%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD016-5 : 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 : n019.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 20.97s 2.97s
% Output : CNFRefutation 20.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 16 unt; 0 nHn; 34 RR)
% Number of literals : 68 ( 0 equ; 36 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(v_is_defined,hypothesis,
defined(v) ).
cnf(sum_6,negated_conjecture,
sum(a,u,q) ).
cnf(sum_7,negated_conjecture,
sum(a,v,r) ).
cnf(sum_8,negated_conjecture,
sum('additive$uidentity',q,r) ).
cnf(not_sum_9,negated_conjecture,
~ sum('additive$uidentity',u,v) ).
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$uidentity') ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c2,plain,
defined(v),
inference(clausification,[status(esa)],[v_is_defined]) ).
cnf(c5,plain,
sum(a,u,q),
inference(clausification,[status(esa)],[sum_6]) ).
cnf(c6,plain,
sum(a,v,r),
inference(clausification,[status(esa)],[sum_7]) ).
cnf(c7,plain,
sum('additive$uidentity',q,r),
inference(clausification,[status(esa)],[sum_8]) ).
cnf(c8,plain,
~ sum('additive$uidentity',u,v),
inference(clausification,[status(esa)],[not_sum_9]) ).
cnf(c9,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c10,plain,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_2]) ).
cnf(c11,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c12,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(d0,plain,
( ~ sum('additive$uidentity',X3,X2)
| ~ sum(X0,X1,X3)
| sum(X0,X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c11,c10]) ).
cnf(d1,plain,
( sum(X0,X1,r)
| ~ sum(X0,X1,q)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( sum(a,u,r)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
sum(a,u,r),
inference(resolution,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
( ~ sum('additive$uinverse'(X0),X3,X2)
| ~ sum(X0,X1,X3)
| sum('additive$uidentity',X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c12,c10]) ).
cnf(d5,plain,
( ~ sum(X2,a,X0)
| sum(X2,r,X1)
| ~ sum(X0,v,X1) ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(d6,plain,
( ~ defined(v)
| sum(X0,r,v)
| ~ sum(X0,a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
( sum(X0,r,v)
| ~ sum(X0,a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
( ~ defined(a)
| sum('additive$uinverse'(a),r,v) ),
inference(resolution,[status(thm)],[d7,c12]) ).
cnf(d9,plain,
sum('additive$uinverse'(a),r,v),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
( sum('additive$uidentity',X0,v)
| ~ sum(a,X0,r)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
( sum('additive$uidentity',X0,v)
| ~ sum(a,X0,r) ),
inference(resolution,[status(thm)],[c0,d10]) ).
cnf(d12,plain,
sum('additive$uidentity',u,v),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c8,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD016-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 02:22:33 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.97/2.97 % SZS status Unsatisfiable for theBenchmark.p
% 20.97/2.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------