%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD009-3 : 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 : n001.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 36.25s 8.50s
% Output : CNFRefutation 36.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 11 unt; 4 nHn; 32 RR)
% Number of literals : 72 ( 0 equ; 43 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(not_sum_3,negated_conjecture,
~ sum('additive$uidentity',a,'additive$uidentity') ).
cnf(not_product_4,negated_conjecture,
~ product(a,X0,b) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
~ sum('additive$uidentity',a,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_3]) ).
cnf(c3,plain,
~ product(a,X0,b),
inference(clausification,[status(esa)],[not_product_4]) ).
cnf(c10,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c11,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c12,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c13,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c21,plain,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c23,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_multiplication]) ).
cnf(d0,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d1,plain,
( ~ defined(X2)
| ~ product(X2,X3,X0)
| ~ product(X3,X1,'multiplicative$uidentity')
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,d0]) ).
cnf(d2,plain,
( ~ defined(X0)
| ~ defined(X1)
| product(multiply(X0,X1),X2,X0)
| ~ product(X1,X2,'multiplicative$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c23]) ).
cnf(d3,plain,
( product(X2,multiply(X1,X0),X1)
| ~ product(X0,X2,'multiplicative$uidentity')
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,c13]) ).
cnf(d4,plain,
( ~ product(X0,a,'multiplicative$uidentity')
| ~ defined(X0)
| ~ defined(b) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
( ~ product(X0,a,'multiplicative$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c1,d4]) ).
cnf(d6,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| ~ defined('multiplicative$uinverse'(a)) ),
inference(resolution,[status(thm)],[d5,c12]) ).
cnf(d7,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined('multiplicative$uinverse'(a)) ),
inference(resolution,[status(thm)],[c0,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)],[c21,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
% 0.00/0.05 % Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n001.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 27 02:26:59 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.25/8.50 % SZS status Unsatisfiable for theBenchmark.p
% 36.25/8.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------