%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD032-3 : 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 : n011.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 13.58s 2.04s
% Output : CNFRefutation 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 13 unt; 4 nHn; 28 RR)
% Number of literals : 58 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(not_sum_2,negated_conjecture,
~ sum('additive$uidentity',a,'additive$uidentity') ).
cnf(product_3,negated_conjecture,
product('multiplicative$uidentity','multiplicative$uinverse'(a),'multiplicative$uidentity') ).
cnf(not_product_4,negated_conjecture,
~ product('multiplicative$uidentity',a,'multiplicative$uidentity') ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
~ sum('additive$uidentity',a,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_2]) ).
cnf(c2,plain,
product('multiplicative$uidentity','multiplicative$uinverse'(a),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[product_3]) ).
cnf(c3,plain,
~ product('multiplicative$uidentity',a,'multiplicative$uidentity'),
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$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c12,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c20,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(d0,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c11]) ).
cnf(d1,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X1,X0)
| ~ product('multiplicative$uidentity',X0,X1)
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d0,c11]) ).
cnf(d2,plain,
( ~ product('multiplicative$uidentity',X0,X1)
| product('multiplicative$uidentity',X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c20,d1]) ).
cnf(d3,plain,
( product('multiplicative$uidentity',X2,X1)
| ~ product('multiplicative$uinverse'(a),X0,X2)
| ~ product('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c9,c2]) ).
cnf(d4,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| ~ product('multiplicative$uidentity',a,X0)
| product('multiplicative$uidentity','multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
( product('multiplicative$uidentity','multiplicative$uidentity',X0)
| ~ product('multiplicative$uidentity',a,X0)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
( product('multiplicative$uidentity','multiplicative$uidentity',X0)
| ~ product('multiplicative$uidentity',a,X0) ),
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
( ~ defined(a)
| product('multiplicative$uidentity','multiplicative$uidentity',a) ),
inference(resolution,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
product('multiplicative$uidentity','multiplicative$uidentity',a),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( product('multiplicative$uidentity',a,'multiplicative$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
product('multiplicative$uidentity',a,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[c20,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c3,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD032-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 02:25:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.58/2.04 % SZS status Unsatisfiable for theBenchmark.p
% 13.58/2.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------