%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD013-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:10:45 AM UTC 2026
% Result : Unsatisfiable 9.15s 3.06s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 15 unt; 0 nHn; 32 RR)
% Number of literals : 60 ( 0 equ; 30 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 : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(sum_6,negated_conjecture,
sum('additive$uidentity',a,b) ).
cnf(sum_7,negated_conjecture,
sum('additive$uidentity',c,d) ).
cnf(sum_8,negated_conjecture,
sum(a,c,u) ).
cnf(not_sum_9,negated_conjecture,
~ sum(d,b,u) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c5,plain,
sum('additive$uidentity',a,b),
inference(clausification,[status(esa)],[sum_6]) ).
cnf(c6,plain,
sum('additive$uidentity',c,d),
inference(clausification,[status(esa)],[sum_7]) ).
cnf(c7,plain,
sum(a,c,u),
inference(clausification,[status(esa)],[sum_8]) ).
cnf(c8,plain,
~ sum(d,b,u),
inference(clausification,[status(esa)],[not_sum_9]) ).
cnf(c9,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c10,plain,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_2]) ).
cnf(c11,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c13,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(d0,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d1,plain,
( ~ sum(X2,'additive$uidentity',X0)
| sum(X2,d,X1)
| ~ sum(X0,c,X1) ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(d2,plain,
( ~ sum(X0,'additive$uidentity',a)
| sum(X0,d,u) ),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( ~ defined(a)
| sum(a,d,u) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
sum(a,d,u),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( ~ sum(X2,a,X0)
| sum(X2,u,X1)
| ~ sum(X0,c,X1) ),
inference(resolution,[status(thm)],[c9,c7]) ).
cnf(d6,plain,
( sum(X0,u,u)
| ~ sum(X0,a,a) ),
inference(resolution,[status(thm)],[d5,c7]) ).
cnf(d7,plain,
( ~ defined(a)
| sum('additive$uidentity',u,u) ),
inference(resolution,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
sum('additive$uidentity',u,u),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( ~ sum('additive$uidentity',X2,X1)
| ~ sum(a,X0,X2)
| sum(b,X0,X1) ),
inference(resolution,[status(thm)],[c10,c5]) ).
cnf(d10,plain,
( sum(b,X0,u)
| ~ sum(a,X0,u) ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
sum(b,d,u),
inference(resolution,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
sum(d,b,u),
inference(resolution,[status(thm)],[d11,c13]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c8,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD013-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.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 02:23:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.15/3.06 % SZS status Unsatisfiable for theBenchmark.p
% 9.15/3.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------