%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD015-3 : 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 : 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 07:10:45 AM UTC 2026
% Result : Unsatisfiable 17.73s 5.30s
% Output : CNFRefutation 17.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 52 ( 16 unt; 2 nHn; 52 RR)
% Number of literals : 124 ( 0 equ; 74 neg)
% Maximal clause size : 4 ( 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 : 77 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(sum_3,negated_conjecture,
sum('additive$uidentity','additive$uinverse'(a),'additive$uinverse'(b)) ).
cnf(not_sum_4,negated_conjecture,
~ sum('additive$uidentity',a,b) ).
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$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,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,
sum('additive$uidentity','additive$uinverse'(a),'additive$uinverse'(b)),
inference(clausification,[status(esa)],[sum_3]) ).
cnf(c3,plain,
~ sum('additive$uidentity',a,b),
inference(clausification,[status(esa)],[not_sum_4]) ).
cnf(c4,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(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$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c8,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c24,plain,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(c26,plain,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[totality_of_order_relation]) ).
cnf(c27,plain,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[compatibility_of_order_relation_and_addition]) ).
cnf(d0,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d1,plain,
( ~ defined(X0)
| sum(X0,'additive$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c8,c7]) ).
cnf(d2,plain,
( ~ sum(X0,X3,X2)
| ~ sum('additive$uinverse'(X0),X1,X3)
| sum('additive$uidentity',X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
sum('additive$uinverse'(a),'additive$uidentity','additive$uinverse'(b)),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d4,plain,
( ~ sum(X3,'additive$uidentity',X1)
| sum(X3,X0,X2)
| ~ sum(X1,X0,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d5,plain,
( ~ defined(X0)
| ~ sum(X1,'additive$uidentity','additive$uinverse'(X0))
| sum(X1,X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( sum('additive$uinverse'(a),b,'additive$uidentity')
| ~ defined(b) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
sum('additive$uinverse'(a),b,'additive$uidentity'),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
( sum('additive$uidentity',b,X0)
| ~ sum(a,'additive$uidentity',X0)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( sum('additive$uidentity',b,X0)
| ~ sum(a,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
( ~ defined(a)
| sum('additive$uidentity',b,a) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
sum('additive$uidentity',b,a),
inference(resolution,[status(thm)],[c0,d10]) ).
cnf(d12,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(a,X1)
| ~ sum(X0,b,X1) ),
inference(resolution,[status(thm)],[d11,c27]) ).
cnf(d13,plain,
( ~ defined(b)
| ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| 'less$uor$uequal'(a,b) ),
inference(resolution,[status(thm)],[d12,c6]) ).
cnf(d14,plain,
( ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| 'less$uor$uequal'(a,b) ),
inference(resolution,[status(thm)],[c1,d13]) ).
cnf(d15,plain,
( 'less$uor$uequal'(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[status(thm)],[c26]) ).
cnf(d16,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'('additive$uidentity',X2)
| ~ sum(X0,'additive$uinverse'(X1),X2) ),
inference(resolution,[status(thm)],[c27,d1]) ).
cnf(d17,plain,
( ~ defined(X0)
| 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| ~ 'less$uor$uequal'(X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
( ~ defined(X0)
| 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
'less$uor$uequal'('additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
'less$uor$uequal'(a,b),
inference(resolution,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
( ~ 'less$uor$uequal'(b,a)
| ~ 'less$uor$uequal'(a,b) ),
inference(resolution,[status(thm)],[c24,c3]) ).
cnf(d22,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(X1,X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c27,c6]) ).
cnf(d23,plain,
( ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| 'less$uor$uequal'(b,a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[d11,d22]) ).
cnf(d24,plain,
( ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| 'less$uor$uequal'(b,a) ),
inference(resolution,[status(thm)],[c1,d23]) ).
cnf(d25,plain,
'less$uor$uequal'(b,a),
inference(resolution,[status(thm)],[d19,d24]) ).
cnf(d26,plain,
~ 'less$uor$uequal'(a,b),
inference(resolution,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[d26,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD015-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n016.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 02:27:16 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.73/5.30 % SZS status Unsatisfiable for theBenchmark.p
% 17.73/5.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------