%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU701^2 : 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 : n022.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 09:36:30 AM UTC 2026
% Result : Theorem 1.69s 1.43s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 10
% Syntax : Number of formulae : 141 ( 97 unt; 0 typ; 3 def)
% Number of atoms : 1575 ( 415 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 2627 ( 153 ~; 127 |; 137 &;1552 @)
% ( 5 <=>; 365 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 19 con; 0-2 aty)
% ( 288 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 494 ( 390 ^; 104 !; 0 ?; 494 :)
% 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_27,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f830,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f642,f703,f733,f829]) ).
thf(f829,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f828]) ).
thf(f828,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f827]) ).
thf(f827,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f826,f820]) ).
thf(f820,plain,
( ( ( in @ sK7 @ ( setadjoin @ sK7 @ emptyset ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f803,f807]) ).
thf(f807,plain,
( ( sK7 = sK9 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f806]) ).
thf(f806,plain,
( ( ( sK7 = sK9 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f805]) ).
thf(f805,plain,
( ( ( $false
| ( sK7 = sK9 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f804]) ).
thf(f804,plain,
( ( ( ( ( sK2 = sK9 )
& $false )
| ( sK7 = sK9 ) )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f801,f183]) ).
thf(f183,plain,
sK4 = $false,
inference(not_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
( ( ~ sK4 ) = $true ),
inference(binary_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ( ~ sK4
=> ( ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( ( sK7 = Y0 )
& ~ sK4 ) ) )
= ( setadjoin @ sK7 @ emptyset ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
( $false
= ( ( in @ sK7 @ sK3 )
=> ( ~ sK4
=> ( ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( ( sK7 = Y0 )
& ~ sK4 ) ) )
= ( setadjoin @ sK7 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f150]) ).
thf(f150,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ~ sK4
=> ( ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( ( Y0 = Y1 )
& ~ sK4 ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
@ sK7 )
= $false ),
inference(sigma_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ~ sK4
=> ( ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( ( Y0 = Y1 )
& ~ sK4 ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( ( ( in @ sK2 @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ~ sK4
=> ( ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( ( Y0 = Y1 )
& ~ sK4 ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
= ( ^ [Y0: $o] :
( ( in @ sK2 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ~ Y0
=> ( ( dsetconstr @ sK3
@ ^ [Y2: $i] :
( ( ( sK2 = Y2 )
& Y0 )
| ( ( Y1 = Y2 )
& ~ Y0 ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( !! @ $o
@ ^ [Y0: $o] :
( ( in @ sK2 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ~ Y0
=> ( ( dsetconstr @ sK3
@ ^ [Y2: $i] :
( ( ( sK2 = Y2 )
& Y0 )
| ( ( Y1 = Y2 )
& ~ Y0 ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
( ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ Y1
=> ( ( dsetconstr @ Y0
@ ^ [Y3: $i] :
( ( ( sK2 = Y3 )
& Y1 )
| ( ( Y2 = Y3 )
& ~ Y1 ) ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ sK2 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ Y1
=> ( ( dsetconstr @ Y0
@ ^ [Y3: $i] :
( ( ( sK2 = Y3 )
& Y1 )
| ( ( Y2 = Y3 )
& ~ Y1 ) ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f82]) ).
thf(f82,plain,
( $false
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f66,f81]) ).
thf(f81,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f49,f61]) ).
thf(f61,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ~ ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ~ ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f28,f24,f26,f29,f27,f30,f25]) ).
thf(f25,plain,
( iffalseProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( iffalseProp1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ~ X0
=> ( in @ X3
@ ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X0 )
| ( X0
& ( X1 = X4 ) ) ) ) ) ) ) )
= iffalseProp1 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ X0
@ ^ [X5: $i] :
( ( ( X3 = X5 )
& ~ X1 )
| ( X1
& ( X2 = X5 ) ) ) ) ) ) ) )
= iffalseProp1 ),
file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',iffalseProp1) ).
thf(f30,plain,
( in__Cong
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( in__Cong
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y3 = Y2 )
=> ( ( in @ Y3 @ Y1 )
= ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
<=> ( in @ X3 @ X1 ) ) ) )
= in__Cong ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X4: $i,X0: $i] :
( ( ( X0 = X4 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( in @ X3 @ X4 )
<=> ( in @ X2 @ X0 ) ) ) )
= in__Cong ),
file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',in__Cong) ).
thf(f27,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( eqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= eqinunit ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i,X3: $i] :
( ( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
= eqinunit ),
file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',eqinunit) ).
thf(f29,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X3: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) )
= uniqinunit ),
file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',uniqinunit) ).
thf(f26,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ X1 ) )
=> ( X0 = X1 ) ) )
= setext ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X4: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X4 ) ) )
= setext ),
file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',setext) ).
thf(f24,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( dsetconstrER
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X0 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',dsetconstrER) ).
thf(f28,plain,
( ( ~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iffalseProp1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iffalseProp1
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ Y2
=> ( ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y0 = Y4 )
& Y2 )
| ( ( Y3 = Y4 )
& ~ Y2 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iffalseProp1
=> ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ X0
=> ( ( dsetconstr @ X1
@ ^ [X4: $i] :
( ( ~ X0
& ( X3 = X4 ) )
| ( X0
& ( X2 = X4 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iffalseProp1
=> ! [X1: $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( dsetconstr @ X0
@ ^ [X5: $i] :
( ( ~ X1
& ( X3 = X5 ) )
| ( X1
& ( X2 = X5 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iffalseProp1
=> ! [X1: $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( dsetconstr @ X0
@ ^ [X5: $i] :
( ( ~ X1
& ( X3 = X5 ) )
| ( X1
& ( X2 = X5 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',iffalseProp2) ).
thf(f801,plain,
( ( ( ( ( sK2 = sK9 )
& sK4 )
| ( sK7 = sK9 ) )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f800]) ).
thf(f800,plain,
( ( $false = $true )
| ( ( ( ( sK2 = sK9 )
& sK4 )
| ( sK7 = sK9 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f799]) ).
thf(f799,plain,
( ( ( ( ( sK2 = sK9 )
& sK4 )
| ( sK7 = sK9 ) )
= $true )
| ( $false
= ( $false
=> ( in @ sK9 @ ( setadjoin @ sK7 @ emptyset ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f798]) ).
thf(f798,plain,
( ( $false
= ( $false
=> ( in @ sK9 @ ( setadjoin @ sK7 @ emptyset ) ) ) )
| ( ( ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) )
@ sK9 )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f786,f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( ( X1 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) )
=> ( X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( X1 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ Y2 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f786,plain,
( ( ( ( in @ sK9
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) ) ) )
=> ( in @ sK9 @ ( setadjoin @ sK7 @ emptyset ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f780]) ).
thf(f780,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) ) )
@ sK9 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f739]) ).
thf(f739,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f638]) ).
thf(f638,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f637]) ).
thf(f637,definition,
( spl0_1
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f803,plain,
( ( ( in @ sK9 @ ( setadjoin @ sK7 @ emptyset ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f802]) ).
thf(f802,plain,
( ( ( $true
=> ( in @ sK9 @ ( setadjoin @ sK7 @ emptyset ) ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f786,f797]) ).
thf(f797,plain,
( ( ( in @ sK9
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f786]) ).
thf(f826,plain,
( ( ( in @ sK7 @ ( setadjoin @ sK7 @ emptyset ) )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f813,f807]) ).
thf(f813,plain,
( ( ( in @ sK7 @ ( setadjoin @ sK9 @ emptyset ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f809]) ).
thf(f809,plain,
( ( ( $true
=> ( in @ sK7 @ ( setadjoin @ sK9 @ emptyset ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f78,f806]) ).
thf(f78,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
=> ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f733,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f732]) ).
thf(f732,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f731]) ).
thf(f731,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f223,f729]) ).
thf(f729,plain,
( ( $false
= ( in @ sK7
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f675,f714]) ).
thf(f714,plain,
( ( sK8 = sK7 )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f685]) ).
thf(f685,plain,
( ( ( sK7 = sK8 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f684]) ).
thf(f684,definition,
( spl0_3
<=> ( ( sK7 = sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f675,plain,
( ( ( in @ sK8
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f663]) ).
thf(f663,plain,
( ( $false
= ( ( in @ sK8 @ ( setadjoin @ sK7 @ emptyset ) )
=> ( in @ sK8
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f657]) ).
thf(f657,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f641]) ).
thf(f641,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f640]) ).
thf(f640,definition,
( spl0_2
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f223,plain,
( ( in @ sK7
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f220]) ).
thf(f220,plain,
( ( $true
=> ( in @ sK7
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f187,f164]) ).
thf(f164,plain,
( ( in @ sK7 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f151]) ).
thf(f187,plain,
! [X0: $i] :
( $true
= ( ( in @ X0 @ sK3 )
=> ( in @ X0
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( X0 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f186]) ).
thf(f186,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK3 )
=> ( in @ X0
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( $true
& ( X0 = Y0 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f185]) ).
thf(f185,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK3 )
=> ( $true
=> ( in @ X0
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( $true
& ( X0 = Y0 ) ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f125,f179]) ).
thf(f125,plain,
! [X0: $o,X1: $i] :
( ( ( in @ X1 @ sK3 )
=> ( ~ X0
=> ( in @ X1
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& X0 )
| ( ~ X0
& ( X1 = Y0 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f122]) ).
thf(f122,plain,
! [X0: $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ~ X0
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& X0 )
| ( ~ X0
& ( Y0 = Y1 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
! [X0: $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ~ X0
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& X0 )
| ( ~ X0
& ( Y0 = Y1 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X0: $o] :
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( ~ X0
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& X0 )
| ( ~ X0
& ( Y0 = Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f100,f109]) ).
thf(f109,plain,
( ( in @ sK2 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f100,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ~ X3
=> ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y1: $i] :
( ( ( X2 = Y1 )
& X3 )
| ( ~ X3
& ( Y0 = Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( ^ [Y0: $o] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ~ Y0
=> ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ( X2 = Y2 )
& Y0 )
| ( ~ Y0
& ( Y1 = Y2 ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( ( !! @ $o
@ ^ [Y0: $o] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ~ Y0
=> ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ( X2 = Y2 )
& Y0 )
| ( ~ Y0
& ( Y1 = Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ~ Y1
=> ( in @ Y2
@ ( dsetconstr @ X1
@ ^ [Y3: $i] :
( ( ( Y0 = Y3 )
& Y1 )
| ( ~ Y1
& ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ~ Y1
=> ( in @ Y2
@ ( dsetconstr @ X1
@ ^ [Y3: $i] :
( ( ( Y0 = Y3 )
& Y1 )
| ( ~ Y1
& ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ Y2
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y2 )
| ( ~ Y2
& ( Y3 = Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f703,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f701,f640,f684]) ).
thf(f701,plain,
( ( ( sK7 = sK8 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f696]) ).
thf(f696,plain,
( ( ( $true
=> ( sK7 = sK8 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f73,f676]) ).
thf(f676,plain,
( ( ( in @ sK8 @ ( setadjoin @ sK7 @ emptyset ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f663]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X2 = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f642,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f635,f640,f637]) ).
thf(f635,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f196]) ).
thf(f196,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) )
=> ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK2 = Y1 )
& sK4 )
| ( sK7 = Y1 ) ) ) )
=> ( in @ Y0 @ ( setadjoin @ sK7 @ emptyset ) ) ) )
=> $false ) )
= $true ),
inference(superposition,[status(thm)],[f58,f182]) ).
thf(f182,plain,
( ( ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( sK7 = Y0 ) ) )
= ( setadjoin @ sK7 @ emptyset ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f181]) ).
thf(f181,plain,
( $false
= ( ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( ( sK7 = Y0 )
& $true ) ) )
= ( setadjoin @ sK7 @ emptyset ) ) ),
inference(boolean_simplification,[status(thm)],[f180]) ).
thf(f180,plain,
( ( $true
=> ( ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& sK4 )
| ( ( sK7 = Y0 )
& $true ) ) )
= ( setadjoin @ sK7 @ emptyset ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f163,f179]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU701^2 : 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
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:31:21 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU701^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Conditionals
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A -> ~phi ->
% 0.30/0.46 % dsetconstr A (^ z:i.phi & z = x | ~phi & z = y) =
% 0.30/0.46 % setadjoin y emptyset))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC203l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.90 v8.2.0, 0.85 v8.1.0, 0.82 v7.5.0, 0.86 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 17 ( 6 unt; 10 typ; 6 def)
% 0.30/0.46 % Number of atoms : 42 ( 16 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 9 ( 6 avg)
% 0.30/0.46 % Number of connectives : 74 ( 4 ~; 2 |; 4 &; 42 @)
% 0.30/0.46 % ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 15 ( 3 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 11 ( 10 usr; 7 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 26 ( 3 ^; 23 !; 0 ?; 26 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=253
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER_type,type,
% 0.30/0.46 dsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER,definition,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setext_type,type,
% 0.30/0.46 setext: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setext,definition,
% 0.30/0.46 ( setext
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit_type,type,
% 0.30/0.46 uniqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit,definition,
% 0.30/0.46 ( uniqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit_type,type,
% 0.30/0.46 eqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit,definition,
% 0.30/0.46 ( eqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong_type,type,
% 0.30/0.46 in__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong,definition,
% 0.30/0.46 ( in__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(iffalseProp1_type,type,
% 0.30/0.46 iffalseProp1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(iffalseProp1,definition,
% 0.30/0.46 ( iffalseProp1
% 0.30/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ~ Xphi
% 0.30/0.46 => ( in @ Xy
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xz: $i] :
% 0.30/0.46 ( ( Xphi
% 0.30/0.46 & ( Xz = Xx ) )
% 0.30/0.46 | ( ~ Xphi
% 0.30/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(iffalseProp2,conjecture,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 => ( setext
% 0.30/0.46 => ( uniqinunit
% 0.30/0.46 => ( eqinunit
% 0.30/0.46 => ( in__Cong
% 0.30/0.46 => ( iffalseProp1
% 0.30/0.46 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ~ Xphi
% 0.30/0.46 => ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xz: $i] :
% 0.30/0.46 ( ( Xphi
% 0.30/0.46 & ( Xz = Xx ) )
% 0.30/0.46 | ( ~ Xphi
% 0.30/0.46 & ( Xz = Xy ) ) ) )
% 0.30/0.46 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.49/1.29 ---- Embedded in THF ---
% 1.49/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.29 %%% Generated on Tue Feb 24 12:31:22 EST 2026
% 1.49/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.29 %%% Logic specification used:
% 1.49/1.29 %%% thf(spec, logic, $$dhol).
% 1.49/1.29
% 1.49/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2DTF20100.p
% See solution above
% 1.49/1.29 ------------------------
% 1.67/1.31 ---- Cleaned THF ---
% 1.67/1.31 thf(in_type,type,
% 1.67/1.31 in: $i > $i > $o ).
% 1.67/1.31
% 1.67/1.31 thf(emptyset_type,type,
% 1.67/1.31 emptyset: $i ).
% 1.67/1.31
% 1.67/1.31 thf(setadjoin_type,type,
% 1.67/1.31 setadjoin: $i > $i > $i ).
% 1.67/1.31
% 1.67/1.31 thf(dsetconstr_type,type,
% 1.67/1.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.67/1.31
% 1.67/1.31 thf(dsetconstrER_type,type,
% 1.67/1.31 dsetconstrER: $o ).
% 1.67/1.31
% 1.67/1.31 thf(dsetconstrER,definition,
% 1.67/1.31 ( dsetconstrER
% 1.67/1.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.67/1.31 ( ( in @ Xx
% 1.67/1.31 @ ( dsetconstr @ A
% 1.67/1.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.67/1.31 => ( Xphi @ Xx ) ) ) ) ).
% 1.67/1.31
% 1.67/1.31 thf(setext_type,type,
% 1.67/1.31 setext: $o ).
% 1.67/1.31
% 1.67/1.31 thf(setext,definition,
% 1.67/1.31 ( setext
% 1.67/1.31 = ( ! [A: $i,B: $i] :
% 1.67/1.31 ( ! [Xx: $i] :
% 1.67/1.31 ( ( in @ Xx @ A )
% 1.67/1.31 => ( in @ Xx @ B ) )
% 1.67/1.31 => ( ! [Xx: $i] :
% 1.67/1.31 ( ( in @ Xx @ B )
% 1.67/1.31 => ( in @ Xx @ A ) )
% 1.67/1.31 => ( A = B ) ) ) ) ) ).
% 1.67/1.31
% 1.67/1.31 thf(uniqinunit_type,type,
% 1.67/1.31 uniqinunit: $o ).
% 1.67/1.31
% 1.67/1.31 thf(uniqinunit,definition,
% 1.67/1.31 ( uniqinunit
% 1.67/1.31 = ( ! [Xx: $i,Xy: $i] :
% 1.67/1.31 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.67/1.31 => ( Xx = Xy ) ) ) ) ).
% 1.67/1.31
% 1.67/1.31 thf(eqinunit_type,type,
% 1.67/1.31 eqinunit: $o ).
% 1.67/1.31
% 1.67/1.31 thf(eqinunit,definition,
% 1.67/1.31 ( eqinunit
% 1.67/1.31 = ( ! [Xx: $i,Xy: $i] :
% 1.67/1.31 ( ( Xx = Xy )
% 1.67/1.31 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.67/1.31
% 1.67/1.31 thf(in__Cong_type,type,
% 1.67/1.31 in__Cong: $o ).
% 1.67/1.31
% 1.67/1.31 thf(in__Cong,definition,
% 1.67/1.31 ( in__Cong
% 1.67/1.31 = ( ! [A: $i,B: $i] :
% 1.67/1.31 ( ( A = B )
% 1.67/1.31 => ! [Xx: $i,Xy: $i] :
% 1.67/1.31 ( ( Xx = Xy )
% 1.67/1.31 => ( ( in @ Xx @ A )
% 1.67/1.31 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 1.67/1.31
% 1.67/1.31 thf(iffalseProp1_type,type,
% 1.67/1.31 iffalseProp1: $o ).
% 1.67/1.31
% 1.67/1.31 thf(iffalseProp1,definition,
% 1.67/1.31 ( iffalseProp1
% 1.67/1.31 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.67/1.31 ( ( in @ Xx @ A )
% 1.67/1.31 => ! [Xy: $i] :
% 1.67/1.31 ( ( in @ Xy @ A )
% 1.67/1.31 => ( ~ Xphi
% 1.67/1.31 => ( in @ Xy
% 1.67/1.31 @ ( dsetconstr @ A
% 1.67/1.31 @ ^ [Xz: $i] :
% 1.67/1.31 ( ( Xphi
% 1.67/1.31 & ( Xz = Xx ) )
% 1.67/1.31 | ( ~ Xphi
% 1.67/1.31 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 1.67/1.31
% 1.67/1.31 thf(iffalseProp2,conjecture,
% 1.67/1.31 ( dsetconstrER
% 1.67/1.31 => ( setext
% 1.67/1.31 => ( uniqinunit
% 1.67/1.31 => ( eqinunit
% 1.67/1.31 => ( in__Cong
% 1.67/1.31 => ( iffalseProp1
% 1.67/1.31 => ! [A: $i,Xphi: $o,Xx: $i] :
% 1.67/1.31 ( ( in @ Xx @ A )
% 1.67/1.31 => ! [Xy: $i] :
% 1.67/1.31 ( ( in @ Xy @ A )
% 1.67/1.31 => ( ~ Xphi
% 1.67/1.31 => ( ( dsetconstr @ A
% 1.67/1.31 @ ^ [Xz: $i] :
% 1.67/1.31 ( ( Xphi
% 1.67/1.31 & ( Xz = Xx ) )
% 1.67/1.31 | ( ~ Xphi
% 1.67/1.31 & ( Xz = Xy ) ) ) )
% 1.67/1.31 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) ) ) ).
% 1.67/1.31 ------------------------
% 1.67/1.32 % (20377)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/18Mi)
% 1.67/1.32 % (20374)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/2Mi)
% 1.67/1.32 % (20374)Instruction limit reached!
% 1.67/1.32 % (20374)------------------------------
% 1.67/1.32 % (20374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (20374)Termination reason: Unknown
% 1.67/1.32 % (20374)Termination phase: Preprocessing 3
% 1.67/1.32
% 1.67/1.32 % (20374)Memory used [KB]: 1023
% 1.67/1.32 % (20374)Time elapsed: 0.002 s
% 1.67/1.32 % (20374)Instructions burned: 3 (million)
% 1.67/1.32 % (20374)------------------------------
% 1.67/1.32 % (20374)------------------------------
% 1.67/1.33 % (20377)Instruction limit reached!
% 1.67/1.33 % (20377)------------------------------
% 1.67/1.33 % (20377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (20377)Termination reason: Unknown
% 1.67/1.33 % (20377)Termination phase: Saturation
% 1.67/1.33
% 1.67/1.33 % (20377)Memory used [KB]: 5628
% 1.67/1.33 % (20377)Time elapsed: 0.008 s
% 1.67/1.33 % (20377)Instructions burned: 20 (million)
% 1.67/1.33 % (20377)------------------------------
% 1.67/1.33 % (20377)------------------------------
% 1.67/1.33 % (20371)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/183Mi)
% 1.67/1.33 % (20372)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_20100 for (2999ds/4Mi)
% 1.67/1.33 % (20373)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_20100 for (2999ds/27Mi)
% 1.67/1.33 % (20375)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_20100 for (2999ds/2Mi)
% 1.67/1.33 % (20376)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_20100 for (2999ds/275Mi)
% 1.67/1.33 % (20375)Instruction limit reached!
% 1.67/1.33 % (20375)------------------------------
% 1.67/1.33 % (20375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (20375)Termination reason: Unknown
% 1.67/1.33 % (20375)Termination phase: shuffling
% 1.67/1.33
% 1.67/1.33 % (20375)Memory used [KB]: 1023
% 1.67/1.33 % (20375)Time elapsed: 0.003 s
% 1.67/1.33 % (20375)Instructions burned: 2 (million)
% 1.67/1.33 % (20375)------------------------------
% 1.67/1.33 % (20375)------------------------------
% 1.67/1.33 % (20372)Instruction limit reached!
% 1.67/1.33 % (20372)------------------------------
% 1.67/1.33 % (20372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (20372)Termination reason: Unknown
% 1.67/1.33 % (20372)Termination phase: Property scanning
% 1.67/1.33
% 1.67/1.33 % (20372)Memory used [KB]: 1023
% 1.67/1.33 % (20372)Time elapsed: 0.004 s
% 1.67/1.33 % (20372)Instructions burned: 4 (million)
% 1.67/1.33 % (20372)------------------------------
% 1.67/1.33 % (20372)------------------------------
% 1.67/1.33 % (20378)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/3Mi)
% 1.67/1.33 % (20378)Instruction limit reached!
% 1.67/1.33 % (20378)------------------------------
% 1.67/1.33 % (20378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (20378)Termination reason: Unknown
% 1.67/1.33 % (20378)Termination phase: Property scanning
% 1.67/1.33
% 1.67/1.33 % (20378)Memory used [KB]: 1023
% 1.67/1.33 % (20378)Time elapsed: 0.003 s
% 1.67/1.33 % (20378)Instructions burned: 5 (million)
% 1.67/1.33 % (20378)------------------------------
% 1.67/1.33 % (20378)------------------------------
% 1.67/1.34 % (20379)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_20100 for (2999ds/37Mi)
% 1.67/1.34 % (20382)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_20100 for (2999ds/1041Mi)
% 1.67/1.35 % (20373)Instruction limit reached!
% 1.67/1.35 % (20373)------------------------------
% 1.67/1.35 % (20373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (20373)Termination reason: Unknown
% 1.67/1.35 % (20373)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (20373)Memory used [KB]: 5628
% 1.67/1.35 % (20373)Time elapsed: 0.019 s
% 1.67/1.35 % (20373)Instructions burned: 27 (million)
% 1.67/1.35 % (20373)------------------------------
% 1.67/1.35 % (20373)------------------------------
% 1.67/1.35 % (20380)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_20100 for (2999ds/15Mi)
% 1.67/1.35 % (20381)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_20100 for (2999ds/3Mi)
% 1.67/1.35 % (20379)Instruction limit reached!
% 1.67/1.35 % (20379)------------------------------
% 1.67/1.35 % (20379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (20379)Termination reason: Unknown
% 1.67/1.35 % (20379)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (20379)Memory used [KB]: 5756
% 1.67/1.35 % (20379)Time elapsed: 0.013 s
% 1.67/1.35 % (20379)Instructions burned: 39 (million)
% 1.67/1.35 % (20379)------------------------------
% 1.67/1.35 % (20379)------------------------------
% 1.67/1.35 % (20381)Instruction limit reached!
% 1.67/1.35 % (20381)------------------------------
% 1.67/1.35 % (20381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (20381)Termination reason: Unknown
% 1.67/1.35 % (20381)Termination phase: Function definition elimination
% 1.67/1.35
% 1.67/1.35 % (20381)Memory used [KB]: 1023
% 1.67/1.35 % (20381)Time elapsed: 0.004 s
% 1.67/1.35 % (20381)Instructions burned: 4 (million)
% 1.67/1.35 % (20381)------------------------------
% 1.67/1.35 % (20381)------------------------------
% 1.67/1.36 % (20380)Instruction limit reached!
% 1.67/1.36 % (20380)------------------------------
% 1.67/1.36 % (20380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (20380)Termination reason: Unknown
% 1.67/1.36 % (20380)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (20380)Memory used [KB]: 5756
% 1.67/1.36 % (20380)Time elapsed: 0.012 s
% 1.67/1.36 % (20380)Instructions burned: 15 (million)
% 1.67/1.36 % (20380)------------------------------
% 1.67/1.36 % (20380)------------------------------
% 1.67/1.36 % (20384)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/16Mi)
% 1.67/1.36 % (20383)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/7Mi)
% 1.67/1.36 % (20384)Instruction limit reached!
% 1.67/1.36 % (20384)------------------------------
% 1.67/1.36 % (20384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (20384)Termination reason: Unknown
% 1.67/1.36 % (20384)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (20384)Memory used [KB]: 5884
% 1.67/1.36 % (20384)Time elapsed: 0.007 s
% 1.67/1.36 % (20384)Instructions burned: 18 (million)
% 1.67/1.36 % (20384)------------------------------
% 1.67/1.36 % (20384)------------------------------
% 1.67/1.37 % (20383)Instruction limit reached!
% 1.67/1.37 % (20383)------------------------------
% 1.67/1.37 % (20383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (20383)Termination reason: Unknown
% 1.67/1.37 % (20383)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (20383)Memory used [KB]: 1023
% 1.67/1.37 % (20383)Time elapsed: 0.006 s
% 1.67/1.37 % (20383)Instructions burned: 8 (million)
% 1.67/1.37 % (20383)------------------------------
% 1.67/1.37 % (20383)------------------------------
% 1.67/1.37 % (20385)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_20100 for (2999ds/3Mi)
% 1.67/1.37 % (20385)Instruction limit reached!
% 1.67/1.37 % (20385)------------------------------
% 1.67/1.37 % (20385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (20385)Termination reason: Unknown
% 1.67/1.37 % (20385)Termination phase: Property scanning
% 1.67/1.37
% 1.67/1.37 % (20385)Memory used [KB]: 1023
% 1.67/1.37 % (20385)Time elapsed: 0.004 s
% 1.67/1.37 % (20385)Instructions burned: 4 (million)
% 1.67/1.37 % (20385)------------------------------
% 1.67/1.37 % (20385)------------------------------
% 1.67/1.37 % (20387)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/7Mi)
% 1.67/1.37 % (20386)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_20100 for (2999ds/3Mi)
% 1.67/1.38 % (20387)Instruction limit reached!
% 1.67/1.38 % (20387)------------------------------
% 1.67/1.38 % (20387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (20387)Termination reason: Unknown
% 1.67/1.38 % (20387)Termination phase: Saturation
% 1.67/1.38
% 1.67/1.38 % (20387)Memory used [KB]: 5500
% 1.67/1.38 % (20387)Time elapsed: 0.003 s
% 1.67/1.38 % (20387)Instructions burned: 7 (million)
% 1.67/1.38 % (20387)------------------------------
% 1.67/1.38 % (20387)------------------------------
% 1.67/1.38 % (20386)Instruction limit reached!
% 1.67/1.38 % (20386)------------------------------
% 1.67/1.38 % (20386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (20386)Termination reason: Unknown
% 1.67/1.38 % (20386)Termination phase: Property scanning
% 1.67/1.38
% 1.67/1.38 % (20386)Memory used [KB]: 1023
% 1.67/1.38 % (20386)Time elapsed: 0.004 s
% 1.67/1.38 % (20386)Instructions burned: 4 (million)
% 1.67/1.38 % (20386)------------------------------
% 1.67/1.38 % (20386)------------------------------
% 1.67/1.38 % (20388)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/3Mi)
% 1.67/1.38 % (20390)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/18Mi)
% 1.67/1.39 % (20388)Instruction limit reached!
% 1.67/1.39 % (20388)------------------------------
% 1.67/1.39 % (20388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (20388)Termination reason: Unknown
% 1.67/1.39 % (20388)Termination phase: Function definition elimination
% 1.67/1.39
% 1.67/1.39 % (20388)Memory used [KB]: 1023
% 1.67/1.39 % (20388)Time elapsed: 0.004 s
% 1.67/1.39 % (20388)Instructions burned: 4 (million)
% 1.67/1.39 % (20388)------------------------------
% 1.67/1.39 % (20388)------------------------------
% 1.67/1.39 % (20389)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/4Mi)
% 1.67/1.39 % (20389)Instruction limit reached!
% 1.67/1.39 % (20389)------------------------------
% 1.67/1.39 % (20389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (20389)Termination reason: Unknown
% 1.67/1.39 % (20389)Termination phase: Property scanning
% 1.67/1.39
% 1.67/1.39 % (20389)Memory used [KB]: 1023
% 1.67/1.39 % (20389)Time elapsed: 0.004 s
% 1.67/1.39 % (20389)Instructions burned: 4 (million)
% 1.67/1.39 % (20389)------------------------------
% 1.67/1.39 % (20389)------------------------------
% 1.67/1.39 % (20390)Instruction limit reached!
% 1.67/1.39 % (20390)------------------------------
% 1.67/1.39 % (20390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (20390)Termination reason: Unknown
% 1.67/1.39 % (20390)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (20390)Memory used [KB]: 5628
% 1.67/1.39 % (20390)Time elapsed: 0.007 s
% 1.67/1.39 % (20390)Instructions burned: 19 (million)
% 1.67/1.39 % (20390)------------------------------
% 1.67/1.39 % (20390)------------------------------
% 1.67/1.39 % (20391)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/710Mi)
% 1.69/1.40 % (20394)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_20100 for (2999ds/21Mi)
% 1.69/1.40 % (20392)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/6Mi)
% 1.69/1.41 % (20393)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_20100 for (2999ds/902Mi)
% 1.69/1.41 % (20392)Instruction limit reached!
% 1.69/1.41 % (20392)------------------------------
% 1.69/1.41 % (20392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (20392)Termination reason: Unknown
% 1.69/1.41 % (20392)Termination phase: Saturation
% 1.69/1.41
% 1.69/1.41 % (20392)Memory used [KB]: 5500
% 1.69/1.41 % (20392)Time elapsed: 0.005 s
% 1.69/1.41 % (20392)Instructions burned: 6 (million)
% 1.69/1.41 % (20392)------------------------------
% 1.69/1.41 % (20392)------------------------------
% 1.69/1.41 % (20394)Instruction limit reached!
% 1.69/1.41 % (20394)------------------------------
% 1.69/1.41 % (20394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (20394)Termination reason: Unknown
% 1.69/1.41 % (20394)Termination phase: Saturation
% 1.69/1.41
% 1.69/1.41 % (20394)Memory used [KB]: 5628
% 1.69/1.41 % (20394)Time elapsed: 0.008 s
% 1.69/1.41 % (20394)Instructions burned: 21 (million)
% 1.69/1.41 % (20394)------------------------------
% 1.69/1.41 % (20394)------------------------------
% 1.69/1.41 % (20371)Instruction limit reached!
% 1.69/1.41 % (20371)------------------------------
% 1.69/1.41 % (20371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (20371)Termination reason: Unknown
% 1.69/1.41 % (20371)Termination phase: Saturation
% 1.69/1.41
% 1.69/1.41 % (20371)Memory used [KB]: 6140
% 1.69/1.41 % (20371)Time elapsed: 0.083 s
% 1.69/1.41 % (20371)Instructions burned: 183 (million)
% 1.69/1.41 % (20371)------------------------------
% 1.69/1.41 % (20371)------------------------------
% 1.69/1.41 % (20393)Refutation not found, incomplete strategy
% 1.69/1.41 % (20393)------------------------------
% 1.69/1.41 % (20393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (20393)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.41
% 1.69/1.41
% 1.69/1.41 % (20393)Memory used [KB]: 5500
% 1.69/1.41 % (20393)Time elapsed: 0.006 s
% 1.69/1.41 % (20393)Instructions burned: 7 (million)
% 1.69/1.41 % (20393)------------------------------
% 1.69/1.41 % (20393)------------------------------
% 1.69/1.42 % (20396)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_20100 for (2999ds/6Mi)
% 1.69/1.42 % (20396)Instruction limit reached!
% 1.69/1.42 % (20396)------------------------------
% 1.69/1.42 % (20396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.42 % (20396)Termination reason: Unknown
% 1.69/1.42 % (20396)Termination phase: Saturation
% 1.69/1.42
% 1.69/1.42 % (20396)Memory used [KB]: 5500
% 1.69/1.42 % (20396)Time elapsed: 0.003 s
% 1.69/1.42 % (20396)Instructions burned: 7 (million)
% 1.69/1.42 % (20396)------------------------------
% 1.69/1.42 % (20396)------------------------------
% 1.69/1.42 % (20397)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/377Mi)
% 1.69/1.42 % (20395)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20100 for (2999ds/5Mi)
% 1.69/1.43 % (20382)First to succeed.
% 1.69/1.43 % (20395)Instruction limit reached!
% 1.69/1.43 % (20395)------------------------------
% 1.69/1.43 % (20395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.43 % (20395)Termination reason: Unknown
% 1.69/1.43 % (20395)Termination phase: Saturation
% 1.69/1.43
% 1.69/1.43 % (20395)Memory used [KB]: 5500
% 1.69/1.43 % (20395)Time elapsed: 0.005 s
% 1.69/1.43 % (20395)Instructions burned: 6 (million)
% 1.69/1.43 % (20395)------------------------------
% 1.69/1.43 % (20395)------------------------------
% 1.69/1.43 % (20399)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_20100 for (2999ds/19Mi)
% 1.69/1.43 % (20398)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_20100 for (2999ds/779Mi)
% 1.69/1.43 % (20382)Refutation found. Thanks to Tanya!
% 1.69/1.43 % SZS status Theorem for DTF2THF_20100
% 1.69/1.43 % SZS output start Proof for DTF2THF_20100
% 1.69/1.43 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.43 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.69/1.43 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.69/1.43 thf(func_def_27, type, ph1: !>[X0: $tType]:(X0)).
% 1.69/1.43 thf(f830,plain,(
% 1.69/1.43 $false),
% 1.69/1.43 inference(avatar_sat_refutation,[status(thm)],[f642,f703,f733,f829])).
% 1.69/1.43 thf(f829,plain,(
% 1.69/1.43 ~spl0_1),
% 1.69/1.43 inference(avatar_contradiction_clause,[status(thm)],[f828])).
% 1.69/1.43 thf(f828,plain,(
% 1.69/1.43 $false | ~spl0_1),
% 1.69/1.43 inference(trivial_inequality_removal,[status(thm)],[f827])).
% 1.69/1.43 thf(f827,plain,(
% 1.69/1.43 ($false = $true) | ~spl0_1),
% 1.69/1.43 inference(forward_demodulation,[status(thm)],[f826,f820])).
% 1.69/1.43 thf(f820,plain,(
% 1.69/1.43 ((in @ sK7 @ (setadjoin @ sK7 @ emptyset)) = $false) | ~spl0_1),
% 1.69/1.43 inference(backward_demodulation,[status(thm)],[f803,f807])).
% 1.69/1.43 thf(f807,plain,(
% 1.69/1.43 (sK7 = sK9) | ~spl0_1),
% 1.69/1.43 inference(equality_proxy_clausification,[status(thm)],[f806])).
% 1.69/1.43 thf(f806,plain,(
% 1.69/1.43 ((sK7 = sK9) = $true) | ~spl0_1),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f805])).
% 1.69/1.43 thf(f805,plain,(
% 1.69/1.43 (($false | (sK7 = sK9)) = $true) | ~spl0_1),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f804])).
% 1.69/1.43 thf(f804,plain,(
% 1.69/1.43 ((((sK2 = sK9) & $false) | (sK7 = sK9)) = $true) | ~spl0_1),
% 1.69/1.43 inference(forward_demodulation,[status(thm)],[f801,f183])).
% 1.69/1.43 thf(f183,plain,(
% 1.69/1.43 (sK4 = $false)),
% 1.69/1.43 inference(not_proxy_clausification,[status(thm)],[f179])).
% 1.69/1.43 thf(f179,plain,(
% 1.69/1.43 ((~ sK4) = $true)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f163])).
% 1.69/1.43 thf(f163,plain,(
% 1.69/1.43 (((~ sK4) => ((dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | ((sK7 = Y0) & (~ sK4))))) = (setadjoin @ sK7 @ emptyset))) = $false)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f151])).
% 1.69/1.43 thf(f151,plain,(
% 1.69/1.43 ($false = ((in @ sK7 @ sK3) => ((~ sK4) => ((dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | ((sK7 = Y0) & (~ sK4))))) = (setadjoin @ sK7 @ emptyset)))))),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f150])).
% 1.69/1.43 thf(f150,plain,(
% 1.69/1.43 (((^[Y0 : $i]: ((in @ Y0 @ sK3) => ((~ sK4) => ((dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | ((Y0 = Y1) & (~ sK4))))) = (setadjoin @ Y0 @ emptyset))))) @ sK7) = $false)),
% 1.69/1.43 inference(sigma_clausification,[status(thm)],[f108])).
% 1.69/1.43 thf(f108,plain,(
% 1.69/1.43 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((~ sK4) => ((dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | ((Y0 = Y1) & (~ sK4))))) = (setadjoin @ Y0 @ emptyset)))))) = $false)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.69/1.43 thf(f107,plain,(
% 1.69/1.43 (((in @ sK2 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((~ sK4) => ((dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | ((Y0 = Y1) & (~ sK4))))) = (setadjoin @ Y0 @ emptyset))))))) = $false)),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f106])).
% 1.69/1.43 thf(f106,plain,(
% 1.69/1.43 ($false = ((^[Y0 : $o]: ((in @ sK2 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((~ Y0) => ((dsetconstr @ sK3 @ (^[Y2 : $i]: (((sK2 = Y2) & Y0) | ((Y1 = Y2) & (~ Y0))))) = (setadjoin @ Y1 @ emptyset)))))))) @ sK4))),
% 1.69/1.43 inference(sigma_clausification,[status(thm)],[f105])).
% 1.69/1.43 thf(f105,plain,(
% 1.69/1.43 ((!! @ $o @ (^[Y0 : $o]: ((in @ sK2 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((~ Y0) => ((dsetconstr @ sK3 @ (^[Y2 : $i]: (((sK2 = Y2) & Y0) | ((Y1 = Y2) & (~ Y0))))) = (setadjoin @ Y1 @ emptyset))))))))) = $false)),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f104])).
% 1.69/1.43 thf(f104,plain,(
% 1.69/1.43 (((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ sK2 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ Y1) => ((dsetconstr @ Y0 @ (^[Y3 : $i]: (((sK2 = Y3) & Y1) | ((Y2 = Y3) & (~ Y1))))) = (setadjoin @ Y2 @ emptyset)))))))))) @ sK3) = $false)),
% 1.69/1.43 inference(sigma_clausification,[status(thm)],[f103])).
% 1.69/1.43 thf(f103,plain,(
% 1.69/1.43 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ sK2 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ Y1) => ((dsetconstr @ Y0 @ (^[Y3 : $i]: (((sK2 = Y3) & Y1) | ((Y2 = Y3) & (~ Y1))))) = (setadjoin @ Y2 @ emptyset))))))))))))),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.69/1.43 thf(f102,plain,(
% 1.69/1.43 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset)))))))))))) @ sK2) = $false)),
% 1.69/1.43 inference(sigma_clausification,[status(thm)],[f86])).
% 1.69/1.43 thf(f86,plain,(
% 1.69/1.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset))))))))))))) = $false)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.69/1.43 thf(f83,plain,(
% 1.69/1.43 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset)))))))))))))))),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f82])).
% 1.69/1.43 thf(f82,plain,(
% 1.69/1.43 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset))))))))))))))))),
% 1.69/1.43 inference(backward_demodulation,[status(thm)],[f66,f81])).
% 1.69/1.43 thf(f81,plain,(
% 1.69/1.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) = $true)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.69/1.43 thf(f66,plain,(
% 1.69/1.43 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset))))))))))))))) = $false)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.69/1.43 thf(f63,plain,(
% 1.69/1.43 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset)))))))))))))))) = $false)),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f62])).
% 1.69/1.43 thf(f62,plain,(
% 1.69/1.43 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset))))))))))))))))) = $false)),
% 1.69/1.43 inference(backward_demodulation,[status(thm)],[f49,f61])).
% 1.69/1.43 thf(f61,plain,(
% 1.69/1.43 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.69/1.43 thf(f49,plain,(
% 1.69/1.43 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset))))))))))))))))) = $false)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.69/1.43 thf(f36,plain,(
% 1.69/1.43 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset)))))))))))))))))))),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.69/1.43 thf(f33,plain,(
% 1.69/1.43 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset))))))))))))))))))))),
% 1.69/1.43 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.69/1.43 thf(f32,plain,(
% 1.69/1.43 ((~ ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset)))))))))))))))))))) = $true)),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.69/1.43 thf(f31,plain,(
% 1.69/1.43 ((~ ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset)))))))))))))))))))) = $true)),
% 1.69/1.43 inference(definition_unfolding,[status(thm)],[f28,f24,f26,f29,f27,f30,f25])).
% 1.69/1.43 thf(f25,plain,(
% 1.69/1.43 (iffalseProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))))),
% 1.69/1.43 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.43 thf(f17,plain,(
% 1.69/1.43 (iffalseProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))))),
% 1.69/1.43 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.43 thf(f16,plain,(
% 1.69/1.43 (! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (~X0 => (in @ X3 @ (dsetconstr @ X2 @ (^[X4 : $i] : (((X3 = X4) & ~X0) | (X0 & (X1 = X4))))))))) = iffalseProp1)),
% 1.69/1.43 inference(rectify,[status(thm)],[f6])).
% 1.69/1.43 thf(f6,axiom,(
% 1.69/1.43 (! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X5 : $i] : (((X3 = X5) & ~X1) | (X1 & (X2 = X5))))))))) = iffalseProp1)),
% 1.69/1.43 file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',iffalseProp1)).
% 1.69/1.43 thf(f30,plain,(
% 1.69/1.43 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))))),
% 1.69/1.43 inference(cnf_transformation,[status(thm)],[f21])).
% 1.69/1.43 thf(f21,plain,(
% 1.69/1.43 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))))),
% 1.69/1.43 inference(fool_elimination,[status(thm)],[f20])).
% 1.69/1.43 thf(f20,plain,(
% 1.69/1.43 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X2 @ X0) <=> (in @ X3 @ X1)))) = in__Cong)),
% 1.69/1.43 inference(rectify,[status(thm)],[f5])).
% 1.69/1.43 thf(f5,axiom,(
% 1.69/1.43 (! [X4 : $i,X0 : $i] : ((X0 = X4) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => ((in @ X3 @ X4) <=> (in @ X2 @ X0)))) = in__Cong)),
% 1.69/1.43 file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',in__Cong)).
% 1.69/1.43 thf(f27,plain,(
% 1.69/1.43 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 1.69/1.43 inference(cnf_transformation,[status(thm)],[f13])).
% 1.69/1.43 thf(f13,plain,(
% 1.69/1.43 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 1.69/1.43 inference(fool_elimination,[status(thm)],[f12])).
% 1.69/1.43 thf(f12,plain,(
% 1.69/1.43 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))) = eqinunit)),
% 1.69/1.43 inference(rectify,[status(thm)],[f4])).
% 1.69/1.43 thf(f4,axiom,(
% 1.69/1.43 (! [X2 : $i,X3 : $i] : ((X2 = X3) => (in @ X2 @ (setadjoin @ X3 @ emptyset))) = eqinunit)),
% 1.69/1.43 file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',eqinunit)).
% 1.69/1.43 thf(f29,plain,(
% 1.69/1.43 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 1.69/1.43 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.43 thf(f23,plain,(
% 1.69/1.43 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 1.69/1.43 inference(fool_elimination,[status(thm)],[f22])).
% 1.69/1.43 thf(f22,plain,(
% 1.69/1.43 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.69/1.43 inference(rectify,[status(thm)],[f3])).
% 1.69/1.43 thf(f3,axiom,(
% 1.69/1.43 (! [X3 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)) = uniqinunit)),
% 1.69/1.43 file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',uniqinunit)).
% 1.69/1.43 thf(f26,plain,(
% 1.69/1.43 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))),
% 1.69/1.43 inference(cnf_transformation,[status(thm)],[f15])).
% 1.69/1.43 thf(f15,plain,(
% 1.69/1.43 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))),
% 1.69/1.43 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.43 thf(f14,plain,(
% 1.69/1.43 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))) = setext)),
% 1.69/1.43 inference(rectify,[status(thm)],[f2])).
% 1.69/1.43 thf(f2,axiom,(
% 1.69/1.43 (! [X4 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X4)) => (! [X2 : $i] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (X0 = X4))) = setext)),
% 1.69/1.43 file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',setext)).
% 1.69/1.43 thf(f24,plain,(
% 1.69/1.43 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2)))))))))),
% 1.69/1.43 inference(cnf_transformation,[status(thm)],[f19])).
% 1.69/1.43 thf(f19,plain,(
% 1.69/1.43 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2)))))))))),
% 1.69/1.43 inference(fool_elimination,[status(thm)],[f18])).
% 1.69/1.43 thf(f18,plain,(
% 1.69/1.43 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X0)) = dsetconstrER)),
% 1.69/1.43 inference(rectify,[status(thm)],[f1])).
% 1.69/1.43 thf(f1,axiom,(
% 1.69/1.43 (! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.69/1.43 file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',dsetconstrER)).
% 1.69/1.43 thf(f28,plain,(
% 1.69/1.43 ((~ (dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iffalseProp1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset)))))))))))))))))))) = $true)),
% 1.69/1.43 inference(cnf_transformation,[status(thm)],[f11])).
% 1.69/1.43 thf(f11,plain,(
% 1.69/1.43 ((~ (dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iffalseProp1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ Y2) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y0 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))) = (setadjoin @ Y3 @ emptyset)))))))))))))))))))) = $true)),
% 1.69/1.43 inference(fool_elimination,[status(thm)],[f10])).
% 1.69/1.43 thf(f10,plain,(
% 1.69/1.43 ~(dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iffalseProp1 => ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => (~X0 => ((dsetconstr @ X1 @ (^[X4 : $i] : ((~X0 & (X3 = X4)) | (X0 & (X2 = X4))))) = (setadjoin @ X3 @ emptyset)))))))))))),
% 1.69/1.43 inference(rectify,[status(thm)],[f8])).
% 1.69/1.43 thf(f8,negated_conjecture,(
% 1.69/1.43 ~(dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iffalseProp1 => ! [X1 : $o,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => ((dsetconstr @ X0 @ (^[X5 : $i] : ((~X1 & (X3 = X5)) | (X1 & (X2 = X5))))) = (setadjoin @ X3 @ emptyset)))))))))))),
% 1.69/1.43 inference(negated_conjecture,[status(cth)],[f7])).
% 1.69/1.43 thf(f7,conjecture,(
% 1.69/1.43 dsetconstrER => (setext => (uniqinunit => (eqinunit => (in__Cong => (iffalseProp1 => ! [X1 : $o,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => ((dsetconstr @ X0 @ (^[X5 : $i] : ((~X1 & (X3 = X5)) | (X1 & (X2 = X5))))) = (setadjoin @ X3 @ emptyset))))))))))),
% 1.69/1.43 file('/export/starexec/sandbox2/tmp/tmp.lsnMrSZRFj/DTF2THF_20100.p',iffalseProp2)).
% 1.69/1.43 thf(f801,plain,(
% 1.69/1.43 ((((sK2 = sK9) & sK4) | (sK7 = sK9)) = $true) | ~spl0_1),
% 1.69/1.43 inference(trivial_inequality_removal,[status(thm)],[f800])).
% 1.69/1.43 thf(f800,plain,(
% 1.69/1.43 ($false = $true) | ((((sK2 = sK9) & sK4) | (sK7 = sK9)) = $true) | ~spl0_1),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f799])).
% 1.69/1.43 thf(f799,plain,(
% 1.69/1.43 ((((sK2 = sK9) & sK4) | (sK7 = sK9)) = $true) | ($false = ($false => (in @ sK9 @ (setadjoin @ sK7 @ emptyset)))) | ~spl0_1),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f798])).
% 1.69/1.43 thf(f798,plain,(
% 1.69/1.43 ($false = ($false => (in @ sK9 @ (setadjoin @ sK7 @ emptyset)))) | (((^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0))) @ sK9) = $true) | ~spl0_1),
% 1.69/1.43 inference(superposition,[status(thm)],[f786,f48])).
% 1.69/1.43 thf(f48,plain,(
% 1.69/1.43 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($false = (in @ X3 @ (dsetconstr @ X2 @ X1))) | ((X1 @ X3) = $true)) )),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.69/1.43 thf(f47,plain,(
% 1.69/1.43 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X3 @ (dsetconstr @ X2 @ X1)) => (X1 @ X3)) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.69/1.43 thf(f46,plain,(
% 1.69/1.43 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ X1)) => (X1 @ Y0))) @ X3) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f45])).
% 1.69/1.43 thf(f45,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ X1)) => (X1 @ Y0)))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.69/1.43 thf(f44,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ Y0 @ X1)) => (X1 @ Y1))))) @ X2) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f43])).
% 1.69/1.43 thf(f43,plain,(
% 1.69/1.43 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ Y0 @ X1)) => (X1 @ Y1)))))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.69/1.43 thf(f42,plain,(
% 1.69/1.43 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2))))))) @ X1) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f37])).
% 1.69/1.43 thf(f37,plain,(
% 1.69/1.43 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) = $true)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.69/1.43 thf(f786,plain,(
% 1.69/1.43 (((in @ sK9 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0))))) => (in @ sK9 @ (setadjoin @ sK7 @ emptyset))) = $false) | ~spl0_1),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f780])).
% 1.69/1.43 thf(f780,plain,(
% 1.69/1.43 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1))))) => (in @ Y0 @ (setadjoin @ sK7 @ emptyset)))) @ sK9)) | ~spl0_1),
% 1.69/1.43 inference(sigma_clausification,[status(thm)],[f739])).
% 1.69/1.43 thf(f739,plain,(
% 1.69/1.43 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1))))) => (in @ Y0 @ (setadjoin @ sK7 @ emptyset))))) = $false) | ~spl0_1),
% 1.69/1.43 inference(not_proxy_clausification,[status(thm)],[f638])).
% 1.69/1.43 thf(f638,plain,(
% 1.69/1.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1))))) => (in @ Y0 @ (setadjoin @ sK7 @ emptyset)))))) = $true) | ~spl0_1),
% 1.69/1.43 inference(avatar_component_clause,[status(thm)],[f637])).
% 1.69/1.43 thf(f637,definition,(
% 1.69/1.43 spl0_1 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1))))) => (in @ Y0 @ (setadjoin @ sK7 @ emptyset)))))) = $true)),
% 1.69/1.43 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.69/1.43 thf(f803,plain,(
% 1.69/1.43 ((in @ sK9 @ (setadjoin @ sK7 @ emptyset)) = $false) | ~spl0_1),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f802])).
% 1.69/1.43 thf(f802,plain,(
% 1.69/1.43 (($true => (in @ sK9 @ (setadjoin @ sK7 @ emptyset))) = $false) | ~spl0_1),
% 1.69/1.43 inference(backward_demodulation,[status(thm)],[f786,f797])).
% 1.69/1.43 thf(f797,plain,(
% 1.69/1.43 ((in @ sK9 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0))))) = $true) | ~spl0_1),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f786])).
% 1.69/1.43 thf(f826,plain,(
% 1.69/1.43 ((in @ sK7 @ (setadjoin @ sK7 @ emptyset)) = $true) | ~spl0_1),
% 1.69/1.43 inference(forward_demodulation,[status(thm)],[f813,f807])).
% 1.69/1.43 thf(f813,plain,(
% 1.69/1.43 ((in @ sK7 @ (setadjoin @ sK9 @ emptyset)) = $true) | ~spl0_1),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f809])).
% 1.69/1.43 thf(f809,plain,(
% 1.69/1.43 (($true => (in @ sK7 @ (setadjoin @ sK9 @ emptyset))) = $true) | ~spl0_1),
% 1.69/1.43 inference(superposition,[status(thm)],[f78,f806])).
% 1.69/1.43 thf(f78,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i] : ((((X2 = X1) => (in @ X2 @ (setadjoin @ X1 @ emptyset))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.69/1.43 thf(f77,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((Y0 = X1) => (in @ Y0 @ (setadjoin @ X1 @ emptyset)))) @ X2) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f76])).
% 1.69/1.43 thf(f76,plain,(
% 1.69/1.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (in @ Y0 @ (setadjoin @ X1 @ emptyset))))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.69/1.43 thf(f75,plain,(
% 1.69/1.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))) @ X1))) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f67])).
% 1.69/1.43 thf(f67,plain,(
% 1.69/1.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) = $true)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.69/1.43 thf(f733,plain,(
% 1.69/1.43 ~spl0_2 | ~spl0_3),
% 1.69/1.43 inference(avatar_contradiction_clause,[status(thm)],[f732])).
% 1.69/1.43 thf(f732,plain,(
% 1.69/1.43 $false | (~spl0_2 | ~spl0_3)),
% 1.69/1.43 inference(trivial_inequality_removal,[status(thm)],[f731])).
% 1.69/1.43 thf(f731,plain,(
% 1.69/1.43 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 1.69/1.43 inference(backward_demodulation,[status(thm)],[f223,f729])).
% 1.69/1.43 thf(f729,plain,(
% 1.69/1.43 ($false = (in @ sK7 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0)))))) | (~spl0_2 | ~spl0_3)),
% 1.69/1.43 inference(backward_demodulation,[status(thm)],[f675,f714])).
% 1.69/1.43 thf(f714,plain,(
% 1.69/1.43 (sK8 = sK7) | ~spl0_3),
% 1.69/1.43 inference(equality_proxy_clausification,[status(thm)],[f685])).
% 1.69/1.43 thf(f685,plain,(
% 1.69/1.43 ((sK7 = sK8) = $true) | ~spl0_3),
% 1.69/1.43 inference(avatar_component_clause,[status(thm)],[f684])).
% 1.69/1.43 thf(f684,definition,(
% 1.69/1.43 spl0_3 <=> ((sK7 = sK8) = $true)),
% 1.69/1.43 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.69/1.43 thf(f675,plain,(
% 1.69/1.43 ((in @ sK8 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0))))) = $false) | ~spl0_2),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f663])).
% 1.69/1.43 thf(f663,plain,(
% 1.69/1.43 ($false = ((in @ sK8 @ (setadjoin @ sK7 @ emptyset)) => (in @ sK8 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0))))))) | ~spl0_2),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f657])).
% 1.69/1.43 thf(f657,plain,(
% 1.69/1.43 (((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK7 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1))))))) @ sK8) = $false) | ~spl0_2),
% 1.69/1.43 inference(sigma_clausification,[status(thm)],[f641])).
% 1.69/1.43 thf(f641,plain,(
% 1.69/1.43 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK7 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1)))))))) = $false) | ~spl0_2),
% 1.69/1.43 inference(avatar_component_clause,[status(thm)],[f640])).
% 1.69/1.43 thf(f640,definition,(
% 1.69/1.43 spl0_2 <=> ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK7 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1)))))))) = $false)),
% 1.69/1.43 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.69/1.43 thf(f223,plain,(
% 1.69/1.43 ((in @ sK7 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0))))) = $true)),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f220])).
% 1.69/1.43 thf(f220,plain,(
% 1.69/1.43 (($true => (in @ sK7 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0)))))) = $true)),
% 1.69/1.43 inference(superposition,[status(thm)],[f187,f164])).
% 1.69/1.43 thf(f164,plain,(
% 1.69/1.43 ((in @ sK7 @ sK3) = $true)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f151])).
% 1.69/1.43 thf(f187,plain,(
% 1.69/1.43 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK3) => (in @ X0 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (X0 = Y0)))))))) )),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f186])).
% 1.69/1.43 thf(f186,plain,(
% 1.69/1.43 ( ! [X0 : $i] : ((((in @ X0 @ sK3) => (in @ X0 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | ($true & (X0 = Y0))))))) = $true)) )),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f185])).
% 1.69/1.43 thf(f185,plain,(
% 1.69/1.43 ( ! [X0 : $i] : ((((in @ X0 @ sK3) => ($true => (in @ X0 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | ($true & (X0 = Y0)))))))) = $true)) )),
% 1.69/1.43 inference(superposition,[status(thm)],[f125,f179])).
% 1.69/1.43 thf(f125,plain,(
% 1.69/1.43 ( ! [X0 : $o,X1 : $i] : ((((in @ X1 @ sK3) => ((~ X0) => (in @ X1 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & X0) | ((~ X0) & (X1 = Y0)))))))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f122])).
% 1.69/1.43 thf(f122,plain,(
% 1.69/1.43 ( ! [X0 : $o,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => ((~ X0) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & X0) | ((~ X0) & (Y0 = Y1))))))))) @ X1))) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f119])).
% 1.69/1.43 thf(f119,plain,(
% 1.69/1.43 ( ! [X0 : $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((~ X0) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & X0) | ((~ X0) & (Y0 = Y1)))))))))) = $true)) )),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f116])).
% 1.69/1.43 thf(f116,plain,(
% 1.69/1.43 ( ! [X0 : $o] : ((($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((~ X0) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & X0) | ((~ X0) & (Y0 = Y1))))))))))) = $true)) )),
% 1.69/1.43 inference(superposition,[status(thm)],[f100,f109])).
% 1.69/1.43 thf(f109,plain,(
% 1.69/1.43 ((in @ sK2 @ sK3) = $true)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.69/1.43 thf(f100,plain,(
% 1.69/1.43 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((in @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((~ X3) => (in @ Y0 @ (dsetconstr @ X1 @ (^[Y1 : $i]: (((X2 = Y1) & X3) | ((~ X3) & (Y0 = Y1))))))))))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f99])).
% 1.69/1.43 thf(f99,plain,(
% 1.69/1.43 ( ! [X2 : $i,X3 : $o,X1 : $i] : ((((^[Y0 : $o]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((~ Y0) => (in @ Y1 @ (dsetconstr @ X1 @ (^[Y2 : $i]: (((X2 = Y2) & Y0) | ((~ Y0) & (Y1 = Y2)))))))))))) @ X3) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f98])).
% 1.69/1.43 thf(f98,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $o @ (^[Y0 : $o]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((~ Y0) => (in @ Y1 @ (dsetconstr @ X1 @ (^[Y2 : $i]: (((X2 = Y2) & Y0) | ((~ Y0) & (Y1 = Y2))))))))))))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.69/1.43 thf(f97,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((~ Y1) => (in @ Y2 @ (dsetconstr @ X1 @ (^[Y3 : $i]: (((Y0 = Y3) & Y1) | ((~ Y1) & (Y2 = Y3)))))))))))))) @ X2) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f96])).
% 1.69/1.43 thf(f96,plain,(
% 1.69/1.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((~ Y1) => (in @ Y2 @ (dsetconstr @ X1 @ (^[Y3 : $i]: (((Y0 = Y3) & Y1) | ((~ Y1) & (Y2 = Y3))))))))))))))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.69/1.43 thf(f95,plain,(
% 1.69/1.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4)))))))))))))))) @ X1) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f87])).
% 1.69/1.43 thf(f87,plain,(
% 1.69/1.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ Y2) => (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((~ Y2) & (Y3 = Y4))))))))))))))))) = $true)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.69/1.43 thf(f703,plain,(
% 1.69/1.43 spl0_3 | ~spl0_2),
% 1.69/1.43 inference(avatar_split_clause,[status(thm)],[f701,f640,f684])).
% 1.69/1.43 thf(f701,plain,(
% 1.69/1.43 ((sK7 = sK8) = $true) | ~spl0_2),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f696])).
% 1.69/1.43 thf(f696,plain,(
% 1.69/1.43 (($true => (sK7 = sK8)) = $true) | ~spl0_2),
% 1.69/1.43 inference(superposition,[status(thm)],[f73,f676])).
% 1.69/1.43 thf(f676,plain,(
% 1.69/1.43 ((in @ sK8 @ (setadjoin @ sK7 @ emptyset)) = $true) | ~spl0_2),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f663])).
% 1.69/1.43 thf(f73,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X2 = X1)) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.69/1.43 thf(f72,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ emptyset)) => (Y0 = X1))) @ X2))) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f65])).
% 1.69/1.43 thf(f65,plain,(
% 1.69/1.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ emptyset)) => (Y0 = X1)))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.69/1.43 thf(f64,plain,(
% 1.69/1.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))) @ X1) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f61])).
% 1.69/1.43 thf(f642,plain,(
% 1.69/1.43 spl0_1 | spl0_2),
% 1.69/1.43 inference(avatar_split_clause,[status(thm)],[f635,f640,f637])).
% 1.69/1.43 thf(f635,plain,(
% 1.69/1.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1))))) => (in @ Y0 @ (setadjoin @ sK7 @ emptyset)))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK7 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1)))))))) = $false)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f199])).
% 1.69/1.43 thf(f199,plain,(
% 1.69/1.43 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK7 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1)))))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1))))) => (in @ Y0 @ (setadjoin @ sK7 @ emptyset))))))) = $true)),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f196])).
% 1.69/1.43 thf(f196,plain,(
% 1.69/1.43 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK7 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK2 = Y1) & sK4) | (sK7 = Y1))))) => (in @ Y0 @ (setadjoin @ sK7 @ emptyset))))) => $false)) = $true)),
% 1.69/1.43 inference(superposition,[status(thm)],[f58,f182])).
% 1.69/1.43 thf(f182,plain,(
% 1.69/1.43 (((dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | (sK7 = Y0)))) = (setadjoin @ sK7 @ emptyset)) = $false)),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f181])).
% 1.69/1.43 thf(f181,plain,(
% 1.69/1.43 ($false = ((dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | ((sK7 = Y0) & $true)))) = (setadjoin @ sK7 @ emptyset)))),
% 1.69/1.43 inference(boolean_simplification,[status(thm)],[f180])).
% 1.69/1.43 thf(f180,plain,(
% 1.69/1.43 (($true => ((dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK2 = Y0) & sK4) | ((sK7 = Y0) & $true)))) = (setadjoin @ sK7 @ emptyset))) = $false)),
% 1.69/1.43 inference(backward_demodulation,[status(thm)],[f163,f179])).
% 1.69/1.43 thf(f58,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (X2 = X1))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.69/1.43 thf(f57,plain,(
% 1.69/1.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (Y0 = X1)))) @ X2) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f56])).
% 1.69/1.43 thf(f56,plain,(
% 1.69/1.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (Y0 = X1))))) = $true)) )),
% 1.69/1.43 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.69/1.43 thf(f55,plain,(
% 1.69/1.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) @ X1) = $true)) )),
% 1.69/1.43 inference(pi_clausification,[status(thm)],[f50])).
% 1.69/1.43 thf(f50,plain,(
% 1.69/1.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) = $true)),
% 1.69/1.43 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.69/1.43 % SZS output end Proof for DTF2THF_20100
% 1.69/1.43 % (20382)------------------------------
% 1.69/1.43 % (20382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.43 % (20382)Termination reason: Refutation
% 1.69/1.43
% 1.69/1.43 % (20382)Memory used [KB]: 6652
% 1.69/1.43 % (20382)Time elapsed: 0.088 s
% 1.69/1.43 % (20382)Instructions burned: 247 (million)
% 1.69/1.43 % (20382)------------------------------
% 1.69/1.43 % (20382)------------------------------
% 1.69/1.43 % (20370)Success in time 0.107 s
%------------------------------------------------------------------------------