%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD031-1 : 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 : n017.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 07:10:49 AM UTC 2026
% Result : Unsatisfiable 26.01s 8.83s
% Output : CNFRefutation 26.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 11 unt; 6 nHn; 32 RR)
% Number of literals : 73 ( 0 equ; 40 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(a_equals_multiplicative_identity_2,negated_conjecture,
equalish(a,'multiplicative$uidentity') ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,'additive$uidentity') ).
cnf(multiplicative_inverses_not_equal,negated_conjecture,
~ equalish('multiplicative$uinverse'(a),'multiplicative$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_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(compatibility_of_equality_and_multiplication,axiom,
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X2,X1)) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
equalish(a,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[a_equals_multiplicative_identity_2]) ).
cnf(c2,plain,
~ equalish(a,'additive$uidentity'),
inference(clausification,[status(esa)],[a_not_equal_to_additive_identity_3]) ).
cnf(c3,plain,
~ equalish('multiplicative$uinverse'(a),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverses_not_equal]) ).
cnf(c9,plain,
( ~ defined(X0)
| equalish(multiply('multiplicative$uidentity',X0),X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c10,plain,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| equalish(multiply(X0,'multiplicative$uinverse'(X0)),'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c18,plain,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c25,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_equality]) ).
cnf(c26,plain,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_equality]) ).
cnf(c28,plain,
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X2,X1)) ),
inference(clausification,[status(esa)],[compatibility_of_equality_and_multiplication]) ).
cnf(d0,plain,
( ~ equalish(X1,multiply(X0,'multiplicative$uinverse'(X0)))
| equalish(X1,'multiplicative$uidentity')
| equalish(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c10,c26]) ).
cnf(d1,plain,
( ~ defined(X1)
| ~ equalish(X0,multiply('multiplicative$uidentity',X1))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c26,c9]) ).
cnf(d2,plain,
( ~ equalish(X1,'multiplicative$uidentity')
| ~ defined(X0)
| equalish(multiply(X1,X0),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c28]) ).
cnf(d3,plain,
( equalish(X0,multiply(X1,X0))
| ~ equalish(X1,'multiplicative$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,c25]) ).
cnf(d4,plain,
( equalish(X0,'additive$uidentity')
| equalish('multiplicative$uinverse'(X0),'multiplicative$uidentity')
| ~ defined(X0)
| ~ equalish(X0,'multiplicative$uidentity')
| ~ defined('multiplicative$uinverse'(X0)) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( equalish(a,'additive$uidentity')
| ~ equalish(a,'multiplicative$uidentity')
| ~ defined('multiplicative$uinverse'(a))
| ~ defined(a) ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
( equalish(a,'additive$uidentity')
| ~ equalish(a,'multiplicative$uidentity')
| ~ defined('multiplicative$uinverse'(a)) ),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
( equalish(a,'additive$uidentity')
| ~ defined('multiplicative$uinverse'(a)) ),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
~ defined('multiplicative$uinverse'(a)),
inference(resolution,[status(thm)],[c2,d7]) ).
cnf(d9,plain,
( defined('multiplicative$uinverse'(a))
| ~ defined(a) ),
inference(resolution,[status(thm)],[c18,c2]) ).
cnf(d10,plain,
defined('multiplicative$uinverse'(a)),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD031-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 02:20:34 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.01/8.83 % SZS status Unsatisfiable for theBenchmark.p
% 26.01/8.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------