%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD030-3 : 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 : n007.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 18.09s 3.11s
% Output : CNFRefutation 18.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 11 unt; 0 nHn; 23 RR)
% Number of literals : 45 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(product_4,negated_conjecture,
product('multiplicative$uidentity',a,d) ).
cnf(not_product_5,negated_conjecture,
~ product(d,b,multiply(a,b)) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
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(c3,plain,
product('multiplicative$uidentity',a,d),
inference(clausification,[status(esa)],[product_4]) ).
cnf(c4,plain,
~ product(d,b,multiply(a,b)),
inference(clausification,[status(esa)],[not_product_5]) ).
cnf(c11,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c12,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c14,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c24,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_multiplication]) ).
cnf(d0,plain,
product(a,'multiplicative$uidentity',d),
inference(resolution,[status(thm)],[c14,c3]) ).
cnf(d1,plain,
( ~ product(a,X2,X1)
| ~ product('multiplicative$uidentity',X0,X2)
| product(d,X0,X1) ),
inference(resolution,[status(thm)],[d0,c11]) ).
cnf(d2,plain,
( ~ defined(X0)
| product(d,X0,X1)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
( ~ defined(a)
| ~ defined(X0)
| product(d,X0,multiply(a,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,c24]) ).
cnf(d4,plain,
( product(d,X0,multiply(a,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
~ defined(b),
inference(resolution,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c1,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD030-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 02:22:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.09/3.11 % SZS status Unsatisfiable for theBenchmark.p
% 18.09/3.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------