%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU705^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 09:36:32 AM UTC 2026
% Result : Theorem 1.86s 1.72s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 9
% Syntax : Number of formulae : 124 ( 73 unt; 0 typ; 2 def)
% Number of atoms : 1348 ( 367 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 2245 ( 110 ~; 164 |; 168 &;1462 @)
% ( 2 <=>; 158 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 15 con; 0-4 aty)
% ( 151 !!; 30 ??; 0 @@+; 0 @@-)
% Number of variables : 479 ( 336 ^; 141 !; 2 ?; 479 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_9,type,
singleton: $i > $o ).
thf(func_def_12,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_31,type,
sK1: $i > $o > $i > $i > $i ).
thf(func_def_36,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f602,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f330,f367,f599]) ).
thf(f599,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[status(thm)],[f598]) ).
thf(f598,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f593]) ).
thf(f593,plain,
( ( $true = $false )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f78,f590]) ).
thf(f590,plain,
( ( ( in @ sK5 @ sK3 )
= $false )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f589]) ).
thf(f589,plain,
( ( ( in @ sK5 @ sK3 )
= $false )
| ( $true = $false )
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f569,f74]) ).
thf(f74,plain,
( $true
= ( in @ sK4 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( in @ sK4 @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK4 = Y1 )
& sK2 )
| ( ( Y0 = Y1 )
& ~ sK2 ) ) ) )
@ sK3 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ sK3
@ ^ [Y2: $i] :
( ( ( Y0 = Y2 )
& sK2 )
| ( ( Y1 = Y2 )
& ~ sK2 ) ) ) )
@ sK3 ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ sK3
@ ^ [Y2: $i] :
( ( ( Y0 = Y2 )
& sK2 )
| ( ( Y1 = Y2 )
& ~ sK2 ) ) ) )
@ sK3 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] :
( ( ( Y1 = Y3 )
& sK2 )
| ( ( Y2 = Y3 )
& ~ sK2 ) ) ) )
@ Y0 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] :
( ( ( Y1 = Y3 )
& sK2 )
| ( ( Y2 = Y3 )
& ~ sK2 ) ) ) )
@ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y0 )
| ( ( Y3 = Y4 )
& ~ Y0 ) ) ) )
@ Y1 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y0 )
| ( ( Y3 = Y4 )
& ~ Y0 ) ) ) )
@ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y0 )
| ( ( Y3 = Y4 )
& ~ Y0 ) ) ) )
@ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y0 )
| ( ( Y3 = Y4 )
& ~ Y0 ) ) ) )
@ Y1 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dsetconstr @ Y1 @ Y0 ) @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y0 )
| ( ( Y3 = Y4 )
& ~ Y0 ) ) ) )
@ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dsetconstr @ Y1 @ Y0 ) @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y0 )
| ( ( Y3 = Y4 )
& ~ Y0 ) ) ) )
@ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dsetconstr @ Y1 @ Y0 ) @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y0 )
| ( ( Y3 = Y4 )
& ~ Y0 ) ) ) )
@ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= Y1 )
& ( in @ Y2 @ Y1 ) ) )
@ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( ( setadjoin @ Y5 @ emptyset )
= Y4 )
& ( in @ Y5 @ Y4 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y1 )
| ( ( Y3 = Y4 )
& ~ Y1 ) ) ) ) ) ) ) ) ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in
@ ( ^ [Y4: $i,Y5: $o,Y6: $i,Y7: $i] :
( setunion
@ ( dsetconstr @ Y4
@ ^ [Y8: $i] :
( ( ( Y6 = Y8 )
& Y5 )
| ( ( Y7 = Y8 )
& ~ Y5 ) ) ) )
@ Y1
@ Y0
@ Y2
@ Y3 )
@ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f27,f28,f31,f32,f26]) ).
thf(f26,plain,
( if
= ( ^ [Y0: $i,Y1: $o,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y1 )
| ( ( Y3 = Y4 )
& ~ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( if
= ( ^ [Y0: $i,Y1: $o,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y1 )
| ( ( Y3 = Y4 )
& ~ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [X0: $i,X1: $o,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ~ X1
& ( X3 = X4 ) )
| ( X1
& ( X2 = X4 ) ) ) ) ) )
= if ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: $i,X3: $o,X2: $i,X5: $i] :
( setunion
@ ( dsetconstr @ X0
@ ^ [X6: $i] :
( ( ~ X3
& ( X5 = X6 ) )
| ( X3
& ( X2 = X6 ) ) ) ) ) )
= if ),
file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',if) ).
thf(f32,plain,
( ifSingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( ( setadjoin @ Y5 @ emptyset )
= Y4 )
& ( in @ Y5 @ Y4 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y1 )
| ( ( Y3 = Y4 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f29]) ).
thf(f29,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i] :
? [X2: $i] :
( ( in @ X2 @ X0 )
& ( ( setadjoin @ X2 @ emptyset )
= X0 ) ) )
= singleton ),
file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',singleton) ).
thf(f25,plain,
( ifSingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( singleton
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y1 )
| ( ( Y3 = Y4 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ifSingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( singleton
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y2 = Y4 )
& Y1 )
| ( ( Y3 = Y4 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( ifSingleton
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( singleton
@ ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ~ X1
& ( X3 = X4 ) )
| ( X1
& ( X0 = X4 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ifSingleton
= ( ! [X2: $i,X3: $o,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X6: $i] :
( ( ~ X3
& ( X5 = X6 ) )
| ( X3
& ( X2 = X6 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',ifSingleton) ).
thf(f31,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= Y1 )
& ( in @ Y2 @ Y1 ) ) )
@ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f30,f29]) ).
thf(f30,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( theprop
= ( !! @ $i
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) )
= theprop ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X4: $i] :
( ( ( singleton @ X4 )
=> ( in @ ( setunion @ X4 ) @ X4 ) )
= theprop ),
file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',theprop) ).
thf(f28,plain,
( sepSubset
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( sepSubset
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i > $o] :
( ( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 )
= sepSubset ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X3: $i > $o] :
( ( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X3 @ X2 ) )
@ X0 )
= sepSubset ),
file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',sepSubset) ).
thf(f27,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetE
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',subsetE) ).
thf(f24,plain,
( ( ~ ( subsetE
=> ( sepSubset
=> ( theprop
=> ( ifSingleton
=> ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( if @ Y1 @ Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ~ ( subsetE
=> ( sepSubset
=> ( theprop
=> ( ifSingleton
=> ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( in @ ( if @ Y1 @ Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( subsetE
=> ( sepSubset
=> ( theprop
=> ( ifSingleton
=> ! [X0: $i,X1: $i,X2: $o] :
( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( if @ X1 @ X2 @ X0 @ X3 ) @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( subsetE
=> ( sepSubset
=> ( theprop
=> ( ifSingleton
=> ! [X2: $i,X0: $i,X3: $o] :
( ( in @ X2 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( in @ ( if @ X0 @ X3 @ X2 @ X5 ) @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( subsetE
=> ( sepSubset
=> ( theprop
=> ( ifSingleton
=> ! [X2: $i,X0: $i,X3: $o] :
( ( in @ X2 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( in @ ( if @ X0 @ X3 @ X2 @ X5 ) @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',ifp) ).
thf(f569,plain,
( ( $false
= ( in @ sK4 @ sK3 ) )
| ( ( in @ sK5 @ sK3 )
= $false )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f568]) ).
thf(f568,plain,
( ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( ( in @ sK5 @ sK3 )
= $false )
| ( $false
= ( in @ sK4 @ sK3 ) )
| ( ( ^ [Y0: $i] : sK4 )
!= ( ^ [Y0: $i] : sK4 ) )
| ( $true = $false )
| ( ( ^ [Y0: $i] : sK5 )
!= ( ^ [Y0: $i] : sK5 ) )
| ~ spl0_5 ),
inference(duplicate_literal_removal,[status(thm)],[f563]) ).
thf(f563,plain,
( ( $false
= ( in @ sK4 @ sK3 ) )
| ( ( ^ [Y0: $i] : sK4 )
!= ( ^ [Y0: $i] : sK4 ) )
| ( $true = $false )
| ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( ( in @ sK5 @ sK3 )
= $false )
| ( ( in @ sK5 @ sK3 )
= $false )
| ( ( ^ [Y0: $i] : sK5 )
!= ( ^ [Y0: $i] : sK5 ) )
| ( $false
= ( in @ sK4 @ sK3 ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f123,f320]) ).
thf(f320,plain,
( ( $false
= ( in @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f318]) ).
thf(f318,definition,
( spl0_5
<=> ( $false
= ( in @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X0: $o,X1: $o,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK1 @ X6 @ X1 @ X5 @ X3 ) @ ( setadjoin @ ( sK1 @ X6 @ X0 @ X4 @ X2 ) @ emptyset ) ) )
| ( $false
= ( in @ X2 @ X6 ) )
| ( $false
= ( in @ X5 @ X6 ) )
| ( ( in @ X3 @ X6 )
= $false )
| ( ( in @ X4 @ X6 )
= $false )
| ( ( ^ [Y0: $i] : X2 )
!= ( ^ [Y0: $i] : X3 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) )
| ( ( ^ [Y0: $i] : X5 )
!= ( ^ [Y0: $i] : X4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f118]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X0: $o,X1: $o,X6: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] : X5 )
!= ( ^ [Y0: $i] : X4 ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) )
| ( $false
= ( in @ X2 @ X6 ) )
| ( $false
= ( in @ X5 @ X6 ) )
| ( ( ^ [Y0: $i] : X2 )
!= ( ^ [Y0: $i] : X3 ) )
| ( $true
= ( in @ ( sK1 @ X6 @ X1 @ X5 @ X3 ) @ ( setadjoin @ ( sK1 @ X6 @ X0 @ X4 @ X2 ) @ emptyset ) ) )
| ( ( ^ [Y0: $i] : X1 )
!= ( ^ [Y0: $i] : X0 ) )
| ( ( in @ X3 @ X6 )
= $false )
| ( ( in @ X4 @ X6 )
= $false ) ),
inference(constrained_superposition,[status(thm)],[f64,f66]) ).
thf(f66,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( sK1 @ X1 @ X2 @ X3 @ X4 ) @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& X2 )
| ( ( X4 = Y0 )
& ~ X2 ) ) ) )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X4 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X3 @ X1 )
= $false )
| ( ( ( setadjoin @ ( sK1 @ X1 @ X2 @ X3 @ X4 ) @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& X2 )
| ( ( X4 = Y0 )
& ~ X2 ) ) ) )
= $true )
| ( ( in @ X4 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ X1 )
= $false )
| ( ( ( ( setadjoin @ ( sK1 @ X1 @ X2 @ X3 @ X4 ) @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& X2 )
| ( ( X4 = Y0 )
& ~ X2 ) ) ) )
& ( in @ ( sK1 @ X1 @ X2 @ X3 @ X4 )
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& X2 )
| ( ( X4 = Y0 )
& ~ X2 ) ) ) ) )
= $true )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ X1 )
= $false )
| ( ( in @ X3 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y1: $i] :
( ( ( X3 = Y1 )
& X2 )
| ( ( X4 = Y1 )
& ~ X2 ) ) ) )
& ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y1: $i] :
( ( ( X3 = Y1 )
& X2 )
| ( ( X4 = Y1 )
& ~ X2 ) ) ) ) )
@ ( sK1 @ X1 @ X2 @ X3 @ X4 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y1: $i] :
( ( ( X3 = Y1 )
& X2 )
| ( ( X4 = Y1 )
& ~ X2 ) ) ) )
& ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y1: $i] :
( ( ( X3 = Y1 )
& X2 )
| ( ( X4 = Y1 )
& ~ X2 ) ) ) ) ) )
= $true )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( in @ X4 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y1: $i] :
( ( ( X3 = Y1 )
& X2 )
| ( ( X4 = Y1 )
& ~ X2 ) ) ) )
& ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y1: $i] :
( ( ( X3 = Y1 )
& X2 )
| ( ( X4 = Y1 )
& ~ X2 ) ) ) ) ) ) ) )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ( X3 = Y2 )
& X2 )
| ( ( Y0 = Y2 )
& ~ X2 ) ) ) )
& ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ( X3 = Y2 )
& X2 )
| ( ( Y0 = Y2 )
& ~ X2 ) ) ) ) ) ) )
@ X4 ) )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ( X3 = Y2 )
& X2 )
| ( ( Y0 = Y2 )
& ~ X2 ) ) ) )
& ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ( X3 = Y2 )
& X2 )
| ( ( Y0 = Y2 )
& ~ X2 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ( X3 = Y2 )
& X2 )
| ( ( Y0 = Y2 )
& ~ X2 ) ) ) )
& ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] :
( ( ( X3 = Y2 )
& X2 )
| ( ( Y0 = Y2 )
& ~ X2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y3: $i] :
( ( ( Y0 = Y3 )
& X2 )
| ( ( Y1 = Y3 )
& ~ X2 ) ) ) )
& ( in @ Y2
@ ( dsetconstr @ X1
@ ^ [Y3: $i] :
( ( ( Y0 = Y3 )
& X2 )
| ( ( Y1 = Y3 )
& ~ X2 ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y3: $i] :
( ( ( Y0 = Y3 )
& X2 )
| ( ( Y1 = Y3 )
& ~ X2 ) ) ) )
& ( in @ Y2
@ ( dsetconstr @ X1
@ ^ [Y3: $i] :
( ( ( Y0 = Y3 )
& X2 )
| ( ( Y1 = Y3 )
& ~ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y0 )
| ( ( Y2 = Y4 )
& ~ Y0 ) ) ) )
& ( in @ Y3
@ ( dsetconstr @ X1
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y0 )
| ( ( Y2 = Y4 )
& ~ Y0 ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y0 )
| ( ( Y2 = Y4 )
& ~ Y0 ) ) ) )
& ( in @ Y3
@ ( dsetconstr @ X1
@ ^ [Y4: $i] :
( ( ( Y1 = Y4 )
& Y0 )
| ( ( Y2 = Y4 )
& ~ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] :
( ( ( Y2 = Y5 )
& Y1 )
| ( ( Y3 = Y5 )
& ~ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f64,plain,
! [X2: $o,X3: $i,X1: $i,X4: $i] :
( ( ( in @ ( sK1 @ X1 @ X2 @ X3 @ X4 )
@ ( dsetconstr @ X1
@ ^ [Y0: $i] :
( ( ( X3 = Y0 )
& X2 )
| ( ( X4 = Y0 )
& ~ X2 ) ) ) )
= $true )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X4 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f78,plain,
( ( in @ sK5 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( in @ sK5 @ sK3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& sK2 )
| ( ( sK5 = Y0 )
& ~ sK2 ) ) ) )
@ sK3 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK4 = Y1 )
& sK2 )
| ( ( Y0 = Y1 )
& ~ sK2 ) ) ) )
@ sK3 ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( in
@ ( setunion
@ ( dsetconstr @ sK3
@ ^ [Y1: $i] :
( ( ( sK4 = Y1 )
& sK2 )
| ( ( Y0 = Y1 )
& ~ sK2 ) ) ) )
@ sK3 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f367,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f366]) ).
thf(f366,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f362]) ).
thf(f362,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f78,f351]) ).
thf(f351,plain,
( ( ( in @ sK5 @ sK3 )
= $false )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f350]) ).
thf(f350,plain,
( ( $true = $false )
| ( ( in @ sK5 @ sK3 )
= $false )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f348,f74]) ).
thf(f348,plain,
( ( ( in @ sK5 @ sK3 )
= $false )
| ( $false
= ( in @ sK4 @ sK3 ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f344]) ).
thf(f344,plain,
( ( ( in @ sK5 @ sK3 )
= $false )
| ( $false
= ( in @ sK4 @ sK3 ) )
| ( $true = $false )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f324,f117]) ).
thf(f117,plain,
! [X2: $o,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ ( setadjoin @ ( sK1 @ X0 @ X2 @ X1 @ X3 ) @ emptyset ) @ X0 ) )
| ( ( in @ X1 @ X0 )
= $false )
| ( $false
= ( in @ X3 @ X0 ) ) ),
inference(superposition,[status(thm)],[f89,f66]) ).
thf(f89,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( subset @ ( dsetconstr @ X2 @ X1 ) @ X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] : ( subset @ ( dsetconstr @ Y0 @ X1 ) @ Y0 )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( dsetconstr @ Y0 @ X1 ) @ Y0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dsetconstr @ Y1 @ Y0 ) @ Y1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dsetconstr @ Y1 @ Y0 ) @ Y1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f324,plain,
( ( $false
= ( subset @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) @ sK3 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f322]) ).
thf(f322,definition,
( spl0_6
<=> ( $false
= ( subset @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f330,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f311,f322,f318]) ).
thf(f311,plain,
( ( $false
= ( in @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) ) )
| ( $false
= ( subset @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f307]) ).
thf(f307,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) ) )
| ( $false
= ( subset @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) @ sK3 ) ) ),
inference(superposition,[status(thm)],[f144,f95]) ).
thf(f95,plain,
! [X0: $i] :
( ( $true
= ( in @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ ( setadjoin @ X0 @ emptyset ) ) )
| ( ( in @ X0 @ ( setadjoin @ X0 @ emptyset ) )
= $false ) ),
inference(equality_resolution,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ X2 @ emptyset )
!= X1 )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( $false
= ( ( setadjoin @ X2 @ emptyset )
= X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( ( setadjoin @ X2 @ emptyset )
= X1 )
& ( in @ X2 @ X1 ) ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= X1 )
& ( in @ Y0 @ X1 ) )
@ X2 ) )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X1: $i] :
( ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= X1 )
& ( in @ Y0 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= X1 )
& ( in @ Y0 @ X1 ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f144,plain,
! [X0: $i] :
( ( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) ) @ X0 ) )
| ( $false
= ( subset @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) ) @ X0 ) )
| ( $false
= ( subset @ X0 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f45,f139]) ).
thf(f139,plain,
( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ sK2 @ sK4 @ sK5 ) @ emptyset ) ) @ sK3 ) ),
inference(equality_resolution,[status(thm)],[f130]) ).
thf(f130,plain,
! [X0: $o] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ X0 @ sK4 @ sK5 ) @ emptyset ) ) @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
! [X0: $o] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ X0 @ sK4 @ sK5 ) @ emptyset ) ) @ sK3 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[status(thm)],[f128,f74]) ).
thf(f128,plain,
! [X0: $o] :
( ( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ X0 @ sK4 @ sK5 ) @ emptyset ) ) @ sK3 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( $false
= ( in @ sK4 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
! [X0: $o] :
( ( $true = $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ X0 @ sK4 @ sK5 ) @ emptyset ) ) @ sK3 ) )
| ( $false
= ( in @ sK4 @ sK3 ) ) ),
inference(forward_demodulation,[status(thm)],[f125,f78]) ).
thf(f125,plain,
! [X0: $o] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( ( in @ sK5 @ sK3 )
= $false )
| ( $false
= ( in @ sK4 @ sK3 ) )
| ( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ X0 @ sK4 @ sK5 ) @ emptyset ) ) @ sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f121]) ).
thf(f121,plain,
! [X0: $o] :
( ( $false
= ( in @ ( setunion @ ( setadjoin @ ( sK1 @ sK3 @ X0 @ sK4 @ sK5 ) @ emptyset ) ) @ sK3 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( $false
= ( in @ sK4 @ sK3 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK2 ) )
| ( ( in @ sK5 @ sK3 )
= $false ) ),
inference(constrained_superposition,[status(thm)],[f77,f66]) ).
thf(f77,plain,
( ( in
@ ( setunion
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& sK2 )
| ( ( sK5 = Y0 )
& ~ sK2 ) ) ) )
@ sK3 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X2 @ X3 ) )
| ( ( subset @ X1 @ X3 )
= $false )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X3 ) )
= $true )
| ( ( subset @ X1 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X3 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ Y0 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU705^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n013.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:31:23 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.46 ---- Original DTF file ---
% 0.18/0.46 thf(spec,logic,$$dhol).
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 % File : SEU705^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.46 % Domain : Set Theory
% 0.18/0.46 % Problem : Conditionals
% 0.18/0.46 % Version : Especial > Reduced > Especial.
% 0.18/0.46 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A ->
% 0.18/0.46 % in (if A phi x y) A))
% 0.18/0.46
% 0.18/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.46 % Source : [Bro08]
% 0.18/0.46 % Names : ZFC207l [Bro08]
% 0.18/0.46
% 0.18/0.46 % Status : Theorem
% 0.18/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.18/0.46 % Syntax : Number of formulae : 19 ( 6 unt; 12 typ; 6 def)
% 0.18/0.46 % Number of atoms : 33 ( 11 equ; 0 cnn)
% 0.18/0.46 % Maximal formula atoms : 7 ( 4 avg)
% 0.18/0.46 % Number of connectives : 59 ( 2 ~; 2 |; 5 &; 39 @)
% 0.18/0.46 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.18/0.46 % Maximal formula depth : 17 ( 3 avg)
% 0.18/0.46 % Number of types : 2 ( 0 usr)
% 0.18/0.46 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.18/0.46 % Number of symbols : 13 ( 12 usr; 5 con; 0-4 aty)
% 0.18/0.46 % Number of variables : 23 ( 8 ^; 14 !; 1 ?; 23 :)
% 0.18/0.46 % SPC : TH0_THM_EQU_NAR
% 0.18/0.46
% 0.18/0.46 % Comments : http://mathgate.info/detsetitem.php?id=261
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 thf(in_type,type,
% 0.18/0.46 in: $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(emptyset_type,type,
% 0.18/0.46 emptyset: $i ).
% 0.18/0.46
% 0.18/0.46 thf(setadjoin_type,type,
% 0.18/0.46 setadjoin: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(setunion_type,type,
% 0.18/0.46 setunion: $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstr_type,type,
% 0.18/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.46
% 0.18/0.46 thf(subset_type,type,
% 0.18/0.46 subset: $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetE_type,type,
% 0.18/0.46 subsetE: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetE,definition,
% 0.18/0.46 ( subsetE
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(sepSubset_type,type,
% 0.18/0.46 sepSubset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(sepSubset,definition,
% 0.18/0.46 ( sepSubset
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.46 ( subset
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(singleton_type,type,
% 0.18/0.46 singleton: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(singleton,definition,
% 0.18/0.46 ( singleton
% 0.18/0.46 = ( ^ [A: $i] :
% 0.18/0.46 ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 & ( A
% 0.18/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(theprop_type,type,
% 0.18/0.46 theprop: $o ).
% 0.18/0.46
% 0.18/0.46 thf(theprop,definition,
% 0.18/0.46 ( theprop
% 0.18/0.46 = ( ! [X: $i] :
% 0.18/0.46 ( ( singleton @ X )
% 0.18/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ifSingleton_type,type,
% 0.18/0.46 ifSingleton: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ifSingleton,definition,
% 0.18/0.46 ( ifSingleton
% 0.18/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ A )
% 0.18/0.46 => ( singleton
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xz: $i] :
% 0.18/0.46 ( ( Xphi
% 0.18/0.46 & ( Xz = Xx ) )
% 0.18/0.46 | ( ~ Xphi
% 0.18/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(if_type,type,
% 0.18/0.46 if: $i > $o > $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(if,definition,
% 0.18/0.46 ( if
% 0.18/0.46 = ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] :
% 0.18/0.46 ( setunion
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xz: $i] :
% 0.18/0.46 ( ( Xphi
% 0.18/0.46 & ( Xz = Xx ) )
% 0.18/0.46 | ( ~ Xphi
% 0.18/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ifp,conjecture,
% 0.18/0.46 ( subsetE
% 0.18/0.46 => ( sepSubset
% 0.18/0.46 => ( theprop
% 0.18/0.46 => ( ifSingleton
% 0.18/0.46 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ A )
% 0.18/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 1.77/1.45 ---- Embedded in THF ---
% 1.77/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.77/1.45 %%% Generated on Tue Feb 24 12:31:24 EST 2026
% 1.77/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 1.77/1.45 %%% Logic specification used:
% 1.77/1.45 %%% thf(spec, logic, $$dhol).
% 1.77/1.45
% 1.77/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2DTF3057.p
% See solution above
% 1.77/1.45 ------------------------
% 1.77/1.46 ---- Cleaned THF ---
% 1.77/1.46 thf(in_type,type,
% 1.77/1.46 in: $i > $i > $o ).
% 1.77/1.46
% 1.77/1.46 thf(emptyset_type,type,
% 1.77/1.46 emptyset: $i ).
% 1.77/1.46
% 1.77/1.46 thf(setadjoin_type,type,
% 1.77/1.46 setadjoin: $i > $i > $i ).
% 1.77/1.46
% 1.77/1.46 thf(setunion_type,type,
% 1.77/1.46 setunion: $i > $i ).
% 1.77/1.46
% 1.77/1.46 thf(dsetconstr_type,type,
% 1.77/1.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.77/1.46
% 1.77/1.46 thf(subset_type,type,
% 1.77/1.46 subset: $i > $i > $o ).
% 1.77/1.46
% 1.77/1.46 thf(subsetE_type,type,
% 1.77/1.46 subsetE: $o ).
% 1.77/1.46
% 1.77/1.46 thf(subsetE,definition,
% 1.77/1.46 ( subsetE
% 1.77/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.77/1.46 ( ( subset @ A @ B )
% 1.77/1.46 => ( ( in @ Xx @ A )
% 1.77/1.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.77/1.46
% 1.77/1.46 thf(sepSubset_type,type,
% 1.77/1.46 sepSubset: $o ).
% 1.77/1.46
% 1.77/1.46 thf(sepSubset,definition,
% 1.77/1.46 ( sepSubset
% 1.77/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 1.77/1.46 ( subset
% 1.77/1.46 @ ( dsetconstr @ A
% 1.77/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.77/1.46 @ A ) ) ) ).
% 1.77/1.46
% 1.77/1.46 thf(singleton_type,type,
% 1.77/1.46 singleton: $i > $o ).
% 1.77/1.46
% 1.77/1.46 thf(singleton,definition,
% 1.77/1.46 ( singleton
% 1.77/1.46 = ( ^ [A: $i] :
% 1.77/1.46 ? [Xx: $i] :
% 1.77/1.46 ( ( in @ Xx @ A )
% 1.77/1.46 & ( A
% 1.77/1.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.77/1.46
% 1.77/1.46 thf(theprop_type,type,
% 1.77/1.46 theprop: $o ).
% 1.77/1.46
% 1.77/1.46 thf(theprop,definition,
% 1.77/1.46 ( theprop
% 1.77/1.46 = ( ! [X: $i] :
% 1.77/1.46 ( ( singleton @ X )
% 1.77/1.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 1.77/1.46
% 1.77/1.46 thf(ifSingleton_type,type,
% 1.77/1.46 ifSingleton: $o ).
% 1.77/1.46
% 1.77/1.46 thf(ifSingleton,definition,
% 1.77/1.46 ( ifSingleton
% 1.77/1.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.77/1.46 ( ( in @ Xx @ A )
% 1.77/1.46 => ! [Xy: $i] :
% 1.77/1.46 ( ( in @ Xy @ A )
% 1.77/1.46 => ( singleton
% 1.77/1.46 @ ( dsetconstr @ A
% 1.77/1.46 @ ^ [Xz: $i] :
% 1.77/1.46 ( ( Xphi
% 1.77/1.46 & ( Xz = Xx ) )
% 1.77/1.46 | ( ~ Xphi
% 1.77/1.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 1.77/1.46
% 1.77/1.46 thf(if_type,type,
% 1.77/1.46 if: $i > $o > $i > $i > $i ).
% 1.77/1.46
% 1.77/1.46 thf(if,definition,
% 1.77/1.46 ( if
% 1.77/1.46 = ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] :
% 1.77/1.46 ( setunion
% 1.77/1.46 @ ( dsetconstr @ A
% 1.77/1.46 @ ^ [Xz: $i] :
% 1.77/1.46 ( ( Xphi
% 1.77/1.46 & ( Xz = Xx ) )
% 1.77/1.46 | ( ~ Xphi
% 1.77/1.46 & ( Xz = Xy ) ) ) ) ) ) ) ).
% 1.77/1.46
% 1.77/1.46 thf(ifp,conjecture,
% 1.77/1.46 ( subsetE
% 1.77/1.46 => ( sepSubset
% 1.77/1.46 => ( theprop
% 1.77/1.46 => ( ifSingleton
% 1.77/1.46 => ! [A: $i,Xphi: $o,Xx: $i] :
% 1.77/1.46 ( ( in @ Xx @ A )
% 1.77/1.46 => ! [Xy: $i] :
% 1.77/1.46 ( ( in @ Xy @ A )
% 1.77/1.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ) ) ).
% 1.77/1.46 ------------------------
% 1.77/1.48 % (3196)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/2Mi)
% 1.77/1.48 % (3194)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_3057 for (2999ds/4Mi)
% 1.77/1.48 % (3197)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_3057 for (2999ds/2Mi)
% 1.77/1.48 % (3195)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_3057 for (2999ds/27Mi)
% 1.77/1.48 % (3193)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/183Mi)
% 1.77/1.48 % (3198)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_3057 for (2999ds/275Mi)
% 1.77/1.48 % (3199)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/18Mi)
% 1.77/1.48 % (3196)Instruction limit reached!
% 1.77/1.48 % (3196)------------------------------
% 1.77/1.48 % (3196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.48 % (3196)Termination reason: Unknown
% 1.77/1.48 % (3196)Termination phase: shuffling
% 1.77/1.48
% 1.77/1.48 % (3197)Instruction limit reached!
% 1.77/1.48 % (3197)------------------------------
% 1.77/1.48 % (3197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.48 % (3197)Termination reason: Unknown
% 1.77/1.48 % (3197)Termination phase: shuffling
% 1.77/1.48
% 1.77/1.48 % (3197)Memory used [KB]: 1023
% 1.77/1.48 % (3197)Time elapsed: 0.002 s
% 1.77/1.48 % (3197)Instructions burned: 2 (million)
% 1.77/1.48 % (3197)------------------------------
% 1.77/1.48 % (3197)------------------------------
% 1.77/1.48 % (3196)Memory used [KB]: 1023
% 1.77/1.48 % (3196)Time elapsed: 0.003 s
% 1.77/1.48 % (3196)Instructions burned: 2 (million)
% 1.77/1.48 % (3196)------------------------------
% 1.77/1.48 % (3196)------------------------------
% 1.77/1.48 % (3194)Instruction limit reached!
% 1.77/1.48 % (3194)------------------------------
% 1.77/1.48 % (3194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.48 % (3194)Termination reason: Unknown
% 1.77/1.48 % (3194)Termination phase: Saturation
% 1.77/1.48
% 1.77/1.48 % (3194)Memory used [KB]: 5500
% 1.77/1.48 % (3194)Time elapsed: 0.004 s
% 1.77/1.48 % (3194)Instructions burned: 5 (million)
% 1.77/1.48 % (3194)------------------------------
% 1.77/1.48 % (3194)------------------------------
% 1.77/1.49 % (3199)Instruction limit reached!
% 1.77/1.49 % (3199)------------------------------
% 1.77/1.49 % (3199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.49 % (3199)Termination reason: Unknown
% 1.77/1.49 % (3199)Termination phase: Saturation
% 1.77/1.49
% 1.77/1.49 % (3199)Memory used [KB]: 5628
% 1.77/1.49 % (3199)Time elapsed: 0.011 s
% 1.77/1.49 % (3199)Instructions burned: 18 (million)
% 1.77/1.49 % (3199)------------------------------
% 1.77/1.49 % (3199)------------------------------
% 1.77/1.49 % (3195)Instruction limit reached!
% 1.77/1.49 % (3195)------------------------------
% 1.77/1.49 % (3195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.49 % (3195)Termination reason: Unknown
% 1.77/1.49 % (3195)Termination phase: Saturation
% 1.77/1.49
% 1.77/1.49 % (3195)Memory used [KB]: 5628
% 1.77/1.49 % (3195)Time elapsed: 0.016 s
% 1.77/1.49 % (3195)Instructions burned: 28 (million)
% 1.77/1.49 % (3195)------------------------------
% 1.77/1.49 % (3195)------------------------------
% 1.77/1.49 % (3200)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/3Mi)
% 1.77/1.49 % (3201)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_3057 for (2999ds/37Mi)
% 1.77/1.50 % (3200)Instruction limit reached!
% 1.77/1.50 % (3200)------------------------------
% 1.77/1.50 % (3200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50 % (3202)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_3057 for (2999ds/15Mi)
% 1.77/1.50 % (3200)Termination reason: Unknown
% 1.77/1.50 % (3200)Termination phase: Property scanning
% 1.77/1.50
% 1.77/1.50 % (3200)Memory used [KB]: 1023
% 1.77/1.50 % (3200)Time elapsed: 0.003 s
% 1.77/1.50 % (3200)Instructions burned: 4 (million)
% 1.77/1.50 % (3200)------------------------------
% 1.77/1.50 % (3200)------------------------------
% 1.86/1.50 % (3202)Instruction limit reached!
% 1.86/1.50 % (3202)------------------------------
% 1.86/1.50 % (3202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.50 % (3203)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_3057 for (2999ds/3Mi)
% 1.86/1.50 % (3202)Termination reason: Unknown
% 1.86/1.50 % (3202)Termination phase: Saturation
% 1.86/1.50
% 1.86/1.50 % (3202)Memory used [KB]: 5756
% 1.86/1.50 % (3202)Time elapsed: 0.009 s
% 1.86/1.50 % (3202)Instructions burned: 15 (million)
% 1.86/1.50 % (3202)------------------------------
% 1.86/1.50 % (3202)------------------------------
% 1.86/1.51 % (3203)Instruction limit reached!
% 1.86/1.51 % (3203)------------------------------
% 1.86/1.51 % (3203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.51 % (3203)Termination reason: Unknown
% 1.86/1.51 % (3203)Termination phase: Property scanning
% 1.86/1.51
% 1.86/1.51 % (3203)Memory used [KB]: 1023
% 1.86/1.51 % (3203)Time elapsed: 0.003 s
% 1.86/1.51 % (3203)Instructions burned: 3 (million)
% 1.86/1.51 % (3203)------------------------------
% 1.86/1.51 % (3203)------------------------------
% 1.86/1.51 % (3204)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_3057 for (2999ds/1041Mi)
% 1.86/1.51 % (3205)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/7Mi)
% 1.86/1.51 % (3201)Instruction limit reached!
% 1.86/1.51 % (3201)------------------------------
% 1.86/1.51 % (3201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.51 % (3201)Termination reason: Unknown
% 1.86/1.51 % (3201)Termination phase: Saturation
% 1.86/1.51
% 1.86/1.51 % (3201)Memory used [KB]: 5756
% 1.86/1.51 % (3201)Time elapsed: 0.020 s
% 1.86/1.51 % (3201)Instructions burned: 38 (million)
% 1.86/1.51 % (3201)------------------------------
% 1.86/1.51 % (3201)------------------------------
% 1.86/1.52 % (3205)Instruction limit reached!
% 1.86/1.52 % (3205)------------------------------
% 1.86/1.52 % (3205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.52 % (3205)Termination reason: Unknown
% 1.86/1.52 % (3205)Termination phase: Saturation
% 1.86/1.52
% 1.86/1.52 % (3205)Memory used [KB]: 1023
% 1.86/1.52 % (3205)Time elapsed: 0.006 s
% 1.86/1.52 % (3205)Instructions burned: 8 (million)
% 1.86/1.52 % (3205)------------------------------
% 1.86/1.52 % (3205)------------------------------
% 1.86/1.52 % (3206)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/16Mi)
% 1.86/1.52 % (3207)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_3057 for (2999ds/3Mi)
% 1.86/1.52 % (3207)Instruction limit reached!
% 1.86/1.52 % (3207)------------------------------
% 1.86/1.52 % (3207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.52 % (3207)Termination reason: Unknown
% 1.86/1.52 % (3207)Termination phase: Property scanning
% 1.86/1.52
% 1.86/1.52 % (3207)Memory used [KB]: 1023
% 1.86/1.52 % (3207)Time elapsed: 0.003 s
% 1.86/1.52 % (3207)Instructions burned: 3 (million)
% 1.86/1.52 % (3207)------------------------------
% 1.86/1.52 % (3207)------------------------------
% 1.86/1.53 % (3206)Instruction limit reached!
% 1.86/1.53 % (3206)------------------------------
% 1.86/1.53 % (3206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.53 % (3206)Termination reason: Unknown
% 1.86/1.53 % (3206)Termination phase: Saturation
% 1.86/1.53
% 1.86/1.53 % (3206)Memory used [KB]: 5884
% 1.86/1.53 % (3206)Time elapsed: 0.010 s
% 1.86/1.53 % (3206)Instructions burned: 16 (million)
% 1.86/1.53 % (3206)------------------------------
% 1.86/1.53 % (3206)------------------------------
% 1.86/1.53 % (3208)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_3057 for (2999ds/3Mi)
% 1.86/1.53 % (3208)Instruction limit reached!
% 1.86/1.53 % (3208)------------------------------
% 1.86/1.53 % (3208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.53 % (3208)Termination reason: Unknown
% 1.86/1.53 % (3208)Termination phase: Property scanning
% 1.86/1.53
% 1.86/1.53 % (3208)Memory used [KB]: 1023
% 1.86/1.53 % (3208)Time elapsed: 0.003 s
% 1.86/1.53 % (3208)Instructions burned: 3 (million)
% 1.86/1.53 % (3208)------------------------------
% 1.86/1.53 % (3208)------------------------------
% 1.86/1.53 % (3209)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/7Mi)
% 1.86/1.53 % (3209)Refutation not found, incomplete strategy
% 1.86/1.53 % (3209)------------------------------
% 1.86/1.53 % (3209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.53 % (3209)Termination reason: Refutation not found, incomplete strategy
% 1.86/1.53
% 1.86/1.53
% 1.86/1.53 % (3209)Memory used [KB]: 5500
% 1.86/1.53 % (3209)Time elapsed: 0.004 s
% 1.86/1.53 % (3209)Instructions burned: 6 (million)
% 1.86/1.53 % (3209)------------------------------
% 1.86/1.53 % (3209)------------------------------
% 1.86/1.54 % (3210)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/3Mi)
% 1.86/1.54 % (3210)Instruction limit reached!
% 1.86/1.54 % (3210)------------------------------
% 1.86/1.54 % (3210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.54 % (3210)Termination reason: Unknown
% 1.86/1.54 % (3210)Termination phase: Function definition elimination
% 1.86/1.54
% 1.86/1.54 % (3210)Memory used [KB]: 1023
% 1.86/1.54 % (3210)Time elapsed: 0.003 s
% 1.86/1.54 % (3210)Instructions burned: 4 (million)
% 1.86/1.54 % (3210)------------------------------
% 1.86/1.54 % (3210)------------------------------
% 1.86/1.54 % (3211)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/4Mi)
% 1.86/1.55 % (3211)Instruction limit reached!
% 1.86/1.55 % (3211)------------------------------
% 1.86/1.55 % (3211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.55 % (3211)Termination reason: Unknown
% 1.86/1.55 % (3211)Termination phase: Function definition elimination
% 1.86/1.55
% 1.86/1.55 % (3211)Memory used [KB]: 1023
% 1.86/1.55 % (3211)Time elapsed: 0.003 s
% 1.86/1.55 % (3211)Instructions burned: 4 (million)
% 1.86/1.55 % (3211)------------------------------
% 1.86/1.55 % (3211)------------------------------
% 1.86/1.55 % (3212)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/18Mi)
% 1.86/1.55 % (3213)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/710Mi)
% 1.86/1.56 % (3212)Instruction limit reached!
% 1.86/1.56 % (3212)------------------------------
% 1.86/1.56 % (3212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.56 % (3214)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/6Mi)
% 1.86/1.56 % (3212)Termination reason: Unknown
% 1.86/1.56 % (3212)Termination phase: Saturation
% 1.86/1.56
% 1.86/1.56 % (3212)Memory used [KB]: 5628
% 1.86/1.56 % (3212)Time elapsed: 0.011 s
% 1.86/1.56 % (3212)Instructions burned: 18 (million)
% 1.86/1.56 % (3212)------------------------------
% 1.86/1.56 % (3212)------------------------------
% 1.86/1.56 % (3214)Instruction limit reached!
% 1.86/1.56 % (3214)------------------------------
% 1.86/1.56 % (3214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.56 % (3214)Termination reason: Unknown
% 1.86/1.56 % (3214)Termination phase: Saturation
% 1.86/1.56
% 1.86/1.56 % (3214)Memory used [KB]: 5500
% 1.86/1.56 % (3214)Time elapsed: 0.005 s
% 1.86/1.56 % (3214)Instructions burned: 8 (million)
% 1.86/1.56 % (3214)------------------------------
% 1.86/1.56 % (3214)------------------------------
% 1.86/1.56 % (3215)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_3057 for (2999ds/902Mi)
% 1.86/1.56 % (3193)Instruction limit reached!
% 1.86/1.56 % (3193)------------------------------
% 1.86/1.56 % (3193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.56 % (3193)Termination reason: Unknown
% 1.86/1.56 % (3193)Termination phase: Saturation
% 1.86/1.56
% 1.86/1.56 % (3193)Memory used [KB]: 6140
% 1.86/1.56 % (3193)Time elapsed: 0.088 s
% 1.86/1.56 % (3193)Instructions burned: 183 (million)
% 1.86/1.56 % (3193)------------------------------
% 1.86/1.56 % (3193)------------------------------
% 1.86/1.57 % (3198)Instruction limit reached!
% 1.86/1.57 % (3198)------------------------------
% 1.86/1.57 % (3198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.57 % (3198)Termination reason: Unknown
% 1.86/1.57 % (3198)Termination phase: Saturation
% 1.86/1.57
% 1.86/1.57 % (3198)Memory used [KB]: 5756
% 1.86/1.57 % (3198)Time elapsed: 0.091 s
% 1.86/1.57 % (3198)Instructions burned: 278 (million)
% 1.86/1.57 % (3198)------------------------------
% 1.86/1.57 % (3198)------------------------------
% 1.86/1.57 % (3216)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_3057 for (2999ds/21Mi)
% 1.86/1.58 % (3217)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/5Mi)
% 1.86/1.58 % (3217)Instruction limit reached!
% 1.86/1.58 % (3217)------------------------------
% 1.86/1.58 % (3217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.58 % (3217)Termination reason: Unknown
% 1.86/1.58 % (3217)Termination phase: Saturation
% 1.86/1.58
% 1.86/1.58 % (3217)Memory used [KB]: 5500
% 1.86/1.58 % (3217)Time elapsed: 0.004 s
% 1.86/1.58 % (3217)Instructions burned: 6 (million)
% 1.86/1.58 % (3217)------------------------------
% 1.86/1.58 % (3217)------------------------------
% 1.86/1.58 % (3218)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_3057 for (2999ds/6Mi)
% 1.86/1.58 % (3219)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/377Mi)
% 1.86/1.58 % (3218)Instruction limit reached!
% 1.86/1.58 % (3218)------------------------------
% 1.86/1.58 % (3218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.58 % (3216)Instruction limit reached!
% 1.86/1.58 % (3216)------------------------------
% 1.86/1.58 % (3216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.58 % (3218)Termination reason: Unknown
% 1.86/1.58 % (3218)Termination phase: Saturation
% 1.86/1.58
% 1.86/1.58 % (3218)Memory used [KB]: 5500
% 1.86/1.58 % (3218)Time elapsed: 0.005 s
% 1.86/1.58 % (3218)Instructions burned: 8 (million)
% 1.86/1.58 % (3218)------------------------------
% 1.86/1.58 % (3218)------------------------------
% 1.86/1.58 % (3216)Termination reason: Unknown
% 1.86/1.58 % (3216)Termination phase: Saturation
% 1.86/1.58
% 1.86/1.58 % (3216)Memory used [KB]: 5628
% 1.86/1.58 % (3216)Time elapsed: 0.013 s
% 1.86/1.58 % (3216)Instructions burned: 22 (million)
% 1.86/1.58 % (3216)------------------------------
% 1.86/1.58 % (3216)------------------------------
% 1.86/1.59 % (3220)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_3057 for (2998ds/779Mi)
% 1.86/1.60 % (3221)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_3057 for (2998ds/19Mi)
% 1.86/1.60 % (3222)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/879Mi)
% 1.86/1.61 % (3221)Refutation not found, incomplete strategy
% 1.86/1.61 % (3221)------------------------------
% 1.86/1.61 % (3221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.61 % (3221)Termination reason: Refutation not found, incomplete strategy
% 1.86/1.61
% 1.86/1.61
% 1.86/1.61 % (3221)Memory used [KB]: 5628
% 1.86/1.61 % (3221)Time elapsed: 0.009 s
% 1.86/1.61 % (3221)Instructions burned: 15 (million)
% 1.86/1.61 % (3221)------------------------------
% 1.86/1.61 % (3221)------------------------------
% 1.86/1.62 % (3223)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/17Mi)
% 1.86/1.63 % (3223)Instruction limit reached!
% 1.86/1.63 % (3223)------------------------------
% 1.86/1.63 % (3223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.63 % (3223)Termination reason: Unknown
% 1.86/1.63 % (3223)Termination phase: Saturation
% 1.86/1.63
% 1.86/1.63 % (3223)Memory used [KB]: 5628
% 1.86/1.63 % (3223)Time elapsed: 0.035 s
% 1.86/1.63 % (3223)Instructions burned: 18 (million)
% 1.86/1.63 % (3223)------------------------------
% 1.86/1.63 % (3223)------------------------------
% 1.86/1.65 % (3224)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/3Mi)
% 1.86/1.65 % (3224)Instruction limit reached!
% 1.86/1.65 % (3224)------------------------------
% 1.86/1.65 % (3224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.65 % (3224)Termination reason: Unknown
% 1.86/1.65 % (3224)Termination phase: Preprocessing 3
% 1.86/1.65
% 1.86/1.65 % (3224)Memory used [KB]: 1023
% 1.86/1.65 % (3224)Time elapsed: 0.003 s
% 1.86/1.65 % (3224)Instructions burned: 3 (million)
% 1.86/1.65 % (3224)------------------------------
% 1.86/1.65 % (3224)------------------------------
% 1.86/1.67 % (3225)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/30Mi)
% 1.86/1.67 % (3225)Refutation not found, incomplete strategy
% 1.86/1.67 % (3225)------------------------------
% 1.86/1.67 % (3225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.67 % (3225)Termination reason: Refutation not found, incomplete strategy
% 1.86/1.67
% 1.86/1.67
% 1.86/1.67 % (3225)Memory used [KB]: 5500
% 1.86/1.67 % (3225)Time elapsed: 0.005 s
% 1.86/1.67 % (3225)Instructions burned: 7 (million)
% 1.86/1.67 % (3225)------------------------------
% 1.86/1.67 % (3225)------------------------------
% 1.86/1.69 % (3226)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/127Mi)
% 1.86/1.72 % (3220)First to succeed.
% 1.86/1.72 % (3220)Refutation found. Thanks to Tanya!
% 1.86/1.72 % SZS status Theorem for DTF2THF_3057
% 1.86/1.72 % SZS output start Proof for DTF2THF_3057
% 1.86/1.72 thf(func_def_0, type, in: $i > $i > $o).
% 1.86/1.72 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.86/1.72 thf(func_def_3, type, setunion: $i > $i).
% 1.86/1.72 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 1.86/1.72 thf(func_def_5, type, subset: $i > $i > $o).
% 1.86/1.72 thf(func_def_9, type, singleton: $i > $o).
% 1.86/1.72 thf(func_def_12, type, if: $i > $o > $i > $i > $i).
% 1.86/1.72 thf(func_def_31, type, sK1: $i > $o > $i > $i > $i).
% 1.86/1.72 thf(func_def_36, type, ph6: !>[X0: $tType]:(X0)).
% 1.86/1.72 thf(f602,plain,(
% 1.86/1.72 $false),
% 1.86/1.72 inference(avatar_sat_refutation,[status(thm)],[f330,f367,f599])).
% 1.86/1.72 thf(f599,plain,(
% 1.86/1.72 ~spl0_5),
% 1.86/1.72 inference(avatar_contradiction_clause,[status(thm)],[f598])).
% 1.86/1.72 thf(f598,plain,(
% 1.86/1.72 $false | ~spl0_5),
% 1.86/1.72 inference(trivial_inequality_removal,[status(thm)],[f593])).
% 1.86/1.72 thf(f593,plain,(
% 1.86/1.72 ($true = $false) | ~spl0_5),
% 1.86/1.72 inference(backward_demodulation,[status(thm)],[f78,f590])).
% 1.86/1.72 thf(f590,plain,(
% 1.86/1.72 ((in @ sK5 @ sK3) = $false) | ~spl0_5),
% 1.86/1.72 inference(trivial_inequality_removal,[status(thm)],[f589])).
% 1.86/1.72 thf(f589,plain,(
% 1.86/1.72 ((in @ sK5 @ sK3) = $false) | ($true = $false) | ~spl0_5),
% 1.86/1.72 inference(forward_demodulation,[status(thm)],[f569,f74])).
% 1.86/1.72 thf(f74,plain,(
% 1.86/1.72 ($true = (in @ sK4 @ sK3))),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.86/1.72 thf(f72,plain,(
% 1.86/1.72 (((in @ sK4 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (setunion @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK4 = Y1) & sK2) | ((Y0 = Y1) & (~ sK2)))))) @ sK3))))) = $false)),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.86/1.72 thf(f71,plain,(
% 1.86/1.72 (((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (in @ (setunion @ (dsetconstr @ sK3 @ (^[Y2 : $i]: (((Y0 = Y2) & sK2) | ((Y1 = Y2) & (~ sK2)))))) @ sK3)))))) @ sK4) = $false)),
% 1.86/1.72 inference(sigma_clausification,[status(thm)],[f70])).
% 1.86/1.72 thf(f70,plain,(
% 1.86/1.72 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (in @ (setunion @ (dsetconstr @ sK3 @ (^[Y2 : $i]: (((Y0 = Y2) & sK2) | ((Y1 = Y2) & (~ sK2)))))) @ sK3))))))) = $false)),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.86/1.72 thf(f69,plain,(
% 1.86/1.72 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (((Y1 = Y3) & sK2) | ((Y2 = Y3) & (~ sK2)))))) @ Y0)))))))) @ sK3))),
% 1.86/1.72 inference(sigma_clausification,[status(thm)],[f68])).
% 1.86/1.72 thf(f68,plain,(
% 1.86/1.72 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (((Y1 = Y3) & sK2) | ((Y2 = Y3) & (~ sK2)))))) @ Y0))))))))))),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.86/1.72 thf(f67,plain,(
% 1.86/1.72 (((^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y2 = Y4) & Y0) | ((Y3 = Y4) & (~ Y0)))))) @ Y1)))))))))) @ sK2) = $false)),
% 1.86/1.72 inference(sigma_clausification,[status(thm)],[f50])).
% 1.86/1.72 thf(f50,plain,(
% 1.86/1.72 ($false = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y2 = Y4) & Y0) | ((Y3 = Y4) & (~ Y0)))))) @ Y1))))))))))))),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.86/1.72 thf(f48,plain,(
% 1.86/1.72 (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1)))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y2 = Y4) & Y0) | ((Y3 = Y4) & (~ Y0)))))) @ Y1)))))))))))) = $false)),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.86/1.72 thf(f46,plain,(
% 1.86/1.72 ($false = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1)))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y2 = Y4) & Y0) | ((Y3 = Y4) & (~ Y0)))))) @ Y1))))))))))))))),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.86/1.72 thf(f36,plain,(
% 1.86/1.72 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1)))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y2 = Y4) & Y0) | ((Y3 = Y4) & (~ Y0)))))) @ Y1)))))))))))))))),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.86/1.72 thf(f35,plain,(
% 1.86/1.72 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1)))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y2 = Y4) & Y0) | ((Y3 = Y4) & (~ Y0)))))) @ Y1))))))))))))))))),
% 1.86/1.72 inference(not_proxy_clausification,[status(thm)],[f34])).
% 1.86/1.72 thf(f34,plain,(
% 1.86/1.72 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1)))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (((Y2 = Y4) & Y0) | ((Y3 = Y4) & (~ Y0)))))) @ Y1)))))))))))))))))),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.86/1.72 thf(f33,plain,(
% 1.86/1.72 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = Y1) & (in @ Y2 @ Y1))))) @ Y0) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((setadjoin @ Y5 @ emptyset) = Y4) & (in @ Y5 @ Y4))))) @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y2 = Y4) & Y1) | ((Y3 = Y4) & (~ Y1)))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (setunion @ (dsetconstr @ Y4 @ (^[Y8 : $i]: (((Y6 = Y8) & Y5) | ((Y7 = Y8) & (~ Y5))))))))))))) @ Y1 @ Y0 @ Y2 @ Y3) @ Y1)))))))))))))))))),
% 1.86/1.72 inference(definition_unfolding,[status(thm)],[f24,f27,f28,f31,f32,f26])).
% 1.86/1.72 thf(f26,plain,(
% 1.86/1.72 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y2 = Y4) & Y1) | ((Y3 = Y4) & (~ Y1))))))))))))))),
% 1.86/1.72 inference(cnf_transformation,[status(thm)],[f13])).
% 1.86/1.72 thf(f13,plain,(
% 1.86/1.72 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y2 = Y4) & Y1) | ((Y3 = Y4) & (~ Y1))))))))))))))),
% 1.86/1.72 inference(fool_elimination,[status(thm)],[f12])).
% 1.86/1.72 thf(f12,plain,(
% 1.86/1.72 ((^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : ((~X1 & (X3 = X4)) | (X1 & (X2 = X4))))))) = if)),
% 1.86/1.72 inference(rectify,[status(thm)],[f6])).
% 1.86/1.72 thf(f6,axiom,(
% 1.86/1.72 ((^[X0 : $i, X3 : $o, X2 : $i, X5 : $i] : (setunion @ (dsetconstr @ X0 @ (^[X6 : $i] : ((~X3 & (X5 = X6)) | (X3 & (X2 = X6))))))) = if)),
% 1.86/1.72 file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',if)).
% 1.86/1.72 thf(f32,plain,(
% 1.86/1.72 (ifSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((setadjoin @ Y5 @ emptyset) = Y4) & (in @ Y5 @ Y4))))) @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y2 = Y4) & Y1) | ((Y3 = Y4) & (~ Y1)))))))))))))))))),
% 1.86/1.72 inference(definition_unfolding,[status(thm)],[f25,f29])).
% 1.86/1.72 thf(f29,plain,(
% 1.86/1.72 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.86/1.72 inference(cnf_transformation,[status(thm)],[f19])).
% 1.86/1.72 thf(f19,plain,(
% 1.86/1.72 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.86/1.72 inference(fool_elimination,[status(thm)],[f18])).
% 1.86/1.72 thf(f18,plain,(
% 1.86/1.72 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 1.86/1.72 inference(rectify,[status(thm)],[f3])).
% 1.86/1.72 thf(f3,axiom,(
% 1.86/1.72 ((^[X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & ((setadjoin @ X2 @ emptyset) = X0)))) = singleton)),
% 1.86/1.72 file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',singleton)).
% 1.86/1.72 thf(f25,plain,(
% 1.86/1.72 (ifSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y2 = Y4) & Y1) | ((Y3 = Y4) & (~ Y1)))))))))))))))))),
% 1.86/1.72 inference(cnf_transformation,[status(thm)],[f21])).
% 1.86/1.72 thf(f21,plain,(
% 1.86/1.72 (ifSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y2 = Y4) & Y1) | ((Y3 = Y4) & (~ Y1)))))))))))))))))),
% 1.86/1.72 inference(fool_elimination,[status(thm)],[f20])).
% 1.86/1.72 thf(f20,plain,(
% 1.86/1.72 (ifSingleton = ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (singleton @ (dsetconstr @ X2 @ (^[X4 : $i] : ((~X1 & (X3 = X4)) | (X1 & (X0 = X4)))))))))),
% 1.86/1.72 inference(rectify,[status(thm)],[f5])).
% 1.86/1.72 thf(f5,axiom,(
% 1.86/1.72 (ifSingleton = ! [X2 : $i,X3 : $o,X0 : $i] : ((in @ X2 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X6 : $i] : ((~X3 & (X5 = X6)) | (X3 & (X2 = X6)))))))))),
% 1.86/1.72 file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',ifSingleton)).
% 1.86/1.72 thf(f31,plain,(
% 1.86/1.72 (theprop = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = Y1) & (in @ Y2 @ Y1))))) @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 1.86/1.72 inference(definition_unfolding,[status(thm)],[f30,f29])).
% 1.86/1.72 thf(f30,plain,(
% 1.86/1.72 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 1.86/1.72 inference(cnf_transformation,[status(thm)],[f23])).
% 1.86/1.72 thf(f23,plain,(
% 1.86/1.72 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 1.86/1.72 inference(fool_elimination,[status(thm)],[f22])).
% 1.86/1.72 thf(f22,plain,(
% 1.86/1.72 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 1.86/1.72 inference(rectify,[status(thm)],[f4])).
% 1.86/1.72 thf(f4,axiom,(
% 1.86/1.72 (! [X4 : $i] : ((singleton @ X4) => (in @ (setunion @ X4) @ X4)) = theprop)),
% 1.86/1.72 file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',theprop)).
% 1.86/1.72 thf(f28,plain,(
% 1.86/1.72 (sepSubset = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ Y1))))))),
% 1.86/1.72 inference(cnf_transformation,[status(thm)],[f15])).
% 1.86/1.72 thf(f15,plain,(
% 1.86/1.72 (sepSubset = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ Y1))))))),
% 1.86/1.72 inference(fool_elimination,[status(thm)],[f14])).
% 1.86/1.72 thf(f14,plain,(
% 1.86/1.72 (! [X0 : $i,X1 : $i > $o] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ X0) = sepSubset)),
% 1.86/1.72 inference(rectify,[status(thm)],[f2])).
% 1.86/1.72 thf(f2,axiom,(
% 1.86/1.72 (! [X0 : $i,X3 : $i > $o] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : (X3 @ X2))) @ X0) = sepSubset)),
% 1.86/1.72 file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',sepSubset)).
% 1.86/1.72 thf(f27,plain,(
% 1.86/1.72 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 1.86/1.72 inference(cnf_transformation,[status(thm)],[f11])).
% 1.86/1.72 thf(f11,plain,(
% 1.86/1.72 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 1.86/1.72 inference(fool_elimination,[status(thm)],[f10])).
% 1.86/1.72 thf(f10,plain,(
% 1.86/1.72 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0))))),
% 1.86/1.72 inference(rectify,[status(thm)],[f1])).
% 1.86/1.72 thf(f1,axiom,(
% 1.86/1.72 (subsetE = ! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.86/1.72 file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',subsetE)).
% 1.86/1.72 thf(f24,plain,(
% 1.86/1.72 ((~ (subsetE => (sepSubset => (theprop => (ifSingleton => (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (if @ Y1 @ Y0 @ Y2 @ Y3) @ Y1)))))))))))))))) = $true)),
% 1.86/1.72 inference(cnf_transformation,[status(thm)],[f17])).
% 1.86/1.72 thf(f17,plain,(
% 1.86/1.72 ((~ (subsetE => (sepSubset => (theprop => (ifSingleton => (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (if @ Y1 @ Y0 @ Y2 @ Y3) @ Y1)))))))))))))))) = $true)),
% 1.86/1.72 inference(fool_elimination,[status(thm)],[f16])).
% 1.86/1.72 thf(f16,plain,(
% 1.86/1.72 ~(subsetE => (sepSubset => (theprop => (ifSingleton => ! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (if @ X1 @ X2 @ X0 @ X3) @ X1)))))))),
% 1.86/1.72 inference(rectify,[status(thm)],[f8])).
% 1.86/1.72 thf(f8,negated_conjecture,(
% 1.86/1.72 ~(subsetE => (sepSubset => (theprop => (ifSingleton => ! [X2 : $i,X0 : $i,X3 : $o] : ((in @ X2 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => (in @ (if @ X0 @ X3 @ X2 @ X5) @ X0)))))))),
% 1.86/1.72 inference(negated_conjecture,[status(cth)],[f7])).
% 1.86/1.72 thf(f7,conjecture,(
% 1.86/1.72 subsetE => (sepSubset => (theprop => (ifSingleton => ! [X2 : $i,X0 : $i,X3 : $o] : ((in @ X2 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => (in @ (if @ X0 @ X3 @ X2 @ X5) @ X0))))))),
% 1.86/1.72 file('/export/starexec/sandbox/tmp/tmp.ph90K1Mmp4/DTF2THF_3057.p',ifp)).
% 1.86/1.72 thf(f569,plain,(
% 1.86/1.72 ($false = (in @ sK4 @ sK3)) | ((in @ sK5 @ sK3) = $false) | ~spl0_5),
% 1.86/1.72 inference(trivial_inequality_removal,[status(thm)],[f568])).
% 1.86/1.72 thf(f568,plain,(
% 1.86/1.72 ((^[Y0 : $i]: (sK2)) != (^[Y0 : $i]: (sK2))) | ((in @ sK5 @ sK3) = $false) | ($false = (in @ sK4 @ sK3)) | ((^[Y0 : $i]: (sK4)) != (^[Y0 : $i]: (sK4))) | ($true = $false) | ((^[Y0 : $i]: (sK5)) != (^[Y0 : $i]: (sK5))) | ~spl0_5),
% 1.86/1.72 inference(duplicate_literal_removal,[status(thm)],[f563])).
% 1.86/1.72 thf(f563,plain,(
% 1.86/1.72 ($false = (in @ sK4 @ sK3)) | ((^[Y0 : $i]: (sK4)) != (^[Y0 : $i]: (sK4))) | ($true = $false) | ((^[Y0 : $i]: (sK2)) != (^[Y0 : $i]: (sK2))) | ((in @ sK5 @ sK3) = $false) | ((in @ sK5 @ sK3) = $false) | ((^[Y0 : $i]: (sK5)) != (^[Y0 : $i]: (sK5))) | ($false = (in @ sK4 @ sK3)) | ~spl0_5),
% 1.86/1.72 inference(superposition,[status(thm)],[f123,f320])).
% 1.86/1.72 thf(f320,plain,(
% 1.86/1.72 ($false = (in @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset))) | ~spl0_5),
% 1.86/1.72 inference(avatar_component_clause,[status(thm)],[f318])).
% 1.86/1.72 thf(f318,definition,(
% 1.86/1.72 spl0_5 <=> ($false = (in @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset)))),
% 1.86/1.72 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.86/1.72 thf(f123,plain,(
% 1.86/1.72 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $o,X6 : $i,X4 : $i,X5 : $i] : (($true = (in @ (sK1 @ X6 @ X1 @ X5 @ X3) @ (setadjoin @ (sK1 @ X6 @ X0 @ X4 @ X2) @ emptyset))) | ($false = (in @ X2 @ X6)) | ($false = (in @ X5 @ X6)) | ((in @ X3 @ X6) = $false) | ((in @ X4 @ X6) = $false) | ((^[Y0 : $i]: (X2)) != (^[Y0 : $i]: (X3))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0))) | ((^[Y0 : $i]: (X5)) != (^[Y0 : $i]: (X4)))) )),
% 1.86/1.72 inference(duplicate_literal_removal,[status(thm)],[f118])).
% 1.86/1.72 thf(f118,plain,(
% 1.86/1.72 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $o,X6 : $i,X4 : $i,X5 : $i] : (((^[Y0 : $i]: (X5)) != (^[Y0 : $i]: (X4))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0))) | ($false = (in @ X2 @ X6)) | ($false = (in @ X5 @ X6)) | ((^[Y0 : $i]: (X2)) != (^[Y0 : $i]: (X3))) | ($true = (in @ (sK1 @ X6 @ X1 @ X5 @ X3) @ (setadjoin @ (sK1 @ X6 @ X0 @ X4 @ X2) @ emptyset))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0))) | ((in @ X3 @ X6) = $false) | ((in @ X4 @ X6) = $false)) )),
% 1.86/1.72 inference(constrained_superposition,[status(thm)],[f64,f66])).
% 1.86/1.72 thf(f66,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (((setadjoin @ (sK1 @ X1 @ X2 @ X3 @ X4) @ emptyset) = (dsetconstr @ X1 @ (^[Y0 : $i]: (((X3 = Y0) & X2) | ((X4 = Y0) & (~ X2)))))) | ((in @ X3 @ X1) = $false) | ((in @ X4 @ X1) = $false)) )),
% 1.86/1.72 inference(equality_proxy_clausification,[status(thm)],[f65])).
% 1.86/1.72 thf(f65,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (((in @ X3 @ X1) = $false) | (((setadjoin @ (sK1 @ X1 @ X2 @ X3 @ X4) @ emptyset) = (dsetconstr @ X1 @ (^[Y0 : $i]: (((X3 = Y0) & X2) | ((X4 = Y0) & (~ X2)))))) = $true) | ((in @ X4 @ X1) = $false)) )),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.86/1.72 thf(f63,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ X1) = $false) | ((((setadjoin @ (sK1 @ X1 @ X2 @ X3 @ X4) @ emptyset) = (dsetconstr @ X1 @ (^[Y0 : $i]: (((X3 = Y0) & X2) | ((X4 = Y0) & (~ X2)))))) & (in @ (sK1 @ X1 @ X2 @ X3 @ X4) @ (dsetconstr @ X1 @ (^[Y0 : $i]: (((X3 = Y0) & X2) | ((X4 = Y0) & (~ X2))))))) = $true) | ((in @ X3 @ X1) = $false)) )),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.86/1.72 thf(f62,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ X1) = $false) | ((in @ X3 @ X1) = $false) | ($true = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ (^[Y1 : $i]: (((X3 = Y1) & X2) | ((X4 = Y1) & (~ X2)))))) & (in @ Y0 @ (dsetconstr @ X1 @ (^[Y1 : $i]: (((X3 = Y1) & X2) | ((X4 = Y1) & (~ X2)))))))) @ (sK1 @ X1 @ X2 @ X3 @ X4)))) )),
% 1.86/1.72 inference(sigma_clausification,[status(thm)],[f61])).
% 1.86/1.72 thf(f61,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ (^[Y1 : $i]: (((X3 = Y1) & X2) | ((X4 = Y1) & (~ X2)))))) & (in @ Y0 @ (dsetconstr @ X1 @ (^[Y1 : $i]: (((X3 = Y1) & X2) | ((X4 = Y1) & (~ X2))))))))) = $true) | ((in @ X4 @ X1) = $false) | ((in @ X3 @ X1) = $false)) )),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.86/1.72 thf(f60,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ X4 @ X1) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ (^[Y1 : $i]: (((X3 = Y1) & X2) | ((X4 = Y1) & (~ X2)))))) & (in @ Y0 @ (dsetconstr @ X1 @ (^[Y1 : $i]: (((X3 = Y1) & X2) | ((X4 = Y1) & (~ X2))))))))))) | ((in @ X3 @ X1) = $false)) )),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.86/1.72 thf(f59,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ (^[Y2 : $i]: (((X3 = Y2) & X2) | ((Y0 = Y2) & (~ X2)))))) & (in @ Y1 @ (dsetconstr @ X1 @ (^[Y2 : $i]: (((X3 = Y2) & X2) | ((Y0 = Y2) & (~ X2))))))))))) @ X4)) | ((in @ X3 @ X1) = $false)) )),
% 1.86/1.72 inference(pi_clausification,[status(thm)],[f58])).
% 1.86/1.72 thf(f58,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i] : (((in @ X3 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ (^[Y2 : $i]: (((X3 = Y2) & X2) | ((Y0 = Y2) & (~ X2)))))) & (in @ Y1 @ (dsetconstr @ X1 @ (^[Y2 : $i]: (((X3 = Y2) & X2) | ((Y0 = Y2) & (~ X2)))))))))))))) )),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.86/1.72 thf(f57,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ (^[Y2 : $i]: (((X3 = Y2) & X2) | ((Y0 = Y2) & (~ X2)))))) & (in @ Y1 @ (dsetconstr @ X1 @ (^[Y2 : $i]: (((X3 = Y2) & X2) | ((Y0 = Y2) & (~ X2))))))))))))))) )),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.86/1.72 thf(f56,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ (^[Y3 : $i]: (((Y0 = Y3) & X2) | ((Y1 = Y3) & (~ X2)))))) & (in @ Y2 @ (dsetconstr @ X1 @ (^[Y3 : $i]: (((Y0 = Y3) & X2) | ((Y1 = Y3) & (~ X2)))))))))))))) @ X3))) )),
% 1.86/1.72 inference(pi_clausification,[status(thm)],[f55])).
% 1.86/1.72 thf(f55,plain,(
% 1.86/1.72 ( ! [X2 : $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ (^[Y3 : $i]: (((Y0 = Y3) & X2) | ((Y1 = Y3) & (~ X2)))))) & (in @ Y2 @ (dsetconstr @ X1 @ (^[Y3 : $i]: (((Y0 = Y3) & X2) | ((Y1 = Y3) & (~ X2))))))))))))))))) )),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.86/1.72 thf(f54,plain,(
% 1.86/1.72 ( ! [X2 : $o,X1 : $i] : (($true = ((^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ X1 @ (^[Y4 : $i]: (((Y1 = Y4) & Y0) | ((Y2 = Y4) & (~ Y0)))))) & (in @ Y3 @ (dsetconstr @ X1 @ (^[Y4 : $i]: (((Y1 = Y4) & Y0) | ((Y2 = Y4) & (~ Y0)))))))))))))))) @ X2))) )),
% 1.86/1.72 inference(pi_clausification,[status(thm)],[f53])).
% 1.86/1.72 thf(f53,plain,(
% 1.86/1.72 ( ! [X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ X1 @ (^[Y4 : $i]: (((Y1 = Y4) & Y0) | ((Y2 = Y4) & (~ Y0)))))) & (in @ Y3 @ (dsetconstr @ X1 @ (^[Y4 : $i]: (((Y1 = Y4) & Y0) | ((Y2 = Y4) & (~ Y0))))))))))))))))))) )),
% 1.86/1.72 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.86/1.72 thf(f52,plain,(
% 1.86/1.72 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1)))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1)))))))))))))))))) @ X1) = $true)) )),
% 1.86/1.72 inference(pi_clausification,[status(thm)],[f51])).
% 1.86/1.72 thf(f51,plain,(
% 1.86/1.72 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1)))))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (((Y2 = Y5) & Y1) | ((Y3 = Y5) & (~ Y1))))))))))))))))))))),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.86/1.72 thf(f64,plain,(
% 1.86/1.72 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (((in @ (sK1 @ X1 @ X2 @ X3 @ X4) @ (dsetconstr @ X1 @ (^[Y0 : $i]: (((X3 = Y0) & X2) | ((X4 = Y0) & (~ X2)))))) = $true) | ((in @ X3 @ X1) = $false) | ((in @ X4 @ X1) = $false)) )),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.86/1.72 thf(f78,plain,(
% 1.86/1.72 ((in @ sK5 @ sK3) = $true)),
% 1.86/1.72 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.86/1.72 thf(f76,plain,(
% 1.86/1.72 (((in @ sK5 @ sK3) => (in @ (setunion @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK4 = Y0) & sK2) | ((sK5 = Y0) & (~ sK2)))))) @ sK3)) = $false)),
% 1.86/1.73 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.86/1.73 thf(f75,plain,(
% 1.86/1.73 (((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (setunion @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK4 = Y1) & sK2) | ((Y0 = Y1) & (~ sK2)))))) @ sK3))) @ sK5) = $false)),
% 1.86/1.73 inference(sigma_clausification,[status(thm)],[f73])).
% 1.86/1.73 thf(f73,plain,(
% 1.86/1.73 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (setunion @ (dsetconstr @ sK3 @ (^[Y1 : $i]: (((sK4 = Y1) & sK2) | ((Y0 = Y1) & (~ sK2)))))) @ sK3)))) = $false)),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.86/1.73 thf(f367,plain,(
% 1.86/1.73 ~spl0_6),
% 1.86/1.73 inference(avatar_contradiction_clause,[status(thm)],[f366])).
% 1.86/1.73 thf(f366,plain,(
% 1.86/1.73 $false | ~spl0_6),
% 1.86/1.73 inference(trivial_inequality_removal,[status(thm)],[f362])).
% 1.86/1.73 thf(f362,plain,(
% 1.86/1.73 ($true = $false) | ~spl0_6),
% 1.86/1.73 inference(backward_demodulation,[status(thm)],[f78,f351])).
% 1.86/1.73 thf(f351,plain,(
% 1.86/1.73 ((in @ sK5 @ sK3) = $false) | ~spl0_6),
% 1.86/1.73 inference(trivial_inequality_removal,[status(thm)],[f350])).
% 1.86/1.73 thf(f350,plain,(
% 1.86/1.73 ($true = $false) | ((in @ sK5 @ sK3) = $false) | ~spl0_6),
% 1.86/1.73 inference(forward_demodulation,[status(thm)],[f348,f74])).
% 1.86/1.73 thf(f348,plain,(
% 1.86/1.73 ((in @ sK5 @ sK3) = $false) | ($false = (in @ sK4 @ sK3)) | ~spl0_6),
% 1.86/1.73 inference(trivial_inequality_removal,[status(thm)],[f344])).
% 1.86/1.73 thf(f344,plain,(
% 1.86/1.73 ((in @ sK5 @ sK3) = $false) | ($false = (in @ sK4 @ sK3)) | ($true = $false) | ~spl0_6),
% 1.86/1.73 inference(superposition,[status(thm)],[f324,f117])).
% 1.86/1.73 thf(f117,plain,(
% 1.86/1.73 ( ! [X2 : $o,X3 : $i,X0 : $i,X1 : $i] : (($true = (subset @ (setadjoin @ (sK1 @ X0 @ X2 @ X1 @ X3) @ emptyset) @ X0)) | ((in @ X1 @ X0) = $false) | ($false = (in @ X3 @ X0))) )),
% 1.86/1.73 inference(superposition,[status(thm)],[f89,f66])).
% 1.86/1.73 thf(f89,plain,(
% 1.86/1.73 ( ! [X2 : $i,X1 : $i > $o] : (($true = (subset @ (dsetconstr @ X2 @ X1) @ X2))) )),
% 1.86/1.73 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.86/1.73 thf(f88,plain,(
% 1.86/1.73 ( ! [X2 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: (subset @ (dsetconstr @ Y0 @ X1) @ Y0)) @ X2))) )),
% 1.86/1.73 inference(pi_clausification,[status(thm)],[f87])).
% 1.86/1.73 thf(f87,plain,(
% 1.86/1.73 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (subset @ (dsetconstr @ Y0 @ X1) @ Y0))) = $true)) )),
% 1.86/1.73 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.86/1.73 thf(f86,plain,(
% 1.86/1.73 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1)))) @ X1) = $true)) )),
% 1.86/1.73 inference(pi_clausification,[status(thm)],[f47])).
% 1.86/1.73 thf(f47,plain,(
% 1.86/1.73 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))))),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.86/1.73 thf(f324,plain,(
% 1.86/1.73 ($false = (subset @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset) @ sK3)) | ~spl0_6),
% 1.86/1.73 inference(avatar_component_clause,[status(thm)],[f322])).
% 1.86/1.73 thf(f322,definition,(
% 1.86/1.73 spl0_6 <=> ($false = (subset @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset) @ sK3))),
% 1.86/1.73 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.86/1.73 thf(f330,plain,(
% 1.86/1.73 spl0_5 | spl0_6),
% 1.86/1.73 inference(avatar_split_clause,[status(thm)],[f311,f322,f318])).
% 1.86/1.73 thf(f311,plain,(
% 1.86/1.73 ($false = (in @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset))) | ($false = (subset @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset) @ sK3))),
% 1.86/1.73 inference(trivial_inequality_removal,[status(thm)],[f307])).
% 1.86/1.73 thf(f307,plain,(
% 1.86/1.73 ($true = $false) | ($false = (in @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset))) | ($false = (subset @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset) @ sK3))),
% 1.86/1.73 inference(superposition,[status(thm)],[f144,f95])).
% 1.86/1.73 thf(f95,plain,(
% 1.86/1.73 ( ! [X0 : $i] : (($true = (in @ (setunion @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) | ((in @ X0 @ (setadjoin @ X0 @ emptyset)) = $false)) )),
% 1.86/1.73 inference(equality_resolution,[status(thm)],[f85])).
% 1.86/1.73 thf(f85,plain,(
% 1.86/1.73 ( ! [X2 : $i,X1 : $i] : (((setadjoin @ X2 @ emptyset) != X1) | ((in @ X2 @ X1) = $false) | ($true = (in @ (setunion @ X1) @ X1))) )),
% 1.86/1.73 inference(equality_proxy_clausification,[status(thm)],[f84])).
% 1.86/1.73 thf(f84,plain,(
% 1.86/1.73 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ X1) = $false) | ($true = (in @ (setunion @ X1) @ X1)) | ($false = ((setadjoin @ X2 @ emptyset) = X1))) )),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.86/1.73 thf(f83,plain,(
% 1.86/1.73 ( ! [X2 : $i,X1 : $i] : (($false = (((setadjoin @ X2 @ emptyset) = X1) & (in @ X2 @ X1))) | ($true = (in @ (setunion @ X1) @ X1))) )),
% 1.86/1.73 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.86/1.73 thf(f82,plain,(
% 1.86/1.73 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = X1) & (in @ Y0 @ X1))) @ X2)) | ($true = (in @ (setunion @ X1) @ X1))) )),
% 1.86/1.73 inference(pi_clausification,[status(thm)],[f81])).
% 1.86/1.73 thf(f81,plain,(
% 1.86/1.73 ( ! [X1 : $i] : (($true = (in @ (setunion @ X1) @ X1)) | ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = X1) & (in @ Y0 @ X1)))))) )),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.86/1.73 thf(f80,plain,(
% 1.86/1.73 ( ! [X1 : $i] : (($true = ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = X1) & (in @ Y0 @ X1)))) => (in @ (setunion @ X1) @ X1)))) )),
% 1.86/1.73 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.86/1.73 thf(f79,plain,(
% 1.86/1.73 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0)))) => (in @ (setunion @ Y0) @ Y0))) @ X1) = $true)) )),
% 1.86/1.73 inference(pi_clausification,[status(thm)],[f49])).
% 1.86/1.73 thf(f49,plain,(
% 1.86/1.73 ($true = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0)))) => (in @ (setunion @ Y0) @ Y0)))))),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.86/1.73 thf(f144,plain,(
% 1.86/1.73 ( ! [X0 : $i] : (($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset)) @ X0)) | ($false = (subset @ X0 @ sK3))) )),
% 1.86/1.73 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.86/1.73 thf(f143,plain,(
% 1.86/1.73 ( ! [X0 : $i] : (($true = $false) | ($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset)) @ X0)) | ($false = (subset @ X0 @ sK3))) )),
% 1.86/1.73 inference(superposition,[status(thm)],[f45,f139])).
% 1.86/1.73 thf(f139,plain,(
% 1.86/1.73 ($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ sK2 @ sK4 @ sK5) @ emptyset)) @ sK3))),
% 1.86/1.73 inference(equality_resolution,[status(thm)],[f130])).
% 1.86/1.73 thf(f130,plain,(
% 1.86/1.73 ( ! [X0 : $o] : (((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK2))) | ($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ X0 @ sK4 @ sK5) @ emptyset)) @ sK3))) )),
% 1.86/1.73 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.86/1.73 thf(f129,plain,(
% 1.86/1.73 ( ! [X0 : $o] : (((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK2))) | ($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ X0 @ sK4 @ sK5) @ emptyset)) @ sK3)) | ($true = $false)) )),
% 1.86/1.73 inference(forward_demodulation,[status(thm)],[f128,f74])).
% 1.86/1.73 thf(f128,plain,(
% 1.86/1.73 ( ! [X0 : $o] : (($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ X0 @ sK4 @ sK5) @ emptyset)) @ sK3)) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK2))) | ($false = (in @ sK4 @ sK3))) )),
% 1.86/1.73 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.86/1.73 thf(f127,plain,(
% 1.86/1.73 ( ! [X0 : $o] : (($true = $false) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK2))) | ($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ X0 @ sK4 @ sK5) @ emptyset)) @ sK3)) | ($false = (in @ sK4 @ sK3))) )),
% 1.86/1.73 inference(forward_demodulation,[status(thm)],[f125,f78])).
% 1.86/1.73 thf(f125,plain,(
% 1.86/1.73 ( ! [X0 : $o] : (((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK2))) | ((in @ sK5 @ sK3) = $false) | ($false = (in @ sK4 @ sK3)) | ($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ X0 @ sK4 @ sK5) @ emptyset)) @ sK3))) )),
% 1.86/1.73 inference(duplicate_literal_removal,[status(thm)],[f121])).
% 1.86/1.73 thf(f121,plain,(
% 1.86/1.73 ( ! [X0 : $o] : (($false = (in @ (setunion @ (setadjoin @ (sK1 @ sK3 @ X0 @ sK4 @ sK5) @ emptyset)) @ sK3)) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK2))) | ($false = (in @ sK4 @ sK3)) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK2))) | ((in @ sK5 @ sK3) = $false)) )),
% 1.86/1.73 inference(constrained_superposition,[status(thm)],[f77,f66])).
% 1.86/1.73 thf(f77,plain,(
% 1.86/1.73 ((in @ (setunion @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (((sK4 = Y0) & sK2) | ((sK5 = Y0) & (~ sK2)))))) @ sK3) = $false)),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.86/1.73 thf(f45,plain,(
% 1.86/1.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X2 @ X3)) | ((subset @ X1 @ X3) = $false) | ((in @ X2 @ X1) = $false)) )),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.86/1.73 thf(f44,plain,(
% 1.86/1.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ X1) => (in @ X2 @ X3)) = $true) | ((subset @ X1 @ X3) = $false)) )),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.86/1.73 thf(f43,plain,(
% 1.86/1.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ X3) => ((in @ X2 @ X1) => (in @ X2 @ X3))))) )),
% 1.86/1.73 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.86/1.73 thf(f42,plain,(
% 1.86/1.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X1 @ Y0) => ((in @ X2 @ X1) => (in @ X2 @ Y0)))) @ X3))) )),
% 1.86/1.73 inference(pi_clausification,[status(thm)],[f41])).
% 1.86/1.73 thf(f41,plain,(
% 1.86/1.73 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0) => ((in @ X2 @ X1) => (in @ X2 @ Y0))))) = $true)) )),
% 1.86/1.73 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.86/1.73 thf(f40,plain,(
% 1.86/1.73 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y1) => ((in @ Y0 @ X1) => (in @ Y0 @ Y1)))))) @ X2))) )),
% 1.86/1.73 inference(pi_clausification,[status(thm)],[f39])).
% 1.86/1.73 thf(f39,plain,(
% 1.86/1.73 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y1) => ((in @ Y0 @ X1) => (in @ Y0 @ Y1))))))))) )),
% 1.86/1.73 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.86/1.73 thf(f38,plain,(
% 1.86/1.73 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2)))))))) @ X1))) )),
% 1.86/1.73 inference(pi_clausification,[status(thm)],[f37])).
% 1.86/1.73 thf(f37,plain,(
% 1.86/1.73 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 1.86/1.73 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.86/1.73 % SZS output end Proof for DTF2THF_3057
% 1.86/1.73 % (3220)------------------------------
% 1.86/1.73 % (3220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.86/1.73 % (3220)Termination reason: Refutation
% 1.86/1.73
% 1.86/1.73 % (3220)Memory used [KB]: 6012
% 1.86/1.73 % (3220)Time elapsed: 0.130 s
% 1.86/1.73 % (3220)Instructions burned: 252 (million)
% 1.86/1.73 % (3220)------------------------------
% 1.86/1.73 % (3220)------------------------------
% 1.86/1.73 % (3192)Success in time 0.261 s
%------------------------------------------------------------------------------