%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU678^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 Feb 25 09:36:12 AM UTC 2026
% Result : Theorem 1.84s 1.47s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of formulae : 144 ( 111 unt; 0 typ; 2 def)
% Number of atoms : 1524 ( 284 equ; 71 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 3539 ( 44 ~; 28 |; 55 &;2746 @)
% ( 2 <=>; 354 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 268 ( 268 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 24 usr; 16 con; 0-3 aty)
% ( 276 !!; 34 ??; 0 @@+; 0 @@-)
% Number of variables : 714 ( 575 ^; 137 !; 2 ?; 714 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_11,type,
breln: $i > $i > $i > $o ).
thf(func_def_12,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_16,type,
func: $i > $i > $i > $o ).
thf(func_def_34,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
sK4: $i > $i ).
thf(f409,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f249,f360,f408]) ).
thf(f408,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f407]) ).
thf(f407,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f406]) ).
thf(f406,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f405]) ).
thf(f405,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f402,f139]) ).
thf(f139,plain,
( ( in @ ( sK4 @ sK5 ) @ sK2 )
= $true ),
inference(boolean_simplification,[status(thm)],[f131]) ).
thf(f131,plain,
( $true
= ( $true
=> ( in @ ( sK4 @ sK5 ) @ sK2 ) ) ),
inference(superposition,[status(thm)],[f121,f126]) ).
thf(f126,plain,
( ( in @ sK5 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( in @ sK5 @ sK3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( in @ ( kpair @ sK5 @ Y1 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y2: $i] : ( (=) @ ( sK4 @ Y2 ) ) ) ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( in @ ( kpair @ sK5 @ Y1 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y2: $i] : ( (=) @ ( sK4 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f123]) ).
thf(f123,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( sK4 @ Y0 ) @ sK2 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( sK4 @ Y0 ) @ sK2 ) ) )
=> ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f111,f87]) ).
thf(f87,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( $true
= ( subset @ ( dpsetconstr @ X3 @ X1 @ X2 ) @ ( cartprod @ X3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( subset @ ( dpsetconstr @ Y0 @ X1 @ X2 ) @ ( cartprod @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i > $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( dpsetconstr @ Y0 @ X1 @ X2 ) @ ( cartprod @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dpsetconstr @ Y1 @ X1 @ Y0 ) @ ( cartprod @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dpsetconstr @ Y1 @ X1 @ Y0 ) @ ( cartprod @ Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( subset @ ( dpsetconstr @ Y2 @ Y0 @ Y1 ) @ ( cartprod @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( subset @ ( dpsetconstr @ Y2 @ Y0 @ Y1 ) @ ( cartprod @ Y2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( subset @ ( dpsetconstr @ Y2 @ Y0 @ Y1 ) @ ( cartprod @ Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y3 @ Y2 @ Y4 )
=> ( in @ ( kpair @ Y2 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( subset @ ( dpsetconstr @ Y2 @ Y0 @ Y1 ) @ ( cartprod @ Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y3 @ Y2 @ Y4 )
=> ( in @ ( kpair @ Y2 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( subset @ ( dpsetconstr @ Y2 @ Y0 @ Y1 ) @ ( cartprod @ Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y3 @ Y2 @ Y4 )
=> ( in @ ( kpair @ Y2 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( subset @ ( dpsetconstr @ Y2 @ Y0 @ Y1 ) @ ( cartprod @ Y2 @ Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( ( setadjoin @ Y6 @ emptyset )
= Y5 )
& ( in @ Y6 @ Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y3 @ Y2 @ Y4 )
=> ( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y2
@ Y0
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y1
@ Y0
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f37,f42,f33,f39,f34,f41]) ).
thf(f41,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f36,f31,f40]) ).
thf(f40,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f32,f35]) ).
thf(f35,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',singleton) ).
thf(f32,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ex1
= ( ^ [X0: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X1: $i] : ( X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',ex1) ).
thf(f31,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X0 @ X4 ) ) )
= breln ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',breln) ).
thf(f36,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) )
= func ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ( ^ [X0: $i,X4: $i,X8: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( in @ ( kpair @ X1 @ X3 ) @ X8 ) ) )
& ( breln @ X0 @ X4 @ X8 ) ) )
= func ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',func) ).
thf(f34,plain,
( dpsetconstrERa
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( dpsetconstrERa
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
( dpsetconstrERa
= ( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ X0 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X2
@ ^ [X5: $i,X6: $i] : ( X1 @ X5 @ X6 ) ) )
=> ( X1 @ X0 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( dpsetconstrERa
= ( ! [X1: $i,X2: $i > $i > $o,X4: $i,X0: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X3 )
@ ( dpsetconstr @ X0 @ X4
@ ^ [X6: $i,X7: $i] : ( X2 @ X6 @ X7 ) ) )
=> ( X2 @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',dpsetconstrERa) ).
thf(f39,plain,
( setOfPairsIsBReln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y2
@ Y0
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f38,f31]) ).
thf(f38,plain,
( setOfPairsIsBReln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( breln @ Y2 @ Y0
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( setOfPairsIsBReln
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( breln @ Y2 @ Y0
@ ( dpsetconstr @ Y2 @ Y0
@ ^ [Y3: $i,Y4: $i] : ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i,X1: $i > $i > $o,X2: $i] :
( ( breln @ X0 @ X2
@ ( dpsetconstr @ X0 @ X2
@ ^ [X3: $i,X4: $i] : ( X1 @ X3 @ X4 ) ) )
= setOfPairsIsBReln ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X0: $i,X2: $i > $i > $o,X4: $i] :
( ( breln @ X0 @ X4
@ ( dpsetconstr @ X0 @ X4
@ ^ [X1: $i,X3: $i] : ( X2 @ X1 @ X3 ) ) )
= setOfPairsIsBReln ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',setOfPairsIsBReln) ).
thf(f33,plain,
( dpsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y3 @ Y2 @ Y4 )
=> ( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( dpsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y3 @ Y2 @ Y4 )
=> ( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i > $i > $o,X1: $i,X2: $i,X3: $i] :
( ( ( in @ X1 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X0 @ X1 @ X4 )
=> ( in @ ( kpair @ X1 @ X4 )
@ ( dpsetconstr @ X3 @ X2
@ ^ [X5: $i,X6: $i] : ( X0 @ X5 @ X6 ) ) ) ) ) )
= dpsetconstrI ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: $i > $i > $o,X1: $i,X4: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X2 @ X1 @ X3 )
=> ( in @ ( kpair @ X1 @ X3 )
@ ( dpsetconstr @ X0 @ X4
@ ^ [X6: $i,X7: $i] : ( X2 @ X6 @ X7 ) ) ) ) ) )
= dpsetconstrI ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',dpsetconstrI) ).
thf(f42,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ^ [Y3: $i,Y4: $i > $o] :
( ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( ( setadjoin @ Y6 @ emptyset )
= Y5 )
& ( in @ Y6 @ Y5 ) ) )
@ ( dsetconstr @ Y3
@ ^ [Y5: $i] : ( Y4 @ Y5 ) ) )
@ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f30,f40]) ).
thf(f30,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ex1 @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ex1I
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ex1 @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( X0 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X0 @ X3 )
=> ( X2 = X3 ) ) )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) )
= ex1I ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
=> ( ( X2 @ X1 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 @ X3 )
=> ( X1 = X3 ) ) )
=> ( ex1 @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
= ex1I ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',ex1I) ).
thf(f37,plain,
( $true
= ( ~ ( ex1I
=> ( dpsetconstrI
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( ~ ( ex1I
=> ( dpsetconstrI
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ex1I
=> ( dpsetconstrI
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ! [X0: $i > $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( X0 @ X3 ) @ X2 ) )
=> ( func @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i,X5: $i] :
( ( X0 @ X4 )
= X5 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ ( ex1I
=> ( dpsetconstrI
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ! [X9: $i > $i,X0: $i,X4: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( X9 @ X1 ) @ X4 ) )
=> ( func @ X0 @ X4
@ ( dpsetconstr @ X0 @ X4
@ ^ [X1: $i,X3: $i] :
( ( X9 @ X1 )
= X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
( ex1I
=> ( dpsetconstrI
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ! [X9: $i > $i,X0: $i,X4: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( X9 @ X1 ) @ X4 ) )
=> ( func @ X0 @ X4
@ ( dpsetconstr @ X0 @ X4
@ ^ [X1: $i,X3: $i] :
( ( X9 @ X1 )
= X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',lamProp) ).
thf(f111,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( sK4 @ Y0 ) @ sK2 ) ) )
=> ( ( subset
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) )
@ ( cartprod @ sK3 @ sK2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK2
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y3: $i] : ( (=) @ ( sK4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f110]) ).
thf(f110,plain,
( ( ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( in @ ( Y0 @ Y1 ) @ sK2 ) ) )
=> ( ( subset
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( Y0 @ Y1 ) ) )
@ ( cartprod @ sK3 @ sK2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y3: $i] :
( in @ ( kpair @ Y1 @ Y3 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y4: $i] : ( (=) @ ( Y0 @ Y4 ) ) ) ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK2
@ ^ [Y3: $i] :
( in @ ( kpair @ Y1 @ Y3 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y4: $i] : ( (=) @ ( Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
( ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( in @ ( Y0 @ Y1 ) @ sK2 ) ) )
=> ( ( subset
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( Y0 @ Y1 ) ) )
@ ( cartprod @ sK3 @ sK2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y3: $i] :
( in @ ( kpair @ Y1 @ Y3 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y4: $i] : ( (=) @ ( Y0 @ Y4 ) ) ) ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK2
@ ^ [Y3: $i] :
( in @ ( kpair @ Y1 @ Y3 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y4: $i] : ( (=) @ ( Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( Y1 @ Y2 ) @ sK2 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y0 @ sK2
@ ^ [Y2: $i] : ( (=) @ ( Y1 @ Y2 ) ) )
@ ( cartprod @ Y0 @ sK2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y4: $i] :
( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ Y0 @ sK2
@ ^ [Y5: $i] : ( (=) @ ( Y1 @ Y5 ) ) ) ) ) )
& ( in @ Y3
@ ( dsetconstr @ sK2
@ ^ [Y4: $i] :
( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ Y0 @ sK2
@ ^ [Y5: $i] : ( (=) @ ( Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ ( Y1 @ Y2 ) @ sK2 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y0 @ sK2
@ ^ [Y2: $i] : ( (=) @ ( Y1 @ Y2 ) ) )
@ ( cartprod @ Y0 @ sK2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y4: $i] :
( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ Y0 @ sK2
@ ^ [Y5: $i] : ( (=) @ ( Y1 @ Y5 ) ) ) ) ) )
& ( in @ Y3
@ ( dsetconstr @ sK2
@ ^ [Y4: $i] :
( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ Y0 @ sK2
@ ^ [Y5: $i] : ( (=) @ ( Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( Y2 @ Y3 ) @ Y0 ) ) )
=> ( ( subset
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y3: $i] : ( (=) @ ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y6: $i] : ( (=) @ ( Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f121,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK3 )
=> ( in @ ( sK4 @ X1 ) @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( sK4 @ Y0 ) @ sK2 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in @ ( sK4 @ Y0 ) @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f402,plain,
( ( $true
= ( ~ ( in @ ( sK4 @ sK5 ) @ sK2 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f401]) ).
thf(f401,plain,
( ( $true
= ( ( in @ ( sK4 @ sK5 ) @ sK2 )
=> $false ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f400]) ).
thf(f400,plain,
( ( ( ( in @ ( sK4 @ sK5 ) @ sK2 )
=> ~ $true )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f399]) ).
thf(f399,plain,
( ( $true
= ( ( in @ ( sK4 @ sK5 ) @ sK2 )
=> ( ( sK4 @ sK5 )
!= ( sK4 @ sK5 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f398]) ).
thf(f398,plain,
( ( ( ( in @ ( sK4 @ sK5 ) @ sK2 )
=> ( ( ( sK4 @ sK5 )
= ( sK4 @ sK5 ) )
=> $false ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f369]) ).
thf(f369,plain,
( ( ( ( in @ ( sK4 @ sK5 ) @ sK2 )
=> ( ( ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) )
@ sK5
@ ( sK4 @ sK5 ) )
=> $false ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f159,f245]) ).
thf(f245,plain,
( ( $false
= ( in @ ( kpair @ sK5 @ ( sK4 @ sK5 ) )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f244]) ).
thf(f244,definition,
( spl0_1
<=> ( $false
= ( in @ ( kpair @ sK5 @ ( sK4 @ sK5 ) )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f159,plain,
! [X2: $i,X0: $i,X1: $i > $i > $o] :
( $true
= ( ( in @ X2 @ X0 )
=> ( ( X1 @ sK5 @ X2 )
=> ( in @ ( kpair @ sK5 @ X2 ) @ ( dpsetconstr @ sK3 @ X0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f156]) ).
thf(f156,plain,
! [X2: $i,X0: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( X1 @ sK5 @ Y0 )
=> ( in @ ( kpair @ sK5 @ Y0 ) @ ( dpsetconstr @ sK3 @ X0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
! [X0: $i,X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( X1 @ sK5 @ Y0 )
=> ( in @ ( kpair @ sK5 @ Y0 ) @ ( dpsetconstr @ sK3 @ X0 @ X1 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f133]) ).
thf(f133,plain,
! [X0: $i,X1: $i > $i > $o] :
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( X1 @ sK5 @ Y0 )
=> ( in @ ( kpair @ sK5 @ Y0 ) @ ( dpsetconstr @ sK3 @ X0 @ X1 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f74,f126]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i > $o] :
( $true
= ( ( in @ X3 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ X3 @ Y0 )
=> ( in @ ( kpair @ X3 @ Y0 ) @ ( dpsetconstr @ X1 @ X2 @ X4 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( in @ X3 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( Y0 @ X3 @ Y1 )
=> ( in @ ( kpair @ X3 @ Y1 ) @ ( dpsetconstr @ X1 @ X2 @ Y0 ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( in @ X3 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( Y0 @ X3 @ Y1 )
=> ( in @ ( kpair @ X3 @ Y1 ) @ ( dpsetconstr @ X1 @ X2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( Y1 @ Y0 @ Y2 )
=> ( in @ ( kpair @ Y0 @ Y2 ) @ ( dpsetconstr @ X1 @ X2 @ Y1 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( Y1 @ Y0 @ Y2 )
=> ( in @ ( kpair @ Y0 @ Y2 ) @ ( dpsetconstr @ X1 @ X2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y1 @ Y3 )
=> ( in @ ( kpair @ Y1 @ Y3 ) @ ( dpsetconstr @ X1 @ Y0 @ Y2 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y2 @ Y1 @ Y3 )
=> ( in @ ( kpair @ Y1 @ Y3 ) @ ( dpsetconstr @ X1 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y3 @ Y2 @ Y4 )
=> ( in @ ( kpair @ Y2 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y3 @ Y2 @ Y4 )
=> ( in @ ( kpair @ Y2 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f360,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f359]) ).
thf(f359,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f358]) ).
thf(f358,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f357,f295]) ).
thf(f295,plain,
( ( ( ( sK4 @ sK5 )
= sK6 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f294]) ).
thf(f294,plain,
( ( ( $true
=> ( ( sK4 @ sK5 )
= sK6 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f267,f292]) ).
thf(f292,plain,
( ( $true
= ( in @ ( kpair @ sK5 @ sK6 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f267]) ).
thf(f267,plain,
( ( ( ( in @ ( kpair @ sK5 @ sK6 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) )
=> ( ( sK4 @ sK5 )
= sK6 ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f263]) ).
thf(f263,plain,
( ( $false
= ( ( in @ sK6 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ sK6 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) )
=> ( ( sK4 @ sK5 )
= sK6 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f261]) ).
thf(f261,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( ( sK4 @ sK5 )
= Y0 ) ) )
@ sK6 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f255]) ).
thf(f255,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( ( sK4 @ sK5 )
= Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( ( sK4 @ sK5 )
= Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f247]) ).
thf(f247,definition,
( spl0_2
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( ( sK4 @ sK5 )
= Y0 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f357,plain,
( ( ( ( sK4 @ sK5 )
= sK6 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f356]) ).
thf(f356,plain,
( ( $true
= ( $true
=> ( ( sK4 @ sK5 )
= sK6 ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f355,f268]) ).
thf(f268,plain,
( ( $true
= ( in @ sK6 @ sK2 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f263]) ).
thf(f355,plain,
( ( $true
= ( ( in @ sK6 @ sK2 )
=> ( ( sK4 @ sK5 )
= sK6 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f354]) ).
thf(f354,plain,
( ( $true
= ( ( in @ sK6 @ sK2 )
=> ( $true
=> ( ( sK4 @ sK5 )
= sK6 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f332]) ).
thf(f332,plain,
( ( $true
= ( ( in @ sK6 @ sK2 )
=> ( $true
=> ( ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) )
@ sK5
@ sK6 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f170,f292]) ).
thf(f170,plain,
! [X2: $i,X0: $i,X1: $i > $i > $o] :
( $true
= ( ( in @ X2 @ X0 )
=> ( ( in @ ( kpair @ sK5 @ X2 ) @ ( dpsetconstr @ sK3 @ X0 @ X1 ) )
=> ( X1 @ sK5 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: $i,X0: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ ( dpsetconstr @ sK3 @ X0 @ X1 ) )
=> ( X1 @ sK5 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X0: $i,X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ ( dpsetconstr @ sK3 @ X0 @ X1 ) )
=> ( X1 @ sK5 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X0: $i,X1: $i > $i > $o] :
( $true
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( in @ ( kpair @ sK5 @ Y0 ) @ ( dpsetconstr @ sK3 @ X0 @ X1 ) )
=> ( X1 @ sK5 @ Y0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f104,f126]) ).
thf(f104,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i] :
( $true
= ( ( in @ X4 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ ( dpsetconstr @ X1 @ X2 @ X3 ) )
=> ( X3 @ X4 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f103]) ).
thf(f103,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X1 @ X2 @ X3 ) )
=> ( X3 @ Y0 @ Y1 ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X1 @ X2 @ X3 ) )
=> ( X3 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X3: $i > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ X1 @ X2 @ Y0 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ X1 @ X2 @ Y0 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ X1 @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ X1 @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f249,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f240,f247,f244]) ).
thf(f240,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( ( sK4 @ sK5 )
= Y0 ) ) ) ) )
= $true )
| ( $false
= ( in @ ( kpair @ sK5 @ ( sK4 @ sK5 ) )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f196]) ).
thf(f196,plain,
( $true
= ( ( in @ ( kpair @ sK5 @ ( sK4 @ sK5 ) )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( ( sK4 @ sK5 )
= Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f195]) ).
thf(f195,plain,
( $true
= ( $true
=> ( ( in @ ( kpair @ sK5 @ ( sK4 @ sK5 ) )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( ( sK4 @ sK5 )
= Y0 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f154,f139]) ).
thf(f154,plain,
! [X0: $i] :
( $true
= ( ( in @ X0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ X0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( X0 = Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f153]) ).
thf(f153,plain,
! [X0: $i] :
( $true
= ( ( in @ X0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ X0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i] : ( (=) @ ( sK4 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
=> ( X0 = Y0 ) ) ) )
=> $false ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f152]) ).
thf(f152,plain,
! [X0: $i] :
( $true
= ( ( in @ X0 @ sK2 )
=> ( ( ^ [Y0: $i] :
( in @ ( kpair @ sK5 @ Y0 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y1: $i] : ( (=) @ ( sK4 @ Y1 ) ) ) )
@ X0 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( ^ [Y1: $i] :
( in @ ( kpair @ sK5 @ Y1 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y2: $i] : ( (=) @ ( sK4 @ Y2 ) ) ) )
@ Y0 )
=> ( X0 = Y0 ) ) ) )
=> $false ) ) ) ),
inference(superposition,[status(thm)],[f59,f125]) ).
thf(f125,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( in @ ( kpair @ sK5 @ Y1 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y2: $i] : ( (=) @ ( sK4 @ Y2 ) ) ) ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK2
@ ^ [Y1: $i] :
( in @ ( kpair @ sK5 @ Y1 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y2: $i] : ( (=) @ ( sK4 @ Y2 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f59,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X1 @ X2 )
=> ( ( X3 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X3 @ Y0 )
=> ( X1 = Y0 ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2 @ X3 ) )
& ( in @ Y0 @ ( dsetconstr @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X1 @ X2 )
=> ( ( Y0 @ X1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( Y0 @ Y1 )
=> ( X1 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2 @ Y0 ) )
& ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ X2 )
=> ( ( Y0 @ X1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( Y0 @ Y1 )
=> ( X1 = Y1 ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2 @ Y0 ) )
& ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ Y0 )
=> ( ( Y1 @ X1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( X1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) )
& ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ Y0 )
=> ( ( Y1 @ X1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( X1 = Y2 ) ) ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ Y0 @ Y1 ) )
& ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 @ Y3 )
=> ( Y0 = Y3 ) ) ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y1 @ Y2 ) )
& ( in @ Y3 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU678^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:30:08 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.46 ---- Original DTF file ---
% 0.18/0.46 thf(spec,logic,$$dhol).
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 % File : SEU678^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.46 % Domain : Set Theory
% 0.18/0.46 % Problem : Functions - Lambda Abstraction
% 0.18/0.46 % Version : Especial > Reduced > Especial.
% 0.18/0.46 % English : (! A:i.! B:i.! f:i>i.(! x:i.in x A -> in (f x) B) ->
% 0.18/0.46 % func A B (dpsetconstr A B (^ x,y:i.f x = y)))
% 0.18/0.46
% 0.18/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.46 % Source : [Bro08]
% 0.18/0.46 % Names : ZFC180l [Bro08]
% 0.18/0.46
% 0.18/0.46 % Status : Theorem
% 0.18/0.46 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.18/0.46 % Syntax : Number of formulae : 25 ( 8 unt; 16 typ; 8 def)
% 0.18/0.46 % Number of atoms : 43 ( 11 equ; 0 cnn)
% 0.18/0.46 % Maximal formula atoms : 8 ( 4 avg)
% 0.18/0.46 % Number of connectives : 102 ( 0 ~; 0 |; 2 &; 82 @)
% 0.18/0.46 % ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% 0.18/0.46 % Maximal formula depth : 14 ( 2 avg)
% 0.18/0.46 % Number of types : 2 ( 0 usr)
% 0.18/0.46 % Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% 0.18/0.46 % Number of symbols : 17 ( 16 usr; 5 con; 0-3 aty)
% 0.18/0.46 % Number of variables : 43 ( 20 ^; 22 !; 1 ?; 43 :)
% 0.18/0.46 % SPC : TH0_THM_EQU_NAR
% 0.18/0.46
% 0.18/0.46 % Comments : http://mathgate.info/detsetitem.php?id=235
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 thf(in_type,type,
% 0.18/0.46 in: $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(emptyset_type,type,
% 0.18/0.46 emptyset: $i ).
% 0.18/0.46
% 0.18/0.46 thf(setadjoin_type,type,
% 0.18/0.46 setadjoin: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstr_type,type,
% 0.18/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.46
% 0.18/0.46 thf(subset_type,type,
% 0.18/0.46 subset: $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(kpair_type,type,
% 0.18/0.46 kpair: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(cartprod_type,type,
% 0.18/0.46 cartprod: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(singleton_type,type,
% 0.18/0.46 singleton: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(singleton,definition,
% 0.18/0.46 ( singleton
% 0.18/0.46 = ( ^ [A: $i] :
% 0.18/0.46 ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 & ( A
% 0.18/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ex1_type,type,
% 0.18/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.18/0.46
% 0.18/0.46 thf(ex1,definition,
% 0.18/0.46 ( ex1
% 0.18/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.18/0.46 ( singleton
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ex1I_type,type,
% 0.18/0.46 ex1I: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ex1I,definition,
% 0.18/0.46 ( ex1I
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ( Xphi @ Xx )
% 0.18/0.46 => ( ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ A )
% 0.18/0.46 => ( ( Xphi @ Xy )
% 0.18/0.46 => ( Xy = Xx ) ) )
% 0.18/0.46 => ( ex1 @ A
% 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(breln_type,type,
% 0.18/0.46 breln: $i > $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(breln,definition,
% 0.18/0.46 ( breln
% 0.18/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstr_type,type,
% 0.18/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrI_type,type,
% 0.18/0.46 dpsetconstrI: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrI,definition,
% 0.18/0.46 ( dpsetconstrI
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.18/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setOfPairsIsBReln_type,type,
% 0.18/0.46 setOfPairsIsBReln: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setOfPairsIsBReln,definition,
% 0.18/0.46 ( setOfPairsIsBReln
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.18/0.46 ( breln @ A @ B
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrERa_type,type,
% 0.18/0.46 dpsetconstrERa: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrERa,definition,
% 0.18/0.46 ( dpsetconstrERa
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(func_type,type,
% 0.18/0.46 func: $i > $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(func,definition,
% 0.18/0.46 ( func
% 0.18/0.46 = ( ^ [A: $i,B: $i,R: $i] :
% 0.18/0.46 ( ( breln @ A @ B @ R )
% 0.18/0.46 & ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ex1 @ B
% 0.18/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(lamProp,conjecture,
% 0.18/0.46 ( ex1I
% 0.18/0.46 => ( dpsetconstrI
% 0.18/0.46 => ( setOfPairsIsBReln
% 0.18/0.46 => ( dpsetconstrERa
% 0.18/0.46 => ! [A: $i,B: $i,Xf: $i > $i] :
% 0.18/0.46 ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.18/0.46 => ( func @ A @ B
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( Xf @ Xx )
% 0.18/0.46 = Xy ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 1.71/1.35 ---- Embedded in THF ---
% 1.71/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.35 %%% Generated on Tue Feb 24 12:30:09 EST 2026
% 1.71/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.35 %%% Logic specification used:
% 1.71/1.35 %%% thf(spec, logic, $$dhol).
% 1.71/1.35
% 1.71/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2DTF6648.p
% See solution above
% 1.71/1.35 ------------------------
% 1.71/1.36 ---- Cleaned THF ---
% 1.71/1.36 thf(in_type,type,
% 1.71/1.36 in: $i > $i > $o ).
% 1.71/1.36
% 1.71/1.36 thf(emptyset_type,type,
% 1.71/1.36 emptyset: $i ).
% 1.71/1.36
% 1.71/1.36 thf(setadjoin_type,type,
% 1.71/1.36 setadjoin: $i > $i > $i ).
% 1.71/1.36
% 1.71/1.36 thf(dsetconstr_type,type,
% 1.71/1.36 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.71/1.36
% 1.71/1.36 thf(subset_type,type,
% 1.71/1.36 subset: $i > $i > $o ).
% 1.71/1.36
% 1.71/1.36 thf(kpair_type,type,
% 1.71/1.36 kpair: $i > $i > $i ).
% 1.71/1.36
% 1.71/1.36 thf(cartprod_type,type,
% 1.71/1.36 cartprod: $i > $i > $i ).
% 1.71/1.36
% 1.71/1.36 thf(singleton_type,type,
% 1.71/1.36 singleton: $i > $o ).
% 1.71/1.36
% 1.71/1.36 thf(singleton,definition,
% 1.71/1.36 ( singleton
% 1.71/1.36 = ( ^ [A: $i] :
% 1.71/1.36 ? [Xx: $i] :
% 1.71/1.36 ( ( in @ Xx @ A )
% 1.71/1.36 & ( A
% 1.71/1.36 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.71/1.36
% 1.71/1.36 thf(ex1_type,type,
% 1.71/1.36 ex1: $i > ( $i > $o ) > $o ).
% 1.71/1.36
% 1.71/1.36 thf(ex1,definition,
% 1.71/1.36 ( ex1
% 1.71/1.36 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.71/1.36 ( singleton
% 1.71/1.36 @ ( dsetconstr @ A
% 1.71/1.36 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.71/1.36
% 1.71/1.36 thf(ex1I_type,type,
% 1.71/1.36 ex1I: $o ).
% 1.71/1.36
% 1.71/1.36 thf(ex1I,definition,
% 1.71/1.36 ( ex1I
% 1.71/1.36 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.71/1.36 ( ( in @ Xx @ A )
% 1.71/1.36 => ( ( Xphi @ Xx )
% 1.71/1.36 => ( ! [Xy: $i] :
% 1.71/1.36 ( ( in @ Xy @ A )
% 1.71/1.36 => ( ( Xphi @ Xy )
% 1.71/1.36 => ( Xy = Xx ) ) )
% 1.71/1.36 => ( ex1 @ A
% 1.71/1.36 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.71/1.36
% 1.71/1.36 thf(breln_type,type,
% 1.71/1.36 breln: $i > $i > $i > $o ).
% 1.71/1.36
% 1.71/1.36 thf(breln,definition,
% 1.71/1.36 ( breln
% 1.71/1.36 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.71/1.36
% 1.71/1.36 thf(dpsetconstr_type,type,
% 1.71/1.36 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.71/1.36
% 1.71/1.36 thf(dpsetconstrI_type,type,
% 1.71/1.36 dpsetconstrI: $o ).
% 1.71/1.36
% 1.71/1.36 thf(dpsetconstrI,definition,
% 1.71/1.36 ( dpsetconstrI
% 1.71/1.36 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 1.71/1.36 ( ( in @ Xx @ A )
% 1.71/1.36 => ! [Xy: $i] :
% 1.71/1.36 ( ( in @ Xy @ B )
% 1.71/1.36 => ( ( Xphi @ Xx @ Xy )
% 1.71/1.36 => ( in @ ( kpair @ Xx @ Xy )
% 1.71/1.36 @ ( dpsetconstr @ A @ B
% 1.71/1.36 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 1.71/1.36
% 1.71/1.36 thf(setOfPairsIsBReln_type,type,
% 1.71/1.36 setOfPairsIsBReln: $o ).
% 1.71/1.36
% 1.71/1.36 thf(setOfPairsIsBReln,definition,
% 1.71/1.36 ( setOfPairsIsBReln
% 1.71/1.36 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 1.71/1.36 ( breln @ A @ B
% 1.71/1.36 @ ( dpsetconstr @ A @ B
% 1.71/1.36 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 1.71/1.36
% 1.71/1.36 thf(dpsetconstrERa_type,type,
% 1.71/1.36 dpsetconstrERa: $o ).
% 1.71/1.36
% 1.71/1.36 thf(dpsetconstrERa,definition,
% 1.71/1.36 ( dpsetconstrERa
% 1.71/1.36 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 1.71/1.36 ( ( in @ Xx @ A )
% 1.71/1.36 => ! [Xy: $i] :
% 1.71/1.36 ( ( in @ Xy @ B )
% 1.71/1.36 => ( ( in @ ( kpair @ Xx @ Xy )
% 1.71/1.36 @ ( dpsetconstr @ A @ B
% 1.71/1.36 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 1.71/1.36 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 1.71/1.36
% 1.71/1.36 thf(func_type,type,
% 1.71/1.36 func: $i > $i > $i > $o ).
% 1.71/1.36
% 1.71/1.36 thf(func,definition,
% 1.71/1.36 ( func
% 1.71/1.36 = ( ^ [A: $i,B: $i,R: $i] :
% 1.71/1.36 ( ( breln @ A @ B @ R )
% 1.71/1.36 & ! [Xx: $i] :
% 1.71/1.36 ( ( in @ Xx @ A )
% 1.71/1.36 => ( ex1 @ B
% 1.71/1.36 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.71/1.36
% 1.71/1.36 thf(lamProp,conjecture,
% 1.71/1.36 ( ex1I
% 1.71/1.36 => ( dpsetconstrI
% 1.71/1.36 => ( setOfPairsIsBReln
% 1.71/1.36 => ( dpsetconstrERa
% 1.71/1.36 => ! [A: $i,B: $i,Xf: $i > $i] :
% 1.71/1.36 ( ! [Xx: $i] :
% 1.71/1.36 ( ( in @ Xx @ A )
% 1.71/1.36 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.71/1.36 => ( func @ A @ B
% 1.71/1.36 @ ( dpsetconstr @ A @ B
% 1.71/1.36 @ ^ [Xx: $i,Xy: $i] :
% 1.71/1.36 ( ( Xf @ Xx )
% 1.71/1.36 = Xy ) ) ) ) ) ) ) ) ).
% 1.71/1.36 ------------------------
% 1.71/1.37 % (6798)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/275Mi)
% 1.71/1.38 % (6795)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/27Mi)
% 1.71/1.38 % (6796)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/2Mi)
% 1.71/1.38 % (6794)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/4Mi)
% 1.71/1.38 % (6796)Instruction limit reached!
% 1.71/1.38 % (6796)------------------------------
% 1.71/1.38 % (6796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.38 % (6796)Termination reason: Unknown
% 1.71/1.38 % (6796)Termination phase: Property scanning
% 1.71/1.38
% 1.71/1.38 % (6796)Memory used [KB]: 1023
% 1.71/1.38 % (6796)Time elapsed: 0.002 s
% 1.71/1.38 % (6796)Instructions burned: 4 (million)
% 1.71/1.38 % (6796)------------------------------
% 1.71/1.38 % (6796)------------------------------
% 1.71/1.38 % (6794)Instruction limit reached!
% 1.71/1.38 % (6794)------------------------------
% 1.71/1.38 % (6794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.38 % (6794)Termination reason: Unknown
% 1.71/1.38 % (6794)Termination phase: Property scanning
% 1.71/1.38
% 1.71/1.38 % (6794)Memory used [KB]: 1023
% 1.71/1.38 % (6794)Time elapsed: 0.003 s
% 1.71/1.38 % (6794)Instructions burned: 4 (million)
% 1.71/1.38 % (6794)------------------------------
% 1.71/1.38 % (6794)------------------------------
% 1.71/1.38 % (6793)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/183Mi)
% 1.71/1.38 % (6798)Refutation not found, incomplete strategy
% 1.71/1.38 % (6798)------------------------------
% 1.71/1.38 % (6798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.38 % (6798)Termination reason: Refutation not found, incomplete strategy
% 1.71/1.38
% 1.71/1.38
% 1.71/1.38 % (6798)Memory used [KB]: 5628
% 1.71/1.38 % (6798)Time elapsed: 0.007 s
% 1.71/1.38 % (6798)Instructions burned: 16 (million)
% 1.71/1.38 % (6798)------------------------------
% 1.71/1.38 % (6798)------------------------------
% 1.71/1.38 % (6797)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/2Mi)
% 1.71/1.38 % (6797)Instruction limit reached!
% 1.71/1.38 % (6797)------------------------------
% 1.71/1.38 % (6797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.38 % (6797)Termination reason: Unknown
% 1.71/1.38 % (6797)Termination phase: Property scanning
% 1.71/1.38
% 1.71/1.38 % (6797)Memory used [KB]: 1023
% 1.71/1.38 % (6797)Time elapsed: 0.003 s
% 1.71/1.38 % (6797)Instructions burned: 4 (million)
% 1.71/1.38 % (6797)------------------------------
% 1.71/1.38 % (6797)------------------------------
% 1.71/1.38 % (6799)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/18Mi)
% 1.71/1.39 % (6795)Instruction limit reached!
% 1.71/1.39 % (6795)------------------------------
% 1.71/1.39 % (6795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.39 % (6795)Termination reason: Unknown
% 1.71/1.39 % (6795)Termination phase: Saturation
% 1.71/1.39
% 1.71/1.39 % (6795)Memory used [KB]: 5756
% 1.71/1.39 % (6795)Time elapsed: 0.011 s
% 1.71/1.39 % (6795)Instructions burned: 29 (million)
% 1.71/1.39 % (6795)------------------------------
% 1.71/1.39 % (6795)------------------------------
% 1.71/1.39 % (6800)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/3Mi)
% 1.71/1.39 % (6801)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/37Mi)
% 1.71/1.39 % (6800)Instruction limit reached!
% 1.71/1.39 % (6800)------------------------------
% 1.71/1.39 % (6800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.39 % (6800)Termination reason: Unknown
% 1.71/1.39 % (6800)Termination phase: Property scanning
% 1.71/1.39
% 1.71/1.39 % (6800)Memory used [KB]: 1023
% 1.71/1.39 % (6800)Time elapsed: 0.002 s
% 1.71/1.39 % (6800)Instructions burned: 4 (million)
% 1.71/1.39 % (6800)------------------------------
% 1.71/1.39 % (6800)------------------------------
% 1.71/1.39 % (6802)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/15Mi)
% 1.71/1.39 % (6803)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/3Mi)
% 1.71/1.39 % (6803)Instruction limit reached!
% 1.71/1.39 % (6803)------------------------------
% 1.71/1.39 % (6803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.39 % (6803)Termination reason: Unknown
% 1.71/1.39 % (6803)Termination phase: Naming
% 1.71/1.39
% 1.71/1.39 % (6803)Memory used [KB]: 1023
% 1.71/1.39 % (6803)Time elapsed: 0.002 s
% 1.71/1.39 % (6803)Instructions burned: 4 (million)
% 1.71/1.39 % (6803)------------------------------
% 1.71/1.39 % (6803)------------------------------
% 1.71/1.40 % (6799)Instruction limit reached!
% 1.71/1.40 % (6799)------------------------------
% 1.71/1.40 % (6799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (6799)Termination reason: Unknown
% 1.71/1.40 % (6799)Termination phase: Saturation
% 1.71/1.40
% 1.71/1.40 % (6799)Memory used [KB]: 5756
% 1.71/1.40 % (6799)Time elapsed: 0.013 s
% 1.71/1.40 % (6799)Instructions burned: 19 (million)
% 1.71/1.40 % (6799)------------------------------
% 1.71/1.40 % (6799)------------------------------
% 1.71/1.40 % (6805)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/1041Mi)
% 1.71/1.40 % (6802)Instruction limit reached!
% 1.71/1.40 % (6802)------------------------------
% 1.71/1.40 % (6802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.40 % (6802)Termination reason: Unknown
% 1.71/1.40 % (6802)Termination phase: Saturation
% 1.71/1.40
% 1.71/1.40 % (6802)Memory used [KB]: 5756
% 1.71/1.40 % (6802)Time elapsed: 0.007 s
% 1.71/1.40 % (6802)Instructions burned: 17 (million)
% 1.71/1.40 % (6802)------------------------------
% 1.71/1.40 % (6802)------------------------------
% 1.84/1.40 % (6801)Instruction limit reached!
% 1.84/1.40 % (6801)------------------------------
% 1.84/1.40 % (6801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.40 % (6801)Termination reason: Unknown
% 1.84/1.40 % (6801)Termination phase: Saturation
% 1.84/1.40
% 1.84/1.40 % (6801)Memory used [KB]: 5756
% 1.84/1.40 % (6801)Time elapsed: 0.013 s
% 1.84/1.40 % (6801)Instructions burned: 38 (million)
% 1.84/1.40 % (6801)------------------------------
% 1.84/1.40 % (6801)------------------------------
% 1.84/1.40 % (6811)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/16Mi)
% 1.84/1.41 % (6813)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/3Mi)
% 1.84/1.41 % (6810)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/7Mi)
% 1.84/1.41 % (6813)Instruction limit reached!
% 1.84/1.41 % (6813)------------------------------
% 1.84/1.41 % (6813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (6813)Termination reason: Unknown
% 1.84/1.41 % (6813)Termination phase: shuffling
% 1.84/1.41
% 1.84/1.41 % (6813)Memory used [KB]: 1023
% 1.84/1.41 % (6813)Time elapsed: 0.002 s
% 1.84/1.41 % (6813)Instructions burned: 4 (million)
% 1.84/1.41 % (6813)------------------------------
% 1.84/1.41 % (6813)------------------------------
% 1.84/1.41 % (6810)Instruction limit reached!
% 1.84/1.41 % (6810)------------------------------
% 1.84/1.41 % (6810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (6810)Termination reason: Unknown
% 1.84/1.41 % (6810)Termination phase: Saturation
% 1.84/1.41
% 1.84/1.41 % (6814)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/7Mi)
% 1.84/1.41 % (6810)Memory used [KB]: 1023
% 1.84/1.41 % (6810)Time elapsed: 0.006 s
% 1.84/1.41 % (6810)Instructions burned: 8 (million)
% 1.84/1.41 % (6810)------------------------------
% 1.84/1.41 % (6810)------------------------------
% 1.84/1.41 % (6811)Instruction limit reached!
% 1.84/1.41 % (6811)------------------------------
% 1.84/1.41 % (6811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (6811)Termination reason: Unknown
% 1.84/1.41 % (6811)Termination phase: Saturation
% 1.84/1.41
% 1.84/1.41 % (6811)Memory used [KB]: 6012
% 1.84/1.41 % (6811)Time elapsed: 0.008 s
% 1.84/1.41 % (6811)Instructions burned: 17 (million)
% 1.84/1.41 % (6811)------------------------------
% 1.84/1.41 % (6811)------------------------------
% 1.84/1.41 % (6814)Instruction limit reached!
% 1.84/1.41 % (6814)------------------------------
% 1.84/1.41 % (6814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.41 % (6814)Termination reason: Unknown
% 1.84/1.41 % (6814)Termination phase: Saturation
% 1.84/1.41
% 1.84/1.41 % (6814)Memory used [KB]: 5500
% 1.84/1.41 % (6814)Time elapsed: 0.004 s
% 1.84/1.41 % (6814)Instructions burned: 7 (million)
% 1.84/1.41 % (6814)------------------------------
% 1.84/1.41 % (6814)------------------------------
% 1.84/1.41 % (6812)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/3Mi)
% 1.84/1.42 % (6812)Instruction limit reached!
% 1.84/1.42 % (6812)------------------------------
% 1.84/1.42 % (6812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.42 % (6812)Termination reason: Unknown
% 1.84/1.42 % (6812)Termination phase: Property scanning
% 1.84/1.42
% 1.84/1.42 % (6812)Memory used [KB]: 1023
% 1.84/1.42 % (6812)Time elapsed: 0.004 s
% 1.84/1.42 % (6812)Instructions burned: 4 (million)
% 1.84/1.42 % (6812)------------------------------
% 1.84/1.42 % (6812)------------------------------
% 1.84/1.42 % (6815)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/3Mi)
% 1.84/1.42 % (6815)Instruction limit reached!
% 1.84/1.42 % (6815)------------------------------
% 1.84/1.42 % (6815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.42 % (6815)Termination reason: Unknown
% 1.84/1.42 % (6815)Termination phase: Property scanning
% 1.84/1.42
% 1.84/1.42 % (6815)Memory used [KB]: 1023
% 1.84/1.42 % (6815)Time elapsed: 0.002 s
% 1.84/1.42 % (6815)Instructions burned: 5 (million)
% 1.84/1.42 % (6815)------------------------------
% 1.84/1.42 % (6815)------------------------------
% 1.84/1.42 % (6817)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/18Mi)
% 1.84/1.42 % (6818)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/710Mi)
% 1.84/1.42 % (6816)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/4Mi)
% 1.84/1.42 % (6816)Instruction limit reached!
% 1.84/1.42 % (6816)------------------------------
% 1.84/1.42 % (6816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.42 % (6816)Termination reason: Unknown
% 1.84/1.42 % (6816)Termination phase: Preprocessing 3
% 1.84/1.42
% 1.84/1.42 % (6816)Memory used [KB]: 1023
% 1.84/1.42 % (6816)Time elapsed: 0.004 s
% 1.84/1.42 % (6816)Instructions burned: 4 (million)
% 1.84/1.42 % (6816)------------------------------
% 1.84/1.42 % (6816)------------------------------
% 1.84/1.43 % (6817)Instruction limit reached!
% 1.84/1.43 % (6817)------------------------------
% 1.84/1.43 % (6817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.43 % (6817)Termination reason: Unknown
% 1.84/1.43 % (6817)Termination phase: Saturation
% 1.84/1.43
% 1.84/1.43 % (6817)Memory used [KB]: 5756
% 1.84/1.43 % (6817)Time elapsed: 0.008 s
% 1.84/1.43 % (6817)Instructions burned: 19 (million)
% 1.84/1.43 % (6817)------------------------------
% 1.84/1.43 % (6817)------------------------------
% 1.84/1.43 % (6820)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/902Mi)
% 1.84/1.43 % (6820)Refutation not found, incomplete strategy
% 1.84/1.43 % (6820)------------------------------
% 1.84/1.43 % (6820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.43 % (6820)Termination reason: Refutation not found, incomplete strategy
% 1.84/1.43
% 1.84/1.43
% 1.84/1.43 % (6820)Memory used [KB]: 5628
% 1.84/1.43 % (6820)Time elapsed: 0.004 s
% 1.84/1.43 % (6820)Instructions burned: 7 (million)
% 1.84/1.43 % (6820)------------------------------
% 1.84/1.43 % (6820)------------------------------
% 1.84/1.43 % (6819)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/6Mi)
% 1.84/1.43 % (6823)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/21Mi)
% 1.84/1.44 % (6819)Instruction limit reached!
% 1.84/1.44 % (6819)------------------------------
% 1.84/1.44 % (6819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.44 % (6819)Termination reason: Unknown
% 1.84/1.44 % (6819)Termination phase: Property scanning
% 1.84/1.44 % (6824)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/5Mi)
% 1.84/1.44
% 1.84/1.44 % (6819)Memory used [KB]: 1023
% 1.84/1.44 % (6819)Time elapsed: 0.006 s
% 1.84/1.44 % (6819)Instructions burned: 6 (million)
% 1.84/1.44 % (6819)------------------------------
% 1.84/1.44 % (6819)------------------------------
% 1.84/1.44 % (6824)Instruction limit reached!
% 1.84/1.44 % (6824)------------------------------
% 1.84/1.44 % (6824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.44 % (6824)Termination reason: Unknown
% 1.84/1.44 % (6824)Termination phase: Property scanning
% 1.84/1.44
% 1.84/1.44 % (6824)Memory used [KB]: 1023
% 1.84/1.44 % (6824)Time elapsed: 0.004 s
% 1.84/1.44 % (6824)Instructions burned: 6 (million)
% 1.84/1.44 % (6824)------------------------------
% 1.84/1.44 % (6824)------------------------------
% 1.84/1.44 % (6825)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/6Mi)
% 1.84/1.44 % (6825)Instruction limit reached!
% 1.84/1.44 % (6825)------------------------------
% 1.84/1.44 % (6825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.44 % (6825)Termination reason: Unknown
% 1.84/1.44 % (6825)Termination phase: Saturation
% 1.84/1.44
% 1.84/1.44 % (6825)Memory used [KB]: 5500
% 1.84/1.44 % (6825)Time elapsed: 0.003 s
% 1.84/1.44 % (6825)Instructions burned: 7 (million)
% 1.84/1.44 % (6825)------------------------------
% 1.84/1.44 % (6825)------------------------------
% 1.84/1.45 % (6823)Instruction limit reached!
% 1.84/1.45 % (6823)------------------------------
% 1.84/1.45 % (6823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.45 % (6823)Termination reason: Unknown
% 1.84/1.45 % (6823)Termination phase: Saturation
% 1.84/1.45
% 1.84/1.45 % (6823)Memory used [KB]: 5628
% 1.84/1.45 % (6823)Time elapsed: 0.013 s
% 1.84/1.45 % (6823)Instructions burned: 21 (million)
% 1.84/1.45 % (6823)------------------------------
% 1.84/1.45 % (6823)------------------------------
% 1.84/1.45 % (6835)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/19Mi)
% 1.84/1.46 % (6834)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/779Mi)
% 1.84/1.46 % (6835)Instruction limit reached!
% 1.84/1.46 % (6835)------------------------------
% 1.84/1.46 % (6835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.46 % (6835)Termination reason: Unknown
% 1.84/1.46 % (6835)Termination phase: Saturation
% 1.84/1.46
% 1.84/1.46 % (6835)Memory used [KB]: 5628
% 1.84/1.46 % (6835)Time elapsed: 0.009 s
% 1.84/1.46 % (6835)Instructions burned: 19 (million)
% 1.84/1.46 % (6835)------------------------------
% 1.84/1.46 % (6835)------------------------------
% 1.84/1.46 % (6836)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/879Mi)
% 1.84/1.47 % (6805)First to succeed.
% 1.84/1.47 % (6793)Instruction limit reached!
% 1.84/1.47 % (6793)------------------------------
% 1.84/1.47 % (6793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.47 % (6793)Termination reason: Unknown
% 1.84/1.47 % (6793)Termination phase: Saturation
% 1.84/1.47
% 1.84/1.47 % (6793)Memory used [KB]: 6396
% 1.84/1.47 % (6793)Time elapsed: 0.093 s
% 1.84/1.47 % (6793)Instructions burned: 183 (million)
% 1.84/1.47 % (6793)------------------------------
% 1.84/1.47 % (6793)------------------------------
% 1.84/1.47 % (6833)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6648 for (2999ds/377Mi)
% 1.84/1.47 % (6805)Refutation found. Thanks to Tanya!
% 1.84/1.47 % SZS status Theorem for DTF2THF_6648
% 1.84/1.47 % SZS output start Proof for DTF2THF_6648
% 1.84/1.47 thf(func_def_0, type, in: $i > $i > $o).
% 1.84/1.47 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.84/1.47 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.84/1.47 thf(func_def_4, type, subset: $i > $i > $o).
% 1.84/1.47 thf(func_def_5, type, kpair: $i > $i > $i).
% 1.84/1.47 thf(func_def_6, type, cartprod: $i > $i > $i).
% 1.84/1.47 thf(func_def_7, type, singleton: $i > $o).
% 1.84/1.47 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 1.84/1.47 thf(func_def_11, type, breln: $i > $i > $i > $o).
% 1.84/1.47 thf(func_def_12, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.84/1.47 thf(func_def_16, type, func: $i > $i > $i > $o).
% 1.84/1.47 thf(func_def_34, type, ph1: !>[X0: $tType]:(X0)).
% 1.84/1.47 thf(func_def_37, type, sK4: $i > $i).
% 1.84/1.47 thf(f409,plain,(
% 1.84/1.47 $false),
% 1.84/1.47 inference(avatar_sat_refutation,[status(thm)],[f249,f360,f408])).
% 1.84/1.47 thf(f408,plain,(
% 1.84/1.47 ~spl0_1),
% 1.84/1.47 inference(avatar_contradiction_clause,[status(thm)],[f407])).
% 1.84/1.47 thf(f407,plain,(
% 1.84/1.47 $false | ~spl0_1),
% 1.84/1.47 inference(trivial_inequality_removal,[status(thm)],[f406])).
% 1.84/1.47 thf(f406,plain,(
% 1.84/1.47 ($true = $false) | ~spl0_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f405])).
% 1.84/1.47 thf(f405,plain,(
% 1.84/1.47 ($true = (~ $true)) | ~spl0_1),
% 1.84/1.47 inference(forward_demodulation,[status(thm)],[f402,f139])).
% 1.84/1.47 thf(f139,plain,(
% 1.84/1.47 ((in @ (sK4 @ sK5) @ sK2) = $true)),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f131])).
% 1.84/1.47 thf(f131,plain,(
% 1.84/1.47 ($true = ($true => (in @ (sK4 @ sK5) @ sK2)))),
% 1.84/1.47 inference(superposition,[status(thm)],[f121,f126])).
% 1.84/1.47 thf(f126,plain,(
% 1.84/1.47 ((in @ sK5 @ sK3) = $true)),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.84/1.47 thf(f124,plain,(
% 1.84/1.47 (((in @ sK5 @ sK3) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y2 : $i]: (= @ (sK4 @ Y2)))))))) & (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y2 : $i]: (= @ (sK4 @ Y2)))))))))))) = $false)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f123])).
% 1.84/1.47 thf(f123,plain,(
% 1.84/1.47 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3)))))))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3))))))))))))) @ sK5))),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f114])).
% 1.84/1.47 thf(f114,plain,(
% 1.84/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3)))))))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3)))))))))))))))),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.84/1.47 thf(f113,plain,(
% 1.84/1.47 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (sK4 @ Y0) @ sK2)))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3)))))))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3))))))))))))))) = $false)),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f112])).
% 1.84/1.47 thf(f112,plain,(
% 1.84/1.47 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (sK4 @ Y0) @ sK2)))) => ($true & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3)))))))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3)))))))))))))))) = $false)),
% 1.84/1.47 inference(forward_demodulation,[status(thm)],[f111,f87])).
% 1.84/1.47 thf(f87,plain,(
% 1.84/1.47 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (subset @ (dpsetconstr @ X3 @ X1 @ X2) @ (cartprod @ X3 @ X1)))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.84/1.47 thf(f86,plain,(
% 1.84/1.47 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (subset @ (dpsetconstr @ Y0 @ X1 @ X2) @ (cartprod @ Y0 @ X1))) @ X3))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f85])).
% 1.84/1.47 thf(f85,plain,(
% 1.84/1.47 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (subset @ (dpsetconstr @ Y0 @ X1 @ X2) @ (cartprod @ Y0 @ X1)))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.84/1.47 thf(f84,plain,(
% 1.84/1.47 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ X1 @ Y0) @ (cartprod @ Y1 @ X1))))) @ X2))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f83])).
% 1.84/1.47 thf(f83,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ X1 @ Y0) @ (cartprod @ Y1 @ X1)))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.84/1.47 thf(f82,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0))))))) @ X1))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f77])).
% 1.84/1.47 thf(f77,plain,(
% 1.84/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))))),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.84/1.47 thf(f61,plain,(
% 1.84/1.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y2)) => (Y2 @ Y3 @ Y4)))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))) @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))))))))))))))))))) = $false)),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.84/1.47 thf(f48,plain,(
% 1.84/1.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y3))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y2)) => (Y2 @ Y3 @ Y4)))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))) @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6))))))))))))))))))))))))) = $false)),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.84/1.47 thf(f45,plain,(
% 1.84/1.47 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y3))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y2)) => (Y2 @ Y3 @ Y4)))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))) @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))))))))))))))))))))))),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f44])).
% 1.84/1.47 thf(f44,plain,(
% 1.84/1.47 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y3))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y2)) => (Y2 @ Y3 @ Y4)))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))) @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6))))))))))))))))))))))))))))),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.84/1.47 thf(f43,plain,(
% 1.84/1.47 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y0 @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y3 @ Y4)))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))))))))))),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f37,f42,f33,f39,f34,f41])).
% 1.84/1.47 thf(f41,plain,(
% 1.84/1.47 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f36,f31,f40])).
% 1.84/1.47 thf(f40,plain,(
% 1.84/1.47 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f32,f35])).
% 1.84/1.47 thf(f35,plain,(
% 1.84/1.47 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f27])).
% 1.84/1.47 thf(f27,plain,(
% 1.84/1.47 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f26])).
% 1.84/1.47 thf(f26,plain,(
% 1.84/1.47 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.84/1.47 inference(rectify,[status(thm)],[f1])).
% 1.84/1.47 thf(f1,axiom,(
% 1.84/1.47 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',singleton)).
% 1.84/1.47 thf(f32,plain,(
% 1.84/1.47 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f15])).
% 1.84/1.47 thf(f15,plain,(
% 1.84/1.47 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f14])).
% 1.84/1.47 thf(f14,plain,(
% 1.84/1.47 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 1.84/1.47 inference(rectify,[status(thm)],[f2])).
% 1.84/1.47 thf(f2,axiom,(
% 1.84/1.47 (ex1 = (^[X0 : $i, X2 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X2 @ X1))))))),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',ex1)).
% 1.84/1.47 thf(f31,plain,(
% 1.84/1.47 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f29])).
% 1.84/1.47 thf(f29,plain,(
% 1.84/1.47 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f28])).
% 1.84/1.47 thf(f28,plain,(
% 1.84/1.47 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 1.84/1.47 inference(rectify,[status(thm)],[f4])).
% 1.84/1.47 thf(f4,axiom,(
% 1.84/1.47 ((^[X0 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X0 @ X4))) = breln)),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',breln)).
% 1.84/1.47 thf(f36,plain,(
% 1.84/1.47 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f13])).
% 1.84/1.47 thf(f13,plain,(
% 1.84/1.47 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f12])).
% 1.84/1.47 thf(f12,plain,(
% 1.84/1.47 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))) = func)),
% 1.84/1.47 inference(rectify,[status(thm)],[f8])).
% 1.84/1.47 thf(f8,axiom,(
% 1.84/1.47 ((^[X0 : $i, X4 : $i, X8 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ex1 @ X4 @ (^[X3 : $i] : (in @ (kpair @ X1 @ X3) @ X8)))) & (breln @ X0 @ X4 @ X8))) = func)),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',func)).
% 1.84/1.47 thf(f34,plain,(
% 1.84/1.47 (dpsetconstrERa = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y3 @ Y4)))))))))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.47 thf(f19,plain,(
% 1.84/1.47 (dpsetconstrERa = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y3 @ Y4)))))))))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f18])).
% 1.84/1.47 thf(f18,plain,(
% 1.84/1.47 (dpsetconstrERa = ! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : ((in @ X0 @ X3) => ! [X4 : $i] : ((in @ X4 @ X2) => ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X2 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (X1 @ X0 @ X4)))))),
% 1.84/1.47 inference(rectify,[status(thm)],[f7])).
% 1.84/1.47 thf(f7,axiom,(
% 1.84/1.47 (dpsetconstrERa = ! [X1 : $i,X2 : $i > $i > $o,X4 : $i,X0 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => ((in @ (kpair @ X1 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X7 : $i] : (X2 @ X6 @ X7)))) => (X2 @ X1 @ X3)))))),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',dpsetconstrERa)).
% 1.84/1.47 thf(f39,plain,(
% 1.84/1.47 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y0 @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f38,f31])).
% 1.84/1.47 thf(f38,plain,(
% 1.84/1.47 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y2 @ Y0 @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f23])).
% 1.84/1.47 thf(f23,plain,(
% 1.84/1.47 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y2 @ Y0 @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f22])).
% 1.84/1.47 thf(f22,plain,(
% 1.84/1.47 (! [X0 : $i,X1 : $i > $i > $o,X2 : $i] : (breln @ X0 @ X2 @ (dpsetconstr @ X0 @ X2 @ (^[X3 : $i, X4 : $i] : (X1 @ X3 @ X4)))) = setOfPairsIsBReln)),
% 1.84/1.47 inference(rectify,[status(thm)],[f6])).
% 1.84/1.47 thf(f6,axiom,(
% 1.84/1.47 (! [X0 : $i,X2 : $i > $i > $o,X4 : $i] : (breln @ X0 @ X4 @ (dpsetconstr @ X0 @ X4 @ (^[X1 : $i, X3 : $i] : (X2 @ X1 @ X3)))) = setOfPairsIsBReln)),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',setOfPairsIsBReln)).
% 1.84/1.47 thf(f33,plain,(
% 1.84/1.47 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f25])).
% 1.84/1.47 thf(f25,plain,(
% 1.84/1.47 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f24])).
% 1.84/1.47 thf(f24,plain,(
% 1.84/1.47 (! [X0 : $i > $i > $o,X1 : $i,X2 : $i,X3 : $i] : ((in @ X1 @ X3) => ! [X4 : $i] : ((in @ X4 @ X2) => ((X0 @ X1 @ X4) => (in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X3 @ X2 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6))))))) = dpsetconstrI)),
% 1.84/1.47 inference(rectify,[status(thm)],[f5])).
% 1.84/1.47 thf(f5,axiom,(
% 1.84/1.47 (! [X2 : $i > $i > $o,X1 : $i,X4 : $i,X0 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => ((X2 @ X1 @ X3) => (in @ (kpair @ X1 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X7 : $i] : (X2 @ X6 @ X7))))))) = dpsetconstrI)),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',dpsetconstrI)).
% 1.84/1.47 thf(f42,plain,(
% 1.84/1.47 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.84/1.47 inference(definition_unfolding,[status(thm)],[f30,f40])).
% 1.84/1.47 thf(f30,plain,(
% 1.84/1.47 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f21])).
% 1.84/1.47 thf(f21,plain,(
% 1.84/1.47 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f20])).
% 1.84/1.47 thf(f20,plain,(
% 1.84/1.47 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X1) => ((X0 @ X3) => (X2 = X3))) => (ex1 @ X1 @ (^[X4 : $i] : (X0 @ X4)))))) = ex1I)),
% 1.84/1.47 inference(rectify,[status(thm)],[f3])).
% 1.84/1.47 thf(f3,axiom,(
% 1.84/1.47 (! [X2 : $i > $o,X0 : $i,X1 : $i] : ((in @ X1 @ X0) => ((X2 @ X1) => (! [X3 : $i] : ((in @ X3 @ X0) => ((X2 @ X3) => (X1 = X3))) => (ex1 @ X0 @ (^[X3 : $i] : (X2 @ X3)))))) = ex1I)),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',ex1I)).
% 1.84/1.47 thf(f37,plain,(
% 1.84/1.47 ($true = (~ (ex1I => (dpsetconstrI => (setOfPairsIsBReln => (dpsetconstrERa => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (func @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))))))))))),
% 1.84/1.47 inference(cnf_transformation,[status(thm)],[f17])).
% 1.84/1.47 thf(f17,plain,(
% 1.84/1.47 ($true = (~ (ex1I => (dpsetconstrI => (setOfPairsIsBReln => (dpsetconstrERa => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (func @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))))))))))),
% 1.84/1.47 inference(fool_elimination,[status(thm)],[f16])).
% 1.84/1.47 thf(f16,plain,(
% 1.84/1.47 ~(ex1I => (dpsetconstrI => (setOfPairsIsBReln => (dpsetconstrERa => ! [X0 : $i > $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X0 @ X3) @ X2)) => (func @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[X4 : $i, X5 : $i] : (((X0 @ X4) = X5))))))))))),
% 1.84/1.47 inference(rectify,[status(thm)],[f10])).
% 1.84/1.47 thf(f10,negated_conjecture,(
% 1.84/1.47 ~(ex1I => (dpsetconstrI => (setOfPairsIsBReln => (dpsetconstrERa => ! [X9 : $i > $i,X0 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ (X9 @ X1) @ X4)) => (func @ X0 @ X4 @ (dpsetconstr @ X0 @ X4 @ (^[X1 : $i, X3 : $i] : (((X9 @ X1) = X3))))))))))),
% 1.84/1.47 inference(negated_conjecture,[status(cth)],[f9])).
% 1.84/1.47 thf(f9,conjecture,(
% 1.84/1.47 ex1I => (dpsetconstrI => (setOfPairsIsBReln => (dpsetconstrERa => ! [X9 : $i > $i,X0 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ (X9 @ X1) @ X4)) => (func @ X0 @ X4 @ (dpsetconstr @ X0 @ X4 @ (^[X1 : $i, X3 : $i] : (((X9 @ X1) = X3)))))))))),
% 1.84/1.47 file('/export/starexec/sandbox2/tmp/tmp.sTS4XQcRQH/DTF2THF_6648.p',lamProp)).
% 1.84/1.47 thf(f111,plain,(
% 1.84/1.47 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (sK4 @ Y0) @ sK2)))) => ((subset @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0)))) @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3)))))))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y3 : $i]: (= @ (sK4 @ Y3)))))))))))))))) = $false)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f110])).
% 1.84/1.47 thf(f110,plain,(
% 1.84/1.47 (((^[Y0 : $i > $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (in @ (Y0 @ Y1) @ sK2)))) => ((subset @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (Y0 @ Y1)))) @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))))))) & (in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4))))))))))))))))) @ sK4) = $false)),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f109])).
% 1.84/1.47 thf(f109,plain,(
% 1.84/1.47 ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (in @ (Y0 @ Y1) @ sK2)))) => ((subset @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (Y0 @ Y1)))) @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))))))) & (in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))))))))))))))))) = $false)),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.84/1.47 thf(f108,plain,(
% 1.84/1.47 ($false = ((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (Y1 @ Y2) @ sK2)))) => ((subset @ (dpsetconstr @ Y0 @ sK2 @ (^[Y2 : $i]: (= @ (Y1 @ Y2)))) @ (cartprod @ Y0 @ sK2)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ sK2 @ (^[Y5 : $i]: (= @ (Y1 @ Y5)))))))) & (in @ Y3 @ (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ sK2 @ (^[Y5 : $i]: (= @ (Y1 @ Y5))))))))))))))))))) @ sK3))),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f107])).
% 1.84/1.47 thf(f107,plain,(
% 1.84/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (Y1 @ Y2) @ sK2)))) => ((subset @ (dpsetconstr @ Y0 @ sK2 @ (^[Y2 : $i]: (= @ (Y1 @ Y2)))) @ (cartprod @ Y0 @ sK2)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ sK2 @ (^[Y5 : $i]: (= @ (Y1 @ Y5)))))))) & (in @ Y3 @ (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ sK2 @ (^[Y5 : $i]: (= @ (Y1 @ Y5)))))))))))))))))))))),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f106])).
% 1.84/1.47 thf(f106,plain,(
% 1.84/1.47 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))) @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6))))))))))))))))))))) @ sK2) = $false)),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f91])).
% 1.84/1.47 thf(f91,plain,(
% 1.84/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))) @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))))))))))))))))))),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.84/1.47 thf(f76,plain,(
% 1.84/1.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y2)) => (Y2 @ Y3 @ Y4)))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))) @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6)))))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y6 : $i]: (= @ (Y2 @ Y6))))))))))))))))))))))) = $false)),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.84/1.47 thf(f121,plain,(
% 1.84/1.47 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (in @ (sK4 @ X1) @ sK2)) = $true)) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.84/1.47 thf(f120,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (sK4 @ Y0) @ sK2))) @ X1))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f115])).
% 1.84/1.47 thf(f115,plain,(
% 1.84/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (sK4 @ Y0) @ sK2)))))),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.84/1.47 thf(f402,plain,(
% 1.84/1.47 ($true = (~ (in @ (sK4 @ sK5) @ sK2))) | ~spl0_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f401])).
% 1.84/1.47 thf(f401,plain,(
% 1.84/1.47 ($true = ((in @ (sK4 @ sK5) @ sK2) => $false)) | ~spl0_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f400])).
% 1.84/1.47 thf(f400,plain,(
% 1.84/1.47 (((in @ (sK4 @ sK5) @ sK2) => (~ $true)) = $true) | ~spl0_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f399])).
% 1.84/1.47 thf(f399,plain,(
% 1.84/1.47 ($true = ((in @ (sK4 @ sK5) @ sK2) => (~ ((sK4 @ sK5) = (sK4 @ sK5))))) | ~spl0_1),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f398])).
% 1.84/1.47 thf(f398,plain,(
% 1.84/1.47 (((in @ (sK4 @ sK5) @ sK2) => (((sK4 @ sK5) = (sK4 @ sK5)) => $false)) = $true) | ~spl0_1),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f369])).
% 1.84/1.47 thf(f369,plain,(
% 1.84/1.47 (((in @ (sK4 @ sK5) @ sK2) => (((^[Y0 : $i]: (= @ (sK4 @ Y0))) @ sK5 @ (sK4 @ sK5)) => $false)) = $true) | ~spl0_1),
% 1.84/1.47 inference(superposition,[status(thm)],[f159,f245])).
% 1.84/1.47 thf(f245,plain,(
% 1.84/1.47 ($false = (in @ (kpair @ sK5 @ (sK4 @ sK5)) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0)))))) | ~spl0_1),
% 1.84/1.47 inference(avatar_component_clause,[status(thm)],[f244])).
% 1.84/1.47 thf(f244,definition,(
% 1.84/1.47 spl0_1 <=> ($false = (in @ (kpair @ sK5 @ (sK4 @ sK5)) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0))))))),
% 1.84/1.47 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.84/1.47 thf(f159,plain,(
% 1.84/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i > $i > $o] : (($true = ((in @ X2 @ X0) => ((X1 @ sK5 @ X2) => (in @ (kpair @ sK5 @ X2) @ (dpsetconstr @ sK3 @ X0 @ X1)))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f156])).
% 1.84/1.47 thf(f156,plain,(
% 1.84/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X0) => ((X1 @ sK5 @ Y0) => (in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1))))) @ X2))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f136])).
% 1.84/1.47 thf(f136,plain,(
% 1.84/1.47 ( ! [X0 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X0) => ((X1 @ sK5 @ Y0) => (in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1)))))))) )),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f133])).
% 1.84/1.47 thf(f133,plain,(
% 1.84/1.47 ( ! [X0 : $i,X1 : $i > $i > $o] : (($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X0) => ((X1 @ sK5 @ Y0) => (in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1))))))))) )),
% 1.84/1.47 inference(superposition,[status(thm)],[f74,f126])).
% 1.84/1.47 thf(f74,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = ((in @ X3 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X4 @ X3 @ Y0) => (in @ (kpair @ X3 @ Y0) @ (dpsetconstr @ X1 @ X2 @ X4))))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.84/1.47 thf(f73,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: ((in @ X3 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((Y0 @ X3 @ Y1) => (in @ (kpair @ X3 @ Y1) @ (dpsetconstr @ X1 @ X2 @ Y0)))))))) @ X4))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f72])).
% 1.84/1.47 thf(f72,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((in @ X3 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((Y0 @ X3 @ Y1) => (in @ (kpair @ X3 @ Y1) @ (dpsetconstr @ X1 @ X2 @ Y0))))))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.84/1.47 thf(f71,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((Y1 @ Y0 @ Y2) => (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ X1 @ X2 @ Y1)))))))))) @ X3))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f70])).
% 1.84/1.47 thf(f70,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((Y1 @ Y0 @ Y2) => (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ X1 @ X2 @ Y1))))))))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.84/1.47 thf(f69,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y1 @ Y3) => (in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ X1 @ Y0 @ Y2)))))))))))) @ X2))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f68])).
% 1.84/1.47 thf(f68,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y1 @ Y3) => (in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ X1 @ Y0 @ Y2))))))))))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.84/1.47 thf(f67,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y3)))))))))))))) @ X1))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f62])).
% 1.84/1.47 thf(f62,plain,(
% 1.84/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y3))))))))))))))))),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.84/1.47 thf(f360,plain,(
% 1.84/1.47 ~spl0_2),
% 1.84/1.47 inference(avatar_contradiction_clause,[status(thm)],[f359])).
% 1.84/1.47 thf(f359,plain,(
% 1.84/1.47 $false | ~spl0_2),
% 1.84/1.47 inference(trivial_inequality_removal,[status(thm)],[f358])).
% 1.84/1.47 thf(f358,plain,(
% 1.84/1.47 ($true = $false) | ~spl0_2),
% 1.84/1.47 inference(forward_demodulation,[status(thm)],[f357,f295])).
% 1.84/1.47 thf(f295,plain,(
% 1.84/1.47 (((sK4 @ sK5) = sK6) = $false) | ~spl0_2),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f294])).
% 1.84/1.47 thf(f294,plain,(
% 1.84/1.47 (($true => ((sK4 @ sK5) = sK6)) = $false) | ~spl0_2),
% 1.84/1.47 inference(backward_demodulation,[status(thm)],[f267,f292])).
% 1.84/1.47 thf(f292,plain,(
% 1.84/1.47 ($true = (in @ (kpair @ sK5 @ sK6) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0)))))) | ~spl0_2),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f267])).
% 1.84/1.47 thf(f267,plain,(
% 1.84/1.47 (((in @ (kpair @ sK5 @ sK6) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0))))) => ((sK4 @ sK5) = sK6)) = $false) | ~spl0_2),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f263])).
% 1.84/1.47 thf(f263,plain,(
% 1.84/1.47 ($false = ((in @ sK6 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0))))) => ((sK4 @ sK5) = sK6)))) | ~spl0_2),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f261])).
% 1.84/1.47 thf(f261,plain,(
% 1.84/1.47 (((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => ((sK4 @ sK5) = Y0)))) @ sK6) = $false) | ~spl0_2),
% 1.84/1.47 inference(sigma_clausification,[status(thm)],[f255])).
% 1.84/1.47 thf(f255,plain,(
% 1.84/1.47 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => ((sK4 @ sK5) = Y0))))) = $false) | ~spl0_2),
% 1.84/1.47 inference(not_proxy_clausification,[status(thm)],[f248])).
% 1.84/1.47 thf(f248,plain,(
% 1.84/1.47 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => ((sK4 @ sK5) = Y0)))))) = $true) | ~spl0_2),
% 1.84/1.47 inference(avatar_component_clause,[status(thm)],[f247])).
% 1.84/1.47 thf(f247,definition,(
% 1.84/1.47 spl0_2 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => ((sK4 @ sK5) = Y0)))))) = $true)),
% 1.84/1.47 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.84/1.47 thf(f357,plain,(
% 1.84/1.47 (((sK4 @ sK5) = sK6) = $true) | ~spl0_2),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f356])).
% 1.84/1.47 thf(f356,plain,(
% 1.84/1.47 ($true = ($true => ((sK4 @ sK5) = sK6))) | ~spl0_2),
% 1.84/1.47 inference(forward_demodulation,[status(thm)],[f355,f268])).
% 1.84/1.47 thf(f268,plain,(
% 1.84/1.47 ($true = (in @ sK6 @ sK2)) | ~spl0_2),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f263])).
% 1.84/1.47 thf(f355,plain,(
% 1.84/1.47 ($true = ((in @ sK6 @ sK2) => ((sK4 @ sK5) = sK6))) | ~spl0_2),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f354])).
% 1.84/1.47 thf(f354,plain,(
% 1.84/1.47 ($true = ((in @ sK6 @ sK2) => ($true => ((sK4 @ sK5) = sK6)))) | ~spl0_2),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f332])).
% 1.84/1.47 thf(f332,plain,(
% 1.84/1.47 ($true = ((in @ sK6 @ sK2) => ($true => ((^[Y0 : $i]: (= @ (sK4 @ Y0))) @ sK5 @ sK6)))) | ~spl0_2),
% 1.84/1.47 inference(superposition,[status(thm)],[f170,f292])).
% 1.84/1.47 thf(f170,plain,(
% 1.84/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i > $i > $o] : (($true = ((in @ X2 @ X0) => ((in @ (kpair @ sK5 @ X2) @ (dpsetconstr @ sK3 @ X0 @ X1)) => (X1 @ sK5 @ X2))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f168])).
% 1.84/1.47 thf(f168,plain,(
% 1.84/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i > $i > $o] : ((((^[Y0 : $i]: ((in @ Y0 @ X0) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1)) => (X1 @ sK5 @ Y0)))) @ X2) = $true)) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f138])).
% 1.84/1.47 thf(f138,plain,(
% 1.84/1.47 ( ! [X0 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X0) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1)) => (X1 @ sK5 @ Y0))))))) )),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f132])).
% 1.84/1.47 thf(f132,plain,(
% 1.84/1.47 ( ! [X0 : $i,X1 : $i > $i > $o] : (($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X0) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1)) => (X1 @ sK5 @ Y0)))))))) )),
% 1.84/1.47 inference(superposition,[status(thm)],[f104,f126])).
% 1.84/1.47 thf(f104,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i] : (($true = ((in @ X4 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X4 @ Y0) @ (dpsetconstr @ X1 @ X2 @ X3)) => (X3 @ X4 @ Y0)))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f103])).
% 1.84/1.47 thf(f103,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ X1 @ X2 @ X3)) => (X3 @ Y0 @ Y1))))))) @ X4))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f102])).
% 1.84/1.47 thf(f102,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ X1 @ X2 @ X3)) => (X3 @ Y0 @ Y1)))))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.84/1.47 thf(f101,plain,(
% 1.84/1.47 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ X1 @ X2 @ Y0)) => (Y0 @ Y1 @ Y2))))))))) @ X3))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f100])).
% 1.84/1.47 thf(f100,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ X1 @ X2 @ Y0)) => (Y0 @ Y1 @ Y2)))))))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f99])).
% 1.84/1.47 thf(f99,plain,(
% 1.84/1.47 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ (dpsetconstr @ X1 @ Y0 @ Y1)) => (Y1 @ Y2 @ Y3))))))))))) @ X2))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f98])).
% 1.84/1.47 thf(f98,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ (dpsetconstr @ X1 @ Y0 @ Y1)) => (Y1 @ Y2 @ Y3)))))))))))))) )),
% 1.84/1.47 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.84/1.47 thf(f97,plain,(
% 1.84/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y2)) => (Y2 @ Y3 @ Y4))))))))))))) @ X1))) )),
% 1.84/1.47 inference(pi_clausification,[status(thm)],[f92])).
% 1.84/1.47 thf(f92,plain,(
% 1.84/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y0 @ Y1 @ Y2)) => (Y2 @ Y3 @ Y4)))))))))))))))),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.84/1.47 thf(f249,plain,(
% 1.84/1.47 spl0_1 | spl0_2),
% 1.84/1.47 inference(avatar_split_clause,[status(thm)],[f240,f247,f244])).
% 1.84/1.47 thf(f240,plain,(
% 1.84/1.47 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => ((sK4 @ sK5) = Y0)))))) = $true) | ($false = (in @ (kpair @ sK5 @ (sK4 @ sK5)) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0))))))),
% 1.84/1.47 inference(binary_proxy_clausification,[status(thm)],[f196])).
% 1.84/1.47 thf(f196,plain,(
% 1.84/1.47 ($true = ((in @ (kpair @ sK5 @ (sK4 @ sK5)) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => ((sK4 @ sK5) = Y0))))))))),
% 1.84/1.47 inference(boolean_simplification,[status(thm)],[f195])).
% 1.84/1.47 thf(f195,plain,(
% 1.84/1.47 ($true = ($true => ((in @ (kpair @ sK5 @ (sK4 @ sK5)) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => ((sK4 @ sK5) = Y0)))))))))),
% 1.84/1.48 inference(superposition,[status(thm)],[f154,f139])).
% 1.84/1.48 thf(f154,plain,(
% 1.84/1.48 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK2) => ((in @ (kpair @ sK5 @ X0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => (X0 = Y0)))))))))) )),
% 1.84/1.48 inference(boolean_simplification,[status(thm)],[f153])).
% 1.84/1.48 thf(f153,plain,(
% 1.84/1.48 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK2) => ((in @ (kpair @ sK5 @ X0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: (= @ (sK4 @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1))))) => (X0 = Y0))))) => $false))))) )),
% 1.84/1.48 inference(beta_eta_normalization,[status(thm)],[f152])).
% 1.84/1.48 thf(f152,plain,(
% 1.84/1.48 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK2) => (((^[Y0 : $i]: (in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y1 : $i]: (= @ (sK4 @ Y1)))))) @ X0) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (((^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y2 : $i]: (= @ (sK4 @ Y2)))))) @ Y0) => (X0 = Y0))))) => $false))))) )),
% 1.84/1.48 inference(superposition,[status(thm)],[f59,f125])).
% 1.84/1.48 thf(f125,plain,(
% 1.84/1.48 ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y2 : $i]: (= @ (sK4 @ Y2)))))))) & (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y2 : $i]: (= @ (sK4 @ Y2))))))))))))),
% 1.84/1.48 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.84/1.48 thf(f59,plain,(
% 1.84/1.48 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X1 @ X2) => ((X3 @ X1) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X3 @ Y0) => (X1 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X2 @ X3)) & (in @ Y0 @ (dsetconstr @ X2 @ X3)))))))))) )),
% 1.84/1.48 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.84/1.48 thf(f58,plain,(
% 1.84/1.48 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((Y0 @ Y1) => (X1 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ Y0)) & (in @ Y1 @ (dsetconstr @ X2 @ Y0))))))))) @ X3))) )),
% 1.84/1.48 inference(pi_clausification,[status(thm)],[f57])).
% 1.84/1.48 thf(f57,plain,(
% 1.84/1.48 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((Y0 @ Y1) => (X1 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ Y0)) & (in @ Y1 @ (dsetconstr @ X2 @ Y0)))))))))))) )),
% 1.84/1.48 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.84/1.48 thf(f56,plain,(
% 1.84/1.48 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (X1 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))))))))) @ X2))) )),
% 1.84/1.48 inference(pi_clausification,[status(thm)],[f55])).
% 1.84/1.48 thf(f55,plain,(
% 1.84/1.48 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (X1 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y2 @ (dsetconstr @ Y0 @ Y1)))))))))))) = $true)) )),
% 1.84/1.48 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.84/1.48 thf(f54,plain,(
% 1.84/1.48 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y2))))))))))))) @ X1) = $true)) )),
% 1.84/1.48 inference(pi_clausification,[status(thm)],[f49])).
% 1.84/1.48 thf(f49,plain,(
% 1.84/1.48 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y2)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y2)))))))))))))))),
% 1.84/1.48 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.84/1.48 % SZS output end Proof for DTF2THF_6648
% 1.84/1.48 % (6805)------------------------------
% 1.84/1.48 % (6805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.48 % (6805)Termination reason: Refutation
% 1.84/1.48
% 1.84/1.48 % (6805)Memory used [KB]: 6652
% 1.84/1.48 % (6805)Time elapsed: 0.077 s
% 1.84/1.48 % (6805)Instructions burned: 194 (million)
% 1.84/1.48 % (6805)------------------------------
% 1.84/1.48 % (6805)------------------------------
% 1.84/1.48 % (6792)Success in time 0.094 s
%------------------------------------------------------------------------------