%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD007-3 : 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 : 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 07:10:43 AM UTC 2026
% Result : Unsatisfiable 13.70s 8.50s
% Output : CNFRefutation 13.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 7 unt; 0 nHn; 24 RR)
% Number of literals : 50 ( 0 equ; 33 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(not_sum_2,negated_conjecture,
~ sum('additive$uidentity','additive$uinverse'('additive$uinverse'(a)),a) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$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(well_definedness_of_additive_inverse,axiom,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
~ sum('additive$uidentity','additive$uinverse'('additive$uinverse'(a)),a),
inference(clausification,[status(esa)],[not_sum_2]) ).
cnf(c3,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(c4,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c5,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c6,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c16,plain,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_additive_inverse]) ).
cnf(d0,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d1,plain,
( ~ defined(X0)
| sum(X0,'additive$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d2,plain,
( ~ sum(X0,X3,X2)
| ~ sum('additive$uinverse'(X0),X1,X3)
| sum('additive$uidentity',X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( ~ defined('additive$uinverse'(X0))
| sum('additive$uidentity','additive$uinverse'('additive$uinverse'(X0)),X1)
| ~ sum(X0,'additive$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ sum(a,'additive$uidentity',a)
| ~ defined('additive$uinverse'(a))
| ~ defined(a) ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
( ~ sum(a,'additive$uidentity',a)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
( ~ defined(a)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
~ defined('additive$uinverse'(a)),
inference(resolution,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
~ defined(a),
inference(resolution,[status(thm)],[d7,c16]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c0,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD007-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.40 % Computer : n006.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Sun Sep 27 02:21:24 UTC 2026
% 0.12/5.41 % CPUTime :
% 0.12/5.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.70/8.50 % SZS status Unsatisfiable for theBenchmark.p
% 13.70/8.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------