%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM609+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 12:28:12 EDT 2022
% Result : Theorem 0.38s 0.62s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 62 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 71 ( 29 ~; 17 |; 15 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5164,hypothesis,
( aSet0(xP)
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& W0 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ).
fof(m__,conjecture,
( ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) )
| aSubsetOf0(xP,xQ) ) ).
fof(subgoal_0,plain,
( ~ ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) )
=> aSubsetOf0(xP,xQ) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ~ ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) )
=> aSubsetOf0(xP,xQ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ aSubsetOf0(xP,xQ)
& ? [W0] :
( ~ aElementOf0(W0,xQ)
& aElementOf0(W0,xP) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [W0] :
( ~ aElementOf0(W0,xQ)
& aElementOf0(W0,xP) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_2,xQ)
& aElementOf0(skolemFOFtoCNF_W0_2,xP) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
aElementOf0(skolemFOFtoCNF_W0_2,xP),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP)
& ! [W0] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(szmzizndt0(xQ),W0) )
& ! [W0] :
( ~ aElementOf0(W0,xP)
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ)
| W0 = szmzizndt0(xQ) ) ) ),
inference(canonicalize,[],[m__5164]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aElementOf0(W0,xP)
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ)
| W0 = szmzizndt0(xQ) ) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aElementOf0(W0,xP)
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ)
| W0 = szmzizndt0(xQ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( ( W0 != szmzizndt0(xQ)
| ~ aElementOf0(W0,xP) )
& ( ~ aElementOf0(W0,xP)
| aElement0(W0) )
& ( ~ aElementOf0(W0,xP)
| aElementOf0(W0,xQ) )
& ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ)
| W0 = szmzizndt0(xQ)
| aElementOf0(W0,xP) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aElementOf0(W0,xP)
| aElementOf0(W0,xQ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
~ aElementOf0(skolemFOFtoCNF_W0_2,xQ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
aElementOf0(skolemFOFtoCNF_W0_2,xP),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ aElementOf0(W0,xP)
| aElementOf0(W0,xQ) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( ~ aElementOf0(skolemFOFtoCNF_W0_2,xP)
| aElementOf0(skolemFOFtoCNF_W0_2,xQ) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(skolemFOFtoCNF_W0_2))]]) ).
cnf(refute_0_3,plain,
aElementOf0(skolemFOFtoCNF_W0_2,xQ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_2,xP) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
~ aElementOf0(skolemFOFtoCNF_W0_2,xQ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
$false,
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0_2,xQ) )],[refute_0_3,refute_0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM609+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 23:08:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.38/0.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.62
% 0.38/0.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.38/0.62
%------------------------------------------------------------------------------