%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD002-3 : 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 : n015.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 07:10:42 AM UTC 2026
% Result : Unsatisfiable 17.57s 2.90s
% Output : CNFRefutation 17.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 38 ( 16 unt; 0 nHn; 38 RR)
% Number of literals : 84 ( 0 equ; 48 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 63 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(product_3,hypothesis,
product('multiplicative$uidentity',a,b) ).
cnf(not_sum_4,negated_conjecture,
~ sum('additive$uidentity',a,b) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(distributivity_1,axiom,
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ) ).
cnf(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
product('multiplicative$uidentity',a,b),
inference(clausification,[status(esa)],[product_3]) ).
cnf(c3,plain,
~ sum('additive$uidentity',a,b),
inference(clausification,[status(esa)],[not_sum_4]) ).
cnf(c6,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c8,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
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$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c13,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c14,plain,
( ~ sum(X3,X5,X6)
| ~ product(X6,X4,X2)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity_1]) ).
cnf(c17,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(d0,plain,
product(a,'multiplicative$uidentity',b),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d1,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d2,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c11]) ).
cnf(d3,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X1,X0)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( product('multiplicative$uidentity',b,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
product('multiplicative$uidentity',b,a),
inference(resolution,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
product(b,'multiplicative$uidentity',a),
inference(resolution,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d8,plain,
( ~ defined(X0)
| sum(X4,X3,X2)
| ~ product(X0,X1,X4)
| ~ product('additive$uidentity',X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,d7]) ).
cnf(d9,plain,
( ~ defined('additive$uidentity')
| sum(X1,'additive$uidentity',X2)
| ~ product(X0,'multiplicative$uidentity',X2)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( sum(X2,'additive$uidentity',X1)
| ~ product(X0,'multiplicative$uidentity',X2)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c17,d9]) ).
cnf(d11,plain,
( ~ defined(X0)
| sum(X1,'additive$uidentity',X0)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( sum(a,'additive$uidentity',b)
| ~ defined(b) ),
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
sum(a,'additive$uidentity',b),
inference(resolution,[status(thm)],[c1,d12]) ).
cnf(d14,plain,
sum('additive$uidentity',a,b),
inference(resolution,[status(thm)],[d13,c8]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[c3,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD002-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n015.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 02:24:14 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.57/2.90 % SZS status Unsatisfiable for theBenchmark.p
% 17.57/2.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------