%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP167-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:25:29 PM UTC 2026
% Result : Unsatisfiable 11.95s 2.15s
% Output : CNFRefutation 11.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 17
% Syntax : Number of clauses : 171 ( 171 unt; 0 nHn; 69 RR)
% Number of literals : 171 ( 170 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 155 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
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(t24,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t48,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t57,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t23,t48]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t18,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t15613,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t57,t18]) ).
cnf(t642,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t15613]) ).
cnf(t643,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t642,t48]) ).
cnf(t663,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t643]) ).
cnf(t646,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t642,t642]) ).
cnf(t684,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t646]) ).
cnf(t15614,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t663,t684]) ).
cnf(t692,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t15614]) ).
cnf(t693,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t692]) ).
cnf(t697,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t24,t693]) ).
cnf(t809,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t697]) ).
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(t27,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t28,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t27,t18]) ).
cnf(t272,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t28]) ).
cnf(t810,plain,
multiply(X1,least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),X1),
inference(cp,[status(thm)],[t809,t272]) ).
cnf(t923,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(orient,[status(thm)],[t810]) ).
cnf(t15,axiom,
sFlat0 = least_upper_bound(a,identity),
introduced(definition) ).
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t58,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t15584,plain,
sFlat0 = least_upper_bound(identity,a),
inference(step,[status(thm)],[t15,t58]) ).
cnf(t73,plain,
least_upper_bound(identity,a) = sFlat0,
inference(orient,[status(thm)],[t15584]) ).
cnf(t926,plain,
multiply(a,least_upper_bound(identity,a)) = multiply(sFlat0,a),
inference(cp,[status(thm)],[t923,t73]) ).
cnf(t15626,plain,
multiply(a,sFlat0) = multiply(sFlat0,a),
inference(step,[status(thm)],[t926,t73]) ).
cnf(t947,plain,
multiply(a,sFlat0) = multiply(sFlat0,a),
inference(orient,[status(thm)],[t15626]) ).
cnf(t959,plain,
multiply(a,multiply(sFlat0,X1)) = multiply(multiply(sFlat0,a),X1),
inference(cp,[status(thm)],[t23,t947]) ).
cnf(t15635,plain,
multiply(a,multiply(sFlat0,X1)) = multiply(sFlat0,multiply(a,X1)),
inference(step,[status(thm)],[t959,t23]) ).
cnf(t1159,plain,
multiply(a,multiply(sFlat0,X1)) = multiply(sFlat0,multiply(a,X1)),
inference(orient,[status(thm)],[t15635]) ).
cnf(t17,axiom,
sFlat2 = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
introduced(definition) ).
cnf(t33,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) = sFlat2,
inference(orient,[status(thm)],[t17]) ).
cnf(t62,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) = sFlat2,
inference(rw,[status(thm)],[t33]) ).
cnf(t15637,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(a,identity)) = sFlat2,
inference(step,[status(thm)],[t62,t58]) ).
cnf(t15638,plain,
multiply(sFlat0,greatest_lower_bound(a,identity)) = sFlat2,
inference(step,[status(thm)],[t15637,t73]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t76,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t15639,plain,
multiply(sFlat0,greatest_lower_bound(identity,a)) = sFlat2,
inference(step,[status(thm)],[t15638,t76]) ).
cnf(t16,axiom,
sFlat1 = greatest_lower_bound(a,identity),
introduced(definition) ).
cnf(t15585,plain,
sFlat1 = greatest_lower_bound(identity,a),
inference(step,[status(thm)],[t16,t76]) ).
cnf(t90,plain,
greatest_lower_bound(identity,a) = sFlat1,
inference(orient,[status(thm)],[t15585]) ).
cnf(t15640,plain,
multiply(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t15639,t90]) ).
cnf(t1286,plain,
multiply(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t15640]) ).
cnf(t1304,plain,
multiply(sFlat0,multiply(sFlat1,X1)) = multiply(sFlat2,X1),
inference(cp,[status(thm)],[t23,t1286]) ).
cnf(t1400,plain,
multiply(sFlat0,multiply(sFlat1,X1)) = multiply(sFlat2,X1),
inference(orient,[status(thm)],[t1304]) ).
cnf(t1410,plain,
multiply(sFlat0,multiply(a,multiply(sFlat1,X1))) = multiply(a,multiply(sFlat2,X1)),
inference(cp,[status(thm)],[t1159,t1400]) ).
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(t26,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t695,plain,
multiply(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t26,t693]) ).
cnf(t786,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(orient,[status(thm)],[t695]) ).
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(t41,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t43,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t41,t18]) ).
cnf(t746,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t43]) ).
cnf(t787,plain,
multiply(X1,greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),X1),
inference(cp,[status(thm)],[t786,t746]) ).
cnf(t832,plain,
multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)),
inference(orient,[status(thm)],[t787]) ).
cnf(t838,plain,
multiply(a,greatest_lower_bound(identity,a)) = multiply(sFlat1,a),
inference(cp,[status(thm)],[t832,t90]) ).
cnf(t15622,plain,
multiply(a,sFlat1) = multiply(sFlat1,a),
inference(step,[status(thm)],[t838,t90]) ).
cnf(t856,plain,
multiply(a,sFlat1) = multiply(sFlat1,a),
inference(orient,[status(thm)],[t15622]) ).
cnf(t869,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(multiply(sFlat1,a),X1),
inference(cp,[status(thm)],[t23,t856]) ).
cnf(t15627,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(sFlat1,multiply(a,X1)),
inference(step,[status(thm)],[t869,t23]) ).
cnf(t998,plain,
multiply(a,multiply(sFlat1,X1)) = multiply(sFlat1,multiply(a,X1)),
inference(orient,[status(thm)],[t15627]) ).
cnf(t15678,plain,
multiply(sFlat0,multiply(sFlat1,multiply(a,X1))) = multiply(a,multiply(sFlat2,X1)),
inference(step,[status(thm)],[t1410,t998]) ).
cnf(t15679,plain,
multiply(sFlat2,multiply(a,X1)) = multiply(a,multiply(sFlat2,X1)),
inference(step,[status(thm)],[t15678,t1400]) ).
cnf(t2034,plain,
multiply(a,multiply(sFlat2,X1)) = multiply(sFlat2,multiply(a,X1)),
inference(orient,[status(thm)],[t15679]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t61,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t22,t58]) ).
cnf(t103,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t61]) ).
cnf(t7,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t20,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t79,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t20,t76]) ).
cnf(t116,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t79]) ).
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(t63,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(t91,plain,
identity = least_upper_bound(identity,sFlat1),
inference(cp,[status(thm)],[t20,t90]) ).
cnf(t15587,plain,
identity = least_upper_bound(sFlat1,identity),
inference(step,[status(thm)],[t91,t58]) ).
cnf(t96,plain,
least_upper_bound(sFlat1,identity) = identity,
inference(orient,[status(thm)],[t15587]) ).
cnf(t97,plain,
least_upper_bound(sFlat1,least_upper_bound(identity,X1)) = least_upper_bound(identity,X1),
inference(cp,[status(thm)],[t63,t96]) ).
cnf(t237,plain,
least_upper_bound(sFlat1,least_upper_bound(identity,X1)) = least_upper_bound(identity,X1),
inference(orient,[status(thm)],[t97]) ).
cnf(t241,plain,
sFlat1 = greatest_lower_bound(sFlat1,least_upper_bound(identity,X1)),
inference(cp,[status(thm)],[t22,t237]) ).
cnf(t242,plain,
greatest_lower_bound(sFlat1,least_upper_bound(identity,X1)) = sFlat1,
inference(orient,[status(thm)],[t241]) ).
cnf(t247,plain,
least_upper_bound(identity,X1) = least_upper_bound(least_upper_bound(identity,X1),sFlat1),
inference(cp,[status(thm)],[t116,t242]) ).
cnf(t15606,plain,
least_upper_bound(identity,X1) = least_upper_bound(identity,least_upper_bound(X1,sFlat1)),
inference(step,[status(thm)],[t247,t63]) ).
cnf(t488,plain,
least_upper_bound(identity,least_upper_bound(X1,sFlat1)) = least_upper_bound(identity,X1),
inference(orient,[status(thm)],[t15606]) ).
cnf(t492,plain,
least_upper_bound(identity,X1) = least_upper_bound(identity,least_upper_bound(sFlat1,X1)),
inference(cp,[status(thm)],[t488,t58]) ).
cnf(t596,plain,
least_upper_bound(identity,least_upper_bound(sFlat1,X1)) = least_upper_bound(identity,X1),
inference(orient,[status(thm)],[t492]) ).
cnf(t602,plain,
least_upper_bound(sFlat1,X1) = greatest_lower_bound(least_upper_bound(sFlat1,X1),least_upper_bound(identity,X1)),
inference(cp,[status(thm)],[t103,t596]) ).
cnf(t15433,plain,
greatest_lower_bound(least_upper_bound(sFlat1,X1),least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t602]) ).
cnf(t694,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t693,t684]) ).
cnf(t15615,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t694,t693]) ).
cnf(t716,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t15615]) ).
cnf(t718,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t48,t716]) ).
cnf(t719,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t718]) ).
cnf(t750,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t746,t719]) ).
cnf(t15819,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t750,t76]) ).
cnf(t6349,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t15819]) ).
cnf(t6378,plain,
greatest_lower_bound(identity,inverse(a)) = multiply(sFlat1,inverse(a)),
inference(cp,[status(thm)],[t6349,t90]) ).
cnf(t6410,plain,
greatest_lower_bound(identity,inverse(a)) = multiply(sFlat1,inverse(a)),
inference(orient,[status(thm)],[t6378]) ).
cnf(t6411,plain,
identity = least_upper_bound(identity,multiply(sFlat1,inverse(a))),
inference(cp,[status(thm)],[t20,t6410]) ).
cnf(t6463,plain,
least_upper_bound(identity,multiply(sFlat1,inverse(a))) = identity,
inference(orient,[status(thm)],[t6411]) ).
cnf(t15460,plain,
least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))) = greatest_lower_bound(least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))),identity),
inference(cp,[status(thm)],[t15433,t6463]) ).
cnf(t16017,plain,
multiply(sFlat1,least_upper_bound(identity,inverse(a))) = greatest_lower_bound(least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))),identity),
inference(step,[status(thm)],[t15460,t809]) ).
cnf(t721,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t272,t719]) ).
cnf(t15811,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t721,t58]) ).
cnf(t6063,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t15811]) ).
cnf(t6091,plain,
least_upper_bound(identity,inverse(a)) = multiply(sFlat0,inverse(a)),
inference(cp,[status(thm)],[t6063,t73]) ).
cnf(t6123,plain,
least_upper_bound(identity,inverse(a)) = multiply(sFlat0,inverse(a)),
inference(orient,[status(thm)],[t6091]) ).
cnf(t16018,plain,
multiply(sFlat1,multiply(sFlat0,inverse(a))) = greatest_lower_bound(least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))),identity),
inference(step,[status(thm)],[t16017,t6123]) ).
cnf(t860,plain,
multiply(least_upper_bound(identity,a),sFlat1) = least_upper_bound(sFlat1,multiply(sFlat1,a)),
inference(cp,[status(thm)],[t272,t856]) ).
cnf(t15623,plain,
multiply(sFlat0,sFlat1) = least_upper_bound(sFlat1,multiply(sFlat1,a)),
inference(step,[status(thm)],[t860,t73]) ).
cnf(t15624,plain,
multiply(sFlat0,sFlat1) = multiply(sFlat1,least_upper_bound(identity,a)),
inference(step,[status(thm)],[t15623,t809]) ).
cnf(t15625,plain,
multiply(sFlat0,sFlat1) = multiply(sFlat1,sFlat0),
inference(step,[status(thm)],[t15624,t73]) ).
cnf(t872,plain,
multiply(sFlat1,sFlat0) = multiply(sFlat0,sFlat1),
inference(orient,[status(thm)],[t15625]) ).
cnf(t886,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(multiply(sFlat0,sFlat1),X1),
inference(cp,[status(thm)],[t23,t872]) ).
cnf(t15633,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(sFlat0,multiply(sFlat1,X1)),
inference(step,[status(thm)],[t886,t23]) ).
cnf(t1086,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(sFlat0,multiply(sFlat1,X1)),
inference(orient,[status(thm)],[t15633]) ).
cnf(t15653,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(sFlat2,X1),
inference(step,[status(thm)],[t1086,t1400]) ).
cnf(t1401,plain,
multiply(sFlat1,multiply(sFlat0,X1)) = multiply(sFlat2,X1),
inference(orient,[status(thm)],[t15653]) ).
cnf(t16019,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(least_upper_bound(sFlat1,multiply(sFlat1,inverse(a))),identity),
inference(step,[status(thm)],[t16018,t1401]) ).
cnf(t16020,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(identity,least_upper_bound(sFlat1,multiply(sFlat1,inverse(a)))),
inference(step,[status(thm)],[t16019,t76]) ).
cnf(t16021,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(identity,multiply(sFlat1,least_upper_bound(identity,inverse(a)))),
inference(step,[status(thm)],[t16020,t809]) ).
cnf(t16022,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(identity,multiply(sFlat1,multiply(sFlat0,inverse(a)))),
inference(step,[status(thm)],[t16021,t6123]) ).
cnf(t16023,plain,
multiply(sFlat2,inverse(a)) = greatest_lower_bound(identity,multiply(sFlat2,inverse(a))),
inference(step,[status(thm)],[t16022,t1401]) ).
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(t80,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(t75,plain,
identity = greatest_lower_bound(identity,sFlat0),
inference(cp,[status(thm)],[t22,t73]) ).
cnf(t15586,plain,
identity = greatest_lower_bound(sFlat0,identity),
inference(step,[status(thm)],[t75,t76]) ).
cnf(t93,plain,
greatest_lower_bound(sFlat0,identity) = identity,
inference(orient,[status(thm)],[t15586]) ).
cnf(t95,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,X1),
inference(cp,[status(thm)],[t80,t93]) ).
cnf(t212,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t95]) ).
cnf(t215,plain,
sFlat0 = least_upper_bound(sFlat0,greatest_lower_bound(identity,X1)),
inference(cp,[status(thm)],[t20,t212]) ).
cnf(t216,plain,
least_upper_bound(sFlat0,greatest_lower_bound(identity,X1)) = sFlat0,
inference(orient,[status(thm)],[t215]) ).
cnf(t220,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(greatest_lower_bound(identity,X1),sFlat0),
inference(cp,[status(thm)],[t103,t216]) ).
cnf(t15603,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(X1,sFlat0)),
inference(step,[status(thm)],[t220,t80]) ).
cnf(t444,plain,
greatest_lower_bound(identity,greatest_lower_bound(X1,sFlat0)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t15603]) ).
cnf(t449,plain,
greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(sFlat0,X1)),
inference(cp,[status(thm)],[t444,t76]) ).
cnf(t572,plain,
greatest_lower_bound(identity,greatest_lower_bound(sFlat0,X1)) = greatest_lower_bound(identity,X1),
inference(orient,[status(thm)],[t449]) ).
cnf(t579,plain,
greatest_lower_bound(sFlat0,X1) = least_upper_bound(greatest_lower_bound(sFlat0,X1),greatest_lower_bound(identity,X1)),
inference(cp,[status(thm)],[t116,t572]) ).
cnf(t15134,plain,
least_upper_bound(greatest_lower_bound(sFlat0,X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(sFlat0,X1),
inference(orient,[status(thm)],[t579]) ).
cnf(t6133,plain,
identity = greatest_lower_bound(identity,multiply(sFlat0,inverse(a))),
inference(cp,[status(thm)],[t22,t6123]) ).
cnf(t6191,plain,
greatest_lower_bound(identity,multiply(sFlat0,inverse(a))) = identity,
inference(orient,[status(thm)],[t6133]) ).
cnf(t15159,plain,
greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))) = least_upper_bound(greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))),identity),
inference(cp,[status(thm)],[t15134,t6191]) ).
cnf(t16008,plain,
multiply(sFlat0,greatest_lower_bound(identity,inverse(a))) = least_upper_bound(greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))),identity),
inference(step,[status(thm)],[t15159,t786]) ).
cnf(t16009,plain,
multiply(sFlat0,multiply(sFlat1,inverse(a))) = least_upper_bound(greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))),identity),
inference(step,[status(thm)],[t16008,t6410]) ).
cnf(t16010,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a))),identity),
inference(step,[status(thm)],[t16009,t1400]) ).
cnf(t16011,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(identity,greatest_lower_bound(sFlat0,multiply(sFlat0,inverse(a)))),
inference(step,[status(thm)],[t16010,t58]) ).
cnf(t16012,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(identity,multiply(sFlat0,greatest_lower_bound(identity,inverse(a)))),
inference(step,[status(thm)],[t16011,t786]) ).
cnf(t16013,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(identity,multiply(sFlat0,multiply(sFlat1,inverse(a)))),
inference(step,[status(thm)],[t16012,t6410]) ).
cnf(t16014,plain,
multiply(sFlat2,inverse(a)) = least_upper_bound(identity,multiply(sFlat2,inverse(a))),
inference(step,[status(thm)],[t16013,t1400]) ).
cnf(t15187,plain,
least_upper_bound(identity,multiply(sFlat2,inverse(a))) = multiply(sFlat2,inverse(a)),
inference(orient,[status(thm)],[t16014]) ).
cnf(t15197,plain,
identity = greatest_lower_bound(identity,multiply(sFlat2,inverse(a))),
inference(cp,[status(thm)],[t22,t15187]) ).
cnf(t15234,plain,
greatest_lower_bound(identity,multiply(sFlat2,inverse(a))) = identity,
inference(orient,[status(thm)],[t15197]) ).
cnf(t16024,plain,
multiply(sFlat2,inverse(a)) = identity,
inference(step,[status(thm)],[t16023,t15234]) ).
cnf(t15488,plain,
multiply(sFlat2,inverse(a)) = identity,
inference(orient,[status(thm)],[t16024]) ).
cnf(t15491,plain,
multiply(sFlat2,multiply(a,inverse(a))) = multiply(a,identity),
inference(cp,[status(thm)],[t2034,t15488]) ).
cnf(t16026,plain,
multiply(sFlat2,identity) = multiply(a,identity),
inference(step,[status(thm)],[t15491,t719]) ).
cnf(t16027,plain,
sFlat2 = multiply(a,identity),
inference(step,[status(thm)],[t16026,t693]) ).
cnf(t16028,plain,
sFlat2 = a,
inference(step,[status(thm)],[t16027,t693]) ).
cnf(t15515,plain,
a = sFlat2,
inference(orient,[status(thm)],[t16028]) ).
cnf(goal_0,negated_conjecture,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != sFlat2,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_0,t15515]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.45 % Computer : n003.cluster.edu
% 0.11/0.45 % Model : x86_64 x86_64
% 0.11/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.45 % Memory : 8046.5625MB
% 0.11/0.45 % OS : Linux 6.8.0-71-generic
% 0.11/0.45 % CPULimit : 300
% 0.11/0.45 % WCLimit : 300
% 0.11/0.45 % DateTime : Wed Sep 23 13:57:51 UTC 2026
% 0.11/0.45 % CPUTime :
% 0.11/0.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.95/2.15 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.95/2.15 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------