%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD025-3 : 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 : n009.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 07:10:48 AM UTC 2026
% Result : Unsatisfiable 21.50s 3.31s
% Output : CNFRefutation 21.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 15 unt; 0 nHn; 34 RR)
% Number of literals : 70 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(c_is_defined,hypothesis,
defined(c) ).
cnf(product_5,negated_conjecture,
product('multiplicative$uidentity',a,b) ).
cnf(product_6,negated_conjecture,
product('multiplicative$uidentity',c,d) ).
cnf(not_product_7,negated_conjecture,
~ product(d,b,multiply(a,c)) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
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$uidentity',X0,X0) ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c2,plain,
defined(c),
inference(clausification,[status(esa)],[c_is_defined]) ).
cnf(c4,plain,
product('multiplicative$uidentity',a,b),
inference(clausification,[status(esa)],[product_5]) ).
cnf(c5,plain,
product('multiplicative$uidentity',c,d),
inference(clausification,[status(esa)],[product_6]) ).
cnf(c6,plain,
~ product(d,b,multiply(a,c)),
inference(clausification,[status(esa)],[not_product_7]) ).
cnf(c12,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c13,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c14,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c16,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c26,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_multiplication]) ).
cnf(d0,plain,
( product(X0,X1,multiply(X1,X0))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c26,c16]) ).
cnf(d1,plain,
product(c,'multiplicative$uidentity',d),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(d2,plain,
( ~ product(c,X2,X1)
| ~ product('multiplicative$uidentity',X0,X2)
| product(d,X0,X1) ),
inference(resolution,[status(thm)],[d1,c13]) ).
cnf(d3,plain,
product(a,'multiplicative$uidentity',b),
inference(resolution,[status(thm)],[c16,c4]) ).
cnf(d4,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c16,c14]) ).
cnf(d5,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c12,c14]) ).
cnf(d6,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X1,X0)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( product('multiplicative$uidentity',b,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
product('multiplicative$uidentity',b,a),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( product(d,b,X0)
| ~ product(c,a,X0) ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ defined(c)
| ~ defined(a)
| product(d,b,multiply(a,c)) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( product(d,b,multiply(a,c))
| ~ defined(c) ),
inference(resolution,[status(thm)],[c0,d10]) ).
cnf(d12,plain,
product(d,b,multiply(a,c)),
inference(resolution,[status(thm)],[c2,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c6,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD025-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 02:23:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.50/3.31 % SZS status Unsatisfiable for theBenchmark.p
% 21.50/3.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------