%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD010-3 : 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 : n018.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 07:10:44 AM UTC 2026
% Result : Unsatisfiable 12.51s 3.26s
% Output : CNFRefutation 12.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 8 unt; 3 nHn; 14 RR)
% Number of literals : 23 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_sum_1,negated_conjecture,
~ sum('additive$uidentity','multiplicative$uidentity','additive$uidentity') ).
cnf(not_product_2,negated_conjecture,
~ product('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity') ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(c0,plain,
~ sum('additive$uidentity','multiplicative$uidentity','additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_1]) ).
cnf(c1,plain,
~ product('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[not_product_2]) ).
cnf(c10,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c11,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c18,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(d0,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c11,c10]) ).
cnf(d1,plain,
( ~ defined('multiplicative$uidentity')
| sum('additive$uidentity','multiplicative$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
~ defined('multiplicative$uidentity'),
inference(resolution,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c18,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD010-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 27 02:23:07 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.51/3.26 % SZS status Unsatisfiable for theBenchmark.p
% 12.51/3.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------