%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD037-1 : 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 : n016.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 07:10:51 AM UTC 2026
% Result : Unsatisfiable 11.58s 10.29s
% Output : CNFRefutation 11.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 10 unt; 7 nHn; 26 RR)
% Number of literals : 61 ( 0 equ; 32 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,'additive$uidentity') ).
cnf(a_equals_b_4,negated_conjecture,
equalish(a,b) ).
cnf(multiplicative_identity_not_equal_to_multiply_5,negated_conjecture,
~ equalish('multiplicative$uidentity',multiply(b,'multiplicative$uinverse'(a))) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(X0,'additive$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(c2,plain,
~ equalish(a,'additive$uidentity'),
inference(clausification,[status(esa)],[a_not_equal_to_additive_identity_3]) ).
cnf(c3,plain,
equalish(a,b),
inference(clausification,[status(esa)],[a_equals_b_4]) ).
cnf(c4,plain,
~ equalish('multiplicative$uidentity',multiply(b,'multiplicative$uinverse'(a))),
inference(clausification,[status(esa)],[multiplicative_identity_not_equal_to_multiply_5]) ).
cnf(c11,plain,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| equalish(multiply(X0,'multiplicative$uinverse'(X0)),'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c19,plain,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c26,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_equality]) ).
cnf(c27,plain,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_equality]) ).
cnf(c29,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('multiplicative$uidentity',multiply(X0,'multiplicative$uinverse'(X0)))
| equalish(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c11,c26]) ).
cnf(d1,plain,
( ~ equalish(X3,multiply(X1,X0))
| equalish(X3,multiply(X2,X0))
| ~ equalish(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c29,c27]) ).
cnf(d2,plain,
( equalish(X0,'additive$uidentity')
| ~ defined(X0)
| ~ equalish(X0,X1)
| equalish('multiplicative$uidentity',multiply(X1,'multiplicative$uinverse'(X0)))
| ~ defined('multiplicative$uinverse'(X0)) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( equalish('multiplicative$uidentity',multiply(X1,'multiplicative$uinverse'(X0)))
| equalish(X0,'additive$uidentity')
| ~ equalish(X0,X1)
| ~ defined(X0)
| equalish(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c19,d2]) ).
cnf(d4,plain,
( equalish(a,'additive$uidentity')
| ~ equalish(a,b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( equalish(a,'additive$uidentity')
| ~ equalish(a,b) ),
inference(resolution,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
~ equalish(a,b),
inference(resolution,[status(thm)],[c2,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c3,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD037-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n016.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 27 02:30:32 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.58/10.29 % SZS status Unsatisfiable for theBenchmark.p
% 11.58/10.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------