%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD022-3 : 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 : n008.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 07:10:47 AM UTC 2026
% Result : Unsatisfiable 36.06s 5.10s
% Output : CNFRefutation 36.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 16 unt; 0 nHn; 32 RR)
% Number of literals : 57 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 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; 0-1 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(c_is_defined,hypothesis,
defined(c) ).
cnf(sum_5,negated_conjecture,
sum(a,c,u) ).
cnf(sum_6,negated_conjecture,
sum(b,c,u) ).
cnf(not_sum_7,negated_conjecture,
~ sum('additive$uidentity',a,b) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
defined(c),
inference(clausification,[status(esa)],[c_is_defined]) ).
cnf(c4,plain,
sum(a,c,u),
inference(clausification,[status(esa)],[sum_5]) ).
cnf(c5,plain,
sum(b,c,u),
inference(clausification,[status(esa)],[sum_6]) ).
cnf(c6,plain,
~ sum('additive$uidentity',a,b),
inference(clausification,[status(esa)],[not_sum_7]) ).
cnf(c7,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c9,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c10,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c11,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(d0,plain,
sum(c,b,u),
inference(resolution,[status(thm)],[c11,c5]) ).
cnf(d1,plain,
( ~ sum(X2,c,X0)
| sum(X2,u,X1)
| ~ sum(X0,b,X1) ),
inference(resolution,[status(thm)],[c7,d0]) ).
cnf(d2,plain,
( ~ defined(b)
| sum(X0,u,b)
| ~ sum(X0,c,'additive$uidentity') ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( sum(X0,u,b)
| ~ sum(X0,c,'additive$uidentity') ),
inference(resolution,[status(thm)],[c1,d2]) ).
cnf(d4,plain,
( ~ defined(c)
| sum('additive$uinverse'(c),u,b) ),
inference(resolution,[status(thm)],[d3,c10]) ).
cnf(d5,plain,
sum('additive$uinverse'(c),u,b),
inference(resolution,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
sum(u,'additive$uinverse'(c),b),
inference(resolution,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
( ~ defined(X0)
| sum(X0,'additive$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c11,c10]) ).
cnf(d8,plain,
( ~ sum(X3,X0,X1)
| sum(X3,'additive$uidentity',X2)
| ~ sum(X1,'additive$uinverse'(X0),X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
( sum(X0,'additive$uidentity',b)
| ~ sum(X0,c,u)
| ~ defined(c) ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( sum(X0,'additive$uidentity',b)
| ~ sum(X0,c,u) ),
inference(resolution,[status(thm)],[c2,d9]) ).
cnf(d11,plain,
sum(a,'additive$uidentity',b),
inference(resolution,[status(thm)],[d10,c4]) ).
cnf(d12,plain,
sum('additive$uidentity',a,b),
inference(resolution,[status(thm)],[d11,c11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c6,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD022-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n008.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 02:24:39 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.06/5.10 % SZS status Unsatisfiable for theBenchmark.p
% 36.06/5.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------