%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU824^2 : 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 : n004.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 09:37:31 AM UTC 2026
% Result : Theorem 1.72s 1.47s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 5
% Syntax : Number of formulae : 97 ( 94 unt; 0 typ; 0 def)
% Number of atoms : 1592 ( 148 equ; 0 cnn)
% Maximal formula atoms : 6 ( 16 avg)
% Number of connectives : 3265 ( 38 ~; 85 |; 174 &;2156 @)
% ( 0 <=>; 477 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 9 con; 0-2 aty)
% ( 312 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 423 ( 371 ^; 50 !; 2 ?; 423 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
nonempty: $i > $o ).
thf(func_def_3,type,
transitiveset: $i > $o ).
thf(func_def_4,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_6,type,
wellorderedByIn: $i > $o ).
thf(func_def_7,type,
ordinal: $i > $o ).
thf(func_def_24,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f314,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f313]) ).
thf(f313,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f312]) ).
thf(f312,plain,
( ( ~ $true ) = $true ),
inference(forward_demodulation,[status(thm)],[f311,f56]) ).
thf(f56,plain,
( $true
= ( in @ sK5 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( in @ sK5 @ sK3 )
=> ( ( in @ sK3 @ sK2 )
=> ( in @ sK4 @ sK3 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( $false
= ( ( in @ sK4 @ sK5 )
=> ( ( in @ sK5 @ sK3 )
=> ( ( in @ sK3 @ sK2 )
=> ( in @ sK4 @ sK3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ sK4 @ Y0 )
=> ( ( in @ Y0 @ sK3 )
=> ( ( in @ sK3 @ sK2 )
=> ( in @ sK4 @ sK3 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ sK4 @ Y0 )
=> ( ( in @ Y0 @ sK3 )
=> ( ( in @ sK3 @ sK2 )
=> ( in @ sK4 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ sK3 )
=> ( ( in @ sK3 @ sK2 )
=> ( in @ Y0 @ sK3 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ sK3 )
=> ( ( in @ sK3 @ sK2 )
=> ( in @ Y0 @ sK3 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> ( ( in @ Y0 @ sK2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> ( ( in @ Y0 @ sK2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> ( ( in @ Y0 @ sK2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f36,f40]) ).
thf(f40,plain,
( ( ( transitiveset @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
= ( ( ( transitiveset @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> ( ( in @ Y0 @ sK2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f28,f32]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( transitiveset @ Y1 )
& ( ^ [Y2: $i] :
( ( ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ( ( in @ Y4 @ Y5 )
& ( in @ Y5 @ Y6 ) )
=> ( in @ Y4 @ Y6 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y4 @ Y5 )
| ( Y4 = Y5 )
| ( in @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ~ ( in @ Y4 @ Y4 ) ) ) )
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y2 ) )
=> ( ( nonempty @ Y3 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y4 @ Y5 )
| ( Y4 = Y5 ) ) ) )
& ( in @ Y4 @ Y3 ) ) ) ) ) ) )
@ Y1 ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( transitiveset @ Y1 )
& ( ^ [Y2: $i] :
( ( ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ( ( in @ Y4 @ Y5 )
& ( in @ Y5 @ Y6 ) )
=> ( in @ Y4 @ Y6 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y4 @ Y5 )
| ( Y4 = Y5 )
| ( in @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ~ ( in @ Y4 @ Y4 ) ) ) )
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y2 ) )
=> ( ( nonempty @ Y3 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y4 @ Y5 )
| ( Y4 = Y5 ) ) ) )
& ( in @ Y4 @ Y3 ) ) ) ) ) ) )
@ Y1 ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f25,f24]) ).
thf(f24,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( ^ [Y1: $i] :
( ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y4 @ Y5 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 )
| ( in @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( nonempty @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 ) ) ) )
& ( in @ Y3 @ Y2 ) ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f23]) ).
thf(f23,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y2 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 )
| ( in @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) ) )
@ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f19]) ).
thf(f19,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( X2 = X3 )
| ( in @ X2 @ X3 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( ( in @ X5 @ X6 )
& ( in @ X4 @ X5 ) )
=> ( in @ X4 @ X6 ) ) ) ) ) ) )
= stricttotalorderedByIn ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
| ( X2 = X3 )
| ( in @ X2 @ X3 ) ) ) )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X1 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ) )
= stricttotalorderedByIn ),
file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',stricttotalorderedByIn) ).
thf(f20,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( stricttotalorderedByIn @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ( in @ X2 @ X1 )
& ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 = X3 )
| ( in @ X2 @ X3 ) ) ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) )
= wellorderedByIn ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X2 )
=> ? [X1: $i] :
( ( in @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( X1 = X3 )
| ( in @ X1 @ X3 ) ) ) ) ) )
& ( stricttotalorderedByIn @ X0 ) ) )
= wellorderedByIn ),
file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',wellorderedByIn) ).
thf(f22,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ordinal
= ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ordinal
= ( ^ [X1: $i] :
( ( wellorderedByIn @ X1 )
& ( transitiveset @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',ordinal) ).
thf(f25,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( transitiveset @ Y1 )
& ( ^ [Y2: $i] :
( ( ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ( ( in @ Y4 @ Y5 )
& ( in @ Y5 @ Y6 ) )
=> ( in @ Y4 @ Y6 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y4 @ Y5 )
| ( Y4 = Y5 )
| ( in @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y3 )
=> ~ ( in @ Y4 @ Y4 ) ) ) )
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y2 ) )
=> ( ( nonempty @ Y3 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y3 )
=> ( ( in @ Y4 @ Y5 )
| ( Y4 = Y5 ) ) ) )
& ( in @ Y4 @ Y3 ) ) ) ) ) ) )
@ Y1 ) )
@ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f18,f24]) ).
thf(f18,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ordinalTransSet
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ordinalTransSet
= ( ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ordinalTransSet
= ( ! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ X2 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',ordinalTransSet) ).
thf(f21,plain,
( ( ~ ( ordinalTransSet
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ~ ( ordinalTransSet
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( ordinal @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y2 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ordinalTransSet
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X2 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ordinalTransSet
=> ! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X0: $i,X1: $i,X4: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X0 @ X4 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X1 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ordinalTransSet
=> ! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X0: $i,X1: $i,X4: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X0 @ X4 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',ordinalTransIn) ).
thf(f311,plain,
( ( ~ ( in @ sK5 @ sK3 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f310]) ).
thf(f310,plain,
( ( $true
=> ~ ( in @ sK5 @ sK3 ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f299,f70]) ).
thf(f70,plain,
( ( in @ sK3 @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( in @ sK3 @ sK2 )
=> ( in @ sK4 @ sK3 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f299,plain,
( $true
= ( ( in @ sK3 @ sK2 )
=> ~ ( in @ sK5 @ sK3 ) ) ),
inference(boolean_simplification,[status(thm)],[f284]) ).
thf(f284,plain,
( ( ( in @ sK3 @ sK2 )
=> ( ( in @ sK5 @ sK3 )
=> $false ) )
= $true ),
inference(superposition,[status(thm)],[f277,f72]) ).
thf(f72,plain,
( $false
= ( in @ sK4 @ sK3 ) ),
inference(boolean_simplification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true
=> ( in @ sK4 @ sK3 ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f55,f70]) ).
thf(f277,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ( in @ sK5 @ X1 )
=> ( in @ sK4 @ X1 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f276]) ).
thf(f276,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( ( $true
& ( in @ sK5 @ X1 ) )
=> ( in @ sK4 @ X1 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f275,f50]) ).
thf(f50,plain,
( $true
= ( in @ sK4 @ sK5 ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f275,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK2 )
=> ( ( ( in @ sK4 @ sK5 )
& ( in @ sK5 @ X1 ) )
=> ( in @ sK4 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f272]) ).
thf(f272,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( ( in @ sK4 @ sK5 )
& ( in @ sK5 @ Y0 ) )
=> ( in @ sK4 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f269]) ).
thf(f269,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( ( in @ sK4 @ sK5 )
& ( in @ sK5 @ Y0 ) )
=> ( in @ sK4 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f267]) ).
thf(f267,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( ( in @ sK4 @ sK5 )
& ( in @ sK5 @ Y0 ) )
=> ( in @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f263,f112]) ).
thf(f112,plain,
( ( in @ sK5 @ sK2 )
= $true ),
inference(boolean_simplification,[status(thm)],[f111]) ).
thf(f111,plain,
( $true
= ( $true
=> ( in @ sK5 @ sK2 ) ) ),
inference(forward_demodulation,[status(thm)],[f105,f70]) ).
thf(f105,plain,
( $true
= ( ( in @ sK3 @ sK2 )
=> ( in @ sK5 @ sK2 ) ) ),
inference(boolean_simplification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( in @ sK3 @ sK2 )
=> ( $true
=> ( in @ sK5 @ sK2 ) ) )
= $true ),
inference(superposition,[status(thm)],[f94,f56]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ sK2 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ sK2 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ sK2 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ sK2 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ sK2 ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f82,f66]) ).
thf(f66,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f40,f62]) ).
thf(f62,plain,
( $true
= ( transitiveset @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f82,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ sK2 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f81]) ).
thf(f81,plain,
( $true
= ( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ sK2 ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f80,f62]) ).
thf(f80,plain,
( $true
= ( ( ( transitiveset @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ sK2 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f77]) ).
thf(f77,plain,
( $true
= ( ( ( transitiveset @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& $true )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ sK2 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f38,f68]) ).
thf(f68,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK2 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f64,f66]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( ( ( transitiveset @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( transitiveset @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 )
| ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f263,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( ( ( in @ sK4 @ X1 )
& ( in @ X1 @ Y0 ) )
=> ( in @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f261]) ).
thf(f261,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f202]) ).
thf(f202,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f201]) ).
thf(f201,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( ( in @ sK4 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ sK4 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(superposition,[status(thm)],[f184,f114]) ).
thf(f114,plain,
( ( in @ sK4 @ sK2 )
= $true ),
inference(boolean_simplification,[status(thm)],[f113]) ).
thf(f113,plain,
( $true
= ( $true
=> ( in @ sK4 @ sK2 ) ) ),
inference(forward_demodulation,[status(thm)],[f102,f112]) ).
thf(f102,plain,
( $true
= ( ( in @ sK5 @ sK2 )
=> ( in @ sK4 @ sK2 ) ) ),
inference(boolean_simplification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( in @ sK5 @ sK2 )
=> ( $true
=> ( in @ sK4 @ sK2 ) ) )
= $true ),
inference(superposition,[status(thm)],[f94,f50]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( ( in @ X1 @ Y0 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f181]) ).
thf(f181,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f167]) ).
thf(f167,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f116,f163]) ).
thf(f163,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 )
| ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU824^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n004.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:34:56 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.44 ---- Original DTF file ---
% 0.20/0.44 thf(spec,logic,$$dhol).
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % File : SEU824^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.44 % Domain : Set Theory
% 0.20/0.44 % Problem : Ordinals
% 0.20/0.44 % Version : Especial > Reduced > Especial.
% 0.20/0.44 % English : (! X:i.ordinal X -> (! x:i.! A:i.! B:i.in x A -> in A B ->
% 0.20/0.44 % in B X -> in x B))
% 0.20/0.44
% 0.20/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.44 % Source : [Bro08]
% 0.20/0.44 % Names : ZFC326l [Bro08]
% 0.20/0.44
% 0.20/0.44 % Status : Theorem
% 0.20/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.20/0.44 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.20/0.44 % Number of atoms : 40 ( 6 equ; 0 cnn)
% 0.20/0.44 % Maximal formula atoms : 6 ( 8 avg)
% 0.20/0.44 % Number of connectives : 81 ( 1 ~; 3 |; 6 &; 53 @)
% 0.20/0.44 % ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% 0.20/0.44 % Maximal formula depth : 12 ( 3 avg)
% 0.20/0.44 % Number of types : 2 ( 0 usr)
% 0.20/0.44 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.20/0.44 % Number of symbols : 9 ( 8 usr; 1 con; 0-2 aty)
% 0.20/0.44 % Number of variables : 19 ( 3 ^; 15 !; 1 ?; 19 :)
% 0.20/0.44 % SPC : TH0_THM_EQU_NAR
% 0.20/0.44
% 0.20/0.44 % Comments : http://mathgate.info/detsetitem.php?id=521
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 thf(in_type,type,
% 0.20/0.44 in: $i > $i > $o ).
% 0.20/0.44
% 0.20/0.44 thf(powerset_type,type,
% 0.20/0.44 powerset: $i > $i ).
% 0.20/0.44
% 0.20/0.44 thf(nonempty_type,type,
% 0.20/0.44 nonempty: $i > $o ).
% 0.20/0.44
% 0.20/0.44 thf(transitiveset_type,type,
% 0.20/0.44 transitiveset: $i > $o ).
% 0.20/0.44
% 0.20/0.44 thf(stricttotalorderedByIn_type,type,
% 0.20/0.44 stricttotalorderedByIn: $i > $o ).
% 0.20/0.44
% 0.20/0.44 thf(stricttotalorderedByIn,definition,
% 0.20/0.44 ( stricttotalorderedByIn
% 0.20/0.44 = ( ^ [A: $i] :
% 0.20/0.44 ( ! [Xx: $i] :
% 0.20/0.44 ( ( in @ Xx @ A )
% 0.20/0.44 => ! [X: $i] :
% 0.20/0.44 ( ( in @ X @ A )
% 0.20/0.44 => ! [Y: $i] :
% 0.20/0.44 ( ( in @ Y @ A )
% 0.20/0.44 => ( ( ( in @ Xx @ X )
% 0.20/0.44 & ( in @ X @ Y ) )
% 0.20/0.44 => ( in @ Xx @ Y ) ) ) ) )
% 0.20/0.44 & ! [X: $i] :
% 0.20/0.44 ( ( in @ X @ A )
% 0.20/0.44 => ! [Y: $i] :
% 0.20/0.44 ( ( in @ Y @ A )
% 0.20/0.44 => ( ( X = Y )
% 0.20/0.44 | ( in @ X @ Y )
% 0.20/0.44 | ( in @ Y @ X ) ) ) )
% 0.20/0.44 & ! [X: $i] :
% 0.20/0.44 ( ( in @ X @ A )
% 0.20/0.44 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(wellorderedByIn_type,type,
% 0.20/0.44 wellorderedByIn: $i > $o ).
% 0.20/0.44
% 0.20/0.44 thf(wellorderedByIn,definition,
% 0.20/0.44 ( wellorderedByIn
% 0.20/0.44 = ( ^ [A: $i] :
% 0.20/0.44 ( ( stricttotalorderedByIn @ A )
% 0.20/0.44 & ! [X: $i] :
% 0.20/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.44 => ( ( nonempty @ X )
% 0.20/0.44 => ? [Xx: $i] :
% 0.20/0.44 ( ( in @ Xx @ X )
% 0.20/0.44 & ! [Y: $i] :
% 0.20/0.44 ( ( in @ Y @ X )
% 0.20/0.44 => ( ( Xx = Y )
% 0.20/0.44 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(ordinal_type,type,
% 0.20/0.44 ordinal: $i > $o ).
% 0.20/0.44
% 0.20/0.44 thf(ordinal,definition,
% 0.20/0.44 ( ordinal
% 0.20/0.44 = ( ^ [Xx: $i] :
% 0.20/0.44 ( ( transitiveset @ Xx )
% 0.20/0.44 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(ordinalTransSet_type,type,
% 0.20/0.44 ordinalTransSet: $o ).
% 0.20/0.44
% 0.20/0.44 thf(ordinalTransSet,definition,
% 0.20/0.44 ( ordinalTransSet
% 0.20/0.44 = ( ! [X: $i] :
% 0.20/0.44 ( ( ordinal @ X )
% 0.20/0.44 => ! [Xx: $i,A: $i] :
% 0.20/0.44 ( ( in @ A @ X )
% 0.20/0.44 => ( ( in @ Xx @ A )
% 0.20/0.44 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(ordinalTransIn,conjecture,
% 0.20/0.44 ( ordinalTransSet
% 0.20/0.44 => ! [X: $i] :
% 0.20/0.44 ( ( ordinal @ X )
% 0.20/0.44 => ! [Xx: $i,A: $i,B: $i] :
% 0.20/0.44 ( ( in @ Xx @ A )
% 0.20/0.44 => ( ( in @ A @ B )
% 0.20/0.44 => ( ( in @ B @ X )
% 0.20/0.44 => ( in @ Xx @ B ) ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 ------------------------
% 1.56/1.37 ---- Embedded in THF ---
% 1.56/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.37 %%% Generated on Tue Feb 24 12:34:57 EST 2026
% 1.56/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.37 %%% Logic specification used:
% 1.56/1.37 %%% thf(spec, logic, $$dhol).
% 1.56/1.37
% 1.56/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2DTF26731.p
% See solution above
% 1.56/1.37 ------------------------
% 1.56/1.38 ---- Cleaned THF ---
% 1.56/1.38 thf(in_type,type,
% 1.56/1.38 in: $i > $i > $o ).
% 1.56/1.38
% 1.56/1.38 thf(powerset_type,type,
% 1.56/1.38 powerset: $i > $i ).
% 1.56/1.38
% 1.56/1.38 thf(nonempty_type,type,
% 1.56/1.38 nonempty: $i > $o ).
% 1.56/1.38
% 1.56/1.38 thf(transitiveset_type,type,
% 1.56/1.38 transitiveset: $i > $o ).
% 1.56/1.38
% 1.56/1.38 thf(stricttotalorderedByIn_type,type,
% 1.56/1.38 stricttotalorderedByIn: $i > $o ).
% 1.56/1.38
% 1.56/1.38 thf(stricttotalorderedByIn,definition,
% 1.56/1.38 ( stricttotalorderedByIn
% 1.56/1.38 = ( ^ [A: $i] :
% 1.56/1.38 ( ! [Xx: $i] :
% 1.56/1.38 ( ( in @ Xx @ A )
% 1.56/1.38 => ! [X: $i] :
% 1.56/1.38 ( ( in @ X @ A )
% 1.56/1.38 => ! [Y: $i] :
% 1.56/1.38 ( ( in @ Y @ A )
% 1.56/1.38 => ( ( ( in @ Xx @ X )
% 1.56/1.38 & ( in @ X @ Y ) )
% 1.56/1.38 => ( in @ Xx @ Y ) ) ) ) )
% 1.56/1.38 & ! [X: $i] :
% 1.56/1.38 ( ( in @ X @ A )
% 1.56/1.38 => ! [Y: $i] :
% 1.56/1.38 ( ( in @ Y @ A )
% 1.56/1.38 => ( ( X = Y )
% 1.56/1.38 | ( in @ X @ Y )
% 1.56/1.38 | ( in @ Y @ X ) ) ) )
% 1.56/1.38 & ! [X: $i] :
% 1.56/1.38 ( ( in @ X @ A )
% 1.56/1.38 => ~ ( in @ X @ X ) ) ) ) ) ).
% 1.56/1.38
% 1.56/1.38 thf(wellorderedByIn_type,type,
% 1.56/1.38 wellorderedByIn: $i > $o ).
% 1.56/1.38
% 1.56/1.38 thf(wellorderedByIn,definition,
% 1.56/1.38 ( wellorderedByIn
% 1.56/1.38 = ( ^ [A: $i] :
% 1.56/1.38 ( ( stricttotalorderedByIn @ A )
% 1.56/1.38 & ! [X: $i] :
% 1.56/1.38 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.38 => ( ( nonempty @ X )
% 1.56/1.38 => ? [Xx: $i] :
% 1.56/1.38 ( ( in @ Xx @ X )
% 1.56/1.38 & ! [Y: $i] :
% 1.56/1.38 ( ( in @ Y @ X )
% 1.56/1.38 => ( ( Xx = Y )
% 1.56/1.38 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 1.56/1.38
% 1.56/1.38 thf(ordinal_type,type,
% 1.56/1.38 ordinal: $i > $o ).
% 1.56/1.38
% 1.56/1.38 thf(ordinal,definition,
% 1.56/1.38 ( ordinal
% 1.56/1.38 = ( ^ [Xx: $i] :
% 1.56/1.38 ( ( transitiveset @ Xx )
% 1.56/1.38 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 1.56/1.38
% 1.56/1.38 thf(ordinalTransSet_type,type,
% 1.56/1.38 ordinalTransSet: $o ).
% 1.56/1.38
% 1.56/1.38 thf(ordinalTransSet,definition,
% 1.56/1.38 ( ordinalTransSet
% 1.56/1.38 = ( ! [X: $i] :
% 1.56/1.38 ( ( ordinal @ X )
% 1.56/1.38 => ! [Xx: $i,A: $i] :
% 1.56/1.38 ( ( in @ A @ X )
% 1.56/1.38 => ( ( in @ Xx @ A )
% 1.56/1.38 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.56/1.38
% 1.56/1.38 thf(ordinalTransIn,conjecture,
% 1.56/1.38 ( ordinalTransSet
% 1.56/1.38 => ! [X: $i] :
% 1.56/1.38 ( ( ordinal @ X )
% 1.56/1.38 => ! [Xx: $i,A: $i,B: $i] :
% 1.56/1.38 ( ( in @ Xx @ A )
% 1.56/1.38 => ( ( in @ A @ B )
% 1.56/1.38 => ( ( in @ B @ X )
% 1.56/1.38 => ( in @ Xx @ B ) ) ) ) ) ) ).
% 1.56/1.38 ------------------------
% 1.72/1.40 % (26828)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/183Mi)
% 1.72/1.40 % (26829)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_26731 for (2999ds/4Mi)
% 1.72/1.40 % (26831)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/2Mi)
% 1.72/1.40 % (26832)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_26731 for (2999ds/2Mi)
% 1.72/1.40 % (26834)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/18Mi)
% 1.72/1.40 % (26833)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_26731 for (2999ds/275Mi)
% 1.72/1.40 % (26830)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_26731 for (2999ds/27Mi)
% 1.72/1.41 % (26831)Instruction limit reached!
% 1.72/1.41 % (26831)------------------------------
% 1.72/1.41 % (26831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (26831)Termination reason: Unknown
% 1.72/1.41 % (26832)Instruction limit reached!
% 1.72/1.41 % (26832)------------------------------
% 1.72/1.41 % (26832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (26831)Termination phase: Property scanning
% 1.72/1.41
% 1.72/1.41 % (26831)Memory used [KB]: 1023
% 1.72/1.41 % (26831)Time elapsed: 0.003 s
% 1.72/1.41 % (26831)Instructions burned: 3 (million)
% 1.72/1.41 % (26831)------------------------------
% 1.72/1.41 % (26831)------------------------------
% 1.72/1.41 % (26832)Termination reason: Unknown
% 1.72/1.41 % (26832)Termination phase: Property scanning
% 1.72/1.41
% 1.72/1.41 % (26832)Memory used [KB]: 1023
% 1.72/1.41 % (26832)Time elapsed: 0.003 s
% 1.72/1.41 % (26832)Instructions burned: 3 (million)
% 1.72/1.41 % (26832)------------------------------
% 1.72/1.41 % (26832)------------------------------
% 1.72/1.41 % (26829)Instruction limit reached!
% 1.72/1.41 % (26829)------------------------------
% 1.72/1.41 % (26829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (26829)Termination reason: Unknown
% 1.72/1.41 % (26829)Termination phase: Saturation
% 1.72/1.41
% 1.72/1.41 % (26829)Memory used [KB]: 5500
% 1.72/1.41 % (26829)Time elapsed: 0.004 s
% 1.72/1.41 % (26829)Instructions burned: 5 (million)
% 1.72/1.41 % (26829)------------------------------
% 1.72/1.41 % (26829)------------------------------
% 1.72/1.41 % (26833)Refutation not found, incomplete strategy
% 1.72/1.41 % (26833)------------------------------
% 1.72/1.41 % (26833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (26833)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.41
% 1.72/1.41
% 1.72/1.41 % (26833)Memory used [KB]: 5500
% 1.72/1.41 % (26833)Time elapsed: 0.004 s
% 1.72/1.41 % (26833)Instructions burned: 4 (million)
% 1.72/1.41 % (26833)------------------------------
% 1.72/1.41 % (26833)------------------------------
% 1.72/1.41 % (26834)Instruction limit reached!
% 1.72/1.41 % (26834)------------------------------
% 1.72/1.41 % (26834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (26834)Termination reason: Unknown
% 1.72/1.41 % (26834)Termination phase: Saturation
% 1.72/1.41
% 1.72/1.41 % (26834)Memory used [KB]: 5500
% 1.72/1.41 % (26834)Time elapsed: 0.010 s
% 1.72/1.41 % (26834)Instructions burned: 19 (million)
% 1.72/1.41 % (26834)------------------------------
% 1.72/1.41 % (26834)------------------------------
% 1.72/1.42 % (26830)Instruction limit reached!
% 1.72/1.42 % (26830)------------------------------
% 1.72/1.42 % (26830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (26830)Termination reason: Unknown
% 1.72/1.42 % (26830)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (26830)Memory used [KB]: 5628
% 1.72/1.42 % (26830)Time elapsed: 0.014 s
% 1.72/1.42 % (26830)Instructions burned: 27 (million)
% 1.72/1.42 % (26830)------------------------------
% 1.72/1.42 % (26830)------------------------------
% 1.72/1.42 % (26835)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/3Mi)
% 1.72/1.42 % (26836)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_26731 for (2999ds/37Mi)
% 1.72/1.42 % (26837)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_26731 for (2999ds/15Mi)
% 1.72/1.42 % (26835)Instruction limit reached!
% 1.72/1.42 % (26835)------------------------------
% 1.72/1.42 % (26835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (26835)Termination reason: Unknown
% 1.72/1.42 % (26835)Termination phase: Function definition elimination
% 1.72/1.42
% 1.72/1.42 % (26835)Memory used [KB]: 1023
% 1.72/1.42 % (26835)Time elapsed: 0.003 s
% 1.72/1.42 % (26835)Instructions burned: 4 (million)
% 1.72/1.42 % (26835)------------------------------
% 1.72/1.42 % (26835)------------------------------
% 1.72/1.42 % (26838)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_26731 for (2999ds/3Mi)
% 1.72/1.42 % (26838)Instruction limit reached!
% 1.72/1.42 % (26838)------------------------------
% 1.72/1.42 % (26838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (26838)Termination reason: Unknown
% 1.72/1.42 % (26838)Termination phase: Function definition elimination
% 1.72/1.42
% 1.72/1.42 % (26838)Memory used [KB]: 1023
% 1.72/1.42 % (26838)Time elapsed: 0.003 s
% 1.72/1.42 % (26838)Instructions burned: 4 (million)
% 1.72/1.42 % (26838)------------------------------
% 1.72/1.42 % (26838)------------------------------
% 1.72/1.43 % (26839)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_26731 for (2999ds/1041Mi)
% 1.72/1.43 % (26837)Instruction limit reached!
% 1.72/1.43 % (26837)------------------------------
% 1.72/1.43 % (26837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (26837)Termination reason: Unknown
% 1.72/1.43 % (26837)Termination phase: Saturation
% 1.72/1.43
% 1.72/1.43 % (26837)Memory used [KB]: 5500
% 1.72/1.43 % (26837)Time elapsed: 0.008 s
% 1.72/1.43 % (26837)Instructions burned: 15 (million)
% 1.72/1.43 % (26837)------------------------------
% 1.72/1.43 % (26837)------------------------------
% 1.72/1.43 % (26840)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/7Mi)
% 1.72/1.44 % (26840)Instruction limit reached!
% 1.72/1.44 % (26840)------------------------------
% 1.72/1.44 % (26840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (26840)Termination reason: Unknown
% 1.72/1.44 % (26840)Termination phase: Saturation
% 1.72/1.44
% 1.72/1.44 % (26840)Memory used [KB]: 1023
% 1.72/1.44 % (26840)Time elapsed: 0.005 s
% 1.72/1.44 % (26840)Instructions burned: 8 (million)
% 1.72/1.44 % (26840)------------------------------
% 1.72/1.44 % (26840)------------------------------
% 1.72/1.44 % (26836)Instruction limit reached!
% 1.72/1.44 % (26836)------------------------------
% 1.72/1.44 % (26836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (26836)Termination reason: Unknown
% 1.72/1.44 % (26836)Termination phase: Saturation
% 1.72/1.44
% 1.72/1.44 % (26836)Memory used [KB]: 5500
% 1.72/1.44 % (26836)Time elapsed: 0.018 s
% 1.72/1.44 % (26836)Instructions burned: 37 (million)
% 1.72/1.44 % (26836)------------------------------
% 1.72/1.44 % (26836)------------------------------
% 1.72/1.44 % (26841)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/16Mi)
% 1.72/1.44 % (26842)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_26731 for (2999ds/3Mi)
% 1.72/1.44 % (26842)Instruction limit reached!
% 1.72/1.44 % (26842)------------------------------
% 1.72/1.44 % (26842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (26842)Termination reason: Unknown
% 1.72/1.44 % (26842)Termination phase: Property scanning
% 1.72/1.44
% 1.72/1.44 % (26842)Memory used [KB]: 1023
% 1.72/1.44 % (26842)Time elapsed: 0.003 s
% 1.72/1.44 % (26842)Instructions burned: 4 (million)
% 1.72/1.44 % (26842)------------------------------
% 1.72/1.44 % (26842)------------------------------
% 1.72/1.44 % (26843)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_26731 for (2999ds/3Mi)
% 1.72/1.45 % (26843)Instruction limit reached!
% 1.72/1.45 % (26843)------------------------------
% 1.72/1.45 % (26843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (26843)Termination reason: Unknown
% 1.72/1.45 % (26843)Termination phase: Property scanning
% 1.72/1.45
% 1.72/1.45 % (26843)Memory used [KB]: 1023
% 1.72/1.45 % (26843)Time elapsed: 0.003 s
% 1.72/1.45 % (26843)Instructions burned: 4 (million)
% 1.72/1.45 % (26843)------------------------------
% 1.72/1.45 % (26843)------------------------------
% 1.72/1.45 % (26841)Instruction limit reached!
% 1.72/1.45 % (26841)------------------------------
% 1.72/1.45 % (26841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (26841)Termination reason: Unknown
% 1.72/1.45 % (26841)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (26841)Memory used [KB]: 5756
% 1.72/1.45 % (26841)Time elapsed: 0.010 s
% 1.72/1.45 % (26841)Instructions burned: 16 (million)
% 1.72/1.45 % (26841)------------------------------
% 1.72/1.45 % (26841)------------------------------
% 1.72/1.45 % (26844)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/7Mi)
% 1.72/1.45 % (26845)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/3Mi)
% 1.72/1.46 % (26844)Instruction limit reached!
% 1.72/1.46 % (26844)------------------------------
% 1.72/1.46 % (26844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (26844)Termination reason: Unknown
% 1.72/1.46 % (26844)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (26844)Memory used [KB]: 5500
% 1.72/1.46 % (26844)Time elapsed: 0.005 s
% 1.72/1.46 % (26844)Instructions burned: 8 (million)
% 1.72/1.46 % (26844)------------------------------
% 1.72/1.46 % (26844)------------------------------
% 1.72/1.46 % (26845)Instruction limit reached!
% 1.72/1.46 % (26845)------------------------------
% 1.72/1.46 % (26845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (26845)Termination reason: Unknown
% 1.72/1.46 % (26845)Termination phase: Function definition elimination
% 1.72/1.46
% 1.72/1.46 % (26845)Memory used [KB]: 1023
% 1.72/1.46 % (26845)Time elapsed: 0.003 s
% 1.72/1.46 % (26845)Instructions burned: 4 (million)
% 1.72/1.46 % (26845)------------------------------
% 1.72/1.46 % (26845)------------------------------
% 1.72/1.46 % (26846)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/4Mi)
% 1.72/1.46 % (26846)Instruction limit reached!
% 1.72/1.46 % (26846)------------------------------
% 1.72/1.46 % (26846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (26846)Termination reason: Unknown
% 1.72/1.46 % (26846)Termination phase: Function definition elimination
% 1.72/1.46
% 1.72/1.46 % (26846)Memory used [KB]: 1023
% 1.72/1.46 % (26846)Time elapsed: 0.003 s
% 1.72/1.46 % (26846)Instructions burned: 4 (million)
% 1.72/1.46 % (26846)------------------------------
% 1.72/1.46 % (26846)------------------------------
% 1.72/1.46 % (26847)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/18Mi)
% 1.72/1.46 % (26848)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/710Mi)
% 1.72/1.47 % (26839)First to succeed.
% 1.72/1.47 % (26847)Instruction limit reached!
% 1.72/1.47 % (26847)------------------------------
% 1.72/1.47 % (26847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (26847)Termination reason: Unknown
% 1.72/1.47 % (26847)Termination phase: Saturation
% 1.72/1.47
% 1.72/1.47 % (26847)Memory used [KB]: 5628
% 1.72/1.47 % (26847)Time elapsed: 0.010 s
% 1.72/1.47 % (26847)Instructions burned: 18 (million)
% 1.72/1.47 % (26847)------------------------------
% 1.72/1.47 % (26847)------------------------------
% 1.72/1.47 % (26849)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26731 for (2999ds/6Mi)
% 1.72/1.47 % (26850)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_26731 for (2999ds/902Mi)
% 1.72/1.47 % (26839)Refutation found. Thanks to Tanya!
% 1.72/1.47 % SZS status Theorem for DTF2THF_26731
% 1.72/1.47 % SZS output start Proof for DTF2THF_26731
% 1.72/1.47 thf(func_def_0, type, in: $i > $i > $o).
% 1.72/1.47 thf(func_def_1, type, powerset: $i > $i).
% 1.72/1.47 thf(func_def_2, type, nonempty: $i > $o).
% 1.72/1.47 thf(func_def_3, type, transitiveset: $i > $o).
% 1.72/1.47 thf(func_def_4, type, stricttotalorderedByIn: $i > $o).
% 1.72/1.47 thf(func_def_6, type, wellorderedByIn: $i > $o).
% 1.72/1.47 thf(func_def_7, type, ordinal: $i > $o).
% 1.72/1.47 thf(func_def_24, type, ph1: !>[X0: $tType]:(X0)).
% 1.72/1.47 thf(f314,plain,(
% 1.72/1.47 $false),
% 1.72/1.47 inference(trivial_inequality_removal,[status(thm)],[f313])).
% 1.72/1.47 thf(f313,plain,(
% 1.72/1.47 ($false = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f312])).
% 1.72/1.47 thf(f312,plain,(
% 1.72/1.47 ((~ $true) = $true)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f311,f56])).
% 1.72/1.47 thf(f56,plain,(
% 1.72/1.47 ($true = (in @ sK5 @ sK3))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.72/1.47 thf(f49,plain,(
% 1.72/1.47 (((in @ sK5 @ sK3) => ((in @ sK3 @ sK2) => (in @ sK4 @ sK3))) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.72/1.47 thf(f48,plain,(
% 1.72/1.47 ($false = ((in @ sK4 @ sK5) => ((in @ sK5 @ sK3) => ((in @ sK3 @ sK2) => (in @ sK4 @ sK3)))))),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.72/1.47 thf(f47,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i]: ((in @ sK4 @ Y0) => ((in @ Y0 @ sK3) => ((in @ sK3 @ sK2) => (in @ sK4 @ sK3))))) @ sK5))),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f46])).
% 1.72/1.47 thf(f46,plain,(
% 1.72/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ sK4 @ Y0) => ((in @ Y0 @ sK3) => ((in @ sK3 @ sK2) => (in @ sK4 @ sK3)))))))),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.72/1.47 thf(f45,plain,(
% 1.72/1.47 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ sK3) => ((in @ sK3 @ sK2) => (in @ Y0 @ sK3))))))) @ sK4) = $false)),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f44])).
% 1.72/1.47 thf(f44,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ sK3) => ((in @ sK3 @ sK2) => (in @ Y0 @ sK3)))))))) = $false)),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.72/1.47 thf(f43,plain,(
% 1.72/1.47 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => ((in @ Y0 @ sK2) => (in @ Y1 @ Y0))))))))) @ sK3))),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f42])).
% 1.72/1.47 thf(f42,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => ((in @ Y0 @ sK2) => (in @ Y1 @ Y0)))))))))) = $false)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f41])).
% 1.72/1.47 thf(f41,plain,(
% 1.72/1.47 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => ((in @ Y0 @ sK2) => (in @ Y1 @ Y0))))))))))))),
% 1.72/1.47 inference(backward_demodulation,[status(thm)],[f36,f40])).
% 1.72/1.47 thf(f40,plain,(
% 1.72/1.47 (((transitiveset @ sK2) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.72/1.47 thf(f36,plain,(
% 1.72/1.47 ($false = (((transitiveset @ sK2) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => ((in @ Y0 @ sK2) => (in @ Y1 @ Y0))))))))))))),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.72/1.47 thf(f35,plain,(
% 1.72/1.47 (((^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => ((in @ Y3 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ Y1)))))))))))) @ sK2) = $false)),
% 1.72/1.47 inference(sigma_clausification,[status(thm)],[f34])).
% 1.72/1.47 thf(f34,plain,(
% 1.72/1.47 ($false = (!! @ $i @ (^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => ((in @ Y3 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ Y1))))))))))))))),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f33])).
% 1.72/1.47 thf(f33,plain,(
% 1.72/1.47 (($true => (!! @ $i @ (^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => ((in @ Y3 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ Y1)))))))))))))) = $false)),
% 1.72/1.47 inference(backward_demodulation,[status(thm)],[f28,f32])).
% 1.72/1.47 thf(f32,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.72/1.47 thf(f28,plain,(
% 1.72/1.47 (((!! @ $i @ (^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => ((in @ Y3 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ Y1)))))))))))))) = $false)),
% 1.72/1.47 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.72/1.47 thf(f27,plain,(
% 1.72/1.47 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => ((in @ Y3 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ Y1))))))))))))))))),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.72/1.47 thf(f26,plain,(
% 1.72/1.47 ((~ ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: ((transitiveset @ Y1) & ((^[Y2 : $i]: (((^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => (((in @ Y4 @ Y5) & (in @ Y5 @ Y6)) => (in @ Y4 @ Y6))))))))))) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => (((in @ Y4 @ Y5) | (Y4 = Y5)) | (in @ Y5 @ Y4))))))))) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (~ (in @ Y4 @ Y4))))))) @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y2)) => ((nonempty @ Y3) => (?? @ $i @ (^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => ((in @ Y4 @ Y5) | (Y4 = Y5))))) & (in @ Y4 @ Y3)))))))))) @ Y1))) @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: ((transitiveset @ Y1) & ((^[Y2 : $i]: (((^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => (((in @ Y4 @ Y5) & (in @ Y5 @ Y6)) => (in @ Y4 @ Y6))))))))))) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => (((in @ Y4 @ Y5) | (Y4 = Y5)) | (in @ Y5 @ Y4))))))))) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (~ (in @ Y4 @ Y4))))))) @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y2)) => ((nonempty @ Y3) => (?? @ $i @ (^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => ((in @ Y4 @ Y5) | (Y4 = Y5))))) & (in @ Y4 @ Y3)))))))))) @ Y1))) @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => ((in @ Y3 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ Y1))))))))))))))) = $true)),
% 1.72/1.47 inference(definition_unfolding,[status(thm)],[f21,f25,f24])).
% 1.72/1.47 thf(f24,plain,(
% 1.72/1.47 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & ((^[Y1 : $i]: (((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => (((in @ Y3 @ Y4) & (in @ Y4 @ Y5)) => (in @ Y3 @ Y5))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (((in @ Y3 @ Y4) | (Y3 = Y4)) | (in @ Y4 @ Y3))))))))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y3))))))) @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((nonempty @ Y2) => (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ Y3 @ Y4) | (Y3 = Y4))))) & (in @ Y3 @ Y2)))))))))) @ Y0))))),
% 1.72/1.47 inference(definition_unfolding,[status(thm)],[f22,f23])).
% 1.72/1.47 thf(f23,plain,(
% 1.72/1.47 (wellorderedByIn = (^[Y0 : $i]: (((^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (((in @ Y2 @ Y3) & (in @ Y3 @ Y4)) => (in @ Y2 @ Y4))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (((in @ Y2 @ Y3) | (Y2 = Y3)) | (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (in @ Y2 @ Y2))))))) @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))))),
% 1.72/1.47 inference(definition_unfolding,[status(thm)],[f20,f19])).
% 1.72/1.47 thf(f19,plain,(
% 1.72/1.47 (stricttotalorderedByIn = (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1))))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f9])).
% 1.72/1.47 thf(f9,plain,(
% 1.72/1.47 (stricttotalorderedByIn = (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1))))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f8])).
% 1.72/1.47 thf(f8,plain,(
% 1.72/1.47 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => ~(in @ X1 @ X1)) & ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) | (X2 = X3) | (in @ X2 @ X3)))) & ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => (((in @ X5 @ X6) & (in @ X4 @ X5)) => (in @ X4 @ X6))))))) = stricttotalorderedByIn)),
% 1.72/1.47 inference(rectify,[status(thm)],[f1])).
% 1.72/1.47 thf(f1,axiom,(
% 1.72/1.47 ((^[X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ~(in @ X2 @ X2)) & ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) | (X2 = X3) | (in @ X2 @ X3)))) & ! [X1 : $i] : ((in @ X1 @ X0) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (((in @ X2 @ X3) & (in @ X1 @ X2)) => (in @ X1 @ X3))))))) = stricttotalorderedByIn)),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',stricttotalorderedByIn)).
% 1.72/1.47 thf(f20,plain,(
% 1.72/1.47 (wellorderedByIn = (^[Y0 : $i]: ((stricttotalorderedByIn @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f15])).
% 1.72/1.47 thf(f15,plain,(
% 1.72/1.47 (wellorderedByIn = (^[Y0 : $i]: ((stricttotalorderedByIn @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f14])).
% 1.72/1.47 thf(f14,plain,(
% 1.72/1.47 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((nonempty @ X1) => ? [X2 : $i] : ((in @ X2 @ X1) & ! [X3 : $i] : ((in @ X3 @ X1) => ((X2 = X3) | (in @ X2 @ X3)))))) & (stricttotalorderedByIn @ X0))) = wellorderedByIn)),
% 1.72/1.47 inference(rectify,[status(thm)],[f2])).
% 1.72/1.47 thf(f2,axiom,(
% 1.72/1.47 ((^[X0 : $i] : (! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((nonempty @ X2) => ? [X1 : $i] : ((in @ X1 @ X2) & ! [X3 : $i] : ((in @ X3 @ X2) => ((X1 = X3) | (in @ X1 @ X3)))))) & (stricttotalorderedByIn @ X0))) = wellorderedByIn)),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',wellorderedByIn)).
% 1.72/1.47 thf(f22,plain,(
% 1.72/1.47 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f17])).
% 1.72/1.47 thf(f17,plain,(
% 1.72/1.47 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f16])).
% 1.72/1.47 thf(f16,plain,(
% 1.72/1.47 (ordinal = (^[X0 : $i] : ((wellorderedByIn @ X0) & (transitiveset @ X0))))),
% 1.72/1.47 inference(rectify,[status(thm)],[f3])).
% 1.72/1.47 thf(f3,axiom,(
% 1.72/1.47 (ordinal = (^[X1 : $i] : ((wellorderedByIn @ X1) & (transitiveset @ X1))))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',ordinal)).
% 1.72/1.47 thf(f25,plain,(
% 1.72/1.47 (ordinalTransSet = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: ((transitiveset @ Y1) & ((^[Y2 : $i]: (((^[Y3 : $i]: (((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => (((in @ Y4 @ Y5) & (in @ Y5 @ Y6)) => (in @ Y4 @ Y6))))))))))) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => (((in @ Y4 @ Y5) | (Y4 = Y5)) | (in @ Y5 @ Y4))))))))) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (~ (in @ Y4 @ Y4))))))) @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y2)) => ((nonempty @ Y3) => (?? @ $i @ (^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) => ((in @ Y4 @ Y5) | (Y4 = Y5))))) & (in @ Y4 @ Y3)))))))))) @ Y1))) @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))))),
% 1.72/1.47 inference(definition_unfolding,[status(thm)],[f18,f24])).
% 1.72/1.47 thf(f18,plain,(
% 1.72/1.47 (ordinalTransSet = (!! @ $i @ (^[Y0 : $i]: ((ordinal @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))))),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f13])).
% 1.72/1.47 thf(f13,plain,(
% 1.72/1.47 (ordinalTransSet = (!! @ $i @ (^[Y0 : $i]: ((ordinal @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))))),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f12])).
% 1.72/1.47 thf(f12,plain,(
% 1.72/1.47 (ordinalTransSet = ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0)))))),
% 1.72/1.47 inference(rectify,[status(thm)],[f4])).
% 1.72/1.47 thf(f4,axiom,(
% 1.72/1.47 (ordinalTransSet = ! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i,X1 : $i] : ((in @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2)))))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',ordinalTransSet)).
% 1.72/1.47 thf(f21,plain,(
% 1.72/1.47 ((~ (ordinalTransSet => (!! @ $i @ (^[Y0 : $i]: ((ordinal @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => ((in @ Y3 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ Y1))))))))))))))) = $true)),
% 1.72/1.47 inference(cnf_transformation,[status(thm)],[f11])).
% 1.72/1.47 thf(f11,plain,(
% 1.72/1.47 ((~ (ordinalTransSet => (!! @ $i @ (^[Y0 : $i]: ((ordinal @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => ((in @ Y3 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ Y1))))))))))))))) = $true)),
% 1.72/1.47 inference(fool_elimination,[status(thm)],[f10])).
% 1.72/1.47 thf(f10,plain,(
% 1.72/1.47 ~(ordinalTransSet => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i,X2 : $i,X3 : $i] : ((in @ X2 @ X1) => ((in @ X1 @ X3) => ((in @ X3 @ X0) => (in @ X2 @ X3))))))),
% 1.72/1.47 inference(rectify,[status(thm)],[f6])).
% 1.72/1.47 thf(f6,negated_conjecture,(
% 1.72/1.47 ~(ordinalTransSet => ! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X0) => ((in @ X0 @ X4) => ((in @ X4 @ X2) => (in @ X1 @ X4))))))),
% 1.72/1.47 inference(negated_conjecture,[status(cth)],[f5])).
% 1.72/1.47 thf(f5,conjecture,(
% 1.72/1.47 ordinalTransSet => ! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X0) => ((in @ X0 @ X4) => ((in @ X4 @ X2) => (in @ X1 @ X4)))))),
% 1.72/1.47 file('/export/starexec/sandbox/tmp/tmp.BFXeH4jjkd/DTF2THF_26731.p',ordinalTransIn)).
% 1.72/1.47 thf(f311,plain,(
% 1.72/1.47 ((~ (in @ sK5 @ sK3)) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f310])).
% 1.72/1.47 thf(f310,plain,(
% 1.72/1.47 (($true => (~ (in @ sK5 @ sK3))) = $true)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f299,f70])).
% 1.72/1.47 thf(f70,plain,(
% 1.72/1.47 ((in @ sK3 @ sK2) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.72/1.47 thf(f55,plain,(
% 1.72/1.47 (((in @ sK3 @ sK2) => (in @ sK4 @ sK3)) = $false)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.72/1.47 thf(f299,plain,(
% 1.72/1.47 ($true = ((in @ sK3 @ sK2) => (~ (in @ sK5 @ sK3))))),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f284])).
% 1.72/1.47 thf(f284,plain,(
% 1.72/1.47 (((in @ sK3 @ sK2) => ((in @ sK5 @ sK3) => $false)) = $true)),
% 1.72/1.47 inference(superposition,[status(thm)],[f277,f72])).
% 1.72/1.47 thf(f72,plain,(
% 1.72/1.47 ($false = (in @ sK4 @ sK3))),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f71])).
% 1.72/1.47 thf(f71,plain,(
% 1.72/1.47 (($true => (in @ sK4 @ sK3)) = $false)),
% 1.72/1.47 inference(backward_demodulation,[status(thm)],[f55,f70])).
% 1.72/1.47 thf(f277,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((in @ sK5 @ X1) => (in @ sK4 @ X1))) = $true)) )),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f276])).
% 1.72/1.47 thf(f276,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => (($true & (in @ sK5 @ X1)) => (in @ sK4 @ X1))) = $true)) )),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f275,f50])).
% 1.72/1.47 thf(f50,plain,(
% 1.72/1.47 ($true = (in @ sK4 @ sK5))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.72/1.47 thf(f275,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => (((in @ sK4 @ sK5) & (in @ sK5 @ X1)) => (in @ sK4 @ X1))))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f272])).
% 1.72/1.47 thf(f272,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => (((in @ sK4 @ sK5) & (in @ sK5 @ Y0)) => (in @ sK4 @ Y0)))) @ X1) = $true)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f269])).
% 1.72/1.47 thf(f269,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (((in @ sK4 @ sK5) & (in @ sK5 @ Y0)) => (in @ sK4 @ Y0))))) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f267])).
% 1.72/1.47 thf(f267,plain,(
% 1.72/1.47 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (((in @ sK4 @ sK5) & (in @ sK5 @ Y0)) => (in @ sK4 @ Y0)))))) = $true)),
% 1.72/1.47 inference(superposition,[status(thm)],[f263,f112])).
% 1.72/1.47 thf(f112,plain,(
% 1.72/1.47 ((in @ sK5 @ sK2) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f111])).
% 1.72/1.47 thf(f111,plain,(
% 1.72/1.47 ($true = ($true => (in @ sK5 @ sK2)))),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f105,f70])).
% 1.72/1.47 thf(f105,plain,(
% 1.72/1.47 ($true = ((in @ sK3 @ sK2) => (in @ sK5 @ sK2)))),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f98])).
% 1.72/1.47 thf(f98,plain,(
% 1.72/1.47 (((in @ sK3 @ sK2) => ($true => (in @ sK5 @ sK2))) = $true)),
% 1.72/1.47 inference(superposition,[status(thm)],[f94,f56])).
% 1.72/1.47 thf(f94,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ sK2) => ((in @ X1 @ X2) => (in @ X1 @ sK2))))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.72/1.47 thf(f93,plain,(
% 1.72/1.47 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ X1 @ Y0) => (in @ X1 @ sK2)))) @ X2))) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f92])).
% 1.72/1.47 thf(f92,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ X1 @ Y0) => (in @ X1 @ sK2))))))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.72/1.47 thf(f89,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) => (in @ Y0 @ sK2)))))) @ X1) = $true)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f84])).
% 1.72/1.47 thf(f84,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) => (in @ Y0 @ sK2))))))) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f83])).
% 1.72/1.47 thf(f83,plain,(
% 1.72/1.47 (($true => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) => (in @ Y0 @ sK2)))))))) = $true)),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f82,f66])).
% 1.72/1.47 thf(f66,plain,(
% 1.72/1.47 ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0)))))) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.72/1.47 thf(f64,plain,(
% 1.72/1.47 (((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f63])).
% 1.72/1.47 thf(f63,plain,(
% 1.72/1.47 (($true & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))) = $true)),
% 1.72/1.47 inference(backward_demodulation,[status(thm)],[f40,f62])).
% 1.72/1.47 thf(f62,plain,(
% 1.72/1.47 ($true = (transitiveset @ sK2))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.72/1.47 thf(f82,plain,(
% 1.72/1.47 (((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0)))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) => (in @ Y0 @ sK2)))))))) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f81])).
% 1.72/1.47 thf(f81,plain,(
% 1.72/1.47 ($true = (($true & (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) => (in @ Y0 @ sK2)))))))))),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f80,f62])).
% 1.72/1.47 thf(f80,plain,(
% 1.72/1.47 ($true = (((transitiveset @ sK2) & (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) => (in @ Y0 @ sK2)))))))))),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f77])).
% 1.72/1.47 thf(f77,plain,(
% 1.72/1.47 ($true = (((transitiveset @ sK2) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (~ (in @ Y0 @ Y0)))))) & $true)) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ Y0 @ Y1) => (in @ Y0 @ sK2)))))))))),
% 1.72/1.47 inference(superposition,[status(thm)],[f38,f68])).
% 1.72/1.47 thf(f68,plain,(
% 1.72/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f67])).
% 1.72/1.47 thf(f67,plain,(
% 1.72/1.47 (($true & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK2)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0))))))))) = $true)),
% 1.72/1.47 inference(backward_demodulation,[status(thm)],[f64,f66])).
% 1.72/1.47 thf(f38,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($true = (((transitiveset @ X1) & ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (~ (in @ Y0 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2))))) & (in @ Y1 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ Y0 @ Y1) => (in @ Y0 @ X1)))))))))) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.72/1.47 thf(f37,plain,(
% 1.72/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (((transitiveset @ Y0) & ((((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (((in @ Y1 @ Y2) & (in @ Y2 @ Y3)) => (in @ Y1 @ Y3))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (((in @ Y1 @ Y2) | (Y1 = Y2)) | (in @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3))))) & (in @ Y2 @ Y1)))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) @ X1))) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f32])).
% 1.72/1.47 thf(f263,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (((in @ sK4 @ X1) & (in @ X1 @ Y0)) => (in @ sK4 @ Y0)))))) = $true)) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f261])).
% 1.72/1.47 thf(f261,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ sK4 @ Y0) & (in @ Y0 @ Y1)) => (in @ sK4 @ Y1))))))) @ X1) = $true)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f202])).
% 1.72/1.47 thf(f202,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ sK4 @ Y0) & (in @ Y0 @ Y1)) => (in @ sK4 @ Y1)))))))) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f201])).
% 1.72/1.47 thf(f201,plain,(
% 1.72/1.47 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ sK4 @ Y0) & (in @ Y0 @ Y1)) => (in @ sK4 @ Y1))))))))) = $true)),
% 1.72/1.47 inference(superposition,[status(thm)],[f184,f114])).
% 1.72/1.47 thf(f114,plain,(
% 1.72/1.47 ((in @ sK4 @ sK2) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f113])).
% 1.72/1.47 thf(f113,plain,(
% 1.72/1.47 ($true = ($true => (in @ sK4 @ sK2)))),
% 1.72/1.47 inference(forward_demodulation,[status(thm)],[f102,f112])).
% 1.72/1.47 thf(f102,plain,(
% 1.72/1.47 ($true = ((in @ sK5 @ sK2) => (in @ sK4 @ sK2)))),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f100])).
% 1.72/1.47 thf(f100,plain,(
% 1.72/1.47 (((in @ sK5 @ sK2) => ($true => (in @ sK4 @ sK2))) = $true)),
% 1.72/1.47 inference(superposition,[status(thm)],[f94,f50])).
% 1.72/1.47 thf(f184,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ X1 @ Y0) & (in @ Y0 @ Y1)) => (in @ X1 @ Y1))))))))) = $true)) )),
% 1.72/1.47 inference(beta_eta_normalization,[status(thm)],[f181])).
% 1.72/1.47 thf(f181,plain,(
% 1.72/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))) @ X1) = $true)) )),
% 1.72/1.47 inference(pi_clausification,[status(thm)],[f168])).
% 1.72/1.47 thf(f168,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) = $true)),
% 1.72/1.47 inference(boolean_simplification,[status(thm)],[f167])).
% 1.72/1.47 thf(f167,plain,(
% 1.72/1.47 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & $true))),
% 1.72/1.47 inference(backward_demodulation,[status(thm)],[f116,f163])).
% 1.72/1.47 thf(f163,plain,(
% 1.72/1.47 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0)))))))) = $true)),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.72/1.47 thf(f116,plain,(
% 1.72/1.47 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((in @ Y0 @ Y1) | (Y0 = Y1)) | (in @ Y1 @ Y0))))))))))),
% 1.72/1.47 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.72/1.47 % SZS output end Proof for DTF2THF_26731
% 1.72/1.47 % (26839)------------------------------
% 1.72/1.47 % (26839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (26839)Termination reason: Refutation
% 1.72/1.47
% 1.72/1.47 % (26839)Memory used [KB]: 6012
% 1.72/1.47 % (26839)Time elapsed: 0.046 s
% 1.72/1.47 % (26839)Instructions burned: 76 (million)
% 1.72/1.47 % (26839)------------------------------
% 1.72/1.47 % (26839)------------------------------
% 1.72/1.47 % (26827)Success in time 0.076 s
%------------------------------------------------------------------------------