%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD013-5 : 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 : n006.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 14.27s 2.22s
% Output : CNFRefutation 14.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 19 unt; 0 nHn; 32 RR)
% Number of literals : 57 ( 0 equ; 27 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 : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d_is_defined,hypothesis,
defined(d) ).
cnf(sum_7,negated_conjecture,
sum('additive$uidentity',a,b) ).
cnf(sum_8,negated_conjecture,
sum('additive$uidentity',c,d) ).
cnf(sum_9,negated_conjecture,
sum(a,c,u) ).
cnf(sum_10,negated_conjecture,
sum(d,b,v) ).
cnf(not_sum_11,negated_conjecture,
~ sum('additive$uidentity',u,v) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(c3,plain,
defined(d),
inference(clausification,[status(esa)],[d_is_defined]) ).
cnf(c6,plain,
sum('additive$uidentity',a,b),
inference(clausification,[status(esa)],[sum_7]) ).
cnf(c7,plain,
sum('additive$uidentity',c,d),
inference(clausification,[status(esa)],[sum_8]) ).
cnf(c8,plain,
sum(a,c,u),
inference(clausification,[status(esa)],[sum_9]) ).
cnf(c9,plain,
sum(d,b,v),
inference(clausification,[status(esa)],[sum_10]) ).
cnf(c10,plain,
~ sum('additive$uidentity',u,v),
inference(clausification,[status(esa)],[not_sum_11]) ).
cnf(c11,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c12,plain,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_2]) ).
cnf(c13,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c15,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(d0,plain,
sum(c,'additive$uidentity',d),
inference(resolution,[status(thm)],[c15,c7]) ).
cnf(d1,plain,
( ~ sum(a,X2,X1)
| ~ sum(c,X0,X2)
| sum(u,X0,X1) ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d2,plain,
( sum(u,'additive$uidentity',X0)
| ~ sum(a,d,X0) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
sum(a,'additive$uidentity',b),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(d4,plain,
sum(b,d,v),
inference(resolution,[status(thm)],[c15,c9]) ).
cnf(d5,plain,
( ~ sum(X3,'additive$uidentity',X1)
| sum(X3,X0,X2)
| ~ sum(X1,X0,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d6,plain,
( ~ sum(X0,'additive$uidentity',b)
| sum(X0,d,v)
| ~ defined(d) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ sum(X0,'additive$uidentity',b)
| sum(X0,d,v) ),
inference(resolution,[status(thm)],[c3,d6]) ).
cnf(d8,plain,
sum(a,d,v),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
sum(u,'additive$uidentity',v),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
sum('additive$uidentity',u,v),
inference(resolution,[status(thm)],[d9,c15]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c10,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD013-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.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 : Sun Sep 27 02:22:26 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.27/2.22 % SZS status Unsatisfiable for theBenchmark.p
% 14.27/2.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------