%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD003-1 : 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 : n007.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 07:10:42 AM UTC 2026
% Result : Unsatisfiable 29.45s 4.62s
% Output : CNFRefutation 29.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 10 unt; 0 nHn; 36 RR)
% Number of literals : 82 ( 0 equ; 55 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(add_not_equal_to_a_3,negated_conjecture,
~ equalish(add(a,add(b,'additive$uinverse'(b))),a) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(X0)),'additive$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X1,X0)
| equalish(X0,X1) ) ).
cnf(transitivity_of_equality,axiom,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ) ).
cnf(compatibility_of_equality_and_addition,axiom,
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(add(X0,X1),add(X2,X1)) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
~ equalish(add(a,add(b,'additive$uinverse'(b))),a),
inference(clausification,[status(esa)],[add_not_equal_to_a_3]) ).
cnf(c4,plain,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c5,plain,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(X0)),'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c6,plain,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c12,plain,
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ),
inference(clausification,[status(esa)],[well_definedness_of_addition]) ).
cnf(c14,plain,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_additive_inverse]) ).
cnf(c24,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_equality]) ).
cnf(c25,plain,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_equality]) ).
cnf(c26,plain,
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(add(X0,X1),add(X2,X1)) ),
inference(clausification,[status(esa)],[compatibility_of_equality_and_addition]) ).
cnf(d0,plain,
( ~ defined(X1)
| ~ equalish(X0,add('additive$uidentity',X1))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c25,c4]) ).
cnf(d1,plain,
( equalish(add(X1,X0),X0)
| ~ defined(X0)
| ~ equalish(X1,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c26,d0]) ).
cnf(d2,plain,
( equalish(X0,add(X1,X0))
| ~ equalish(X1,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c24]) ).
cnf(d3,plain,
( ~ equalish(X2,add(X1,X0))
| equalish(X2,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c6,c25]) ).
cnf(d4,plain,
( ~ equalish(X0,'additive$uidentity')
| ~ defined(X1)
| equalish(X1,add(X1,X0))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( equalish(add(X0,X1),X0)
| ~ equalish(X1,'additive$uidentity')
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d4,c24]) ).
cnf(d6,plain,
( ~ equalish(add(b,'additive$uinverse'(b)),'additive$uidentity')
| ~ defined(a)
| ~ defined(add(b,'additive$uinverse'(b))) ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
( ~ equalish(add(b,'additive$uinverse'(b)),'additive$uidentity')
| ~ defined(add(b,'additive$uinverse'(b))) ),
inference(resolution,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
( ~ defined(b)
| ~ defined(add(b,'additive$uinverse'(b))) ),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
~ defined(add(b,'additive$uinverse'(b))),
inference(resolution,[status(thm)],[c1,d8]) ).
cnf(d10,plain,
( ~ defined('additive$uinverse'(b))
| ~ defined(b) ),
inference(resolution,[status(thm)],[d9,c12]) ).
cnf(d11,plain,
~ defined('additive$uinverse'(b)),
inference(resolution,[status(thm)],[c1,d10]) ).
cnf(d12,plain,
~ defined(b),
inference(resolution,[status(thm)],[d11,c14]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c1,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD003-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 02:18:54 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.45/4.62 % SZS status Unsatisfiable for theBenchmark.p
% 29.45/4.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------