%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 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 06:50:38 AM UTC 2026
% Result : Unsatisfiable 12.89s 2.23s
% Output : CNFRefutation 12.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 8 unt; 5 nHn; 8 RR)
% Number of literals : 23 ( 12 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_NatBin_OSuc__pred_H_0,axiom,
( X0 = 'c$uSuc'('c$uminus'(X0,'c$u1','tc$unat'))
| ~ 'c$uless'('c$u0',X0,'tc$unat') ) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( X0 = 'c$u0'
| 'c$uless'('c$u0',X0,'tc$unat') ) ).
cnf(cls_conjecture_2,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$uf'('c$uSuc'(X0)),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('c$uSuc'(X0)),'t$ua'),'t$ua'),'t$ua') ).
cnf(cls_conjecture_3,negated_conjecture,
'v$ux' != 'c$u0' ).
cnf(cls_conjecture_4,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'t$ua'),'t$ua') ).
cnf(c0,plain,
( X0 = 'c$uSuc'('c$uminus'(X0,'c$u1','tc$unat'))
| ~ 'c$uless'('c$u0',X0,'tc$unat') ),
inference(clausification,[status(esa)],[cls_NatBin_OSuc__pred_H_0]) ).
cnf(c1,plain,
( X0 = 'c$u0'
| 'c$uless'('c$u0',X0,'tc$unat') ),
inference(clausification,[status(esa)],[cls_Nat_Onot__gr0_0]) ).
cnf(c2,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$uf'('c$uSuc'(X0)),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('c$uSuc'(X0)),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c3,plain,
'v$ux' != 'c$u0',
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c4,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(d0,plain,
( X0 = 'c$uSuc'('c$uminus'(X0,'c$u1','tc$unat'))
| X0 = 'c$u0' ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( X0 = 'c$u0'
| 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('c$uSuc'('c$uminus'(X0,'c$u1','tc$unat'))),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( X0 = 'c$u0'
| X0 = 'c$u0'
| 'c$ulessequals'('c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d3,plain,
'v$ux' = 'c$u0',
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c3,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.56 % Computer : n001.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Sat Sep 26 22:11:44 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.89/2.23 % SZS status Unsatisfiable for theBenchmark.p
% 12.89/2.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------