%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD021-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Sun Sep 27 07:10:47 AM UTC 2026
% Result : Unsatisfiable 19.14s 2.87s
% Output : CNFRefutation 19.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 9 unt; 0 nHn; 18 RR)
% Number of literals : 35 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(sum_3,negated_conjecture,
sum('additive$uidentity',m,'additive$uidentity') ).
cnf(not_sum_4,negated_conjecture,
~ sum(m,a,a) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c2,plain,
sum('additive$uidentity',m,'additive$uidentity'),
inference(clausification,[status(esa)],[sum_3]) ).
cnf(c3,plain,
~ sum(m,a,a),
inference(clausification,[status(esa)],[not_sum_4]) ).
cnf(c4,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c6,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c8,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(d0,plain,
sum(m,'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d1,plain,
( ~ sum(X3,'additive$uidentity',X1)
| sum(X3,X0,X2)
| ~ sum(X1,X0,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d2,plain,
( ~ defined(X0)
| ~ sum(X1,'additive$uidentity','additive$uidentity')
| sum(X1,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( sum(m,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
~ defined(a),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c0,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD021-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 02:25:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.14/2.87 % SZS status Unsatisfiable for theBenchmark.p
% 19.14/2.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------