%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD013-3 : 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 : n010.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 45.41s 25.85s
% Output : CNFRefutation 45.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 63 ( 29 unt; 0 nHn; 63 RR)
% Number of literals : 120 ( 0 equ; 59 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(c_is_defined,hypothesis,
defined(c) ).
cnf(d_is_defined,hypothesis,
defined(d) ).
cnf(sum_5,negated_conjecture,
sum('additive$uidentity',a,b) ).
cnf(sum_6,negated_conjecture,
sum('additive$uidentity',c,d) ).
cnf(not_sum_7,negated_conjecture,
~ sum(a,c,add(d,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$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(totality_of_addition,axiom,
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(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,
defined(c),
inference(clausification,[status(esa)],[c_is_defined]) ).
cnf(c3,plain,
defined(d),
inference(clausification,[status(esa)],[d_is_defined]) ).
cnf(c4,plain,
sum('additive$uidentity',a,b),
inference(clausification,[status(esa)],[sum_5]) ).
cnf(c5,plain,
sum('additive$uidentity',c,d),
inference(clausification,[status(esa)],[sum_6]) ).
cnf(c6,plain,
~ sum(a,c,add(d,b)),
inference(clausification,[status(esa)],[not_sum_7]) ).
cnf(c7,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(c8,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(c9,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c10,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c11,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c20,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(c25,plain,
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_addition]) ).
cnf(d0,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c11,c9]) ).
cnf(d1,plain,
sum(a,'additive$uidentity',b),
inference(resolution,[status(thm)],[c11,c4]) ).
cnf(d2,plain,
( ~ sum(X2,a,X0)
| sum(X2,b,X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c7,d1]) ).
cnf(d3,plain,
( ~ defined(X1)
| sum(X0,b,X1)
| ~ sum(X0,a,X1) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ defined(a)
| sum('additive$uidentity',b,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
sum('additive$uidentity',b,a),
inference(resolution,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
sum(b,'additive$uidentity',a),
inference(resolution,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
( ~ sum(b,X2,X1)
| ~ sum('additive$uidentity',X0,X2)
| sum(a,X0,X1) ),
inference(resolution,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
( sum(X0,b,b)
| ~ sum(X0,a,a) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d9,plain,
( ~ defined(a)
| sum('additive$uidentity',b,b) ),
inference(resolution,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
sum('additive$uidentity',b,b),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
sum(b,'additive$uidentity',b),
inference(resolution,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
( ~ defined(a)
| sum('additive$uinverse'(a),b,'additive$uidentity')
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[d3,c10]) ).
cnf(d13,plain,
( sum('additive$uinverse'(a),b,'additive$uidentity')
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d12]) ).
cnf(d14,plain,
sum('additive$uinverse'(a),b,'additive$uidentity'),
inference(resolution,[status(thm)],[c20,d13]) ).
cnf(d15,plain,
( ~ sum('additive$uinverse'(a),X2,X1)
| ~ sum(b,X0,X2)
| sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d14,c8]) ).
cnf(d16,plain,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ sum(b,X0,b) ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
sum('additive$uidentity','additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
sum(c,'additive$uidentity',d),
inference(resolution,[status(thm)],[c11,c5]) ).
cnf(d19,plain,
( ~ sum(X2,c,X0)
| sum(X2,d,X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c7,d18]) ).
cnf(d20,plain,
( ~ defined(X1)
| sum(X0,d,X1)
| ~ sum(X0,c,X1) ),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
( ~ defined(c)
| sum('additive$uidentity',d,c)
| ~ defined(c) ),
inference(resolution,[status(thm)],[d20,c9]) ).
cnf(d22,plain,
sum('additive$uidentity',d,c),
inference(resolution,[status(thm)],[c2,d21]) ).
cnf(d23,plain,
( ~ sum(X2,'additive$uidentity',X0)
| sum(X2,c,X1)
| ~ sum(X0,d,X1) ),
inference(resolution,[status(thm)],[d22,c7]) ).
cnf(d24,plain,
( ~ sum(X0,'additive$uidentity','additive$uidentity')
| sum(X0,c,c) ),
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
sum('additive$uidentity',c,c),
inference(resolution,[status(thm)],[d24,d17]) ).
cnf(d26,plain,
( ~ sum(b,c,X0)
| sum(a,c,X0) ),
inference(resolution,[status(thm)],[d25,d7]) ).
cnf(d27,plain,
( sum(X1,X0,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c25,c11]) ).
cnf(d28,plain,
( ~ sum(b,X2,X1)
| ~ sum('additive$uidentity',X0,X2)
| sum(b,X0,X1) ),
inference(resolution,[status(thm)],[d11,c8]) ).
cnf(d29,plain,
( sum(b,c,X0)
| ~ sum(b,d,X0) ),
inference(resolution,[status(thm)],[d28,c5]) ).
cnf(d30,plain,
( ~ defined(d)
| ~ defined(b)
| sum(b,c,add(d,b)) ),
inference(resolution,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
( sum(b,c,add(d,b))
| ~ defined(d) ),
inference(resolution,[status(thm)],[c1,d30]) ).
cnf(d32,plain,
sum(b,c,add(d,b)),
inference(resolution,[status(thm)],[c3,d31]) ).
cnf(d33,plain,
sum(a,c,add(d,b)),
inference(resolution,[status(thm)],[d32,d26]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[c6,d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD013-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.48 % Computer : n010.cluster.edu
% 0.11/15.48 % Model : x86_64 x86_64
% 0.11/15.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.48 % Memory : 8046.5625MB
% 0.11/15.48 % OS : Linux 6.8.0-71-generic
% 0.11/15.49 % CPULimit : 300
% 0.11/15.49 % WCLimit : 300
% 0.11/15.49 % DateTime : Sun Sep 27 02:23:33 UTC 2026
% 0.11/15.49 % CPUTime :
% 0.11/15.49 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.41/25.85 % SZS status Unsatisfiable for theBenchmark.p
% 45.41/25.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------