TSTP Solution File: NUM588+3 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : NUM588+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n019.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 : 300s
% DateTime : Wed Aug 31 18:00:57 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 541 ( 64 equ)
% Maximal formula atoms : 80 ( 21 avg)
% Number of connectives : 689 ( 173 ~; 125 |; 347 &)
% ( 10 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 12 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 135 ( 99 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f864,plain,
$false,
inference(subsumption_resolution,[],[f863,f635]) ).
fof(f635,plain,
aElementOf0(sK46,sK45),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
( aElementOf0(sK43,szNzAzT0)
& ! [X2] :
( ~ aElementOf0(X2,sK44)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ! [X3] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,sK43))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X3) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aSet0(sK44)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK43)) )
& isCountable0(sK44)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(sK44,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& ~ aSubsetOf0(sK45,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(sK45,sK44)
& ~ aElementOf0(sK45,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ! [X6] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK43))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X6) ) )
& ! [X7] :
( aElementOf0(X7,sK44)
| ~ aElementOf0(X7,sK45) )
& ~ aElementOf0(sK46,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(sK46,sK45)
& xk = sbrdtbr0(sK45)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,sK43))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X9) )
& aSet0(sK45)
& aElementOf0(sK45,slbdtsldtrb0(sK44,xk)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45,sK46])],[f368,f372,f371,f370,f369]) ).
fof(f369,plain,
( ? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ! [X3] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& isCountable0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X5,X1)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X6] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,X0))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0))
| ~ aElement0(X6) ) )
& ! [X7] :
( aElementOf0(X7,X1)
| ~ aElementOf0(X7,X5) )
& ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X9) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) )
=> ( aElementOf0(sK43,szNzAzT0)
& ? [X1] :
( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ! [X3] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,sK43))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X3) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aSet0(X1)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK43)) )
& isCountable0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(X5,X1)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ! [X6] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK43))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X6) ) )
& ! [X7] :
( aElementOf0(X7,X1)
| ~ aElementOf0(X7,X5) )
& ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(X8,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,sK43))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X9) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f370,plain,
( ? [X1] :
( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ! [X3] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,sK43))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X3) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aSet0(X1)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK43)) )
& isCountable0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(X5,X1)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ! [X6] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK43))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X6) ) )
& ! [X7] :
( aElementOf0(X7,X1)
| ~ aElementOf0(X7,X5) )
& ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(X8,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,sK43))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X9) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) )
=> ( ! [X2] :
( ~ aElementOf0(X2,sK44)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ! [X3] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,sK43))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X3) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& aSet0(sK44)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK43)) )
& isCountable0(sK44)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(sK44,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(X5,sK44)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ! [X6] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK43))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X6) ) )
& ! [X7] :
( aElementOf0(X7,sK44)
| ~ aElementOf0(X7,X5) )
& ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(X8,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,sK43))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X9) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(sK44,xk)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f371,plain,
( ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(X5,sK44)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ! [X6] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK43))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X6) ) )
& ! [X7] :
( aElementOf0(X7,sK44)
| ~ aElementOf0(X7,X5) )
& ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(X8,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,sK43))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X9) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(sK44,xk)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK43)),sdtlpdtrp0(xN,sK43))
& ~ aSubsetOf0(sK45,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aSubsetOf0(sK45,sK44)
& ~ aElementOf0(sK45,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))),xk))
& ! [X6] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,sK43)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK43))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) )
& ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
| szmzizndt0(sdtlpdtrp0(xN,sK43)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK43))
| ~ aElement0(X6) ) )
& ! [X7] :
( aElementOf0(X7,sK44)
| ~ aElementOf0(X7,sK45) )
& ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(X8,sK45) )
& xk = sbrdtbr0(sK45)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,sK43))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK43)),X9) )
& aSet0(sK45)
& aElementOf0(sK45,slbdtsldtrb0(sK44,xk)) ) ),
introduced(choice_axiom,[]) ).
fof(f372,plain,
( ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(X8,sK45) )
=> ( ~ aElementOf0(sK46,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43))))
& aElementOf0(sK46,sK45) ) ),
introduced(choice_axiom,[]) ).
fof(f368,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ! [X3] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& isCountable0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X5,X1)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X6] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,X0))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0))
| ~ aElement0(X6) ) )
& ! [X7] :
( aElementOf0(X7,X1)
| ~ aElementOf0(X7,X5) )
& ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X9) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(rectify,[],[f367]) ).
fof(f367,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ! [X3] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& isCountable0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X5,X1)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X8] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| ~ aElement0(X8) ) )
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(flattening,[],[f366]) ).
fof(f366,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ! [X3] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& isCountable0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X5,X1)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X8] :
( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| ~ aElement0(X8) ) )
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ! [X3] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
<=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1)
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& isCountable0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X5] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSubsetOf0(X5,X1)
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X8] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) )
<=> aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X5) )
& sbrdtbr0(X5) = xk
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aSet0(X5)
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(flattening,[],[f201]) ).
fof(f201,plain,
? [X0] :
( ? [X1] :
( ? [X5] :
( ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X5) )
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) )
<=> aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aSubsetOf0(X5,X1)
& aElementOf0(X5,slbdtsldtrb0(X1,xk))
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSet0(X5)
& sbrdtbr0(X5) = xk )
& aSet0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
<=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& isCountable0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4) )
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
<=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& isCountable0(X1) )
=> ! [X5] :
( ( aSubsetOf0(X5,X1)
& aElementOf0(X5,slbdtsldtrb0(X1,xk))
& ! [X6] :
( aElementOf0(X6,X5)
=> aElementOf0(X6,X1) )
& aSet0(X5)
& sbrdtbr0(X5) = xk )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( aElementOf0(X7,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) ) )
=> ( ( ! [X8] :
( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& aElement0(X8) )
<=> aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ! [X9] :
( aElementOf0(X9,X5)
=> aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ),
inference(rectify,[],[f89]) ).
fof(f89,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElementOf0(X2,sdtlpdtrp0(xN,X0))
& aElement0(X2)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& isCountable0(X1)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) ) )
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2)
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) ) )
=> ( ( ! [X3] :
( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
<=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f88]) ).
fof(f88,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElementOf0(X2,sdtlpdtrp0(xN,X0))
& aElement0(X2)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& isCountable0(X1)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) ) )
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2)
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) ) )
=> ( ( ! [X3] :
( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
<=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f863,plain,
~ aElementOf0(sK46,sK45),
inference(resolution,[],[f861,f637]) ).
fof(f637,plain,
! [X7] :
( aElementOf0(X7,sK44)
| ~ aElementOf0(X7,sK45) ),
inference(cnf_transformation,[],[f373]) ).
fof(f861,plain,
~ aElementOf0(sK46,sK44),
inference(resolution,[],[f801,f818]) ).
fof(f818,plain,
~ aElementOf0(sK46,sF59),
inference(definition_folding,[],[f636,f800,f799,f798,f798]) ).
fof(f798,plain,
sdtlpdtrp0(xN,sK43) = sF57,
introduced(function_definition,[]) ).
fof(f799,plain,
szmzizndt0(sF57) = sF58,
introduced(function_definition,[]) ).
fof(f800,plain,
sF59 = sdtmndt0(sF57,sF58),
introduced(function_definition,[]) ).
fof(f636,plain,
~ aElementOf0(sK46,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))),
inference(cnf_transformation,[],[f373]) ).
fof(f801,plain,
! [X2] :
( aElementOf0(X2,sF59)
| ~ aElementOf0(X2,sK44) ),
inference(definition_folding,[],[f656,f800,f799,f798,f798]) ).
fof(f656,plain,
! [X2] :
( ~ aElementOf0(X2,sK44)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK43),szmzizndt0(sdtlpdtrp0(xN,sK43)))) ),
inference(cnf_transformation,[],[f373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM588+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 07:15:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.50 % (10840)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.51 % (10855)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.51 % (10855)Instruction limit reached!
% 0.20/0.51 % (10855)------------------------------
% 0.20/0.51 % (10855)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (10848)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.52 % (10855)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (10855)Termination reason: Unknown
% 0.20/0.52 % (10855)Termination phase: Property scanning
% 0.20/0.52
% 0.20/0.52 % (10855)Memory used [KB]: 1918
% 0.20/0.52 % (10855)Time elapsed: 0.005 s
% 0.20/0.52 % (10855)Instructions burned: 9 (million)
% 0.20/0.52 % (10855)------------------------------
% 0.20/0.52 % (10855)------------------------------
% 0.20/0.52 % (10840)First to succeed.
% 0.20/0.52 % (10854)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.52 % (10840)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (10840)------------------------------
% 0.20/0.52 % (10840)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (10840)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (10840)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (10840)Memory used [KB]: 6652
% 0.20/0.52 % (10840)Time elapsed: 0.085 s
% 0.20/0.52 % (10840)Instructions burned: 19 (million)
% 0.20/0.52 % (10840)------------------------------
% 0.20/0.52 % (10840)------------------------------
% 0.20/0.52 % (10833)Success in time 0.167 s
%------------------------------------------------------------------------------