%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 01:25:36 PM UTC 2026
% Result : Unsatisfiable 8.23s 6.73s
% Output : CNFRefutation 8.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of clauses : 101 ( 101 unt; 0 nHn; 47 RR)
% Number of literals : 101 ( 100 equ; 12 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t107,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t18,axiom,
sFlat0 = least_upper_bound(a,identity),
introduced(definition) ).
cnf(t1497,plain,
sFlat0 = least_upper_bound(identity,a),
inference(step,[status(thm)],[t18,t107]) ).
cnf(t121,plain,
least_upper_bound(identity,a) = sFlat0,
inference(orient,[status(thm)],[t1497]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t88,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t19,axiom,
sFlat1 = greatest_lower_bound(a,identity),
introduced(definition) ).
cnf(t1496,plain,
sFlat1 = greatest_lower_bound(identity,a),
inference(step,[status(thm)],[t19,t88]) ).
cnf(t104,plain,
greatest_lower_bound(identity,a) = sFlat1,
inference(orient,[status(thm)],[t1496]) ).
cnf(t20,axiom,
sFlat2 = inverse(greatest_lower_bound(a,identity)),
introduced(definition) ).
cnf(t1498,plain,
sFlat2 = inverse(greatest_lower_bound(identity,a)),
inference(step,[status(thm)],[t20,t88]) ).
cnf(t1499,plain,
sFlat2 = inverse(sFlat1),
inference(step,[status(thm)],[t1498,t104]) ).
cnf(t127,plain,
inverse(sFlat1) = sFlat2,
inference(orient,[status(thm)],[t1499]) ).
cnf(t10,axiom,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t65,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t10]) ).
cnf(t2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t28,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t68,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t65,t28]) ).
cnf(t1071,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t68]) ).
cnf(t13,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t29,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t54,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t64,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t29,t54]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t1553,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t64,t23]) ).
cnf(t1036,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t1553]) ).
cnf(t1072,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(cp,[status(thm)],[t1071,t1036]) ).
cnf(t1094,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(orient,[status(thm)],[t1072]) ).
cnf(t55,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t54,t28]) ).
cnf(t166,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t55]) ).
cnf(t176,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t29,t166]) ).
cnf(t1554,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t176,t23]) ).
cnf(t1049,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t1554]) ).
cnf(t1051,plain,
inverse(X1) = multiply(X2,inverse(multiply(X1,X2))),
inference(cp,[status(thm)],[t1049,t65]) ).
cnf(t1079,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(orient,[status(thm)],[t1051]) ).
cnf(t15,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t33,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t15]) ).
cnf(t34,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t33,t23]) ).
cnf(t281,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t34]) ).
cnf(t16,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t32,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t0,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t124,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t125,plain,
inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)),
inference(cp,[status(thm)],[t65,t124]) ).
cnf(t1502,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(step,[status(thm)],[t125,t23]) ).
cnf(t177,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t1502]) ).
cnf(t181,plain,
multiply(X1,identity) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t28,t177]) ).
cnf(t1503,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t181,t28]) ).
cnf(t182,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t1503]) ).
cnf(t183,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t32,t182]) ).
cnf(t1224,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t183]) ).
cnf(t17,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t39,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
cnf(t40,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t39,t23]) ).
cnf(t673,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t40]) ).
cnf(t1225,plain,
multiply(X1,least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),X1),
inference(cp,[status(thm)],[t1224,t673]) ).
cnf(t1323,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(orient,[status(thm)],[t1225]) ).
cnf(t1333,plain,
multiply(a,least_upper_bound(identity,a)) = multiply(sFlat0,a),
inference(cp,[status(thm)],[t1323,t121]) ).
cnf(t1561,plain,
multiply(a,sFlat0) = multiply(sFlat0,a),
inference(step,[status(thm)],[t1333,t121]) ).
cnf(t1355,plain,
multiply(a,sFlat0) = multiply(sFlat0,a),
inference(orient,[status(thm)],[t1561]) ).
cnf(t1359,plain,
multiply(greatest_lower_bound(identity,a),sFlat0) = greatest_lower_bound(sFlat0,multiply(sFlat0,a)),
inference(cp,[status(thm)],[t281,t1355]) ).
cnf(t1562,plain,
multiply(sFlat1,sFlat0) = greatest_lower_bound(sFlat0,multiply(sFlat0,a)),
inference(step,[status(thm)],[t1359,t104]) ).
cnf(t14,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(t30,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t185,plain,
multiply(X1,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t30,t182]) ).
cnf(t1258,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(orient,[status(thm)],[t185]) ).
cnf(t1563,plain,
multiply(sFlat1,sFlat0) = multiply(sFlat0,greatest_lower_bound(identity,a)),
inference(step,[status(thm)],[t1562,t1258]) ).
cnf(t1564,plain,
multiply(sFlat1,sFlat0) = multiply(sFlat0,sFlat1),
inference(step,[status(thm)],[t1563,t104]) ).
cnf(t1371,plain,
multiply(sFlat1,sFlat0) = multiply(sFlat0,sFlat1),
inference(orient,[status(thm)],[t1564]) ).
cnf(t1376,plain,
sFlat0 = multiply(inverse(sFlat1),multiply(sFlat0,sFlat1)),
inference(cp,[status(thm)],[t1036,t1371]) ).
cnf(t1565,plain,
sFlat0 = multiply(sFlat2,multiply(sFlat0,sFlat1)),
inference(step,[status(thm)],[t1376,t127]) ).
cnf(t1392,plain,
multiply(sFlat2,multiply(sFlat0,sFlat1)) = sFlat0,
inference(orient,[status(thm)],[t1565]) ).
cnf(t1410,plain,
inverse(sFlat2) = multiply(multiply(sFlat0,sFlat1),inverse(sFlat0)),
inference(cp,[status(thm)],[t1079,t1392]) ).
cnf(t131,plain,
sFlat1 = inverse(sFlat2),
inference(cp,[status(thm)],[t28,t127]) ).
cnf(t132,plain,
inverse(sFlat2) = sFlat1,
inference(orient,[status(thm)],[t131]) ).
cnf(t1569,plain,
sFlat1 = multiply(multiply(sFlat0,sFlat1),inverse(sFlat0)),
inference(step,[status(thm)],[t1410,t132]) ).
cnf(t1570,plain,
sFlat1 = multiply(sFlat0,multiply(sFlat1,inverse(sFlat0))),
inference(step,[status(thm)],[t1569,t29]) ).
cnf(t1461,plain,
multiply(sFlat0,multiply(sFlat1,inverse(sFlat0))) = sFlat1,
inference(orient,[status(thm)],[t1570]) ).
cnf(t1476,plain,
inverse(multiply(sFlat1,inverse(sFlat0))) = multiply(inverse(sFlat1),sFlat0),
inference(cp,[status(thm)],[t1094,t1461]) ).
cnf(t129,plain,
inverse(multiply(sFlat1,X1)) = multiply(inverse(X1),sFlat2),
inference(cp,[status(thm)],[t65,t127]) ).
cnf(t237,plain,
inverse(multiply(sFlat1,X1)) = multiply(inverse(X1),sFlat2),
inference(orient,[status(thm)],[t129]) ).
cnf(t1571,plain,
multiply(inverse(inverse(sFlat0)),sFlat2) = multiply(inverse(sFlat1),sFlat0),
inference(step,[status(thm)],[t1476,t237]) ).
cnf(t1572,plain,
multiply(sFlat0,sFlat2) = multiply(inverse(sFlat1),sFlat0),
inference(step,[status(thm)],[t1571,t28]) ).
cnf(t1573,plain,
multiply(sFlat0,sFlat2) = multiply(sFlat2,sFlat0),
inference(step,[status(thm)],[t1572,t127]) ).
cnf(t1477,plain,
multiply(sFlat2,sFlat0) = multiply(sFlat0,sFlat2),
inference(orient,[status(thm)],[t1573]) ).
cnf(goal_0,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[goal_0,t107]) ).
cnf(g0_1,plain,
multiply(sFlat0,inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_0,t121]) ).
cnf(g0_2,plain,
multiply(sFlat0,inverse(greatest_lower_bound(identity,a))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_1,t88]) ).
cnf(g0_3,plain,
multiply(sFlat0,inverse(sFlat1)) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_2,t104]) ).
cnf(g0_4,plain,
multiply(sFlat0,sFlat2) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_3,t127]) ).
cnf(g0_5,plain,
multiply(sFlat0,sFlat2) != multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_4,t88]) ).
cnf(g0_6,plain,
multiply(sFlat0,sFlat2) != multiply(inverse(sFlat1),least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_5,t104]) ).
cnf(g0_7,plain,
multiply(sFlat0,sFlat2) != multiply(sFlat2,least_upper_bound(a,identity)),
inference(rw,[status(thm)],[g0_6,t127]) ).
cnf(g0_8,plain,
multiply(sFlat0,sFlat2) != multiply(sFlat2,least_upper_bound(identity,a)),
inference(rw,[status(thm)],[g0_7,t107]) ).
cnf(g0_9,plain,
multiply(sFlat0,sFlat2) != multiply(sFlat2,sFlat0),
inference(rw,[status(thm)],[g0_8,t121]) ).
cnf(g0_10,plain,
multiply(sFlat0,sFlat2) != multiply(sFlat0,sFlat2),
inference(rw,[status(thm)],[g0_9,t1477]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n016.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 14:07:46 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.23/6.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.23/6.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------