%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD028-3 : 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 : n016.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 07:10:49 AM UTC 2026
% Result : Unsatisfiable 22.80s 6.78s
% Output : CNFRefutation 22.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 18 unt; 7 nHn; 39 RR)
% Number of literals : 76 ( 0 equ; 34 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 : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(v_is_defined,hypothesis,
defined(v) ).
cnf(not_sum_5,negated_conjecture,
~ sum('additive$uidentity',a,'additive$uidentity') ).
cnf(product_6,negated_conjecture,
product(a,u,b) ).
cnf(product_7,negated_conjecture,
product(a,v,b) ).
cnf(not_product_8,negated_conjecture,
~ product('multiplicative$uidentity',u,v) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ) ).
cnf(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(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c3,plain,
defined(v),
inference(clausification,[status(esa)],[v_is_defined]) ).
cnf(c4,plain,
~ sum('additive$uidentity',a,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_5]) ).
cnf(c5,plain,
product(a,u,b),
inference(clausification,[status(esa)],[product_6]) ).
cnf(c6,plain,
product(a,v,b),
inference(clausification,[status(esa)],[product_7]) ).
cnf(c7,plain,
~ product('multiplicative$uidentity',u,v),
inference(clausification,[status(esa)],[not_product_8]) ).
cnf(c13,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c14,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c15,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c16,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(c17,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(d0,plain,
( product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c16,c17]) ).
cnf(d1,plain,
product(u,a,b),
inference(resolution,[status(thm)],[c17,c5]) ).
cnf(d2,plain,
( product(u,X2,X1)
| ~ product(a,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[c13,d1]) ).
cnf(d3,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c17,c15]) ).
cnf(d4,plain,
product(v,a,b),
inference(resolution,[status(thm)],[c17,c6]) ).
cnf(d5,plain,
( ~ product(v,X2,X1)
| ~ product(a,X0,X2)
| product(b,X0,X1) ),
inference(resolution,[status(thm)],[c14,d4]) ).
cnf(d6,plain,
( ~ defined(v)
| product(b,X0,v)
| ~ product(a,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( product(b,X0,v)
| ~ product(a,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c3,d6]) ).
cnf(d8,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| product(b,'multiplicative$uinverse'(a),v) ),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( product(b,'multiplicative$uinverse'(a),v)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
product(b,'multiplicative$uinverse'(a),v),
inference(resolution,[status(thm)],[c4,d9]) ).
cnf(d11,plain,
( product(u,X0,v)
| ~ product(a,'multiplicative$uinverse'(a),X0) ),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| product(u,'multiplicative$uidentity',v) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( product(u,'multiplicative$uidentity',v)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d12]) ).
cnf(d14,plain,
product(u,'multiplicative$uidentity',v),
inference(resolution,[status(thm)],[c4,d13]) ).
cnf(d15,plain,
product('multiplicative$uidentity',u,v),
inference(resolution,[status(thm)],[d14,c17]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[c7,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : FLD028-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % Computer : n016.cluster.edu
% 0.10/0.45 % Model : x86_64 x86_64
% 0.10/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.45 % Memory : 8046.5625MB
% 0.10/0.45 % OS : Linux 6.8.0-71-generic
% 0.10/0.45 % CPULimit : 300
% 0.10/0.45 % WCLimit : 300
% 0.10/0.45 % DateTime : Sun Sep 27 02:29:16 UTC 2026
% 0.10/0.45 % CPUTime :
% 0.10/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.80/6.78 % SZS status Unsatisfiable for theBenchmark.p
% 22.80/6.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------