TSTP Solution File: NUM588+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM588+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 12:28:00 EDT 2022
% Result : Theorem 0.56s 0.74s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 9 unt; 1 def)
% Number of atoms : 331 ( 28 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 405 ( 106 ~; 56 |; 198 &)
% ( 19 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 77 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
& aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(W1) )
=> ! [W2] :
( ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
=> ( ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) ) ) ).
fof(definition_0,definition,
! [W0,W2] :
( definitionFOFtoCNF_6(W0,W2)
<=> ( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ).
fof(subgoal_0,plain,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
& aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(W1) )
=> ! [W2] :
( ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
& ~ ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
& aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(W1) )
=> ! [W2] :
( ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) )
& aSubsetOf0(W2,W1)
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W3)
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
& ~ ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [W0] :
( aElementOf0(W0,szNzAzT0)
& ? [W1] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aSet0(W1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(W1)
& ? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aSet0(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aSubsetOf0(W2,W1)
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& ! [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& ! [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W2] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& ! [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ~ aElement0(W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [W0,W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ~ definitionFOFtoCNF_6(W0,W2)
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElement0(W2)
& aElementOf0(W2,sdtlpdtrp0(xN,W0)) ) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_2,plain,
? [W0] :
( aElementOf0(W0,szNzAzT0)
& ? [W1] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aSet0(W1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(W1)
& ? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aSet0(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aSubsetOf0(W2,W1)
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& ! [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& ! [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& ! [W2] : definitionFOFtoCNF_6(W0,W2)
& ! [W2] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_1]) ).
fof(normalize_0_3,plain,
( aElementOf0(skolemFOFtoCNF_W0,szNzAzT0)
& ? [W1] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
& aSet0(W1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& isCountable0(W1)
& ? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
& aSet0(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aSubsetOf0(W2,W1)
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& ! [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W3) )
& ! [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
<=> ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| W3 = szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)) ) ) )
& ! [W2] : definitionFOFtoCNF_6(skolemFOFtoCNF_W0,W2)
& ! [W2] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))) )
& ! [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W2) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W1] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
& aSet0(W1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& isCountable0(W1)
& ? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
& aSet0(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aSubsetOf0(W2,W1)
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,W1) )
& ! [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W3) )
& ! [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
<=> ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| W3 = szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)) ) ) )
& ! [W2] : definitionFOFtoCNF_6(skolemFOFtoCNF_W0,W2)
& ! [W2] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))) )
& ! [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W2) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aSet0(skolemFOFtoCNF_W1_6)
& aSubsetOf0(skolemFOFtoCNF_W1_6,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& isCountable0(skolemFOFtoCNF_W1_6)
& ? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(skolemFOFtoCNF_W1_6,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
& aSet0(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aSubsetOf0(W2,skolemFOFtoCNF_W1_6)
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,skolemFOFtoCNF_W1_6) )
& ! [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W3) )
& ! [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
<=> ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| W3 = szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)) ) ) )
& ! [W2] : definitionFOFtoCNF_6(skolemFOFtoCNF_W0,W2)
& ! [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W2) )
& ! [W2] :
( ~ aElementOf0(W2,skolemFOFtoCNF_W1_6)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(skolemFOFtoCNF_W1_6,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
& aSet0(W2)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aSubsetOf0(W2,skolemFOFtoCNF_W1_6)
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,skolemFOFtoCNF_W1_6) )
& ! [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W3) )
& ! [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
<=> ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| W3 = szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)) ) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
aSet0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))),xk))
& ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& sbrdtbr0(W2) = xk
& aElementOf0(W2,slbdtsldtrb0(skolemFOFtoCNF_W1_6,xk))
& aSet0(W2)
& aSubsetOf0(W2,skolemFOFtoCNF_W1_6)
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aElementOf0(W3,W2) )
& ! [W3] :
( ~ aElementOf0(W3,W2)
| aElementOf0(W3,skolemFOFtoCNF_W1_6) )
& ! [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W3) )
& ! [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
<=> ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| W3 = szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)) ) ) ),
inference(simplify,[],[normalize_0_6,normalize_0_7,normalize_0_8]) ).
fof(normalize_0_10,plain,
( ~ aElementOf0(skolemFOFtoCNF_W2_13,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))),xk))
& ~ aSubsetOf0(skolemFOFtoCNF_W2_13,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& sbrdtbr0(skolemFOFtoCNF_W2_13) = xk
& aElementOf0(skolemFOFtoCNF_W2_13,slbdtsldtrb0(skolemFOFtoCNF_W1_6,xk))
& aSet0(skolemFOFtoCNF_W2_13)
& aSubsetOf0(skolemFOFtoCNF_W2_13,skolemFOFtoCNF_W1_6)
& ? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aElementOf0(W3,skolemFOFtoCNF_W2_13) )
& ! [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)),W3) )
& ! [W3] :
( ~ aElementOf0(W3,skolemFOFtoCNF_W2_13)
| aElementOf0(W3,skolemFOFtoCNF_W1_6) )
& ! [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
<=> ( ~ aElement0(W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,skolemFOFtoCNF_W0))
| W3 = szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)) ) ) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
? [W3] :
( ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aElementOf0(W3,skolemFOFtoCNF_W2_13) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
( ~ aElementOf0(skolemFOFtoCNF_W3_13,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0))))
& aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W2_13) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W2_13),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [W3] :
( ~ aElementOf0(W3,skolemFOFtoCNF_W2_13)
| aElementOf0(W3,skolemFOFtoCNF_W1_6) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_15,plain,
! [W3] :
( ~ aElementOf0(W3,skolemFOFtoCNF_W2_13)
| aElementOf0(W3,skolemFOFtoCNF_W1_6) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [W2] :
( ~ aElementOf0(W2,skolemFOFtoCNF_W1_6)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_17,plain,
! [W2] :
( ~ aElementOf0(W2,skolemFOFtoCNF_W1_6)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
~ aElementOf0(skolemFOFtoCNF_W3_13,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W2_13),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_1,plain,
( ~ aElementOf0(W3,skolemFOFtoCNF_W2_13)
| aElementOf0(W3,skolemFOFtoCNF_W1_6) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_2,plain,
( ~ aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W2_13)
| aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W1_6) ),
inference(subst,[],[refute_0_1:[bind(W3,$fot(skolemFOFtoCNF_W3_13))]]) ).
cnf(refute_0_3,plain,
aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W1_6),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W2_13) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ aElementOf0(W2,skolemFOFtoCNF_W1_6)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_5,plain,
( ~ aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W1_6)
| aElementOf0(skolemFOFtoCNF_W3_13,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))) ),
inference(subst,[],[refute_0_4:[bind(W2,$fot(skolemFOFtoCNF_W3_13))]]) ).
cnf(refute_0_6,plain,
aElementOf0(skolemFOFtoCNF_W3_13,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W3_13,skolemFOFtoCNF_W1_6) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
~ aElementOf0(skolemFOFtoCNF_W3_13,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W3_13,sdtmndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0),szmzizndt0(sdtlpdtrp0(xN,skolemFOFtoCNF_W0)))) )],[refute_0_6,refute_0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM588+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n009.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 : Wed Jul 6 21:23:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.56/0.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.74
% 0.56/0.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.56/0.75
%------------------------------------------------------------------------------