%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP171-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 01:25:31 PM UTC 2026
% Result : Unsatisfiable 5.10s 1.80s
% Output : CNFRefutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 31 RR)
% Number of literals : 55 ( 54 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t11,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)],[t11]) ).
cnf(t3,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t76,plain,
least_upper_bound(identity,b) = b,
inference(orient,[status(thm)],[t3]) ).
cnf(t77,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(b,X1),
inference(cp,[status(thm)],[t63,t76]) ).
cnf(t148,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(b,X1),
inference(orient,[status(thm)],[t77]) ).
cnf(t150,plain,
identity = greatest_lower_bound(identity,least_upper_bound(b,X1)),
inference(cp,[status(thm)],[t23,t148]) ).
cnf(t151,plain,
greatest_lower_bound(identity,least_upper_bound(b,X1)) = identity,
inference(orient,[status(thm)],[t150]) ).
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t59,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t152,plain,
identity = greatest_lower_bound(identity,least_upper_bound(X1,b)),
inference(cp,[status(thm)],[t151,t59]) ).
cnf(t155,plain,
greatest_lower_bound(identity,least_upper_bound(X1,b)) = identity,
inference(orient,[status(thm)],[t152]) ).
cnf(t16,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(t28,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t16]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t29,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t28,t19]) ).
cnf(t227,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t29]) ).
cnf(t17,axiom,
sFlat0 = multiply(a,b),
introduced(definition) ).
cnf(t39,plain,
multiply(a,b) = sFlat0,
inference(orient,[status(thm)],[t17]) ).
cnf(t231,plain,
multiply(least_upper_bound(identity,a),b) = least_upper_bound(b,sFlat0),
inference(cp,[status(thm)],[t227,t39]) ).
cnf(t2,axiom,
least_upper_bound(identity,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t73,plain,
least_upper_bound(identity,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t273,plain,
multiply(a,b) = least_upper_bound(b,sFlat0),
inference(step,[status(thm)],[t231,t73]) ).
cnf(t274,plain,
sFlat0 = least_upper_bound(b,sFlat0),
inference(step,[status(thm)],[t273,t39]) ).
cnf(t275,plain,
sFlat0 = least_upper_bound(sFlat0,b),
inference(step,[status(thm)],[t274,t59]) ).
cnf(t243,plain,
least_upper_bound(sFlat0,b) = sFlat0,
inference(orient,[status(thm)],[t275]) ).
cnf(t245,plain,
identity = greatest_lower_bound(identity,sFlat0),
inference(cp,[status(thm)],[t155,t243]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t79,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t276,plain,
identity = greatest_lower_bound(sFlat0,identity),
inference(step,[status(thm)],[t245,t79]) ).
cnf(t18,axiom,
sFlat1 = greatest_lower_bound(identity,multiply(a,b)),
introduced(definition) ).
cnf(t259,plain,
sFlat1 = greatest_lower_bound(identity,sFlat0),
inference(step,[status(thm)],[t18,t39]) ).
cnf(t260,plain,
sFlat1 = greatest_lower_bound(sFlat0,identity),
inference(step,[status(thm)],[t259,t79]) ).
cnf(t93,plain,
greatest_lower_bound(sFlat0,identity) = sFlat1,
inference(orient,[status(thm)],[t260]) ).
cnf(t277,plain,
identity = sFlat1,
inference(step,[status(thm)],[t276,t93]) ).
cnf(t248,plain,
identity = sFlat1,
inference(orient,[status(thm)],[t277]) ).
cnf(t62,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t23,t59]) ).
cnf(t102,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t62]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t94,plain,
sFlat0 = least_upper_bound(sFlat0,sFlat1),
inference(cp,[status(thm)],[t21,t93]) ).
cnf(t100,plain,
least_upper_bound(sFlat0,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t94]) ).
cnf(t105,plain,
sFlat1 = greatest_lower_bound(sFlat1,sFlat0),
inference(cp,[status(thm)],[t102,t100]) ).
cnf(t261,plain,
sFlat1 = greatest_lower_bound(sFlat0,sFlat1),
inference(step,[status(thm)],[t105,t79]) ).
cnf(t108,plain,
greatest_lower_bound(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t261]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(identity,multiply(a,b)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(sFlat1,multiply(a,b)) != identity,
inference(rw,[status(thm)],[goal_0,t248]) ).
cnf(g0_1,plain,
greatest_lower_bound(sFlat1,sFlat0) != identity,
inference(rw,[status(thm)],[g0_0,t39]) ).
cnf(g0_2,plain,
greatest_lower_bound(sFlat0,sFlat1) != identity,
inference(rw,[status(thm)],[g0_1,t79]) ).
cnf(g0_3,plain,
sFlat1 != identity,
inference(rw,[status(thm)],[g0_2,t108]) ).
cnf(g0_4,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_3,t248]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP171-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 13:58:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.10/1.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.10/1.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------