%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD027-3 : 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 : n001.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 35.34s 4.92s
% Output : CNFRefutation 35.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 23 unt; 9 nHn; 49 RR)
% Number of literals : 94 ( 0 equ; 42 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(not_sum_3,negated_conjecture,
~ sum('additive$uidentity',a,'additive$uidentity') ).
cnf(not_sum_4,negated_conjecture,
~ sum('additive$uidentity',b,'additive$uidentity') ).
cnf(product_5,negated_conjecture,
product('multiplicative$uidentity','multiplicative$uinverse'(a),'multiplicative$uinverse'(b)) ).
cnf(not_product_6,negated_conjecture,
~ product('multiplicative$uidentity',a,b) ).
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$uidentity') ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
~ sum('additive$uidentity',a,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_3]) ).
cnf(c3,plain,
~ sum('additive$uidentity',b,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_4]) ).
cnf(c4,plain,
product('multiplicative$uidentity','multiplicative$uinverse'(a),'multiplicative$uinverse'(b)),
inference(clausification,[status(esa)],[product_5]) ).
cnf(c5,plain,
~ product('multiplicative$uidentity',a,b),
inference(clausification,[status(esa)],[not_product_6]) ).
cnf(c11,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c13,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c14,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(c15,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c22,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(c23,plain,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_inverse]) ).
cnf(d0,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c15,c13]) ).
cnf(d1,plain,
( ~ defined(X0)
| product(X0,X3,X2)
| ~ product('multiplicative$uidentity',X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,d0]) ).
cnf(d2,plain,
( ~ product(X0,'multiplicative$uinverse'(a),X1)
| product(X0,'multiplicative$uinverse'(b),X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c14,c15]) ).
cnf(d4,plain,
( ~ defined('multiplicative$uinverse'(a))
| product('multiplicative$uidentity','multiplicative$uinverse'(b),'multiplicative$uinverse'(a))
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d2,c13]) ).
cnf(d5,plain,
( product('multiplicative$uidentity','multiplicative$uinverse'(b),'multiplicative$uinverse'(a))
| ~ defined('multiplicative$uinverse'(a)) ),
inference(resolution,[status(thm)],[c22,d4]) ).
cnf(d6,plain,
( defined('multiplicative$uinverse'(a))
| ~ defined(a) ),
inference(resolution,[status(thm)],[c23,c2]) ).
cnf(d7,plain,
defined('multiplicative$uinverse'(a)),
inference(resolution,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
product('multiplicative$uidentity','multiplicative$uinverse'(b),'multiplicative$uinverse'(a)),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ product(X0,'multiplicative$uinverse'(b),X1)
| product(X0,'multiplicative$uinverse'(a),X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( sum('additive$uidentity',b,'additive$uidentity')
| ~ defined(b)
| product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity')
| ~ defined(b) ),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
( product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity')
| sum('additive$uidentity',b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c1,d10]) ).
cnf(d12,plain,
product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
( product(b,'multiplicative$uinverse'(b),'multiplicative$uidentity')
| ~ defined(b) ),
inference(resolution,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
product(b,'multiplicative$uinverse'(b),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[c1,d13]) ).
cnf(d15,plain,
product('multiplicative$uinverse'(b),b,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d14,c15]) ).
cnf(d16,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| product(a,'multiplicative$uinverse'(b),'multiplicative$uidentity')
| ~ defined(a) ),
inference(resolution,[status(thm)],[d2,d3]) ).
cnf(d17,plain,
( product(a,'multiplicative$uinverse'(b),'multiplicative$uidentity')
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d16]) ).
cnf(d18,plain,
product(a,'multiplicative$uinverse'(b),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[c2,d17]) ).
cnf(d19,plain,
( product(a,X2,X1)
| ~ product('multiplicative$uinverse'(b),X0,X2)
| ~ product('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d18,c11]) ).
cnf(d20,plain,
( ~ product('multiplicative$uidentity',b,X0)
| product(a,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
( ~ defined(b)
| product(a,'multiplicative$uidentity',b) ),
inference(resolution,[status(thm)],[d20,c13]) ).
cnf(d22,plain,
product(a,'multiplicative$uidentity',b),
inference(resolution,[status(thm)],[c1,d21]) ).
cnf(d23,plain,
product('multiplicative$uidentity',a,b),
inference(resolution,[status(thm)],[d22,c15]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[c5,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD027-3 : 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 : n001.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 02:30:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.34/4.92 % SZS status Unsatisfiable for theBenchmark.p
% 35.34/4.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------