%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW225+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 : n018.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 09:11:33 AM UTC 2026
% Result : Theorem 48.76s 14.06s
% Output : CNFRefutation 48.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 2 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096,axiom,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'),hAPP('v$uf','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))) ).
fof(fact_Suc__le__mono,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uNat$uOSuc'(X1),'c$uNat$uOSuc'(X0))
<=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat',X1,X0) ) ).
fof(fact_real__of__nat__le__iff,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),X1),hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),X0))
<=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat',X1,X0) ) ).
fof(conj_0,conjecture,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),'c$uNat$uOSuc'('c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))),hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),'c$uNat$uOSuc'(hAPP('v$uf','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))))) ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),'c$uNat$uOSuc'('c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))),hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),'c$uNat$uOSuc'(hAPP('v$uf','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))))),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c2,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'),hAPP('v$uf','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))),
inference(clausification,[status(esa)],[fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096]) ).
cnf(c15,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat',X0,X1)
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uNat$uOSuc'(X0),'c$uNat$uOSuc'(X1)) ),
inference(clausification,[status(esa)],[fact_Suc__le__mono]) ).
cnf(c55,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat',X0,X1)
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),X0),hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),X1)) ),
inference(clausification,[status(esa)],[fact_real__of__nat__le__iff]) ).
cnf(c1007,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),'c$uNat$uOSuc'('c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))),hAPP('c$uRealDef$uOreal'('tc$uNat$uOnat'),'c$uNat$uOSuc'(hAPP('v$uf','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uNat$uOSuc'('c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2')),'c$uNat$uOSuc'(hAPP('v$uf','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2')))),
inference(resolution,[status(thm)],[c55,c1007]) ).
cnf(d1,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'),hAPP('v$uf','c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uN1','v$uN2'))),
inference(resolution,[status(thm)],[d0,c15]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[c2,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW225+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n018.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 15:31:41 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.76/14.06 % SZS status Theorem for theBenchmark.p
% 48.76/14.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------