%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV255-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 09:01:46 AM UTC 2026
% Result : Unsatisfiable 117.77s 24.04s
% Output : CNFRefutation 117.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 17 unt; 2 nHn; 19 RR)
% Number of literals : 55 ( 8 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 53 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Nat_Oadd__leE_1,axiom,
( 'c$ulessequals'(X0,X2,'tc$unat')
| ~ 'c$ulessequals'('c$uplus'(X0,X1,'tc$unat'),X2,'tc$unat') ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'(X0,'v$uxb'(X0),'tc$unat') ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 'c$ulessequals'('v$ux',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ 'c$ulessequals'('v$uxa',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'('v$umsg2','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ) ).
cnf(cls_conjecture_3,negated_conjecture,
( 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg')
| 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg2','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ) ).
cnf(clsarity_nat_7,axiom,
'class$uOrderings$uOlinorder'('tc$unat') ).
cnf(cls_Nat_OOne__nat__def_0,axiom,
'c$u1' = 'c$uSuc'('c$u0') ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
'c$uplus'(X0,'c$u0','tc$unat') = X0 ).
cnf(cls_Nat_Oadd__Suc__right_0,axiom,
'c$uplus'(X0,'c$uSuc'(X1),'tc$unat') = 'c$uSuc'('c$uplus'(X0,X1,'tc$unat')) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
( 'c$ulessequals'(X1,X3,X0)
| ~ 'c$ulessequals'('c$uOrderings$uOmax'(X1,X2,X0),X3,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1,axiom,
( 'c$ulessequals'(X2,X3,X0)
| ~ 'c$ulessequals'('c$uOrderings$uOmax'(X1,X2,X0),X3,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(c15,plain,
( 'c$ulessequals'(X0,X2,'tc$unat')
| ~ 'c$ulessequals'('c$uplus'(X0,X1,'tc$unat'),X2,'tc$unat') ),
inference(clausification,[status(esa)],[cls_Nat_Oadd__leE_1]) ).
cnf(c16,plain,
'c$ulessequals'(X0,'v$uxb'(X0),'tc$unat'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c17,plain,
( ~ 'c$ulessequals'('v$ux',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c18,plain,
( ~ 'c$ulessequals'('v$uxa',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'('v$umsg2','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c19,plain,
( 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg')
| 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg2','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c262,plain,
'class$uOrderings$uOlinorder'('tc$unat'),
inference(clausification,[status(esa)],[clsarity_nat_7]) ).
cnf(c2035,plain,
'c$uSuc'('c$u0') = 'c$u1',
inference(clausification,[status(esa)],[cls_Nat_OOne__nat__def_0]) ).
cnf(c2045,plain,
'c$uplus'(X0,'c$u0','tc$unat') = X0,
inference(clausification,[status(esa)],[cls_Nat_Oadd__0__right_0]) ).
cnf(c2046,plain,
'c$uSuc'('c$uplus'(X0,X1,'tc$unat')) = 'c$uplus'(X0,'c$uSuc'(X1),'tc$unat'),
inference(clausification,[status(esa)],[cls_Nat_Oadd__Suc__right_0]) ).
cnf(c2283,plain,
( 'c$ulessequals'(X0,X3,X2)
| ~ 'class$uOrderings$uOlinorder'(X2)
| ~ 'c$ulessequals'('c$uOrderings$uOmax'(X0,X1,X2),X3,X2) ),
inference(clausification,[status(esa)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0]) ).
cnf(c2284,plain,
( 'c$ulessequals'(X1,X3,X2)
| ~ 'class$uOrderings$uOlinorder'(X2)
| ~ 'c$ulessequals'('c$uOrderings$uOmax'(X0,X1,X2),X3,X2) ),
inference(clausification,[status(esa)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1]) ).
cnf(d0,plain,
'c$uSuc'(X0) = 'c$uplus'(X0,'c$uSuc'('c$u0'),'tc$unat'),
inference(superposition,[status(thm)],[c2045,c2046]) ).
cnf(d1,plain,
'c$uSuc'(X0) = 'c$uplus'(X0,'c$u1','tc$unat'),
inference(demodulation,[status(thm)],[d0,c2035]) ).
cnf(d2,plain,
( 'c$ulessequals'(X0,X1,'tc$unat')
| ~ 'c$ulessequals'('c$uSuc'(X0),X1,'tc$unat') ),
inference(superposition,[status(thm)],[d1,c15]) ).
cnf(d3,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$unat')
| 'c$ulessequals'(X0,'v$uxb'('c$uOrderings$uOmax'(X0,X1,'tc$unat')),'tc$unat') ),
inference(resolution,[status(thm)],[c2283,c16]) ).
cnf(d4,plain,
'c$ulessequals'(X0,'v$uxb'('c$uOrderings$uOmax'(X0,X1,'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[c262,d3]) ).
cnf(d5,plain,
'c$ulessequals'(X0,'v$uxb'('c$uOrderings$uOmax'('c$uSuc'(X0),X1,'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$unat')
| 'c$ulessequals'(X0,'v$uxb'('c$uOrderings$uOmax'(X1,X0,'tc$unat')),'tc$unat') ),
inference(resolution,[status(thm)],[c2284,c16]) ).
cnf(d7,plain,
'c$ulessequals'(X0,'v$uxb'('c$uOrderings$uOmax'(X1,X0,'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[c262,d6]) ).
cnf(d8,plain,
( ~ 'c$ulessequals'('v$uxa','v$uxb'(X0),'tc$unat')
| 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(resolution,[status(thm)],[c19,c18]) ).
cnf(d9,plain,
( ~ 'c$ulessequals'('v$ux','v$uxb'(X0),'tc$unat')
| ~ 'c$ulessequals'('v$uxa','v$uxb'(X0),'tc$unat') ),
inference(resolution,[status(thm)],[d8,c17]) ).
cnf(d10,plain,
~ 'c$ulessequals'('v$ux','v$uxb'('c$uOrderings$uOmax'(X0,'v$uxa','tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV255-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.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 : Sat Sep 26 13:24:19 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 117.77/24.04 % SZS status Unsatisfiable for theBenchmark.p
% 117.77/24.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------