%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 01:25:30 PM UTC 2026
% Result : Unsatisfiable 5.99s 1.25s
% Output : CNFRefutation 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 5 RR)
% Number of literals : 60 ( 59 equ; 2 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t113,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/sandbox/benchmark/theBenchmark.p') ).
cnf(t118,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t119,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t113,t118]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t567,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t119,t24]) ).
cnf(t286,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t567]) ).
cnf(t16,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(t60,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t16]) ).
cnf(t63,plain,
multiply(greatest_lower_bound(X1,identity),X2) = greatest_lower_bound(multiply(X1,X2),X2),
inference(cp,[status(thm)],[t60,t24]) ).
cnf(t3,axiom,
greatest_lower_bound(X1,identity) = negative_part(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t42,plain,
greatest_lower_bound(X1,identity) = negative_part(X1),
inference(orient,[status(thm)],[t3]) ).
cnf(t576,plain,
multiply(negative_part(X1),X2) = greatest_lower_bound(multiply(X1,X2),X2),
inference(step,[status(thm)],[t63,t42]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t577,plain,
multiply(negative_part(X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(step,[status(thm)],[t576,t25]) ).
cnf(t509,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(negative_part(X2),X1),
inference(orient,[status(thm)],[t577]) ).
cnf(t515,plain,
multiply(negative_part(inverse(X1)),X1) = greatest_lower_bound(X1,identity),
inference(cp,[status(thm)],[t509,t118]) ).
cnf(t578,plain,
multiply(negative_part(inverse(X1)),X1) = negative_part(X1),
inference(step,[status(thm)],[t515,t42]) ).
cnf(t525,plain,
multiply(negative_part(inverse(X1)),X1) = negative_part(X1),
inference(orient,[status(thm)],[t578]) ).
cnf(t527,plain,
X1 = multiply(inverse(negative_part(inverse(X1))),negative_part(X1)),
inference(cp,[status(thm)],[t286,t525]) ).
cnf(t287,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t286,t118]) ).
cnf(t305,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t287]) ).
cnf(t290,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t286,t286]) ).
cnf(t376,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t290]) ).
cnf(t572,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t305,t376]) ).
cnf(t384,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t572]) ).
cnf(t385,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t384]) ).
cnf(t386,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t385,t376]) ).
cnf(t573,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t386,t385]) ).
cnf(t391,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t573]) ).
cnf(t10,axiom,
greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t74,plain,
greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)),
inference(orient,[status(thm)],[t10]) ).
cnf(t288,plain,
X1 = multiply(inverse(identity),X1),
inference(cp,[status(thm)],[t286,t24]) ).
cnf(t299,plain,
multiply(inverse(identity),X1) = X1,
inference(orient,[status(thm)],[t288]) ).
cnf(t300,plain,
X1 = multiply(inverse(inverse(identity)),X1),
inference(cp,[status(thm)],[t286,t299]) ).
cnf(t346,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(orient,[status(thm)],[t300]) ).
cnf(t347,plain,
inverse(identity) = identity,
inference(cp,[status(thm)],[t346,t118]) ).
cnf(t353,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t347]) ).
cnf(t354,plain,
inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(cp,[status(thm)],[t74,t353]) ).
cnf(t4,axiom,
least_upper_bound(X1,identity) = positive_part(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t93,plain,
least_upper_bound(X1,identity) = positive_part(X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t80,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t96,plain,
positive_part(X1) = least_upper_bound(identity,X1),
inference(cp,[status(thm)],[t93,t80]) ).
cnf(t136,plain,
least_upper_bound(identity,X1) = positive_part(X1),
inference(orient,[status(thm)],[t96]) ).
cnf(t568,plain,
inverse(positive_part(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t354,t136]) ).
cnf(t45,plain,
negative_part(X1) = greatest_lower_bound(identity,X1),
inference(cp,[status(thm)],[t42,t25]) ).
cnf(t130,plain,
greatest_lower_bound(identity,X1) = negative_part(X1),
inference(orient,[status(thm)],[t45]) ).
cnf(t569,plain,
inverse(positive_part(X1)) = negative_part(inverse(X1)),
inference(step,[status(thm)],[t568,t130]) ).
cnf(t356,plain,
inverse(positive_part(X1)) = negative_part(inverse(X1)),
inference(orient,[status(thm)],[t569]) ).
cnf(t392,plain,
positive_part(X1) = inverse(negative_part(inverse(X1))),
inference(cp,[status(thm)],[t391,t356]) ).
cnf(t409,plain,
inverse(negative_part(inverse(X1))) = positive_part(X1),
inference(orient,[status(thm)],[t392]) ).
cnf(t579,plain,
X1 = multiply(positive_part(X1),negative_part(X1)),
inference(step,[status(thm)],[t527,t409]) ).
cnf(t537,plain,
multiply(positive_part(X1),negative_part(X1)) = X1,
inference(orient,[status(thm)],[t579]) ).
cnf(goal_0,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a != a,
inference(rw,[status(thm)],[goal_0,t537]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 13:56:34 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.99/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.99/1.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------