TSTP Solution File: NUM588+3 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n028.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 18:05:58 EDT 2022
% Result : Theorem 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 4 unt; 0 def)
% Number of atoms : 536 ( 61 equ)
% Maximal formula atoms : 80 ( 26 avg)
% Number of connectives : 686 ( 170 ~; 125 |; 347 &)
% ( 10 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 12 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 135 ( 99 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f830,plain,
$false,
inference(subsumption_resolution,[],[f829,f467]) ).
fof(f467,plain,
~ aElementOf0(sK25,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
( aElementOf0(sK22,szNzAzT0)
& aSet0(sK23)
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X2
| ~ aElementOf0(X2,sdtlpdtrp0(xN,sK22))
| ~ aElement0(X2) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,sK22)) != X2
& aElementOf0(X2,sdtlpdtrp0(xN,sK22))
& aElement0(X2) )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ) )
& ! [X4] :
( ( ( aElementOf0(X4,sdtlpdtrp0(xN,sK22))
& szmzizndt0(sdtlpdtrp0(xN,sK22)) != X4
& aElement0(X4) )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK22))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X4
| ~ aElement0(X4) ) )
& aSet0(sK24)
& ~ aSubsetOf0(sK24,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& aElementOf0(sK25,sK24)
& ~ aElementOf0(sK25,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& ! [X6] :
( ~ aElementOf0(X6,sK24)
| aElementOf0(X6,sK23) )
& ~ aElementOf0(sK24,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,sK22))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X7) )
& aElementOf0(sK24,slbdtsldtrb0(sK23,xk))
& xk = sbrdtbr0(sK24)
& aSubsetOf0(sK24,sK23)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& isCountable0(sK23)
& ! [X8] :
( ~ aElementOf0(X8,sK23)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aSubsetOf0(sK23,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ! [X9] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X9)
| ~ aElementOf0(X9,sdtlpdtrp0(xN,sK22)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25])],[f278,f282,f281,f280,f279]) ).
fof(f279,plain,
( ? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X2
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| ~ aElement0(X2) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X2
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& aElement0(X2) )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ? [X3] :
( ! [X4] :
( ( ( aElementOf0(X4,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X4
& aElement0(X4) )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X4
| ~ aElement0(X4) ) )
& aSet0(X3)
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X6] :
( ~ aElementOf0(X6,X3)
| aElementOf0(X6,X1) )
& ~ aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(X3,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X3) = xk
& aSubsetOf0(X3,X1)
& aSet0(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))
& isCountable0(X1)
& ! [X8] :
( ~ aElementOf0(X8,X1)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X9)
| ~ aElementOf0(X9,sdtlpdtrp0(xN,X0)) ) ) )
=> ( aElementOf0(sK22,szNzAzT0)
& ? [X1] :
( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X2
| ~ aElementOf0(X2,sdtlpdtrp0(xN,sK22))
| ~ aElement0(X2) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,sK22)) != X2
& aElementOf0(X2,sdtlpdtrp0(xN,sK22))
& aElement0(X2) )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ) )
& ? [X3] :
( ! [X4] :
( ( ( aElementOf0(X4,sdtlpdtrp0(xN,sK22))
& szmzizndt0(sdtlpdtrp0(xN,sK22)) != X4
& aElement0(X4) )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK22))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X4
| ~ aElement0(X4) ) )
& aSet0(X3)
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& ! [X6] :
( ~ aElementOf0(X6,X3)
| aElementOf0(X6,X1) )
& ~ aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,sK22))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X7) )
& aElementOf0(X3,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X3) = xk
& aSubsetOf0(X3,X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& isCountable0(X1)
& ! [X8] :
( ~ aElementOf0(X8,X1)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ! [X9] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X9)
| ~ aElementOf0(X9,sdtlpdtrp0(xN,sK22)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f280,plain,
( ? [X1] :
( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X2
| ~ aElementOf0(X2,sdtlpdtrp0(xN,sK22))
| ~ aElement0(X2) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,sK22)) != X2
& aElementOf0(X2,sdtlpdtrp0(xN,sK22))
& aElement0(X2) )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ) )
& ? [X3] :
( ! [X4] :
( ( ( aElementOf0(X4,sdtlpdtrp0(xN,sK22))
& szmzizndt0(sdtlpdtrp0(xN,sK22)) != X4
& aElement0(X4) )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK22))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X4
| ~ aElement0(X4) ) )
& aSet0(X3)
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& ! [X6] :
( ~ aElementOf0(X6,X3)
| aElementOf0(X6,X1) )
& ~ aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,sK22))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X7) )
& aElementOf0(X3,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X3) = xk
& aSubsetOf0(X3,X1)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& isCountable0(X1)
& ! [X8] :
( ~ aElementOf0(X8,X1)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ! [X9] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X9)
| ~ aElementOf0(X9,sdtlpdtrp0(xN,sK22)) ) )
=> ( aSet0(sK23)
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X2
| ~ aElementOf0(X2,sdtlpdtrp0(xN,sK22))
| ~ aElement0(X2) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,sK22)) != X2
& aElementOf0(X2,sdtlpdtrp0(xN,sK22))
& aElement0(X2) )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ) )
& ? [X3] :
( ! [X4] :
( ( ( aElementOf0(X4,sdtlpdtrp0(xN,sK22))
& szmzizndt0(sdtlpdtrp0(xN,sK22)) != X4
& aElement0(X4) )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK22))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X4
| ~ aElement0(X4) ) )
& aSet0(X3)
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& ! [X6] :
( ~ aElementOf0(X6,X3)
| aElementOf0(X6,sK23) )
& ~ aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,sK22))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X7) )
& aElementOf0(X3,slbdtsldtrb0(sK23,xk))
& sbrdtbr0(X3) = xk
& aSubsetOf0(X3,sK23)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& isCountable0(sK23)
& ! [X8] :
( ~ aElementOf0(X8,sK23)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aSubsetOf0(sK23,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ! [X9] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X9)
| ~ aElementOf0(X9,sdtlpdtrp0(xN,sK22)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f281,plain,
( ? [X3] :
( ! [X4] :
( ( ( aElementOf0(X4,sdtlpdtrp0(xN,sK22))
& szmzizndt0(sdtlpdtrp0(xN,sK22)) != X4
& aElement0(X4) )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK22))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X4
| ~ aElement0(X4) ) )
& aSet0(X3)
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& ! [X6] :
( ~ aElementOf0(X6,X3)
| aElementOf0(X6,sK23) )
& ~ aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,sK22))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X7) )
& aElementOf0(X3,slbdtsldtrb0(sK23,xk))
& sbrdtbr0(X3) = xk
& aSubsetOf0(X3,sK23)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
=> ( ! [X4] :
( ( ( aElementOf0(X4,sdtlpdtrp0(xN,sK22))
& szmzizndt0(sdtlpdtrp0(xN,sK22)) != X4
& aElement0(X4) )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK22))
| szmzizndt0(sdtlpdtrp0(xN,sK22)) = X4
| ~ aElement0(X4) ) )
& aSet0(sK24)
& ~ aSubsetOf0(sK24,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
& ? [X5] :
( aElementOf0(X5,sK24)
& ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK22)),sdtlpdtrp0(xN,sK22))
& ! [X6] :
( ~ aElementOf0(X6,sK24)
| aElementOf0(X6,sK23) )
& ~ aElementOf0(sK24,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,sK22))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK22)),X7) )
& aElementOf0(sK24,slbdtsldtrb0(sK23,xk))
& xk = sbrdtbr0(sK24)
& aSubsetOf0(sK24,sK23)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ) ),
introduced(choice_axiom,[]) ).
fof(f282,plain,
( ? [X5] :
( aElementOf0(X5,sK24)
& ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) )
=> ( aElementOf0(sK25,sK24)
& ~ aElementOf0(sK25,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ) ),
introduced(choice_axiom,[]) ).
fof(f278,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X2
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| ~ aElement0(X2) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X2
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& aElement0(X2) )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ? [X3] :
( ! [X4] :
( ( ( aElementOf0(X4,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X4
& aElement0(X4) )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X4
| ~ aElement0(X4) ) )
& aSet0(X3)
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X5] :
( aElementOf0(X5,X3)
& ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X6] :
( ~ aElementOf0(X6,X3)
| aElementOf0(X6,X1) )
& ~ aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(X3,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X3) = xk
& aSubsetOf0(X3,X1)
& aSet0(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))
& isCountable0(X1)
& ! [X8] :
( ~ aElementOf0(X8,X1)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X9)
| ~ aElementOf0(X9,sdtlpdtrp0(xN,X0)) ) ) ),
inference(rectify,[],[f277]) ).
fof(f277,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ? [X5] :
( ! [X8] :
( ( ( aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElement0(X8) )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
| ~ aElement0(X8) ) )
& aSet0(X5)
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X9] :
( aElementOf0(X9,X5)
& ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X1) )
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(X5,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X5) = xk
& aSubsetOf0(X5,X1)
& aSet0(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))
& isCountable0(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))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) ) ) ),
inference(flattening,[],[f276]) ).
fof(f276,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ? [X5] :
( ! [X8] :
( ( ( aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElement0(X8) )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
| ~ aElement0(X8) ) )
& aSet0(X5)
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X9] :
( aElementOf0(X9,X5)
& ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X1) )
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(X5,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X5) = xk
& aSubsetOf0(X5,X1)
& aSet0(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))
& isCountable0(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))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) ) ) ),
inference(nnf_transformation,[],[f219]) ).
fof(f219,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ? [X1] :
( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& ? [X5] :
( ! [X8] :
( ( aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElement0(X8) )
<=> aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X5)
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X9] :
( aElementOf0(X9,X5)
& ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X1) )
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(X5,slbdtsldtrb0(X1,xk))
& sbrdtbr0(X5) = xk
& aSubsetOf0(X5,X1)
& aSet0(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))
& isCountable0(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))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) ) ) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
? [X0] :
( ? [X1] :
( ? [X5] :
( ~ aSubsetOf0(X5,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)))) )
& ! [X8] :
( ( aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElement0(X8) )
<=> aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aElementOf0(X5,slbdtsldtrb0(X1,xk))
& aSubsetOf0(X5,X1)
& aSet0(X5)
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X1) )
& sbrdtbr0(X5) = xk )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1)
& ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
=> ! [X5] :
( ( aElementOf0(X5,slbdtsldtrb0(X1,xk))
& aSubsetOf0(X5,X1)
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X5)
=> aElementOf0(X6,X1) )
& sbrdtbr0(X5) = xk )
=> ( ( ! [X7] :
( aElementOf0(X7,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X8] :
( ( aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
& aElement0(X8) )
<=> aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aSubsetOf0(X5,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)))) ) ) ) ) ) ) ),
inference(rectify,[],[f89]) ).
fof(f89,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),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 ) )
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& isCountable0(X1) )
=> ! [X2] :
( ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk))
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& 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] :
( ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),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 ) )
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& isCountable0(X1) )
=> ! [X2] :
( ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk))
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& 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(f829,plain,
aElementOf0(sK25,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))),
inference(resolution,[],[f826,f468]) ).
fof(f468,plain,
aElementOf0(sK25,sK24),
inference(cnf_transformation,[],[f283]) ).
fof(f826,plain,
! [X0] :
( ~ aElementOf0(X0,sK24)
| aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ),
inference(resolution,[],[f455,f465]) ).
fof(f465,plain,
! [X6] :
( aElementOf0(X6,sK23)
| ~ aElementOf0(X6,sK24) ),
inference(cnf_transformation,[],[f283]) ).
fof(f455,plain,
! [X8] :
( ~ aElementOf0(X8,sK23)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ),
inference(cnf_transformation,[],[f283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM588+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 07:22:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.21/0.50 % (29308)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.51 % (29300)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.51 % (29290)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (29292)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52 % (29296)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.52 % (29287)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.52 % (29289)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52 % (29313)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.53 % (29309)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.53 % (29304)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.53 % (29288)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.53 % (29297)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.53 % (29291)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.21/0.53 % (29301)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.21/0.53 % (29308)First to succeed.
% 0.21/0.54 % (29312)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.54 % (29315)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.21/0.54 % (29286)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.54 % (29293)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.54 % (29302)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.54 % (29305)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.54 % (29298)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.54 % (29299)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.54 % (29303)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.21/0.55 % (29314)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.55 % (29311)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.55 % (29310)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.55 % (29308)Refutation found. Thanks to Tanya!
% 0.21/0.55 % SZS status Theorem for theBenchmark
% 0.21/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.55 % (29308)------------------------------
% 0.21/0.55 % (29308)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.55 % (29308)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.55 % (29308)Termination reason: Refutation
% 0.21/0.55
% 0.21/0.55 % (29308)Memory used [KB]: 1663
% 0.21/0.55 % (29308)Time elapsed: 0.131 s
% 0.21/0.55 % (29308)Instructions burned: 21 (million)
% 0.21/0.55 % (29308)------------------------------
% 0.21/0.55 % (29308)------------------------------
% 0.21/0.55 % (29278)Success in time 0.203 s
%------------------------------------------------------------------------------