%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU821^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n025.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 09:37:30 AM UTC 2026
% Result : Theorem 1.50s 1.29s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 492 ( 74 equ; 0 cnn)
% Maximal formula atoms : 6 ( 12 avg)
% Number of connectives : 912 ( 24 ~; 32 |; 67 &; 598 @)
% ( 0 <=>; 117 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 10 usr; 6 con; 0-2 aty)
% ( 67 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 133 ( 95 ^; 30 !; 8 ?; 133 :)
% 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_25,type,
sK3: $i > $i ).
thf(f83,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
$false = $true,
inference(superposition,[status(thm)],[f79,f21]) ).
thf(f21,plain,
( ( in @ sK1 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK1 @ sK1 )
= $true )
& ( ( ordinal @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f18,f17]) ).
thf(f17,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
=> ( ? [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $true )
& ( ( in @ X1 @ X1 )
= $true ) )
& ( ( ordinal @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $true )
& ( ( in @ X1 @ X1 )
= $true ) )
=> ( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK1 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
~ ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ X1 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ~ ( in @ X0 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ~ ( in @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2THF_6802.p',ordinalIrrefl) ).
thf(f79,plain,
( ( in @ sK1 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $false = $true )
| ( ( in @ sK1 @ sK1 )
= $false ) ),
inference(superposition,[status(thm)],[f54,f22]) ).
thf(f22,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f54,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $false )
| ( ( in @ X1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $false )
| ( ( ~ ( in @ X1 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ~ ( in @ X1 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( transitiveset @ sK0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK0 ) )
=> ( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK0 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
=> ( ( in @ Y1 @ Y0 )
| ( Y0 = Y1 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( nonempty @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 ) ) ) ) ) ) ) ) )
& ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) )
& ( !! @ $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 @ Y4 @ Y3 )
| ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) )
@ Y1 ) )
@ Y0 ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f20,f27]) ).
thf(f27,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( nonempty @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( Y3 = Y4 ) ) ) ) ) ) ) ) )
& ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) )
& ( !! @ $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 @ Y4 @ Y3 )
| ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) ) ) ) )
@ Y1 ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f26]) ).
thf(f26,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) )
& ( !! @ $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 @ Y3 @ Y2 )
| ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f24]) ).
thf(f24,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $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 @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) )
& ( !! @ $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 @ Y2 @ Y1 )
| ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
| ( X1 = X2 )
| ( in @ X2 @ X1 ) ) ) )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( ( in @ X4 @ X5 )
& ( in @ X3 @ X4 ) )
=> ( in @ X3 @ X5 ) ) ) ) )
& ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ~ ( in @ X6 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( stricttotalorderedByIn
= ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 )
| ( in @ X3 @ X2 ) ) ) )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X1 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2THF_6802.p',stricttotalorderedByIn) ).
thf(f23,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( stricttotalorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( stricttotalorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( wellorderedByIn
= ( ^ [X0: $i] :
( ( stricttotalorderedByIn @ X0 )
& ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 = X3 )
| ( in @ X2 @ X3 ) ) )
& ( in @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( wellorderedByIn
= ( ^ [X0: $i] :
( ( stricttotalorderedByIn @ X0 )
& ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X2 )
=> ? [X1: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( X1 = X3 )
| ( in @ X1 @ X3 ) ) )
& ( in @ X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2THF_6802.p',wellorderedByIn) ).
thf(f25,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) )
= ordinal ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: $i] :
( ( wellorderedByIn @ X1 )
& ( transitiveset @ X1 ) ) )
= ordinal ),
file('/export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2THF_6802.p',ordinal) ).
thf(f20,plain,
( ( ordinal @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU821^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:35:12 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SEU821^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.44 % Domain : Set Theory
% 0.18/0.44 % Problem : Ordinals
% 0.18/0.44 % Version : Especial > Reduced > Especial.
% 0.18/0.44 % English : (! X:i.ordinal X -> (! A:i.in A X -> ~(in A A)))
% 0.18/0.44
% 0.18/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.44 % Source : [Bro08]
% 0.18/0.44 % Names : ZFC323l [Bro08]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.18/0.44 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.18/0.44 % Number of atoms : 31 ( 5 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 3 ( 7 avg)
% 0.18/0.44 % Number of connectives : 65 ( 2 ~; 3 |; 6 &; 42 @)
% 0.18/0.44 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 8 ( 3 avg)
% 0.18/0.44 % Number of types : 2 ( 0 usr)
% 0.18/0.44 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 8 ( 7 usr; 0 con; 1-2 aty)
% 0.18/0.44 % Number of variables : 14 ( 3 ^; 10 !; 1 ?; 14 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : http://mathgate.info/detsetitem.php?id=518
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(in_type,type,
% 0.18/0.44 in: $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(powerset_type,type,
% 0.18/0.44 powerset: $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(nonempty_type,type,
% 0.18/0.44 nonempty: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(transitiveset_type,type,
% 0.18/0.44 transitiveset: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(stricttotalorderedByIn_type,type,
% 0.18/0.44 stricttotalorderedByIn: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(stricttotalorderedByIn,definition,
% 0.18/0.44 ( stricttotalorderedByIn
% 0.18/0.44 = ( ^ [A: $i] :
% 0.18/0.44 ( ! [Xx: $i] :
% 0.18/0.44 ( ( in @ Xx @ A )
% 0.18/0.44 => ! [X: $i] :
% 0.18/0.44 ( ( in @ X @ A )
% 0.18/0.44 => ! [Y: $i] :
% 0.18/0.44 ( ( in @ Y @ A )
% 0.18/0.44 => ( ( ( in @ Xx @ X )
% 0.18/0.44 & ( in @ X @ Y ) )
% 0.18/0.44 => ( in @ Xx @ Y ) ) ) ) )
% 0.18/0.44 & ! [X: $i] :
% 0.18/0.44 ( ( in @ X @ A )
% 0.18/0.44 => ! [Y: $i] :
% 0.18/0.44 ( ( in @ Y @ A )
% 0.18/0.44 => ( ( X = Y )
% 0.18/0.44 | ( in @ X @ Y )
% 0.18/0.44 | ( in @ Y @ X ) ) ) )
% 0.18/0.44 & ! [X: $i] :
% 0.18/0.44 ( ( in @ X @ A )
% 0.18/0.44 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(wellorderedByIn_type,type,
% 0.18/0.44 wellorderedByIn: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(wellorderedByIn,definition,
% 0.18/0.44 ( wellorderedByIn
% 0.18/0.44 = ( ^ [A: $i] :
% 0.18/0.44 ( ( stricttotalorderedByIn @ A )
% 0.18/0.44 & ! [X: $i] :
% 0.18/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.18/0.44 => ( ( nonempty @ X )
% 0.18/0.44 => ? [Xx: $i] :
% 0.18/0.44 ( ( in @ Xx @ X )
% 0.18/0.44 & ! [Y: $i] :
% 0.18/0.44 ( ( in @ Y @ X )
% 0.18/0.44 => ( ( Xx = Y )
% 0.18/0.44 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(ordinal_type,type,
% 0.18/0.44 ordinal: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(ordinal,definition,
% 0.18/0.44 ( ordinal
% 0.18/0.44 = ( ^ [Xx: $i] :
% 0.18/0.44 ( ( transitiveset @ Xx )
% 0.18/0.44 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(ordinalIrrefl,conjecture,
% 0.18/0.44 ! [X: $i] :
% 0.18/0.44 ( ( ordinal @ X )
% 0.18/0.44 => ! [A: $i] :
% 0.18/0.44 ( ( in @ A @ X )
% 0.18/0.44 => ~ ( in @ A @ A ) ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.50/1.24 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 12:35:13 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2DTF6802.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(in_type,type,
% 1.50/1.26 in: $i > $i > $o ).
% 1.50/1.26
% 1.50/1.26 thf(powerset_type,type,
% 1.50/1.26 powerset: $i > $i ).
% 1.50/1.26
% 1.50/1.26 thf(nonempty_type,type,
% 1.50/1.26 nonempty: $i > $o ).
% 1.50/1.26
% 1.50/1.26 thf(transitiveset_type,type,
% 1.50/1.26 transitiveset: $i > $o ).
% 1.50/1.26
% 1.50/1.26 thf(stricttotalorderedByIn_type,type,
% 1.50/1.26 stricttotalorderedByIn: $i > $o ).
% 1.50/1.26
% 1.50/1.26 thf(stricttotalorderedByIn,definition,
% 1.50/1.26 ( stricttotalorderedByIn
% 1.50/1.26 = ( ^ [A: $i] :
% 1.50/1.26 ( ! [Xx: $i] :
% 1.50/1.26 ( ( in @ Xx @ A )
% 1.50/1.26 => ! [X: $i] :
% 1.50/1.26 ( ( in @ X @ A )
% 1.50/1.26 => ! [Y: $i] :
% 1.50/1.26 ( ( in @ Y @ A )
% 1.50/1.26 => ( ( ( in @ Xx @ X )
% 1.50/1.26 & ( in @ X @ Y ) )
% 1.50/1.26 => ( in @ Xx @ Y ) ) ) ) )
% 1.50/1.26 & ! [X: $i] :
% 1.50/1.26 ( ( in @ X @ A )
% 1.50/1.26 => ! [Y: $i] :
% 1.50/1.26 ( ( in @ Y @ A )
% 1.50/1.26 => ( ( X = Y )
% 1.50/1.26 | ( in @ X @ Y )
% 1.50/1.26 | ( in @ Y @ X ) ) ) )
% 1.50/1.26 & ! [X: $i] :
% 1.50/1.26 ( ( in @ X @ A )
% 1.50/1.26 => ~ ( in @ X @ X ) ) ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(wellorderedByIn_type,type,
% 1.50/1.26 wellorderedByIn: $i > $o ).
% 1.50/1.26
% 1.50/1.26 thf(wellorderedByIn,definition,
% 1.50/1.26 ( wellorderedByIn
% 1.50/1.26 = ( ^ [A: $i] :
% 1.50/1.26 ( ( stricttotalorderedByIn @ A )
% 1.50/1.26 & ! [X: $i] :
% 1.50/1.26 ( ( in @ X @ ( powerset @ A ) )
% 1.50/1.26 => ( ( nonempty @ X )
% 1.50/1.26 => ? [Xx: $i] :
% 1.50/1.26 ( ( in @ Xx @ X )
% 1.50/1.26 & ! [Y: $i] :
% 1.50/1.26 ( ( in @ Y @ X )
% 1.50/1.26 => ( ( Xx = Y )
% 1.50/1.26 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(ordinal_type,type,
% 1.50/1.26 ordinal: $i > $o ).
% 1.50/1.26
% 1.50/1.26 thf(ordinal,definition,
% 1.50/1.26 ( ordinal
% 1.50/1.26 = ( ^ [Xx: $i] :
% 1.50/1.26 ( ( transitiveset @ Xx )
% 1.50/1.26 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(ordinalIrrefl,conjecture,
% 1.50/1.26 ! [X: $i] :
% 1.50/1.26 ( ( ordinal @ X )
% 1.50/1.26 => ! [A: $i] :
% 1.50/1.26 ( ( in @ A @ X )
% 1.50/1.26 => ~ ( in @ A @ A ) ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.27 % (7048)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_6802 for (2999ds/275Mi)
% 1.50/1.27 % (7047)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_6802 for (2999ds/2Mi)
% 1.50/1.27 % (7048)Refutation not found, incomplete strategy
% 1.50/1.27 % (7048)------------------------------
% 1.50/1.27 % (7048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (7048)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.27
% 1.50/1.27
% 1.50/1.27 % (7048)Memory used [KB]: 5500
% 1.50/1.27 % (7048)Time elapsed: 0.002 s
% 1.50/1.27 % (7048)Instructions burned: 2 (million)
% 1.50/1.27 % (7048)------------------------------
% 1.50/1.27 % (7048)------------------------------
% 1.50/1.27 % (7047)Instruction limit reached!
% 1.50/1.27 % (7047)------------------------------
% 1.50/1.27 % (7047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (7047)Termination reason: Unknown
% 1.50/1.27 % (7047)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (7047)Memory used [KB]: 1023
% 1.50/1.27 % (7047)Time elapsed: 0.002 s
% 1.50/1.27 % (7047)Instructions burned: 3 (million)
% 1.50/1.27 % (7047)------------------------------
% 1.50/1.27 % (7047)------------------------------
% 1.50/1.28 % (7043)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6802 for (2999ds/183Mi)
% 1.50/1.28 % (7044)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_6802 for (2999ds/4Mi)
% 1.50/1.28 % (7045)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_6802 for (2999ds/27Mi)
% 1.50/1.28 % (7046)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6802 for (2999ds/2Mi)
% 1.50/1.28 % (7049)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6802 for (2999ds/18Mi)
% 1.50/1.28 % (7046)Instruction limit reached!
% 1.50/1.28 % (7046)------------------------------
% 1.50/1.28 % (7046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (7046)Termination reason: Unknown
% 1.50/1.28 % (7046)Termination phase: shuffling
% 1.50/1.28
% 1.50/1.28 % (7046)Memory used [KB]: 895
% 1.50/1.28 % (7046)Time elapsed: 0.003 s
% 1.50/1.28 % (7046)Instructions burned: 2 (million)
% 1.50/1.28 % (7046)------------------------------
% 1.50/1.28 % (7046)------------------------------
% 1.50/1.28 % (7044)Instruction limit reached!
% 1.50/1.28 % (7044)------------------------------
% 1.50/1.28 % (7044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (7044)Termination reason: Unknown
% 1.50/1.28 % (7044)Termination phase: Property scanning
% 1.50/1.28
% 1.50/1.28 % (7044)Memory used [KB]: 1023
% 1.50/1.28 % (7044)Time elapsed: 0.004 s
% 1.50/1.28 % (7044)Instructions burned: 4 (million)
% 1.50/1.28 % (7044)------------------------------
% 1.50/1.28 % (7044)------------------------------
% 1.50/1.28 % (7051)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_6802 for (2999ds/37Mi)
% 1.50/1.28 % (7050)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6802 for (2999ds/3Mi)
% 1.50/1.29 % (7043)First to succeed.
% 1.50/1.29 % (7050)Instruction limit reached!
% 1.50/1.29 % (7050)------------------------------
% 1.50/1.29 % (7050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (7050)Termination reason: Unknown
% 1.50/1.29 % (7050)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (7050)Memory used [KB]: 5500
% 1.50/1.29 % (7050)Time elapsed: 0.003 s
% 1.50/1.29 % (7050)Instructions burned: 4 (million)
% 1.50/1.29 % (7050)------------------------------
% 1.50/1.29 % (7050)------------------------------
% 1.50/1.29 % (7045)Also succeeded, but the first one will report.
% 1.50/1.29 % (7049)Also succeeded, but the first one will report.
% 1.50/1.29 % (7043)Refutation found. Thanks to Tanya!
% 1.50/1.29 % SZS status Theorem for DTF2THF_6802
% 1.50/1.29 % SZS output start Proof for DTF2THF_6802
% 1.50/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.50/1.29 thf(func_def_1, type, powerset: $i > $i).
% 1.50/1.29 thf(func_def_2, type, nonempty: $i > $o).
% 1.50/1.29 thf(func_def_3, type, transitiveset: $i > $o).
% 1.50/1.29 thf(func_def_4, type, stricttotalorderedByIn: $i > $o).
% 1.50/1.29 thf(func_def_6, type, wellorderedByIn: $i > $o).
% 1.50/1.29 thf(func_def_7, type, ordinal: $i > $o).
% 1.50/1.29 thf(func_def_25, type, sK3: $i > $i).
% 1.50/1.29 thf(f83,plain,(
% 1.50/1.29 $false),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.50/1.29 thf(f81,plain,(
% 1.50/1.29 ($false = $true)),
% 1.50/1.29 inference(superposition,[status(thm)],[f79,f21])).
% 1.50/1.29 thf(f21,plain,(
% 1.50/1.29 ((in @ sK1 @ sK1) = $true)),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f19])).
% 1.50/1.29 thf(f19,plain,(
% 1.50/1.29 (((in @ sK1 @ sK0) = $true) & ((in @ sK1 @ sK1) = $true)) & ((ordinal @ sK0) = $true)),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f18,f17])).
% 1.50/1.29 thf(f17,plain,(
% 1.50/1.29 ? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((in @ X1 @ X1) = $true)) & ((ordinal @ X0) = $true)) => (? [X1 : $i] : (((in @ X1 @ sK0) = $true) & ((in @ X1 @ X1) = $true)) & ((ordinal @ sK0) = $true))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f18,plain,(
% 1.50/1.29 ? [X1 : $i] : (((in @ X1 @ sK0) = $true) & ((in @ X1 @ X1) = $true)) => (((in @ sK1 @ sK0) = $true) & ((in @ sK1 @ sK1) = $true))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f16,plain,(
% 1.50/1.29 ? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((in @ X1 @ X1) = $true)) & ((ordinal @ X0) = $true))),
% 1.50/1.29 inference(ennf_transformation,[status(thm)],[f15])).
% 1.50/1.29 thf(f15,plain,(
% 1.50/1.29 ~! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((in @ X1 @ X1) != $true)))),
% 1.50/1.29 inference(flattening,[status(thm)],[f14])).
% 1.50/1.29 thf(f14,plain,(
% 1.50/1.29 ~! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ~((in @ X1 @ X1) = $true)))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f13])).
% 1.50/1.29 thf(f13,plain,(
% 1.50/1.29 ~! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => ~(in @ X1 @ X1)))),
% 1.50/1.29 inference(rectify,[status(thm)],[f5])).
% 1.50/1.29 thf(f5,negated_conjecture,(
% 1.50/1.29 ~! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i] : ((in @ X0 @ X2) => ~(in @ X0 @ X0)))),
% 1.50/1.29 inference(negated_conjecture,[status(cth)],[f4])).
% 1.50/1.29 thf(f4,conjecture,(
% 1.50/1.29 ! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i] : ((in @ X0 @ X2) => ~(in @ X0 @ X0)))),
% 1.50/1.29 file('/export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2THF_6802.p',ordinalIrrefl)).
% 1.50/1.29 thf(f79,plain,(
% 1.50/1.29 ((in @ sK1 @ sK1) = $false)),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.50/1.29 thf(f75,plain,(
% 1.50/1.29 ($false = $true) | ((in @ sK1 @ sK1) = $false)),
% 1.50/1.29 inference(superposition,[status(thm)],[f54,f22])).
% 1.50/1.29 thf(f22,plain,(
% 1.50/1.29 ((in @ sK1 @ sK0) = $true)),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f19])).
% 1.50/1.29 thf(f54,plain,(
% 1.50/1.29 ( ! [X1 : $i] : (((in @ X1 @ sK0) = $false) | ((in @ X1 @ X1) = $false)) )),
% 1.50/1.29 inference(not_proxy_clausification,[status(thm)],[f53])).
% 1.50/1.29 thf(f53,plain,(
% 1.50/1.29 ( ! [X1 : $i] : (((in @ X1 @ sK0) = $false) | ((~ (in @ X1 @ X1)) = $true)) )),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.50/1.29 thf(f52,plain,(
% 1.50/1.29 ( ! [X1 : $i] : ((((in @ X1 @ sK0) => (~ (in @ X1 @ X1))) = $true)) )),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.50/1.29 thf(f51,plain,(
% 1.50/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK0) => (~ (in @ Y0 @ Y0)))) @ X1) = $true)) )),
% 1.50/1.29 inference(pi_clausification,[status(thm)],[f50])).
% 1.50/1.29 thf(f50,plain,(
% 1.50/1.29 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (~ (in @ Y0 @ Y0))))) = $true)),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.50/1.29 thf(f48,plain,(
% 1.50/1.29 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK0) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) = $true)),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.50/1.29 thf(f32,plain,(
% 1.50/1.29 ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK0) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (((in @ Y1 @ Y0) | (Y0 = Y1)) | (in @ Y0 @ Y1))))))))) = $true)),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.50/1.29 thf(f30,plain,(
% 1.50/1.29 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK0)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2)))))))))))) & (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK0) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (((in @ Y1 @ Y0) | (Y0 = Y1)) | (in @ Y0 @ Y1)))))))))) = $true)),
% 1.50/1.29 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.50/1.29 thf(f29,plain,(
% 1.50/1.29 (((transitiveset @ sK0) & ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ sK0)) => ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y1 @ Y2) | (Y1 = Y2)))))))))))) & (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (~ (in @ Y0 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK0) => (((in @ Y0 @ Y1) & (in @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) => (((in @ Y1 @ Y0) | (Y0 = Y1)) | (in @ Y0 @ Y1))))))))))) = $true)),
% 1.50/1.29 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.50/1.29 thf(f28,plain,(
% 1.50/1.29 (((^[Y0 : $i]: ((transitiveset @ Y0) & ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((nonempty @ Y2) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ Y3 @ Y4) | (Y3 = Y4)))))))))))) & ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y3))))) & (!! @ $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 @ Y4 @ Y3) | (Y3 = Y4)) | (in @ Y3 @ Y4)))))))))) @ Y1))) @ Y0))) @ sK0) = $true)),
% 1.50/1.29 inference(definition_unfolding,[status(thm)],[f20,f27])).
% 1.50/1.29 thf(f27,plain,(
% 1.50/1.29 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((nonempty @ Y2) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ Y3 @ Y4) | (Y3 = Y4)))))))))))) & ((^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y3))))) & (!! @ $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 @ Y4 @ Y3) | (Y3 = Y4)) | (in @ Y3 @ Y4)))))))))) @ Y1))) @ Y0))))),
% 1.50/1.29 inference(definition_unfolding,[status(thm)],[f25,f26])).
% 1.50/1.29 thf(f26,plain,(
% 1.50/1.29 (wellorderedByIn = (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3)))))))))))) & ((^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (in @ Y2 @ Y2))))) & (!! @ $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 @ Y3 @ Y2) | (Y2 = Y3)) | (in @ Y2 @ Y3)))))))))) @ Y0))))),
% 1.50/1.29 inference(definition_unfolding,[status(thm)],[f23,f24])).
% 1.50/1.29 thf(f24,plain,(
% 1.50/1.29 (stricttotalorderedByIn = (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1))))) & (!! @ $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 @ Y2 @ Y1) | (Y1 = Y2)) | (in @ Y1 @ Y2)))))))))))),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.29 thf(f10,plain,(
% 1.50/1.29 (stricttotalorderedByIn = (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ Y1))))) & (!! @ $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 @ Y2 @ Y1) | (Y1 = Y2)) | (in @ Y1 @ Y2)))))))))))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f9])).
% 1.50/1.29 thf(f9,plain,(
% 1.50/1.29 (stricttotalorderedByIn = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X1 @ X2) | (X1 = X2) | (in @ X2 @ X1)))) & ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => (((in @ X4 @ X5) & (in @ X3 @ X4)) => (in @ X3 @ X5))))) & ! [X6 : $i] : ((in @ X6 @ X0) => ~(in @ X6 @ X6)))))),
% 1.50/1.29 inference(rectify,[status(thm)],[f1])).
% 1.50/1.29 thf(f1,axiom,(
% 1.50/1.29 (stricttotalorderedByIn = (^[X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X2 @ X3) | (X2 = X3) | (in @ X3 @ X2)))) & ! [X1 : $i] : ((in @ X1 @ X0) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (((in @ X2 @ X3) & (in @ X1 @ X2)) => (in @ X1 @ X3))))) & ! [X2 : $i] : ((in @ X2 @ X0) => ~(in @ X2 @ X2)))))),
% 1.50/1.29 file('/export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2THF_6802.p',stricttotalorderedByIn)).
% 1.50/1.29 thf(f23,plain,(
% 1.50/1.29 (wellorderedByIn = (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3)))))))))))) & (stricttotalorderedByIn @ Y0))))),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.50/1.29 thf(f8,plain,(
% 1.50/1.29 (wellorderedByIn = (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((nonempty @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y2 @ Y3) | (Y2 = Y3)))))))))))) & (stricttotalorderedByIn @ Y0))))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.29 thf(f7,plain,(
% 1.50/1.29 (wellorderedByIn = (^[X0 : $i] : ((stricttotalorderedByIn @ X0) & ! [X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((nonempty @ X1) => ? [X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => ((X2 = X3) | (in @ X2 @ X3))) & (in @ X2 @ X1)))))))),
% 1.50/1.29 inference(rectify,[status(thm)],[f2])).
% 1.50/1.29 thf(f2,axiom,(
% 1.50/1.29 (wellorderedByIn = (^[X0 : $i] : ((stricttotalorderedByIn @ X0) & ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((nonempty @ X2) => ? [X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => ((X1 = X3) | (in @ X1 @ X3))) & (in @ X1 @ X2)))))))),
% 1.50/1.29 file('/export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2THF_6802.p',wellorderedByIn)).
% 1.50/1.29 thf(f25,plain,(
% 1.50/1.29 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))))),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.50/1.29 thf(f12,plain,(
% 1.50/1.29 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f11])).
% 1.50/1.29 thf(f11,plain,(
% 1.50/1.29 ((^[X0 : $i] : ((wellorderedByIn @ X0) & (transitiveset @ X0))) = ordinal)),
% 1.50/1.29 inference(rectify,[status(thm)],[f3])).
% 1.50/1.29 thf(f3,axiom,(
% 1.50/1.29 ((^[X1 : $i] : ((wellorderedByIn @ X1) & (transitiveset @ X1))) = ordinal)),
% 1.50/1.29 file('/export/starexec/sandbox2/tmp/tmp.YCZVktaBNK/DTF2THF_6802.p',ordinal)).
% 1.50/1.29 thf(f20,plain,(
% 1.50/1.29 ((ordinal @ sK0) = $true)),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f19])).
% 1.50/1.29 % SZS output end Proof for DTF2THF_6802
% 1.50/1.29 % (7043)------------------------------
% 1.50/1.29 % (7043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (7043)Termination reason: Refutation
% 1.50/1.29
% 1.50/1.29 % (7043)Memory used [KB]: 5628
% 1.50/1.29 % (7043)Time elapsed: 0.010 s
% 1.50/1.29 % (7043)Instructions burned: 9 (million)
% 1.50/1.29 % (7043)------------------------------
% 1.50/1.29 % (7043)------------------------------
% 1.50/1.29 % (7042)Success in time 0.023 s
%------------------------------------------------------------------------------