%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV281-1 : 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 : n009.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 09:01:53 AM UTC 2026
% Result : Unsatisfiable 180.20s 31.42s
% Output : CNFRefutation 180.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of clauses : 52 ( 37 unt; 4 nHn; 20 RR)
% Number of literals : 70 ( 40 equ; 17 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 : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 70 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Nat_Ole__add1_0,axiom,
'c$ulessequals'(X0,'c$uplus'(X0,X1,'tc$unat'),'tc$unat') ).
cnf(cls_Nat_Oless__Suc__eq__le_0,axiom,
( 'c$ulessequals'(X0,X1,'tc$unat')
| ~ 'c$uless'(X0,'c$uSuc'(X1),'tc$unat') ) ).
cnf(cls_Public_ONonce__supply__lemma_0,axiom,
( ~ 'c$ulessequals'('v$usko$u$uurX'(X1),X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uEvent$uOused'(X1),'tc$uMessage$uOmsg') ) ).
cnf(cls_conjecture_0,negated_conjecture,
( 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uEvent$uOused'('v$uevs'),'tc$uMessage$uOmsg')
| 'c$uin'('c$uMessage$uOmsg$uONonce'(X1),'c$uEvent$uOused'('v$uevs$uH'),'tc$uMessage$uOmsg')
| X0 = X1 ) ).
cnf(cls_Nat_OlessI_0,axiom,
'c$uless'(X0,'c$uSuc'(X0),'tc$unat') ).
cnf(cls_Binomial_Obinomial__Suc__Suc_0,axiom,
'c$uBinomial$uObinomial'('c$uSuc'(X0),'c$uSuc'(X1)) = 'c$uplus'('c$uBinomial$uObinomial'(X0,X1),'c$uBinomial$uObinomial'(X0,'c$uSuc'(X1)),'tc$unat') ).
cnf(cls_Binomial_Obinomial__Suc__n_0,axiom,
'c$uBinomial$uObinomial'('c$uSuc'(X0),X0) = 'c$uSuc'(X0) ).
cnf(cls_Divides_ODIVISION__BY__ZERO__MOD_0,axiom,
'c$uDivides$uOop$uAmod'(X0,'c$u0','tc$unat') = X0 ).
cnf(cls_Divides_Omod__add__self2_0,axiom,
'c$uDivides$uOop$uAmod'('c$uplus'(X0,X1,'tc$unat'),X1,'tc$unat') = 'c$uDivides$uOop$uAmod'(X0,X1,'tc$unat') ).
cnf(cls_IntDef_Oint__0__neq__1_0,axiom,
'c$u0' != 'c$u1' ).
cnf(cls_Nat_OOne__nat__def_0,axiom,
'c$u1' = 'c$uSuc'('c$u0') ).
cnf(cls_Nat_OSuc__le__mono_0,axiom,
( 'c$ulessequals'(X0,X1,'tc$unat')
| ~ 'c$ulessequals'('c$uSuc'(X0),'c$uSuc'(X1),'tc$unat') ) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
'c$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_Nat_Onat__add__left__cancel_0,axiom,
( X1 = X2
| 'c$uplus'(X0,X1,'tc$unat') != 'c$uplus'(X0,X2,'tc$unat') ) ).
cnf(cls_Nat_Oop_A_L_Oadd__Suc_0,axiom,
'c$uplus'('c$uSuc'(X0),X1,'tc$unat') = 'c$uSuc'('c$uplus'(X0,X1,'tc$unat')) ).
cnf(c0,plain,
'c$ulessequals'(X0,'c$uplus'(X0,X1,'tc$unat'),'tc$unat'),
inference(clausification,[status(esa)],[cls_Nat_Ole__add1_0]) ).
cnf(c2,plain,
( 'c$ulessequals'(X0,X1,'tc$unat')
| ~ 'c$uless'(X0,'c$uSuc'(X1),'tc$unat') ),
inference(clausification,[status(esa)],[cls_Nat_Oless__Suc__eq__le_0]) ).
cnf(c4,plain,
( ~ 'c$ulessequals'('v$usko$u$uurX'(X1),X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uEvent$uOused'(X1),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_Public_ONonce__supply__lemma_0]) ).
cnf(c5,plain,
( 'c$uin'('c$uMessage$uOmsg$uONonce'(X1),'c$uEvent$uOused'('v$uevs'),'tc$uMessage$uOmsg')
| X0 = X1
| 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uEvent$uOused'('v$uevs$uH'),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c70,plain,
'c$uless'(X0,'c$uSuc'(X0),'tc$unat'),
inference(clausification,[status(esa)],[cls_Nat_OlessI_0]) ).
cnf(c1167,plain,
'c$uplus'('c$uBinomial$uObinomial'(X0,X1),'c$uBinomial$uObinomial'(X0,'c$uSuc'(X1)),'tc$unat') = 'c$uBinomial$uObinomial'('c$uSuc'(X0),'c$uSuc'(X1)),
inference(clausification,[status(esa)],[cls_Binomial_Obinomial__Suc__Suc_0]) ).
cnf(c1168,plain,
'c$uSuc'(X0) = 'c$uBinomial$uObinomial'('c$uSuc'(X0),X0),
inference(clausification,[status(esa)],[cls_Binomial_Obinomial__Suc__n_0]) ).
cnf(c1217,plain,
'c$uDivides$uOop$uAmod'(X0,'c$u0','tc$unat') = X0,
inference(clausification,[status(esa)],[cls_Divides_ODIVISION__BY__ZERO__MOD_0]) ).
cnf(c1238,plain,
'c$uDivides$uOop$uAmod'(X0,X1,'tc$unat') = 'c$uDivides$uOop$uAmod'('c$uplus'(X0,X1,'tc$unat'),X1,'tc$unat'),
inference(clausification,[status(esa)],[cls_Divides_Omod__add__self2_0]) ).
cnf(c1375,plain,
'c$u1' != 'c$u0',
inference(clausification,[status(esa)],[cls_IntDef_Oint__0__neq__1_0]) ).
cnf(c2021,plain,
'c$uSuc'('c$u0') = 'c$u1',
inference(clausification,[status(esa)],[cls_Nat_OOne__nat__def_0]) ).
cnf(c2024,plain,
( 'c$ulessequals'(X0,X1,'tc$unat')
| ~ 'c$ulessequals'('c$uSuc'(X0),'c$uSuc'(X1),'tc$unat') ),
inference(clausification,[status(esa)],[cls_Nat_OSuc__le__mono_0]) ).
cnf(c2031,plain,
'c$uplus'(X0,'c$u0','tc$unat') = X0,
inference(clausification,[status(esa)],[cls_Nat_Oadd__0__right_0]) ).
cnf(c2032,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(c2086,plain,
( X1 = X2
| 'c$uplus'(X0,X1,'tc$unat') != 'c$uplus'(X0,X2,'tc$unat') ),
inference(clausification,[status(esa)],[cls_Nat_Onat__add__left__cancel_0]) ).
cnf(c2106,plain,
'c$uSuc'('c$uplus'(X0,X1,'tc$unat')) = 'c$uplus'('c$uSuc'(X0),X1,'tc$unat'),
inference(clausification,[status(esa)],[cls_Nat_Oop_A_L_Oadd__Suc_0]) ).
cnf(d0,plain,
'c$ulessequals'(X0,X0,'tc$unat'),
inference(resolution,[status(thm)],[c70,c2]) ).
cnf(d1,plain,
( ~ 'c$ulessequals'('v$usko$u$uurX'('v$uevs'),X1,'tc$unat')
| 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uEvent$uOused'('v$uevs$uH'),'tc$uMessage$uOmsg')
| X0 = X1 ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d2,plain,
( 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uEvent$uOused'('v$uevs$uH'),'tc$uMessage$uOmsg')
| X0 = 'v$usko$u$uurX'('v$uevs') ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ 'c$ulessequals'('v$usko$u$uurX'('v$uevs$uH'),X0,'tc$unat')
| X0 = 'v$usko$u$uurX'('v$uevs') ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
'v$usko$u$uurX'('v$uevs$uH') = 'v$usko$u$uurX'('v$uevs'),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'c$ulessequals'('c$uBinomial$uObinomial'(X0,X1),'c$uBinomial$uObinomial'('c$uSuc'(X0),'c$uSuc'(X1)),'tc$unat'),
inference(superposition,[status(thm)],[c1167,c0]) ).
cnf(d6,plain,
'c$ulessequals'('c$uBinomial$uObinomial'('c$uSuc'(X0),X0),'c$uSuc'('c$uSuc'(X0)),'tc$unat'),
inference(superposition,[status(thm)],[c1168,d5]) ).
cnf(d7,plain,
'c$ulessequals'('c$uSuc'(X0),'c$uSuc'('c$uSuc'(X0)),'tc$unat'),
inference(demodulation,[status(thm)],[d6,c1168]) ).
cnf(d8,plain,
'c$ulessequals'(X0,'c$uSuc'(X0),'tc$unat'),
inference(resolution,[status(thm)],[d7,c2024]) ).
cnf(d9,plain,
'c$uSuc'('v$usko$u$uurX'('v$uevs$uH')) = 'v$usko$u$uurX'('v$uevs'),
inference(resolution,[status(thm)],[d3,d8]) ).
cnf(d10,plain,
'c$uSuc'('v$usko$u$uurX'('v$uevs')) = 'v$usko$u$uurX'('v$uevs'),
inference(demodulation,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
'c$uDivides$uOop$uAmod'(X0,'c$u0','tc$unat') = 'c$uplus'(X0,'c$u0','tc$unat'),
inference(superposition,[status(thm)],[c1238,c1217]) ).
cnf(d12,plain,
X0 = 'c$uplus'(X0,'c$u0','tc$unat'),
inference(demodulation,[status(thm)],[d11,c1217]) ).
cnf(d13,plain,
( X1 = 'c$u0'
| 'c$uplus'(X0,X1,'tc$unat') != X0 ),
inference(superposition,[status(thm)],[d12,c2086]) ).
cnf(d14,plain,
'c$uplus'(X0,'c$uSuc'(X1),'tc$unat') = 'c$uplus'('c$uSuc'(X0),X1,'tc$unat'),
inference(demodulation,[status(thm)],[c2106,c2032]) ).
cnf(d15,plain,
'c$uplus'(X0,'c$uSuc'('c$u0'),'tc$unat') = 'c$uSuc'(X0),
inference(superposition,[status(thm)],[d14,c2031]) ).
cnf(d16,plain,
'c$uplus'(X0,'c$u1','tc$unat') = 'c$uSuc'(X0),
inference(demodulation,[status(thm)],[d15,c2021]) ).
cnf(d17,plain,
( 'c$u1' = 'c$u0'
| 'c$uSuc'(X0) != X0 ),
inference(superposition,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
'c$uSuc'(X0) != X0,
inference(resolution,[status(thm)],[c1375,d17]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV281-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 13:27:20 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 180.20/31.42 % SZS status Unsatisfiable for theBenchmark.p
% 180.20/31.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------