%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD043-3 : 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 : n016.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 17.21s 9.29s
% Output : CNFRefutation 17.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 11 unt; 0 nHn; 29 RR)
% Number of literals : 67 ( 0 equ; 40 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(product_3,negated_conjecture,
product('additive$uidentity',a,b) ).
cnf(not_sum_4,negated_conjecture,
~ sum('additive$uidentity',b,'additive$uidentity') ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(distributivity_1,axiom,
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ) ).
cnf(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
product('additive$uidentity',a,b),
inference(clausification,[status(esa)],[product_3]) ).
cnf(c3,plain,
~ sum('additive$uidentity',b,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_4]) ).
cnf(c5,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(c6,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c7,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c8,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c14,plain,
( ~ sum(X3,X5,X6)
| ~ product(X6,X4,X2)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity_1]) ).
cnf(c17,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(d0,plain,
( ~ sum('additive$uinverse'(X0),X3,X2)
| ~ sum(X0,X1,X3)
| sum('additive$uidentity',X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d1,plain,
( ~ defined(X0)
| sum('additive$uidentity',X1,'additive$uidentity')
| ~ sum(X0,X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d3,plain,
( ~ defined(X0)
| sum(X4,X3,X2)
| ~ product(X0,X1,X4)
| ~ product('additive$uidentity',X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
( sum(X1,b,X2)
| ~ product(X0,a,X2)
| ~ product(X0,a,X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( sum(b,b,X0)
| ~ product('additive$uidentity',a,X0)
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( sum(b,b,X0)
| ~ product('additive$uidentity',a,X0) ),
inference(resolution,[status(thm)],[c17,d5]) ).
cnf(d7,plain,
sum(b,b,b),
inference(resolution,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
( sum('additive$uidentity',b,'additive$uidentity')
| ~ defined(b) ),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
sum('additive$uidentity',b,'additive$uidentity'),
inference(resolution,[status(thm)],[c1,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c3,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD043-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n016.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sun Sep 27 02:31:22 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.21/9.29 % SZS status Unsatisfiable for theBenchmark.p
% 17.21/9.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------