%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD034-3 : 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 : n020.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 07:10:50 AM UTC 2026
% Result : Unsatisfiable 14.32s 2.24s
% Output : CNFRefutation 14.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 9 unt; 0 nHn; 18 RR)
% Number of literals : 34 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(product_3,negated_conjecture,
product('multiplicative$uidentity',m,'multiplicative$uidentity') ).
cnf(not_product_4,negated_conjecture,
~ product(m,a,a) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c2,plain,
product('multiplicative$uidentity',m,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[product_3]) ).
cnf(c3,plain,
~ product(m,a,a),
inference(clausification,[status(esa)],[not_product_4]) ).
cnf(c9,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c11,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c13,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(d0,plain,
product(m,'multiplicative$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d1,plain,
( product(m,X2,X1)
| ~ product('multiplicative$uidentity',X0,X2)
| ~ product('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d2,plain,
( ~ defined(X1)
| ~ product('multiplicative$uidentity',X1,X0)
| product(m,X0,X1) ),
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d3,plain,
( ~ defined(X0)
| product(m,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,c11]) ).
cnf(d4,plain,
~ defined(a),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c0,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD034-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 02:27:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.32/2.24 % SZS status Unsatisfiable for theBenchmark.p
% 14.32/2.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------