%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD039-3 : 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 : 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 : Sun Sep 27 07:10:52 AM UTC 2026
% Result : Unsatisfiable 11.90s 1.94s
% Output : CNFRefutation 11.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 10 unt; 0 nHn; 22 RR)
% Number of literals : 41 ( 0 equ; 21 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sum_3,negated_conjecture,
sum('additive$uidentity','multiplicative$uidentity','additive$uidentity') ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(different_identities,axiom,
~ sum('additive$uidentity','additive$uidentity','multiplicative$uidentity') ).
cnf(c2,plain,
sum('additive$uidentity','multiplicative$uidentity','additive$uidentity'),
inference(clausification,[status(esa)],[sum_3]) ).
cnf(c3,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c5,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c7,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c19,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(c28,plain,
~ sum('additive$uidentity','additive$uidentity','multiplicative$uidentity'),
inference(clausification,[status(esa)],[different_identities]) ).
cnf(d0,plain,
sum('multiplicative$uidentity','additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d1,plain,
( ~ sum(X2,'multiplicative$uidentity',X0)
| sum(X2,'additive$uidentity',X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( ~ sum(X0,'multiplicative$uidentity','multiplicative$uidentity')
| sum(X0,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ defined('multiplicative$uidentity')
| sum('additive$uidentity','additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
sum('additive$uidentity','additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c19,d3]) ).
cnf(d5,plain,
( ~ sum(X2,'additive$uidentity',X0)
| sum(X2,'additive$uidentity',X1)
| ~ sum(X0,'multiplicative$uidentity',X1) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(d6,plain,
( ~ defined('multiplicative$uidentity')
| ~ sum(X0,'additive$uidentity','additive$uidentity')
| sum(X0,'additive$uidentity','multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( sum(X0,'additive$uidentity','multiplicative$uidentity')
| ~ sum(X0,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[c19,d6]) ).
cnf(d8,plain,
sum('additive$uidentity','additive$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c28,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD039-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 02:26:02 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.90/1.94 % SZS status Unsatisfiable for theBenchmark.p
% 11.90/1.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------