%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 09:11:31 AM UTC 2026
% Result : Theorem 46.95s 7.30s
% Output : CNFRefutation 46.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 21 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 2 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 24 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,X1)
=> 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP('v$uf',X0),hAPP('v$uf',X1)) ) ).
fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,X1)
=> 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP('v$uga',X0),hAPP('v$uga',X1)) ) ).
fof(fact_o__apply,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP('c$uFun$uOcomp'(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)) ).
fof(conj_0,conjecture,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,X1)
=> 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP(hAPP('c$uFun$uOcomp'('tc$uNat$uOnat','tc$uNat$uOnat','tc$uNat$uOnat','v$uf'),'v$uga'),X0),hAPP(hAPP('c$uFun$uOcomp'('tc$uNat$uOnat','tc$uNat$uOnat','tc$uNat$uOnat','v$uf'),'v$uga'),X1)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,X1)
=> 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP(hAPP('c$uFun$uOcomp'('tc$uNat$uOnat','tc$uNat$uOnat','tc$uNat$uOnat','v$uf'),'v$uga'),X0),hAPP(hAPP('c$uFun$uOcomp'('tc$uNat$uOnat','tc$uNat$uOnat','tc$uNat$uOnat','v$uf'),'v$uga'),X1)) ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c1,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP('v$uf',X0),hAPP('v$uf',X1))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,X1) ),
inference(clausification,[status(esa)],[fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096]) ).
cnf(c2,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP('v$uga',X0),hAPP('v$uga',X1))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',X0,X1) ),
inference(clausification,[status(esa)],[fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096]) ).
cnf(c6,plain,
hAPP(hAPP('c$uFun$uOcomp'(X0,X1,X2,X3),X4),X5) = hAPP(X3,hAPP(X4,X5)),
inference(clausification,[status(esa)],[fact_o__apply]) ).
cnf(c1643,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',sK2687,sK2688),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c1644,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP(hAPP('c$uFun$uOcomp'('tc$uNat$uOnat','tc$uNat$uOnat','tc$uNat$uOnat','v$uf'),'v$uga'),sK2687),hAPP(hAPP('c$uFun$uOcomp'('tc$uNat$uOnat','tc$uNat$uOnat','tc$uNat$uOnat','v$uf'),'v$uga'),sK2688)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP('v$uf',hAPP('v$uga',sK2687)),hAPP(hAPP('c$uFun$uOcomp'('tc$uNat$uOnat','tc$uNat$uOnat','tc$uNat$uOnat','v$uf'),'v$uga'),sK2688)),
inference(demodulation,[status(thm)],[c1644,c6]) ).
cnf(d1,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP('v$uf',hAPP('v$uga',sK2687)),hAPP('v$uf',hAPP('v$uga',sK2688))),
inference(demodulation,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',hAPP('v$uga',sK2687),hAPP('v$uga',sK2688)),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uNat$uOnat',sK2687,sK2688),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c1643,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 15:29:25 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.95/7.30 % SZS status Theorem for theBenchmark.p
% 46.95/7.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------