%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 09:11:30 AM UTC 2026
% Result : Theorem 50.97s 13.37s
% Output : CNFRefutation 50.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 18 unt; 0 def)
% Number of atoms : 24 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 4 sgn 3 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_o,axiom,
~ 'c$uParity$uOeven$u$uodd$u$uclass$uOeven'('tc$uNat$uOnat','v$una') ).
fof(fact_nat__mult__commute,axiom,
! [X0,X1] : 'c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',X1,X0) = 'c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',X0,X1) ).
fof(fact_numeral__2__eq__2,axiom,
'c$uInt$uOnumber$u$uclass$uOnumber$u$uof'('tc$uNat$uOnat','c$uInt$uOBit0'('c$uInt$uOBit1'('c$uInt$uOPls'))) = 'c$uNat$uOSuc'('c$uNat$uOSuc'('c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))) ).
fof(fact_odd__Suc__mult__two__ex,axiom,
! [X0] :
( ~ 'c$uParity$uOeven$u$uodd$u$uclass$uOeven'('tc$uNat$uOnat',X0)
<=> ? [X1] : X0 = 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat','c$uInt$uOnumber$u$uclass$uOnumber$u$uof'('tc$uNat$uOnat','c$uInt$uOBit0'('c$uInt$uOBit1'('c$uInt$uOPls'))),X1)) ) ).
fof(fact_One__nat__def,axiom,
'c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat') = 'c$uNat$uOSuc'('c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')) ).
fof(conj_0,conjecture,
? [X0] : 'v$una' = 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat','c$uInt$uOnumber$u$uclass$uOnumber$u$uof'('tc$uNat$uOnat','c$uInt$uOBit0'('c$uInt$uOBit1'('c$uInt$uOPls'))),X0)) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] : 'v$una' = 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat','c$uInt$uOnumber$u$uclass$uOnumber$u$uof'('tc$uNat$uOnat','c$uInt$uOBit0'('c$uInt$uOBit1'('c$uInt$uOPls'))),X0)),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c0,plain,
~ 'c$uParity$uOeven$u$uodd$u$uclass$uOeven'('tc$uNat$uOnat','v$una'),
inference(clausification,[status(esa)],[fact_o]) ).
cnf(c58,plain,
'c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',X0,X1) = 'c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',X1,X0),
inference(clausification,[status(esa)],[fact_nat__mult__commute]) ).
cnf(c59,plain,
'c$uInt$uOnumber$u$uclass$uOnumber$u$uof'('tc$uNat$uOnat','c$uInt$uOBit0'('c$uInt$uOBit1'('c$uInt$uOPls'))) = 'c$uNat$uOSuc'('c$uNat$uOSuc'('c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))),
inference(clausification,[status(esa)],[fact_numeral__2__eq__2]) ).
cnf(c64,plain,
( X0 = 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat','c$uInt$uOnumber$u$uclass$uOnumber$u$uof'('tc$uNat$uOnat','c$uInt$uOBit0'('c$uInt$uOBit1'('c$uInt$uOPls'))),sK70(X0)))
| 'c$uParity$uOeven$u$uodd$u$uclass$uOeven'('tc$uNat$uOnat',X0) ),
inference(clausification,[status(esa)],[fact_odd__Suc__mult__two__ex]) ).
cnf(c1105,plain,
'c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat') = 'c$uNat$uOSuc'('c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),
inference(clausification,[status(esa)],[fact_One__nat__def]) ).
cnf(c1823,plain,
'v$una' != 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat','c$uInt$uOnumber$u$uclass$uOnumber$u$uof'('tc$uNat$uOnat','c$uInt$uOBit0'('c$uInt$uOBit1'('c$uInt$uOPls'))),X0)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'c$uParity$uOeven$u$uodd$u$uclass$uOeven'('tc$uNat$uOnat',X0)
| X0 = 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat','c$uNat$uOSuc'('c$uNat$uOSuc'('c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))),sK70(X0))) ),
inference(demodulation,[status(thm)],[c64,c59]) ).
cnf(d1,plain,
'v$una' = 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat','c$uNat$uOSuc'('c$uNat$uOSuc'('c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))),sK70('v$una'))),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
'v$una' = 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',sK70('v$una'),'c$uNat$uOSuc'('c$uNat$uOSuc'('c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))))),
inference(demodulation,[status(thm)],[d1,c58]) ).
cnf(d3,plain,
'v$una' = 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',sK70('v$una'),'c$uNat$uOSuc'('c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),
inference(demodulation,[status(thm)],[d2,c1105]) ).
cnf(d4,plain,
'v$una' != 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',X0,'c$uInt$uOnumber$u$uclass$uOnumber$u$uof'('tc$uNat$uOnat','c$uInt$uOBit0'('c$uInt$uOBit1'('c$uInt$uOPls'))))),
inference(superposition,[status(thm)],[c58,c1823]) ).
cnf(d5,plain,
'v$una' != 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',X0,'c$uNat$uOSuc'('c$uNat$uOSuc'('c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))))),
inference(demodulation,[status(thm)],[d4,c59]) ).
cnf(d6,plain,
'v$una' != 'c$uNat$uOSuc'('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uNat$uOnat',X0,'c$uNat$uOSuc'('c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),
inference(demodulation,[status(thm)],[d5,c1105]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n006.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
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 15:27:25 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.97/13.37 % SZS status Theorem for theBenchmark.p
% 50.97/13.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------