%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD010-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 13.10s 7.25s
% Output : CNFRefutation 13.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 10 unt; 10 nHn; 28 RR)
% Number of literals : 58 ( 0 equ; 24 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiplicative_inv_not_equal_to_multiplicative_id_2,negated_conjecture,
~ equalish('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity') ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| equalish(multiply('multiplicative$uidentity',X0),X0) ) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| equalish(multiply(X0,'multiplicative$uinverse'(X0)),'multiplicative$uidentity') ) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X1,X0)
| equalish(X0,X1) ) ).
cnf(transitivity_of_equality,axiom,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ) ).
cnf(different_identities,axiom,
~ equalish('additive$uidentity','multiplicative$uidentity') ).
cnf(c0,plain,
~ equalish('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inv_not_equal_to_multiplicative_id_2]) ).
cnf(c6,plain,
( ~ defined(X0)
| equalish(multiply('multiplicative$uidentity',X0),X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c7,plain,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| equalish(multiply(X0,'multiplicative$uinverse'(X0)),'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c14,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(c15,plain,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c22,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_equality]) ).
cnf(c23,plain,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_equality]) ).
cnf(c27,plain,
~ equalish('additive$uidentity','multiplicative$uidentity'),
inference(clausification,[status(esa)],[different_identities]) ).
cnf(d0,plain,
( equalish('multiplicative$uidentity',multiply(X0,'multiplicative$uinverse'(X0)))
| ~ defined(X0)
| equalish(X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[c7,c22]) ).
cnf(d1,plain,
( ~ defined(X1)
| ~ equalish(X0,multiply('multiplicative$uidentity',X1))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c23,c6]) ).
cnf(d2,plain,
( ~ defined('multiplicative$uidentity')
| equalish('multiplicative$uidentity','additive$uidentity')
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity'))
| equalish('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ defined('multiplicative$uinverse'('multiplicative$uidentity'))
| equalish('multiplicative$uidentity','additive$uidentity')
| equalish('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
( equalish('additive$uidentity',X0)
| defined('multiplicative$uinverse'(X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c15,c22]) ).
cnf(d5,plain,
( defined('multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d4,c27]) ).
cnf(d6,plain,
defined('multiplicative$uinverse'('multiplicative$uidentity')),
inference(resolution,[status(thm)],[c14,d5]) ).
cnf(d7,plain,
( equalish('multiplicative$uidentity','additive$uidentity')
| equalish('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
( equalish('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity')
| equalish('multiplicative$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d7,c22]) ).
cnf(d9,plain,
equalish('multiplicative$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
equalish('additive$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[d9,c22]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c27,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD010-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.53 % Computer : n015.cluster.edu
% 0.10/5.53 % Model : x86_64 x86_64
% 0.10/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.53 % Memory : 8046.5625MB
% 0.10/5.53 % OS : Linux 6.8.0-71-generic
% 0.10/5.53 % CPULimit : 300
% 0.10/5.53 % WCLimit : 300
% 0.10/5.53 % DateTime : Sun Sep 27 02:24:35 UTC 2026
% 0.10/5.53 % CPUTime :
% 0.10/5.53 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.10/7.25 % SZS status Unsatisfiable for theBenchmark.p
% 13.10/7.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------