inference(orient,[status(thm)],[t4690]) ).
cnf(t350,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(greatest_lower_bound(b,X1),sFlat3),
inference(cp,[status(thm)],[t168,t348]) ).
cnf(t11,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(t117,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(t4709,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(b,greatest_lower_bound(X1,sFlat3)),
inference(step,[status(thm)],[t350,t117]) ).
cnf(t664,plain,
greatest_lower_bound(b,greatest_lower_bound(X1,sFlat3)) = greatest_lower_bound(b,X1),
inference(orient,[status(thm)],[t4709]) ).
cnf(t667,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(b,greatest_lower_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t664,t113]) ).
cnf(t864,plain,
greatest_lower_bound(b,greatest_lower_bound(sFlat3,X1)) = greatest_lower_bound(b,X1),
inference(orient,[status(thm)],[t667]) ).
cnf(t867,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = greatest_lower_bound(b,sFlat3),
inference(cp,[status(thm)],[t864,t28]) ).
cnf(t4738,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = greatest_lower_bound(sFlat3,b),
inference(step,[status(thm)],[t867,t113]) ).
cnf(t175,plain,
b = greatest_lower_bound(b,sFlat3),
inference(cp,[status(thm)],[t168,t110]) ).
cnf(t4680,plain,
b = greatest_lower_bound(sFlat3,b),
inference(step,[status(thm)],[t175,t113]) ).
cnf(t184,plain,
greatest_lower_bound(sFlat3,b) = b,
inference(orient,[status(thm)],[t4680]) ).
cnf(t4739,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = b,
inference(step,[status(thm)],[t4738,t184]) ).
cnf(t984,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = b,
inference(orient,[status(thm)],[t4739]) ).
cnf(t1390,plain,
b = greatest_lower_bound(b,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t984,t1389]) ).
cnf(t1416,plain,
greatest_lower_bound(b,multiply(sFlat2,sFlat3)) = b,
inference(orient,[status(thm)],[t1390]) ).
cnf(t1417,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(multiply(sFlat2,sFlat3),b),
inference(cp,[status(thm)],[t199,t1416]) ).
cnf(t4778,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(b,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1417,t89]) ).
cnf(t1510,plain,
least_upper_bound(b,multiply(sFlat2,sFlat3)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t4778]) ).
cnf(t4876,plain,
least_upper_bound(b,sFlat4) = multiply(sFlat2,sFlat3),
inference(step,[status(thm)],[t1510,t3533]) ).
cnf(t4877,plain,
least_upper_bound(b,sFlat4) = sFlat4,
inference(step,[status(thm)],[t4876,t3533]) ).
cnf(t3568,plain,
least_upper_bound(b,sFlat4) = sFlat4,
inference(rw,[status(thm)],[t4877]) ).
cnf(t4889,plain,
least_upper_bound(sFlat4,b) = sFlat4,
inference(step,[status(thm)],[t3568,t89]) ).
cnf(t3585,plain,
least_upper_bound(sFlat4,b) = sFlat4,
inference(orient,[status(thm)],[t4889]) ).
cnf(t3589,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t94,t3585]) ).
cnf(t3855,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t3589]) ).
cnf(t4927,plain,
least_upper_bound(sFlat4,X1) = least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)),
inference(step,[status(thm)],[t3884,t3855]) ).
cnf(t4323,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t4927]) ).
cnf(t4865,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(step,[status(thm)],[t1389,t3533]) ).
cnf(t3534,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(orient,[status(thm)],[t4865]) ).
cnf(t4328,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = least_upper_bound(sFlat4,sFlat4),
inference(cp,[status(thm)],[t4323,t3534]) ).
cnf(t4928,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(step,[status(thm)],[t4328,t25]) ).
cnf(t4345,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(orient,[status(thm)],[t4928]) ).
cnf(t201,plain,
least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1),
inference(cp,[status(thm)],[t199,t28]) ).
cnf(t4698,plain,
least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t201,t94]) ).
cnf(t497,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t4698]) ).
cnf(t307,plain,
least_upper_bound(sFlat2,greatest_lower_bound(a,X1)) = least_upper_bound(identity,a),
inference(cp,[status(thm)],[t304,t26]) ).
cnf(t4688,plain,
least_upper_bound(sFlat2,greatest_lower_bound(a,X1)) = sFlat2,
inference(step,[status(thm)],[t307,t107]) ).
cnf(t314,plain,
least_upper_bound(sFlat2,greatest_lower_bound(a,X1)) = sFlat2,
inference(orient,[status(thm)],[t4688]) ).
cnf(t316,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(greatest_lower_bound(a,X1),sFlat2),
inference(cp,[status(thm)],[t168,t314]) ).
cnf(t4706,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(a,greatest_lower_bound(X1,sFlat2)),
inference(step,[status(thm)],[t316,t117]) ).
cnf(t621,plain,
greatest_lower_bound(a,greatest_lower_bound(X1,sFlat2)) = greatest_lower_bound(a,X1),
inference(orient,[status(thm)],[t4706]) ).
cnf(t624,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(a,greatest_lower_bound(sFlat2,X1)),
inference(cp,[status(thm)],[t621,t113]) ).
cnf(t836,plain,
greatest_lower_bound(a,greatest_lower_bound(sFlat2,X1)) = greatest_lower_bound(a,X1),
inference(orient,[status(thm)],[t624]) ).
cnf(t839,plain,
greatest_lower_bound(a,least_upper_bound(sFlat2,X1)) = greatest_lower_bound(a,sFlat2),
inference(cp,[status(thm)],[t836,t28]) ).
cnf(t4736,plain,
greatest_lower_bound(a,least_upper_bound(sFlat2,X1)) = greatest_lower_bound(sFlat2,a),
inference(step,[status(thm)],[t839,t113]) ).
cnf(t174,plain,
a = greatest_lower_bound(a,sFlat2),
inference(cp,[status(thm)],[t168,t107]) ).
cnf(t4679,plain,
a = greatest_lower_bound(sFlat2,a),
inference(step,[status(thm)],[t174,t113]) ).
cnf(t181,plain,
greatest_lower_bound(sFlat2,a) = a,
inference(orient,[status(thm)],[t4679]) ).
cnf(t4737,plain,
greatest_lower_bound(a,least_upper_bound(sFlat2,X1)) = a,
inference(step,[status(thm)],[t4736,t181]) ).
cnf(t967,plain,
greatest_lower_bound(a,least_upper_bound(sFlat2,X1)) = a,
inference(orient,[status(thm)],[t4737]) ).
cnf(t313,plain,
identity = greatest_lower_bound(identity,least_upper_bound(sFlat2,X1)),
inference(cp,[status(thm)],[t28,t304]) ).
cnf(t322,plain,
greatest_lower_bound(identity,least_upper_bound(sFlat2,X1)) = identity,
inference(orient,[status(thm)],[t313]) ).
cnf(t332,plain,
least_upper_bound(sFlat2,X1) = least_upper_bound(least_upper_bound(sFlat2,X1),identity),
inference(cp,[status(thm)],[t199,t322]) ).
cnf(t4707,plain,
least_upper_bound(sFlat2,X1) = least_upper_bound(sFlat2,least_upper_bound(X1,identity)),
inference(step,[status(thm)],[t332,t94]) ).
cnf(t627,plain,
least_upper_bound(sFlat2,least_upper_bound(X1,identity)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t4707]) ).
cnf(t267,plain,
multiply(least_upper_bound(identity,a),b) = least_upper_bound(b,sFlat0),
inference(cp,[status(thm)],[t262,t79]) ).
cnf(t4686,plain,
multiply(sFlat2,b) = least_upper_bound(b,sFlat0),
inference(step,[status(thm)],[t267,t107]) ).
cnf(t4687,plain,
multiply(sFlat2,b) = least_upper_bound(sFlat0,b),
inference(step,[status(thm)],[t4686,t89]) ).
cnf(t274,plain,
least_upper_bound(sFlat0,b) = multiply(sFlat2,b),
inference(orient,[status(thm)],[t4687]) ).
cnf(t277,plain,
least_upper_bound(sFlat0,least_upper_bound(b,X1)) = least_upper_bound(multiply(sFlat2,b),X1),
inference(cp,[status(thm)],[t94,t274]) ).
cnf(t1757,plain,
least_upper_bound(multiply(sFlat2,b),X1) = least_upper_bound(sFlat0,least_upper_bound(b,X1)),
inference(orient,[status(thm)],[t277]) ).
cnf(t1776,plain,
least_upper_bound(sFlat2,multiply(sFlat2,b)) = least_upper_bound(sFlat2,least_upper_bound(sFlat0,least_upper_bound(b,identity))),
inference(cp,[status(thm)],[t627,t1757]) ).
cnf(t166,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t31,t163]) ).
cnf(t1655,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t166]) ).
cnf(t4800,plain,
multiply(sFlat2,least_upper_bound(identity,b)) = least_upper_bound(sFlat2,least_upper_bound(sFlat0,least_upper_bound(b,identity))),
inference(step,[status(thm)],[t1776,t1655]) ).
cnf(t4801,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(sFlat2,least_upper_bound(sFlat0,least_upper_bound(b,identity))),
inference(step,[status(thm)],[t4800,t110]) ).
cnf(t240,plain,
least_upper_bound(sFlat1,X1) = least_upper_bound(sFlat0,least_upper_bound(X1,identity)),
inference(cp,[status(thm)],[t234,t89]) ).
cnf(t562,plain,
least_upper_bound(sFlat0,least_upper_bound(X1,identity)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t240]) ).
cnf(t4802,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(sFlat2,least_upper_bound(sFlat1,b)),
inference(step,[status(thm)],[t4801,t562]) ).
cnf(t236,plain,
least_upper_bound(sFlat1,b) = least_upper_bound(sFlat0,sFlat3),
inference(cp,[status(thm)],[t234,t110]) ).
cnf(t249,plain,
least_upper_bound(sFlat1,b) = least_upper_bound(sFlat0,sFlat3),
inference(orient,[status(thm)],[t236]) ).
cnf(t4803,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(sFlat2,least_upper_bound(sFlat0,sFlat3)),
inference(step,[status(thm)],[t4802,t249]) ).
cnf(t1784,plain,
least_upper_bound(sFlat2,least_upper_bound(sFlat0,sFlat3)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t4803]) ).
cnf(t1785,plain,
a = greatest_lower_bound(a,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t967,t1784]) ).
cnf(t1791,plain,
greatest_lower_bound(a,multiply(sFlat2,sFlat3)) = a,
inference(orient,[status(thm)],[t1785]) ).
cnf(t1792,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(multiply(sFlat2,sFlat3),a),
inference(cp,[status(thm)],[t199,t1791]) ).
cnf(t4804,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(a,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1792,t89]) ).
cnf(t1794,plain,
least_upper_bound(a,multiply(sFlat2,sFlat3)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t4804]) ).
cnf(t4873,plain,
least_upper_bound(a,sFlat4) = multiply(sFlat2,sFlat3),
inference(step,[status(thm)],[t1794,t3533]) ).
cnf(t4874,plain,
least_upper_bound(a,sFlat4) = sFlat4,
inference(step,[status(thm)],[t4873,t3533]) ).
cnf(t3566,plain,
least_upper_bound(a,sFlat4) = sFlat4,
inference(rw,[status(thm)],[t4874]) ).
cnf(t4887,plain,
least_upper_bound(sFlat4,a) = sFlat4,
inference(step,[status(thm)],[t3566,t89]) ).
cnf(t3576,plain,
least_upper_bound(sFlat4,a) = sFlat4,
inference(orient,[status(thm)],[t4887]) ).
cnf(t3578,plain,
least_upper_bound(sFlat2,sFlat4) = least_upper_bound(identity,sFlat4),
inference(cp,[status(thm)],[t592,t3576]) ).
cnf(t4895,plain,
least_upper_bound(sFlat2,sFlat4) = least_upper_bound(sFlat4,identity),
inference(step,[status(thm)],[t3578,t89]) ).
cnf(t4896,plain,
least_upper_bound(sFlat2,sFlat4) = sFlat4,
inference(step,[status(thm)],[t4895,t3590]) ).
cnf(t3638,plain,
least_upper_bound(sFlat2,sFlat4) = sFlat4,
inference(orient,[status(thm)],[t4896]) ).
cnf(t3643,plain,
least_upper_bound(sFlat2,least_upper_bound(sFlat4,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t94,t3638]) ).
cnf(t4075,plain,
least_upper_bound(sFlat2,least_upper_bound(sFlat4,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t3643]) ).
cnf(t4084,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)],[t497,t4075]) ).
cnf(t4948,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)],[t4084,t94]) ).
cnf(t4949,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)],[t4948,t94]) ).
cnf(t4950,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,least_upper_bound(X1,sFlat4)),
inference(step,[status(thm)],[t4949,t497]) ).
cnf(t4951,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,X1),
inference(step,[status(thm)],[t4950,t497]) ).
cnf(t4609,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t4951]) ).
cnf(t4952,plain,
least_upper_bound(sFlat4,sFlat0) = sFlat4,
inference(step,[status(thm)],[t4345,t4609]) ).
cnf(t4622,plain,
least_upper_bound(sFlat4,sFlat0) = sFlat4,
inference(rw,[status(thm)],[t4952]) ).
cnf(t4953,plain,
least_upper_bound(sFlat0,sFlat4) = sFlat4,
inference(step,[status(thm)],[t4622,t89]) ).
cnf(t4623,plain,
least_upper_bound(sFlat0,sFlat4) = sFlat4,
inference(orient,[status(thm)],[t4953]) ).
cnf(t4958,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat1,
inference(step,[status(thm)],[t3761,t4623]) ).
cnf(t4959,plain,
sFlat5 = sFlat1,
inference(step,[status(thm)],[t4958,t3620]) ).
cnf(t4636,plain,
sFlat5 = sFlat1,
inference(rw,[status(thm)],[t4959]) ).
cnf(t4637,plain,
sFlat5 = sFlat1,
inference(orient,[status(thm)],[t4636]) ).
cnf(t4960,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat1,
inference(step,[status(thm)],[t3620,t4637]) ).
cnf(t4638,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat1,
inference(orient,[status(thm)],[t4960]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[goal_0,t89]) ).
cnf(g0_1,plain,
greatest_lower_bound(least_upper_bound(identity,sFlat0),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_0,t79]) ).
cnf(g0_2,plain,
greatest_lower_bound(least_upper_bound(sFlat0,identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_1,t89]) ).
cnf(g0_3,plain,
greatest_lower_bound(sFlat1,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_2,t104]) ).
cnf(g0_4,plain,
greatest_lower_bound(sFlat1,multiply(least_upper_bound(identity,a),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_3,t89]) ).
cnf(g0_5,plain,
greatest_lower_bound(sFlat1,multiply(sFlat2,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_4,t107]) ).
cnf(g0_6,plain,
greatest_lower_bound(sFlat1,multiply(sFlat2,least_upper_bound(identity,b))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_5,t89]) ).
cnf(g0_7,plain,
greatest_lower_bound(sFlat1,multiply(sFlat2,sFlat3)) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_6,t110]) ).
cnf(g0_8,plain,
greatest_lower_bound(sFlat1,sFlat4) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_7,t3533]) ).
cnf(g0_9,plain,
sFlat1 != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_8,t4638]) ).
cnf(g0_10,plain,
sFlat1 != least_upper_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[g0_9,t89]) ).
cnf(g0_11,plain,
sFlat1 != least_upper_bound(identity,sFlat0),
inference(rw,[status(thm)],[g0_10,t79]) ).
cnf(g0_12,plain,
sFlat1 != least_upper_bound(sFlat0,identity),
inference(rw,[status(thm)],[g0_11,t89]) ).
cnf(g0_13,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_12,t104]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 14:04:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.50/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.50/1.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------