%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV238^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 09:40:38 AM UTC 2026
% Result : Theorem 1.58s 1.38s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 1364 ( 318 equ; 0 cnn)
% Maximal formula atoms : 40 ( 20 avg)
% Number of connectives : 3396 ( 189 ~; 195 |; 299 &;2120 @)
% ( 9 <=>; 248 =>; 0 <=; 2 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 446 ( 446 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 14 usr; 11 con; 0-2 aty)
% ( 167 !!; 167 ??; 0 @@+; 0 @@-)
% Number of variables : 772 ( 525 ^; 155 !; 92 ?; 772 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_10,type,
sK0: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_12,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_16,type,
sK6: $i > $o ).
thf(func_def_19,type,
ph8:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK9: $i > $o ).
thf(func_def_21,type,
sK10: $i > $o ).
thf(f270,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f44,f49,f141,f269]) ).
thf(f269,plain,
( ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f268]) ).
thf(f268,plain,
( $false
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(subsumption_resolution,[status(thm)],[f267,f150]) ).
thf(f150,plain,
( ( ( sK6 @ ( sK1 @ sK6 ) )
= $true )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(subsumption_resolution,[status(thm)],[f148,f48]) ).
thf(f48,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
!= $true )
| spl7_4 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl7_4
<=> ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition]) ).
thf(f148,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
= $true )
| ( ( sK6 @ ( sK1 @ sK6 ) )
= $true )
| ~ spl7_2
| ~ spl7_3 ),
inference(trivial_inequality_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ( $true != $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
= $true )
| ( ( sK6 @ ( sK1 @ sK6 ) )
= $true )
| ~ spl7_2
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f29,f143]) ).
thf(f143,plain,
( ( ( sK0 @ sK6 @ sK5 )
= $true )
| ~ spl7_2
| ~ spl7_3 ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
( ( $true != $true )
| ( ( sK0 @ sK6 @ sK5 )
= $true )
| ~ spl7_2
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f43,f39]) ).
thf(f39,plain,
( ( ( sK6 @ sK5 )
= $true )
| ~ spl7_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl7_2
<=> ( ( sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f43,plain,
( ! [X12: $i] :
( ( ( sK6 @ X12 )
!= $true )
| ( ( sK0 @ sK6 @ X12 )
= $true ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl7_3
<=> ! [X12: $i] :
( ( ( sK6 @ X12 )
!= $true )
| ( ( sK0 @ sK6 @ X12 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition]) ).
thf(f29,plain,
! [X1: $i > $o,X5: $i] :
( ( ( sK0 @ X1 @ X5 )
!= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X5 )
= $true )
| ( $true
= ( X1 @ ( sK1 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X1: $i > $o] :
( ( ( $true
= ( X1 @ ( sK1 @ X1 ) ) )
& ! [X3: $i > $o] :
( ( ( ( sK0 @ X3 @ ( sK2 @ X3 ) )
!= $true )
& ( ( X3 @ ( sK2 @ X3 ) )
= $true ) )
| ( ( X3 @ ( sK1 @ X1 ) )
!= $true ) ) )
| ! [X5: $i] :
( ( ( sK0 @ X1 @ X5 )
!= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X5 )
= $true ) ) )
& ( ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) )
| ( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK4 )
= $true )
& ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK4 )
!= $true ) )
| ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) )
& ( ( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) )
& ! [X8: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X8 )
!= $true )
| ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X8 )
= $true ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) )
& ( ! [X9: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true )
| ( $true
= ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 ) ) )
| ( ( ( sK6 @ sK5 )
= $true )
& ! [X12: $i] :
( ( ( sK0 @ sK6 @ X12 )
= $true )
| ( ( sK6 @ X12 )
!= $true ) )
& ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f11,f18,f17,f16,f15,f14,f13,f12]) ).
thf(f12,plain,
( ? [X0: ( $i > $o ) > $i > $o] :
( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ! [X3: $i > $o] :
( ? [X4: $i] :
( ( ( X0 @ X3 @ X4 )
!= $true )
& ( ( X3 @ X4 )
= $true ) )
| ( ( X3 @ X2 )
!= $true ) ) )
| ! [X5: $i] :
( ( $true
!= ( X0 @ X1 @ X5 ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X5 )
= $true ) ) )
& ? [X6: $i] :
( ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
!= $true )
| ? [X7: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X7 )
= $true )
& ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X7 )
!= $true ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
!= $true ) )
& ( ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
= $true )
& ! [X8: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X8 )
!= $true )
| ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X8 )
= $true ) ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
= $true ) ) )
& ( ! [X9: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true )
| ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 )
= $true ) )
| ? [X10: $i] :
( ? [X11: $i > $o] :
( ( ( X11 @ X10 )
= $true )
& ! [X12: $i] :
( ( ( X0 @ X11 @ X12 )
= $true )
| ( $true
!= ( X11 @ X12 ) ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X10 )
!= $true ) ) ) )
=> ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ! [X3: $i > $o] :
( ? [X4: $i] :
( ( ( sK0 @ X3 @ X4 )
!= $true )
& ( ( X3 @ X4 )
= $true ) )
| ( ( X3 @ X2 )
!= $true ) ) )
| ! [X5: $i] :
( ( ( sK0 @ X1 @ X5 )
!= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X5 )
= $true ) ) )
& ? [X6: $i] :
( ( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
!= $true )
| ? [X7: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X7 )
= $true )
& ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X7 )
!= $true ) )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
!= $true ) )
& ( ( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
= $true )
& ! [X8: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X8 )
!= $true )
| ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X8 )
= $true ) ) )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
= $true ) ) )
& ( ! [X9: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true )
| ( $true
= ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 ) ) )
| ? [X10: $i] :
( ? [X11: $i > $o] :
( ( ( X11 @ X10 )
= $true )
& ! [X12: $i] :
( ( $true
= ( sK0 @ X11 @ X12 ) )
| ( $true
!= ( X11 @ X12 ) ) ) )
& ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X10 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ! [X3: $i > $o] :
( ? [X4: $i] :
( ( ( sK0 @ X3 @ X4 )
!= $true )
& ( ( X3 @ X4 )
= $true ) )
| ( ( X3 @ X2 )
!= $true ) ) )
=> ( ( $true
= ( X1 @ ( sK1 @ X1 ) ) )
& ! [X3: $i > $o] :
( ? [X4: $i] :
( ( ( sK0 @ X3 @ X4 )
!= $true )
& ( ( X3 @ X4 )
= $true ) )
| ( ( X3 @ ( sK1 @ X1 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X3: $i > $o] :
( ? [X4: $i] :
( ( ( sK0 @ X3 @ X4 )
!= $true )
& ( ( X3 @ X4 )
= $true ) )
=> ( ( ( sK0 @ X3 @ ( sK2 @ X3 ) )
!= $true )
& ( ( X3 @ ( sK2 @ X3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X6: $i] :
( ( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
!= $true )
| ? [X7: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X7 )
= $true )
& ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X7 )
!= $true ) )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
!= $true ) )
& ( ( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
= $true )
& ! [X8: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X8 )
!= $true )
| ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X8 )
= $true ) ) )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
= $true ) ) )
=> ( ( ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) )
| ? [X7: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X7 )
= $true )
& ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X7 )
!= $true ) )
| ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) )
& ( ( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) )
& ! [X8: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X8 )
!= $true )
| ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X8 )
= $true ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X7: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X7 )
= $true )
& ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X7 )
!= $true ) )
=> ( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK4 )
= $true )
& ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X10: $i] :
( ? [X11: $i > $o] :
( ( ( X11 @ X10 )
= $true )
& ! [X12: $i] :
( ( $true
= ( sK0 @ X11 @ X12 ) )
| ( $true
!= ( X11 @ X12 ) ) ) )
& ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X10 )
!= $true ) )
=> ( ? [X11: $i > $o] :
( ( $true
= ( X11 @ sK5 ) )
& ! [X12: $i] :
( ( $true
= ( sK0 @ X11 @ X12 ) )
| ( $true
!= ( X11 @ X12 ) ) ) )
& ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X11: $i > $o] :
( ( $true
= ( X11 @ sK5 ) )
& ! [X12: $i] :
( ( $true
= ( sK0 @ X11 @ X12 ) )
| ( $true
!= ( X11 @ X12 ) ) ) )
=> ( ( ( sK6 @ sK5 )
= $true )
& ! [X12: $i] :
( ( ( sK0 @ sK6 @ X12 )
= $true )
| ( ( sK6 @ X12 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: ( $i > $o ) > $i > $o] :
( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ! [X3: $i > $o] :
( ? [X4: $i] :
( ( ( X0 @ X3 @ X4 )
!= $true )
& ( ( X3 @ X4 )
= $true ) )
| ( ( X3 @ X2 )
!= $true ) ) )
| ! [X5: $i] :
( ( $true
!= ( X0 @ X1 @ X5 ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X5 )
= $true ) ) )
& ? [X6: $i] :
( ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
!= $true )
| ? [X7: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X7 )
= $true )
& ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X7 )
!= $true ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
!= $true ) )
& ( ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
= $true )
& ! [X8: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X8 )
!= $true )
| ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X8 )
= $true ) ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X6 )
= $true ) ) )
& ( ! [X9: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true )
| ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 )
= $true ) )
| ? [X10: $i] :
( ? [X11: $i > $o] :
( ( ( X11 @ X10 )
= $true )
& ! [X12: $i] :
( ( ( X0 @ X11 @ X12 )
= $true )
| ( $true
!= ( X11 @ X12 ) ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X10 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X0: ( $i > $o ) > $i > $o] :
( ! [X5: $i > $o] :
( ? [X6: $i] :
( ( ( X5 @ X6 )
= $true )
& ! [X7: $i > $o] :
( ? [X8: $i] :
( ( ( X0 @ X7 @ X8 )
!= $true )
& ( ( X7 @ X8 )
= $true ) )
| ( ( X7 @ X6 )
!= $true ) ) )
| ! [X9: $i] :
( ( ( X0 @ X5 @ X9 )
!= $true )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X9 )
= $true ) ) )
& ? [X10: $i] :
( ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
!= $true )
| ? [X11: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X11 )
= $true )
& ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X11 )
!= $true ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
!= $true ) )
& ( ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true )
& ! [X11: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X11 )
!= $true )
| ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X11 )
= $true ) ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true ) ) )
& ( ! [X4: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X4 )
!= $true )
| ( $true
= ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 ) ) )
| ? [X1: $i] :
( ? [X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
& ! [X3: $i] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: ( $i > $o ) > $i > $o] :
( ! [X5: $i > $o] :
( ? [X6: $i] :
( ( ( X5 @ X6 )
= $true )
& ! [X7: $i > $o] :
( ? [X8: $i] :
( ( ( X0 @ X7 @ X8 )
!= $true )
& ( ( X7 @ X8 )
= $true ) )
| ( ( X7 @ X6 )
!= $true ) ) )
| ! [X9: $i] :
( ( ( X0 @ X5 @ X9 )
!= $true )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X9 )
= $true ) ) )
& ? [X10: $i] :
( ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
!= $true )
| ? [X11: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X11 )
= $true )
& ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X11 )
!= $true ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
!= $true ) )
& ( ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true )
& ! [X11: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X11 )
!= $true )
| ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X11 )
= $true ) ) )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true ) ) )
& ( ! [X4: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X4 )
!= $true )
| ( $true
= ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 ) ) )
| ? [X1: $i] :
( ? [X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
& ! [X3: $i] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: ( $i > $o ) > $i > $o] :
( ! [X5: $i > $o] :
( ? [X6: $i] :
( ( ( X5 @ X6 )
= $true )
& ! [X7: $i > $o] :
( ? [X8: $i] :
( ( ( X0 @ X7 @ X8 )
!= $true )
& ( ( X7 @ X8 )
= $true ) )
| ( ( X7 @ X6 )
!= $true ) ) )
| ! [X9: $i] :
( ( ( X0 @ X5 @ X9 )
!= $true )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X9 )
= $true ) ) )
& ? [X10: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true )
<~> ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true )
& ! [X11: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X11 )
!= $true )
| ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X11 )
= $true ) ) ) )
& ( ! [X4: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X4 )
!= $true )
| ( $true
= ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 ) ) )
| ? [X1: $i] :
( ? [X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
& ! [X3: $i] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( $i > $o ) > $i > $o] :
( ? [X10: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true )
<~> ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true )
& ! [X11: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X11 )
!= $true )
| ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X11 )
= $true ) ) ) )
& ! [X5: $i > $o] :
( ? [X6: $i] :
( ( ( X5 @ X6 )
= $true )
& ! [X7: $i > $o] :
( ? [X8: $i] :
( ( ( X0 @ X7 @ X8 )
!= $true )
& ( ( X7 @ X8 )
= $true ) )
| ( ( X7 @ X6 )
!= $true ) ) )
| ! [X9: $i] :
( ( ( X0 @ X5 @ X9 )
!= $true )
| ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X9 )
= $true ) ) )
& ( ! [X4: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X4 )
!= $true )
| ( $true
= ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 ) ) )
| ? [X1: $i] :
( ? [X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
& ! [X3: $i] :
( ( ( X0 @ X2 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ( ! [X5: $i > $o] :
( ! [X6: $i] :
( ( ( X5 @ X6 )
= $true )
=> ? [X7: $i > $o] :
( ! [X8: $i] :
( ( ( X7 @ X8 )
= $true )
=> ( ( X0 @ X7 @ X8 )
= $true ) )
& ( ( X7 @ X6 )
= $true ) ) )
=> ! [X9: $i] :
( ( ( X0 @ X5 @ X9 )
= $true )
=> ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X9 )
= $true ) ) )
& ( ! [X1: $i] :
( ? [X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
& ! [X3: $i] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X0 @ X2 @ X3 )
= $true ) ) )
=> ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
= $true ) )
=> ! [X4: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true )
=> ( $true
= ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 ) ) ) ) )
=> ! [X10: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true )
<=> ( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X10 )
= $true )
& ! [X11: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X11 )
= $true )
=> ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X11 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ( ( ! [X1: $i] :
( ? [X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
& ! [X3: $i] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X0 @ X2 @ X3 )
= $true ) ) )
=> ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
= $true ) )
=> ! [X7: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X7 )
= $true )
=> ( ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X7 )
= $true ) ) )
& ! [X14: $i > $o] :
( ! [X15: $i] :
( ( ( X14 @ X15 )
= $true )
=> ? [X16: $i > $o] :
( ! [X17: $i] :
( ( ( X16 @ X17 )
= $true )
=> ( ( X0 @ X16 @ X17 )
= $true ) )
& ( ( X16 @ X15 )
= $true ) ) )
=> ! [X18: $i] :
( ( ( X0 @ X14 @ X18 )
= $true )
=> ( $true
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X18 ) ) ) ) )
=> ! [X22: $i] :
( ( ! [X23: $i] :
( ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X23 )
= $true )
=> ( $true
= ( X0
@ ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X23 ) ) )
& ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X22 )
= $true ) )
<=> ( ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( X0 @ Y1 @ Y2 ) ) ) ) )
@ X22 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ( ( ! [X1: $i] :
( ? [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X0 @ X2 @ X3 ) )
& ( X2 @ X1 ) )
=> ( X0
@ ^ [X4: $i] :
? [X5: $i > $o] :
( ( X5 @ X4 )
& ! [X6: $i] :
( ( X5 @ X6 )
=> ( X0 @ X5 @ X6 ) ) )
@ X1 ) )
=> ! [X7: $i] :
( ( X0
@ ^ [X8: $i] :
? [X9: $i > $o] :
( ! [X10: $i] :
( ( X9 @ X10 )
=> ( X0 @ X9 @ X10 ) )
& ( X9 @ X8 ) )
@ X7 )
=> ( X0
@ ( X0
@ ^ [X11: $i] :
? [X12: $i > $o] :
( ( X12 @ X11 )
& ! [X13: $i] :
( ( X12 @ X13 )
=> ( X0 @ X12 @ X13 ) ) ) )
@ X7 ) ) )
& ! [X14: $i > $o] :
( ! [X15: $i] :
( ( X14 @ X15 )
=> ? [X16: $i > $o] :
( ! [X17: $i] :
( ( X16 @ X17 )
=> ( X0 @ X16 @ X17 ) )
& ( X16 @ X15 ) ) )
=> ! [X18: $i] :
( ( X0 @ X14 @ X18 )
=> ( X0
@ ^ [X19: $i] :
? [X20: $i > $o] :
( ( X20 @ X19 )
& ! [X21: $i] :
( ( X20 @ X21 )
=> ( X0 @ X20 @ X21 ) ) )
@ X18 ) ) ) )
=> ! [X22: $i] :
( ( ! [X23: $i] :
( ( X0
@ ^ [X24: $i] :
? [X25: $i > $o] :
( ! [X26: $i] :
( ( X25 @ X26 )
=> ( X0 @ X25 @ X26 ) )
& ( X25 @ X24 ) )
@ X23 )
=> ( X0
@ ( X0
@ ^ [X27: $i] :
? [X28: $i > $o] :
( ( X28 @ X27 )
& ! [X29: $i] :
( ( X28 @ X29 )
=> ( X0 @ X28 @ X29 ) ) ) )
@ X23 ) )
& ( X0
@ ^ [X30: $i] :
? [X31: $i > $o] :
( ! [X32: $i] :
( ( X31 @ X32 )
=> ( X0 @ X31 @ X32 ) )
& ( X31 @ X30 ) )
@ X22 ) )
<=> ( X0
@ ^ [X33: $i] :
? [X34: $i > $o] :
( ! [X35: $i] :
( ( X34 @ X35 )
=> ( X0 @ X34 @ X35 ) )
& ( X34 @ X33 ) )
@ X22 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i > $o] :
( ( ( ! [X1: $i] :
( ? [X3: $i > $o] :
( ! [X2: $i] :
( ( X3 @ X2 )
=> ( X0 @ X3 @ X2 ) )
& ( X3 @ X1 ) )
=> ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X3 @ X2 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) ) )
@ X1 ) )
=> ! [X1: $i] :
( ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
& ( X3 @ X2 ) )
@ X1 )
=> ( X0
@ ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X3 @ X2 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) ) ) )
@ X1 ) ) )
& ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ? [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
& ( X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0
@ ^ [X4: $i] :
? [X3: $i > $o] :
( ( X3 @ X4 )
& ! [X5: $i] :
( ( X3 @ X5 )
=> ( X0 @ X3 @ X5 ) ) )
@ X2 ) ) ) )
=> ! [X1: $i] :
( ( ! [X2: $i] :
( ( X0
@ ^ [X4: $i] :
? [X3: $i > $o] :
( ! [X5: $i] :
( ( X3 @ X5 )
=> ( X0 @ X3 @ X5 ) )
& ( X3 @ X4 ) )
@ X2 )
=> ( X0
@ ( X0
@ ^ [X4: $i] :
? [X3: $i > $o] :
( ( X3 @ X4 )
& ! [X5: $i] :
( ( X3 @ X5 )
=> ( X0 @ X3 @ X5 ) ) ) )
@ X2 ) )
& ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
& ( X3 @ X2 ) )
@ X1 ) )
<=> ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
& ( X3 @ X2 ) )
@ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i > $o] :
( ( ( ! [X1: $i] :
( ? [X3: $i > $o] :
( ! [X2: $i] :
( ( X3 @ X2 )
=> ( X0 @ X3 @ X2 ) )
& ( X3 @ X1 ) )
=> ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X3 @ X2 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) ) )
@ X1 ) )
=> ! [X1: $i] :
( ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
& ( X3 @ X2 ) )
@ X1 )
=> ( X0
@ ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X3 @ X2 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) ) ) )
@ X1 ) ) )
& ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ? [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
& ( X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0
@ ^ [X4: $i] :
? [X3: $i > $o] :
( ( X3 @ X4 )
& ! [X5: $i] :
( ( X3 @ X5 )
=> ( X0 @ X3 @ X5 ) ) )
@ X2 ) ) ) )
=> ! [X1: $i] :
( ( ! [X2: $i] :
( ( X0
@ ^ [X4: $i] :
? [X3: $i > $o] :
( ! [X5: $i] :
( ( X3 @ X5 )
=> ( X0 @ X3 @ X5 ) )
& ( X3 @ X4 ) )
@ X2 )
=> ( X0
@ ( X0
@ ^ [X4: $i] :
? [X3: $i > $o] :
( ( X3 @ X4 )
& ! [X5: $i] :
( ( X3 @ X5 )
=> ( X0 @ X3 @ X5 ) ) ) )
@ X2 ) )
& ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
& ( X3 @ X2 ) )
@ X1 ) )
<=> ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
& ( X3 @ X2 ) )
@ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7TYe0oTisK/DTF2THF_21112.p',cTHM2D_pme) ).
thf(f267,plain,
( ( ( sK6 @ ( sK1 @ sK6 ) )
!= $true )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(subsumption_resolution,[status(thm)],[f257,f48]) ).
thf(f257,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
= $true )
| ( ( sK6 @ ( sK1 @ sK6 ) )
!= $true )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(trivial_inequality_removal,[status(thm)],[f254]) ).
thf(f254,plain,
( ( $true != $true )
| ( ( sK6 @ ( sK1 @ sK6 ) )
!= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
= $true )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(superposition,[status(thm)],[f186,f143]) ).
thf(f186,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
!= $true )
| ( $true
!= ( sK6 @ ( sK1 @ X0 ) ) )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
= $true ) )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(trivial_inequality_removal,[status(thm)],[f181]) ).
thf(f181,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $true != $true )
| ( $true
!= ( sK6 @ ( sK1 @ X0 ) ) )
| ( ( sK0 @ X0 @ X1 )
!= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
= $true ) )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(superposition,[status(thm)],[f28,f166]) ).
thf(f166,plain,
( ( ( sK0 @ sK6 @ ( sK2 @ sK6 ) )
= $true )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( ( sK0 @ sK6 @ ( sK2 @ sK6 ) )
= $true )
| ( $true != $true )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(superposition,[status(thm)],[f43,f162]) ).
thf(f162,plain,
( ( $true
= ( sK6 @ ( sK2 @ sK6 ) ) )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ( $true != $true )
| ( $true
= ( sK6 @ ( sK2 @ sK6 ) ) )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(superposition,[status(thm)],[f151,f150]) ).
thf(f151,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( sK1 @ sK6 ) )
!= $true )
| ( ( X0 @ ( sK2 @ X0 ) )
= $true ) )
| ~ spl7_2
| ~ spl7_3
| spl7_4 ),
inference(subsumption_resolution,[status(thm)],[f147,f48]) ).
thf(f147,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( sK1 @ sK6 ) )
!= $true )
| ( ( X0 @ ( sK2 @ X0 ) )
= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
= $true ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(trivial_inequality_removal,[status(thm)],[f145]) ).
thf(f145,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( sK2 @ X0 ) )
= $true )
| ( $true != $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
= $true )
| ( ( X0 @ ( sK1 @ sK6 ) )
!= $true ) )
| ~ spl7_2
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f27,f143]) ).
thf(f27,plain,
! [X3: $i > $o,X1: $i > $o,X5: $i] :
( ( ( sK0 @ X1 @ X5 )
!= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X5 )
= $true )
| ( ( X3 @ ( sK1 @ X1 ) )
!= $true )
| ( ( X3 @ ( sK2 @ X3 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f28,plain,
! [X3: $i > $o,X1: $i > $o,X5: $i] :
( ( ( sK0 @ X3 @ ( sK2 @ X3 ) )
!= $true )
| ( ( sK0 @ X1 @ X5 )
!= $true )
| ( ( X3 @ ( sK1 @ X1 ) )
!= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f141,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[status(thm)],[f140]) ).
thf(f140,plain,
( $false
| ~ spl7_1 ),
inference(subsumption_resolution,[status(thm)],[f139,f51]) ).
thf(f51,plain,
( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK4 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f30,f32]) ).
thf(f32,plain,
( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) )
| ( $true
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f30,plain,
( ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK4 )
!= $true )
| ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) )
| ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK4 )
!= $true )
| ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f139,plain,
( ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK4 )
= $true )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $true != $true )
| ( ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ sK4 )
= $true )
| ~ spl7_1 ),
inference(superposition,[status(thm)],[f35,f50]) ).
thf(f50,plain,
( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK4 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f31,f32]) ).
thf(f31,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK4 )
= $true )
| ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK4 )
= $true )
| ( $true
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f35,plain,
( ! [X9: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true )
| ( $true
= ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 ) ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl7_1
<=> ! [X9: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true )
| ( $true
= ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f49,plain,
( spl7_1
| ~ spl7_4 ),
inference(avatar_split_clause,[status(thm)],[f20,f46,f34]) ).
thf(f20,plain,
! [X9: $i] :
( ( $true
= ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 ) )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ sK5 )
!= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f44,plain,
( spl7_3
| spl7_1 ),
inference(avatar_split_clause,[status(thm)],[f21,f34,f42]) ).
thf(f21,plain,
! [X9: $i,X12: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true )
| ( ( sK6 @ X12 )
!= $true )
| ( $true
= ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 ) )
| ( ( sK0 @ sK6 @ X12 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f40,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f22,f37,f34]) ).
thf(f22,plain,
! [X9: $i] :
( ( ( sK6 @ sK5 )
= $true )
| ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X9 )
!= $true )
| ( $true
= ( sK0
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV238^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:42:46 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.34/0.48 ---- Original DTF file ---
% 0.34/0.48 thf(spec,logic,$$dhol).
% 0.34/0.48 %------------------------------------------------------------------------------
% 0.34/0.48 % File : SEV238^5 : TPTP v9.2.1. Released v4.0.0.
% 0.34/0.48 % Domain : Set Theory (Sets of sets)
% 0.34/0.48 % Problem : TPS problem THM2D
% 0.34/0.48 % Version : Especial.
% 0.34/0.48 % English :
% 0.34/0.48
% 0.34/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.34/0.48 % Source : [Bro09]
% 0.34/0.48 % Names : tps_0480 [Bro09]
% 0.34/0.48 % : THM2D [TPS]
% 0.34/0.48
% 0.34/0.48 % Status : Theorem
% 0.34/0.48 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.17 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.67 v4.0.1, 0.33 v4.0.0
% 0.34/0.48 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.34/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.34/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.34/0.48 % Number of connectives : 92 ( 0 ~; 0 |; 12 &; 61 @)
% 0.34/0.48 % ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% 0.34/0.48 % Maximal formula depth : 18 ( 18 avg)
% 0.34/0.48 % Number of types : 2 ( 0 usr)
% 0.34/0.48 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.34/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.34/0.48 % Number of variables : 36 ( 8 ^; 18 !; 10 ?; 36 :)
% 0.34/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.34/0.48
% 0.34/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.34/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.34/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.34/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.34/0.48 % : Polymorphic definitions expanded.
% 0.34/0.48 %------------------------------------------------------------------------------
% 0.34/0.48 thf(cTHM2D_pme,conjecture,
% 0.34/0.48 ! [K: ( $i > $o ) > $i > $o] :
% 0.34/0.48 ( ( ! [Xx: $i > $o] :
% 0.34/0.48 ( ! [Xx0: $i] :
% 0.34/0.48 ( ( Xx @ Xx0 )
% 0.34/0.48 => ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx1: $i] :
% 0.34/0.48 ( ( S @ Xx1 )
% 0.34/0.48 => ( K @ S @ Xx1 ) )
% 0.34/0.48 & ( S @ Xx0 ) ) )
% 0.34/0.48 => ! [Xx0: $i] :
% 0.34/0.48 ( ( K @ Xx @ Xx0 )
% 0.34/0.48 => ( K
% 0.34/0.48 @ ^ [Xx1: $i] :
% 0.34/0.48 ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx2: $i] :
% 0.34/0.48 ( ( S @ Xx2 )
% 0.34/0.48 => ( K @ S @ Xx2 ) )
% 0.34/0.48 & ( S @ Xx1 ) )
% 0.34/0.48 @ Xx0 ) ) )
% 0.34/0.48 & ( ! [Xx: $i] :
% 0.34/0.48 ( ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx0: $i] :
% 0.34/0.48 ( ( S @ Xx0 )
% 0.34/0.48 => ( K @ S @ Xx0 ) )
% 0.34/0.48 & ( S @ Xx ) )
% 0.34/0.48 => ( K
% 0.34/0.48 @ ^ [Xx0: $i] :
% 0.34/0.48 ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx1: $i] :
% 0.34/0.48 ( ( S @ Xx1 )
% 0.34/0.48 => ( K @ S @ Xx1 ) )
% 0.34/0.48 & ( S @ Xx0 ) )
% 0.34/0.48 @ Xx ) )
% 0.34/0.48 => ! [Xx: $i] :
% 0.34/0.48 ( ( K
% 0.34/0.48 @ ^ [Xx0: $i] :
% 0.34/0.48 ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx1: $i] :
% 0.34/0.48 ( ( S @ Xx1 )
% 0.34/0.48 => ( K @ S @ Xx1 ) )
% 0.34/0.48 & ( S @ Xx0 ) )
% 0.34/0.48 @ Xx )
% 0.34/0.48 => ( K
% 0.34/0.48 @ ( K
% 0.34/0.48 @ ^ [Xx0: $i] :
% 0.34/0.48 ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx1: $i] :
% 0.34/0.48 ( ( S @ Xx1 )
% 0.34/0.48 => ( K @ S @ Xx1 ) )
% 0.34/0.48 & ( S @ Xx0 ) ) )
% 0.34/0.48 @ Xx ) ) ) )
% 0.34/0.48 => ! [Xx: $i] :
% 0.34/0.48 ( ( K
% 0.34/0.48 @ ^ [Xx0: $i] :
% 0.34/0.48 ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx1: $i] :
% 0.34/0.48 ( ( S @ Xx1 )
% 0.34/0.48 => ( K @ S @ Xx1 ) )
% 0.34/0.48 & ( S @ Xx0 ) )
% 0.34/0.48 @ Xx )
% 0.34/0.48 <=> ( ! [Xx0: $i] :
% 0.34/0.48 ( ( K
% 0.34/0.48 @ ^ [Xx1: $i] :
% 0.34/0.48 ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx2: $i] :
% 0.34/0.48 ( ( S @ Xx2 )
% 0.34/0.48 => ( K @ S @ Xx2 ) )
% 0.34/0.48 & ( S @ Xx1 ) )
% 0.34/0.48 @ Xx0 )
% 0.34/0.48 => ( K
% 0.34/0.48 @ ( K
% 0.34/0.48 @ ^ [Xx1: $i] :
% 0.34/0.48 ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx2: $i] :
% 0.34/0.48 ( ( S @ Xx2 )
% 0.34/0.48 => ( K @ S @ Xx2 ) )
% 0.34/0.48 & ( S @ Xx1 ) ) )
% 0.34/0.48 @ Xx0 ) )
% 0.34/0.48 & ( K
% 0.34/0.48 @ ^ [Xx0: $i] :
% 0.34/0.48 ? [S: $i > $o] :
% 0.34/0.48 ( ! [Xx1: $i] :
% 0.34/0.48 ( ( S @ Xx1 )
% 0.34/0.48 => ( K @ S @ Xx1 ) )
% 0.34/0.48 & ( S @ Xx0 ) )
% 0.34/0.48 @ Xx ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 %------------------------------------------------------------------------------
% 0.34/0.48 ------------------------
% 1.45/1.24 ---- Embedded in THF ---
% 1.45/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.24 %%% Generated on Tue Feb 24 12:42:47 EST 2026
% 1.45/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.24 %%% Logic specification used:
% 1.45/1.24 %%% thf(spec, logic, $$dhol).
% 1.45/1.24
% 1.45/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7TYe0oTisK/DTF2DTF21112.p
% See solution above
% 1.45/1.24 ------------------------
% 1.45/1.25 ---- Cleaned THF ---
% 1.45/1.25 thf(cTHM2D_pme,conjecture,
% 1.45/1.25 ! [K: ( $i > $o ) > $i > $o] :
% 1.45/1.25 ( ( ! [Xx: $i > $o] :
% 1.45/1.25 ( ! [Xx0: $i] :
% 1.45/1.25 ( ( Xx @ Xx0 )
% 1.45/1.25 => ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx1: $i] :
% 1.45/1.25 ( ( S @ Xx1 )
% 1.45/1.25 => ( K @ S @ Xx1 ) )
% 1.45/1.25 & ( S @ Xx0 ) ) )
% 1.45/1.25 => ! [Xx0: $i] :
% 1.45/1.25 ( ( K @ Xx @ Xx0 )
% 1.45/1.25 => ( K
% 1.45/1.25 @ ^ [Xx1: $i] :
% 1.45/1.25 ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx2: $i] :
% 1.45/1.25 ( ( S @ Xx2 )
% 1.45/1.25 => ( K @ S @ Xx2 ) )
% 1.45/1.25 & ( S @ Xx1 ) )
% 1.45/1.25 @ Xx0 ) ) )
% 1.45/1.25 & ( ! [Xx: $i] :
% 1.45/1.25 ( ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx0: $i] :
% 1.45/1.25 ( ( S @ Xx0 )
% 1.45/1.25 => ( K @ S @ Xx0 ) )
% 1.45/1.25 & ( S @ Xx ) )
% 1.45/1.25 => ( K
% 1.45/1.25 @ ^ [Xx0: $i] :
% 1.45/1.25 ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx1: $i] :
% 1.45/1.25 ( ( S @ Xx1 )
% 1.45/1.25 => ( K @ S @ Xx1 ) )
% 1.45/1.25 & ( S @ Xx0 ) )
% 1.45/1.25 @ Xx ) )
% 1.45/1.25 => ! [Xx: $i] :
% 1.45/1.25 ( ( K
% 1.45/1.25 @ ^ [Xx0: $i] :
% 1.45/1.25 ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx1: $i] :
% 1.45/1.25 ( ( S @ Xx1 )
% 1.45/1.25 => ( K @ S @ Xx1 ) )
% 1.45/1.25 & ( S @ Xx0 ) )
% 1.45/1.25 @ Xx )
% 1.45/1.25 => ( K
% 1.45/1.25 @ ( K
% 1.45/1.25 @ ^ [Xx0: $i] :
% 1.45/1.25 ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx1: $i] :
% 1.45/1.25 ( ( S @ Xx1 )
% 1.45/1.25 => ( K @ S @ Xx1 ) )
% 1.45/1.25 & ( S @ Xx0 ) ) )
% 1.45/1.25 @ Xx ) ) ) )
% 1.45/1.25 => ! [Xx: $i] :
% 1.45/1.25 ( ( K
% 1.45/1.25 @ ^ [Xx0: $i] :
% 1.45/1.25 ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx1: $i] :
% 1.45/1.25 ( ( S @ Xx1 )
% 1.45/1.25 => ( K @ S @ Xx1 ) )
% 1.45/1.25 & ( S @ Xx0 ) )
% 1.45/1.25 @ Xx )
% 1.45/1.25 <=> ( ! [Xx0: $i] :
% 1.45/1.25 ( ( K
% 1.45/1.25 @ ^ [Xx1: $i] :
% 1.45/1.25 ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx2: $i] :
% 1.45/1.25 ( ( S @ Xx2 )
% 1.45/1.25 => ( K @ S @ Xx2 ) )
% 1.45/1.25 & ( S @ Xx1 ) )
% 1.45/1.25 @ Xx0 )
% 1.45/1.25 => ( K
% 1.45/1.25 @ ( K
% 1.45/1.25 @ ^ [Xx1: $i] :
% 1.45/1.25 ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx2: $i] :
% 1.45/1.25 ( ( S @ Xx2 )
% 1.45/1.25 => ( K @ S @ Xx2 ) )
% 1.45/1.25 & ( S @ Xx1 ) ) )
% 1.45/1.25 @ Xx0 ) )
% 1.45/1.25 & ( K
% 1.45/1.25 @ ^ [Xx0: $i] :
% 1.45/1.25 ? [S: $i > $o] :
% 1.45/1.25 ( ! [Xx1: $i] :
% 1.45/1.25 ( ( S @ Xx1 )
% 1.45/1.25 => ( K @ S @ Xx1 ) )
% 1.45/1.25 & ( S @ Xx0 ) )
% 1.45/1.25 @ Xx ) ) ) ) ).
% 1.45/1.25 ------------------------
% 1.45/1.27 % (21234)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/183Mi)
% 1.45/1.28 % (21237)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/2Mi)
% 1.45/1.28 % (21236)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_21112 for (2999ds/27Mi)
% 1.45/1.28 % (21239)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_21112 for (2999ds/275Mi)
% 1.45/1.28 % (21240)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/18Mi)
% 1.45/1.28 % (21238)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_21112 for (2999ds/2Mi)
% 1.45/1.28 % (21237)Instruction limit reached!
% 1.45/1.28 % (21237)------------------------------
% 1.45/1.28 % (21237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (21237)Termination reason: Unknown
% 1.45/1.28 % (21237)Termination phase: Preprocessing 3
% 1.45/1.28
% 1.45/1.28 % (21237)Memory used [KB]: 1023
% 1.45/1.28 % (21237)Time elapsed: 0.003 s
% 1.45/1.28 % (21237)Instructions burned: 3 (million)
% 1.45/1.28 % (21238)Instruction limit reached!
% 1.45/1.28 % (21238)------------------------------
% 1.45/1.28 % (21238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (21238)Termination reason: Unknown
% 1.45/1.28 % (21238)Termination phase: shuffling
% 1.45/1.28
% 1.45/1.28 % (21238)Memory used [KB]: 1023
% 1.45/1.28 % (21238)Time elapsed: 0.002 s
% 1.45/1.28 % (21238)Instructions burned: 2 (million)
% 1.45/1.28 % (21238)------------------------------
% 1.45/1.28 % (21238)------------------------------
% 1.45/1.28 % (21237)------------------------------
% 1.45/1.28 % (21237)------------------------------
% 1.45/1.28 % (21236)Refutation not found, incomplete strategy
% 1.45/1.28 % (21236)------------------------------
% 1.45/1.28 % (21236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (21236)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.28
% 1.45/1.28
% 1.45/1.28 % (21236)Memory used [KB]: 5628
% 1.45/1.28 % (21236)Time elapsed: 0.009 s
% 1.45/1.28 % (21236)Instructions burned: 14 (million)
% 1.45/1.28 % (21236)------------------------------
% 1.45/1.28 % (21236)------------------------------
% 1.45/1.29 % (21235)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_21112 for (2999ds/4Mi)
% 1.45/1.29 % (21240)Instruction limit reached!
% 1.45/1.29 % (21240)------------------------------
% 1.45/1.29 % (21240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (21240)Termination reason: Unknown
% 1.45/1.29 % (21240)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (21240)Memory used [KB]: 5628
% 1.45/1.29 % (21240)Time elapsed: 0.011 s
% 1.45/1.29 % (21240)Instructions burned: 18 (million)
% 1.45/1.29 % (21240)------------------------------
% 1.45/1.29 % (21240)------------------------------
% 1.45/1.29 % (21235)Instruction limit reached!
% 1.45/1.29 % (21235)------------------------------
% 1.45/1.29 % (21235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (21235)Termination reason: Unknown
% 1.45/1.29 % (21235)Termination phase: Preprocessing 3
% 1.45/1.29
% 1.45/1.29 % (21235)Memory used [KB]: 1023
% 1.45/1.29 % (21235)Time elapsed: 0.003 s
% 1.45/1.29 % (21235)Instructions burned: 5 (million)
% 1.45/1.29 % (21235)------------------------------
% 1.45/1.29 % (21235)------------------------------
% 1.45/1.29 % (21242)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_21112 for (2999ds/37Mi)
% 1.45/1.29 % (21241)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/3Mi)
% 1.45/1.30 % (21241)Instruction limit reached!
% 1.45/1.30 % (21241)------------------------------
% 1.45/1.30 % (21241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.30 % (21241)Termination reason: Unknown
% 1.45/1.30 % (21241)Termination phase: Naming
% 1.45/1.30
% 1.45/1.30 % (21241)Memory used [KB]: 1023
% 1.45/1.30 % (21241)Time elapsed: 0.003 s
% 1.45/1.30 % (21241)Instructions burned: 3 (million)
% 1.45/1.30 % (21241)------------------------------
% 1.45/1.30 % (21241)------------------------------
% 1.58/1.30 % (21245)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_21112 for (2999ds/1041Mi)
% 1.58/1.30 % (21243)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_21112 for (2999ds/15Mi)
% 1.58/1.30 % (21244)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_21112 for (2999ds/3Mi)
% 1.58/1.30 % (21244)Instruction limit reached!
% 1.58/1.30 % (21244)------------------------------
% 1.58/1.30 % (21244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.30 % (21244)Termination reason: Unknown
% 1.58/1.30 % (21244)Termination phase: Preprocessing 3
% 1.58/1.30
% 1.58/1.30 % (21244)Memory used [KB]: 1023
% 1.58/1.30 % (21244)Time elapsed: 0.003 s
% 1.58/1.30 % (21244)Instructions burned: 3 (million)
% 1.58/1.30 % (21244)------------------------------
% 1.58/1.30 % (21244)------------------------------
% 1.58/1.31 % (21243)Instruction limit reached!
% 1.58/1.31 % (21243)------------------------------
% 1.58/1.31 % (21243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (21243)Termination reason: Unknown
% 1.58/1.31 % (21243)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (21243)Memory used [KB]: 5756
% 1.58/1.31 % (21243)Time elapsed: 0.010 s
% 1.58/1.31 % (21243)Instructions burned: 16 (million)
% 1.58/1.31 % (21243)------------------------------
% 1.58/1.31 % (21243)------------------------------
% 1.58/1.31 % (21242)Instruction limit reached!
% 1.58/1.31 % (21242)------------------------------
% 1.58/1.31 % (21242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (21242)Termination reason: Unknown
% 1.58/1.31 % (21242)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (21242)Memory used [KB]: 5756
% 1.58/1.31 % (21242)Time elapsed: 0.019 s
% 1.58/1.31 % (21242)Instructions burned: 37 (million)
% 1.58/1.31 % (21242)------------------------------
% 1.58/1.31 % (21242)------------------------------
% 1.58/1.31 % (21246)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/7Mi)
% 1.58/1.31 % (21239)Refutation not found, incomplete strategy
% 1.58/1.31 % (21239)------------------------------
% 1.58/1.31 % (21239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (21239)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.31
% 1.58/1.31
% 1.58/1.31 % (21239)Memory used [KB]: 5756
% 1.58/1.31 % (21239)Time elapsed: 0.038 s
% 1.58/1.31 % (21239)Instructions burned: 77 (million)
% 1.58/1.31 % (21239)------------------------------
% 1.58/1.31 % (21239)------------------------------
% 1.58/1.32 % (21246)Instruction limit reached!
% 1.58/1.32 % (21246)------------------------------
% 1.58/1.32 % (21246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (21246)Termination reason: Unknown
% 1.58/1.32 % (21246)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (21246)Memory used [KB]: 1023
% 1.58/1.32 % (21246)Time elapsed: 0.005 s
% 1.58/1.32 % (21246)Instructions burned: 7 (million)
% 1.58/1.32 % (21246)------------------------------
% 1.58/1.32 % (21246)------------------------------
% 1.58/1.32 % (21247)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/16Mi)
% 1.58/1.32 % (21234)Instruction limit reached!
% 1.58/1.32 % (21234)------------------------------
% 1.58/1.32 % (21234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (21234)Termination reason: Unknown
% 1.58/1.32 % (21234)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (21234)Memory used [KB]: 6780
% 1.58/1.32 % (21234)Time elapsed: 0.052 s
% 1.58/1.32 % (21234)Instructions burned: 183 (million)
% 1.58/1.32 % (21234)------------------------------
% 1.58/1.32 % (21234)------------------------------
% 1.58/1.33 % (21248)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_21112 for (2999ds/3Mi)
% 1.58/1.33 % (21248)Instruction limit reached!
% 1.58/1.33 % (21248)------------------------------
% 1.58/1.33 % (21248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (21248)Termination reason: Unknown
% 1.58/1.33 % (21248)Termination phase: Property scanning
% 1.58/1.33
% 1.58/1.33 % (21248)Memory used [KB]: 1023
% 1.58/1.33 % (21248)Time elapsed: 0.003 s
% 1.58/1.33 % (21248)Instructions burned: 3 (million)
% 1.58/1.33 % (21248)------------------------------
% 1.58/1.33 % (21248)------------------------------
% 1.58/1.33 % (21247)Instruction limit reached!
% 1.58/1.33 % (21247)------------------------------
% 1.58/1.33 % (21247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (21247)Termination reason: Unknown
% 1.58/1.33 % (21247)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (21247)Memory used [KB]: 5628
% 1.58/1.33 % (21247)Time elapsed: 0.010 s
% 1.58/1.33 % (21247)Instructions burned: 16 (million)
% 1.58/1.33 % (21247)------------------------------
% 1.58/1.33 % (21247)------------------------------
% 1.58/1.33 % (21252)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/4Mi)
% 1.58/1.33 % (21250)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/7Mi)
% 1.58/1.33 % (21251)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/3Mi)
% 1.58/1.33 % (21252)Instruction limit reached!
% 1.58/1.33 % (21252)------------------------------
% 1.58/1.33 % (21252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (21252)Termination reason: Unknown
% 1.58/1.33 % (21252)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (21252)Memory used [KB]: 5500
% 1.58/1.33 % (21252)Time elapsed: 0.003 s
% 1.58/1.33 % (21252)Instructions burned: 7 (million)
% 1.58/1.33 % (21252)------------------------------
% 1.58/1.33 % (21252)------------------------------
% 1.58/1.33 % (21249)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_21112 for (2999ds/3Mi)
% 1.58/1.33 % (21251)Instruction limit reached!
% 1.58/1.33 % (21251)------------------------------
% 1.58/1.33 % (21251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (21251)Termination reason: Unknown
% 1.58/1.33 % (21251)Termination phase: Property scanning
% 1.58/1.33
% 1.58/1.33 % (21251)Memory used [KB]: 1023
% 1.58/1.33 % (21251)Time elapsed: 0.003 s
% 1.58/1.33 % (21251)Instructions burned: 3 (million)
% 1.58/1.33 % (21251)------------------------------
% 1.58/1.33 % (21251)------------------------------
% 1.58/1.33 % (21250)Instruction limit reached!
% 1.58/1.33 % (21250)------------------------------
% 1.58/1.33 % (21250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (21250)Termination reason: Unknown
% 1.58/1.33 % (21250)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (21250)Memory used [KB]: 5500
% 1.58/1.33 % (21250)Time elapsed: 0.005 s
% 1.58/1.33 % (21250)Instructions burned: 8 (million)
% 1.58/1.33 % (21250)------------------------------
% 1.58/1.33 % (21250)------------------------------
% 1.58/1.33 % (21249)Instruction limit reached!
% 1.58/1.33 % (21249)------------------------------
% 1.58/1.33 % (21249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (21249)Termination reason: Unknown
% 1.58/1.33 % (21249)Termination phase: Preprocessing 3
% 1.58/1.33
% 1.58/1.33 % (21249)Memory used [KB]: 1023
% 1.58/1.33 % (21249)Time elapsed: 0.003 s
% 1.58/1.33 % (21249)Instructions burned: 4 (million)
% 1.58/1.33 % (21249)------------------------------
% 1.58/1.33 % (21249)------------------------------
% 1.58/1.34 % (21255)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/6Mi)
% 1.58/1.34 % (21256)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_21112 for (2999ds/902Mi)
% 1.58/1.34 % (21255)Instruction limit reached!
% 1.58/1.34 % (21255)------------------------------
% 1.58/1.34 % (21255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (21255)Termination reason: Unknown
% 1.58/1.34 % (21255)Termination phase: Saturation
% 1.58/1.34
% 1.58/1.34 % (21255)Memory used [KB]: 5500
% 1.58/1.34 % (21255)Time elapsed: 0.003 s
% 1.58/1.34 % (21255)Instructions burned: 6 (million)
% 1.58/1.34 % (21255)------------------------------
% 1.58/1.34 % (21255)------------------------------
% 1.58/1.34 % (21253)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/18Mi)
% 1.58/1.34 % (21254)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/710Mi)
% 1.58/1.35 % (21245)Refutation not found, incomplete strategy
% 1.58/1.35 % (21245)------------------------------
% 1.58/1.35 % (21245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (21245)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.35
% 1.58/1.35
% 1.58/1.35 % (21245)Memory used [KB]: 5756
% 1.58/1.35 % (21245)Time elapsed: 0.077 s
% 1.58/1.35 % (21245)Instructions burned: 136 (million)
% 1.58/1.35 % (21245)------------------------------
% 1.58/1.35 % (21245)------------------------------
% 1.58/1.35 % (21258)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/5Mi)
% 1.58/1.35 % (21258)Instruction limit reached!
% 1.58/1.35 % (21258)------------------------------
% 1.58/1.35 % (21258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (21258)Termination reason: Unknown
% 1.58/1.35 % (21258)Termination phase: Saturation
% 1.58/1.35
% 1.58/1.35 % (21258)Memory used [KB]: 5500
% 1.58/1.35 % (21258)Time elapsed: 0.004 s
% 1.58/1.35 % (21258)Instructions burned: 5 (million)
% 1.58/1.35 % (21258)------------------------------
% 1.58/1.35 % (21258)------------------------------
% 1.58/1.35 % (21253)Refutation not found, incomplete strategy
% 1.58/1.35 % (21253)------------------------------
% 1.58/1.35 % (21253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (21253)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.35
% 1.58/1.35
% 1.58/1.35 % (21253)Memory used [KB]: 5628
% 1.58/1.35 % (21253)Time elapsed: 0.010 s
% 1.58/1.35 % (21253)Instructions burned: 17 (million)
% 1.58/1.35 % (21253)------------------------------
% 1.58/1.35 % (21253)------------------------------
% 1.58/1.35 % (21259)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/6Mi)
% 1.58/1.35 % (21259)Instruction limit reached!
% 1.58/1.35 % (21259)------------------------------
% 1.58/1.35 % (21259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (21259)Termination reason: Unknown
% 1.58/1.35 % (21259)Termination phase: Saturation
% 1.58/1.35
% 1.58/1.35 % (21259)Memory used [KB]: 5500
% 1.58/1.35 % (21259)Time elapsed: 0.003 s
% 1.58/1.35 % (21259)Instructions burned: 7 (million)
% 1.58/1.35 % (21259)------------------------------
% 1.58/1.35 % (21259)------------------------------
% 1.58/1.36 % (21257)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/21Mi)
% 1.58/1.36 % (21257)Instruction limit reached!
% 1.58/1.36 % (21257)------------------------------
% 1.58/1.36 % (21257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (21257)Termination reason: Unknown
% 1.58/1.36 % (21257)Termination phase: Saturation
% 1.58/1.36
% 1.58/1.36 % (21257)Memory used [KB]: 5628
% 1.58/1.36 % (21257)Time elapsed: 0.033 s
% 1.58/1.36 % (21257)Instructions burned: 22 (million)
% 1.58/1.36 % (21257)------------------------------
% 1.58/1.36 % (21257)------------------------------
% 1.58/1.36 % (21260)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/377Mi)
% 1.58/1.36 % (21263)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/879Mi)
% 1.58/1.37 % (21262)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/19Mi)
% 1.58/1.37 % (21261)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/779Mi)
% 1.58/1.37 % (21256)Refutation not found, incomplete strategy
% 1.58/1.37 % (21256)------------------------------
% 1.58/1.37 % (21256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.37 % (21256)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.37
% 1.58/1.37
% 1.58/1.37 % (21256)Memory used [KB]: 5884
% 1.58/1.37 % (21256)Time elapsed: 0.033 s
% 1.58/1.37 % (21256)Instructions burned: 71 (million)
% 1.58/1.37 % (21256)------------------------------
% 1.58/1.37 % (21256)------------------------------
% 1.58/1.38 % (21263)First to succeed.
% 1.58/1.38 % (21262)Instruction limit reached!
% 1.58/1.38 % (21262)------------------------------
% 1.58/1.38 % (21262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (21262)Termination reason: Unknown
% 1.58/1.38 % (21262)Termination phase: Saturation
% 1.58/1.38
% 1.58/1.38 % (21262)Memory used [KB]: 5500
% 1.58/1.38 % (21262)Time elapsed: 0.011 s
% 1.58/1.38 % (21262)Instructions burned: 20 (million)
% 1.58/1.38 % (21262)------------------------------
% 1.58/1.38 % (21262)------------------------------
% 1.58/1.38 % (21264)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21112 for (2999ds/17Mi)
% 1.58/1.38 % (21263)Refutation found. Thanks to Tanya!
% 1.58/1.38 % SZS status Theorem for DTF2THF_21112
% 1.58/1.38 % SZS output start Proof for DTF2THF_21112
% 1.58/1.38 thf(func_def_10, type, sK0: ($i > $o) > $i > $o).
% 1.58/1.38 thf(func_def_11, type, sK1: ($i > $o) > $i).
% 1.58/1.38 thf(func_def_12, type, sK2: ($i > $o) > $i).
% 1.58/1.38 thf(func_def_16, type, sK6: $i > $o).
% 1.58/1.38 thf(func_def_19, type, ph8: !>[X0: $tType]:(X0)).
% 1.58/1.38 thf(func_def_20, type, sK9: $i > $o).
% 1.58/1.38 thf(func_def_21, type, sK10: $i > $o).
% 1.58/1.38 thf(f270,plain,(
% 1.58/1.38 $false),
% 1.58/1.38 inference(avatar_sat_refutation,[status(thm)],[f40,f44,f49,f141,f269])).
% 1.58/1.38 thf(f269,plain,(
% 1.58/1.38 ~spl7_2 | ~spl7_3 | spl7_4),
% 1.58/1.38 inference(avatar_contradiction_clause,[status(thm)],[f268])).
% 1.58/1.38 thf(f268,plain,(
% 1.58/1.38 $false | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(subsumption_resolution,[status(thm)],[f267,f150])).
% 1.58/1.38 thf(f150,plain,(
% 1.58/1.38 ((sK6 @ (sK1 @ sK6)) = $true) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(subsumption_resolution,[status(thm)],[f148,f48])).
% 1.58/1.38 thf(f48,plain,(
% 1.58/1.38 ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) != $true) | spl7_4),
% 1.58/1.38 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.58/1.38 thf(f46,definition,(
% 1.58/1.38 spl7_4 <=> ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) = $true)),
% 1.58/1.38 introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition])).
% 1.58/1.38 thf(f148,plain,(
% 1.58/1.38 ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) = $true) | ((sK6 @ (sK1 @ sK6)) = $true) | (~spl7_2 | ~spl7_3)),
% 1.58/1.38 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 1.58/1.38 thf(f146,plain,(
% 1.58/1.38 ($true != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) = $true) | ((sK6 @ (sK1 @ sK6)) = $true) | (~spl7_2 | ~spl7_3)),
% 1.58/1.38 inference(superposition,[status(thm)],[f29,f143])).
% 1.58/1.38 thf(f143,plain,(
% 1.58/1.38 ((sK0 @ sK6 @ sK5) = $true) | (~spl7_2 | ~spl7_3)),
% 1.58/1.38 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.58/1.38 thf(f142,plain,(
% 1.58/1.38 ($true != $true) | ((sK0 @ sK6 @ sK5) = $true) | (~spl7_2 | ~spl7_3)),
% 1.58/1.38 inference(superposition,[status(thm)],[f43,f39])).
% 1.58/1.38 thf(f39,plain,(
% 1.58/1.38 ((sK6 @ sK5) = $true) | ~spl7_2),
% 1.58/1.38 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.58/1.38 thf(f37,definition,(
% 1.58/1.38 spl7_2 <=> ((sK6 @ sK5) = $true)),
% 1.58/1.38 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 1.58/1.38 thf(f43,plain,(
% 1.58/1.38 ( ! [X12 : $i] : (((sK6 @ X12) != $true) | ((sK0 @ sK6 @ X12) = $true)) ) | ~spl7_3),
% 1.58/1.38 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.58/1.38 thf(f42,definition,(
% 1.58/1.38 spl7_3 <=> ! [X12 : $i] : (((sK6 @ X12) != $true) | ((sK0 @ sK6 @ X12) = $true))),
% 1.58/1.38 introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition])).
% 1.58/1.38 thf(f29,plain,(
% 1.58/1.38 ( ! [X1 : $i > $o,X5 : $i] : (((sK0 @ X1 @ X5) != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5) = $true) | ($true = (X1 @ (sK1 @ X1)))) )),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 thf(f19,plain,(
% 1.58/1.38 ! [X1 : $i > $o] : ((($true = (X1 @ (sK1 @ X1))) & ! [X3 : $i > $o] : ((((sK0 @ X3 @ (sK2 @ X3)) != $true) & ((X3 @ (sK2 @ X3)) = $true)) | ((X3 @ (sK1 @ X1)) != $true))) | ! [X5 : $i] : (((sK0 @ X1 @ X5) != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5) = $true))) & ((($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3)) | (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4) = $true) & ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK4) != $true)) | ($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))) & ((($true = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3)) & ! [X8 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X8) != $true) | ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X8) = $true))) | ($true = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3)))) & (! [X9 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X9) != $true) | ($true = (sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9))) | ((((sK6 @ sK5) = $true) & ! [X12 : $i] : (((sK0 @ sK6 @ X12) = $true) | ((sK6 @ X12) != $true))) & ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) != $true)))),
% 1.58/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f11,f18,f17,f16,f15,f14,f13,f12])).
% 1.58/1.38 thf(f12,plain,(
% 1.58/1.38 ? [X0 : ($i > $o) > $i > $o] : (! [X1 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) = $true) & ! [X3 : $i > $o] : (? [X4 : $i] : (((X0 @ X3 @ X4) != $true) & ((X3 @ X4) = $true)) | ((X3 @ X2) != $true))) | ! [X5 : $i] : (($true != (X0 @ X1 @ X5)) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5) = $true))) & ? [X6 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6) != $true) | ? [X7 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X7) = $true) & ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7) != $true)) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6) != $true)) & ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6) = $true) & ! [X8 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X8) != $true) | ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X8) = $true))) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6) = $true))) & (! [X9 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X9) != $true) | ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9) = $true)) | ? [X10 : $i] : (? [X11 : $i > $o] : (((X11 @ X10) = $true) & ! [X12 : $i] : (((X0 @ X11 @ X12) = $true) | ($true != (X11 @ X12)))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10) != $true)))) => (! [X1 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) = $true) & ! [X3 : $i > $o] : (? [X4 : $i] : (((sK0 @ X3 @ X4) != $true) & ((X3 @ X4) = $true)) | ((X3 @ X2) != $true))) | ! [X5 : $i] : (((sK0 @ X1 @ X5) != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5) = $true))) & ? [X6 : $i] : ((((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6) != $true) | ? [X7 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X7) = $true) & ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7) != $true)) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6) != $true)) & ((((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6) = $true) & ! [X8 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X8) != $true) | ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X8) = $true))) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6) = $true))) & (! [X9 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X9) != $true) | ($true = (sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9))) | ? [X10 : $i] : (? [X11 : $i > $o] : (((X11 @ X10) = $true) & ! [X12 : $i] : (($true = (sK0 @ X11 @ X12)) | ($true != (X11 @ X12)))) & ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10) != $true))))),
% 1.58/1.38 introduced(definition,[],[choice_axiom])).
% 1.58/1.38 thf(f13,plain,(
% 1.58/1.38 ! [X1 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) = $true) & ! [X3 : $i > $o] : (? [X4 : $i] : (((sK0 @ X3 @ X4) != $true) & ((X3 @ X4) = $true)) | ((X3 @ X2) != $true))) => (($true = (X1 @ (sK1 @ X1))) & ! [X3 : $i > $o] : (? [X4 : $i] : (((sK0 @ X3 @ X4) != $true) & ((X3 @ X4) = $true)) | ((X3 @ (sK1 @ X1)) != $true))))),
% 1.58/1.38 introduced(definition,[],[choice_axiom])).
% 1.58/1.38 thf(f14,plain,(
% 1.58/1.38 ! [X3 : $i > $o] : (? [X4 : $i] : (((sK0 @ X3 @ X4) != $true) & ((X3 @ X4) = $true)) => (((sK0 @ X3 @ (sK2 @ X3)) != $true) & ((X3 @ (sK2 @ X3)) = $true)))),
% 1.58/1.38 introduced(definition,[],[choice_axiom])).
% 1.58/1.38 thf(f15,plain,(
% 1.58/1.38 ? [X6 : $i] : ((((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6) != $true) | ? [X7 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X7) = $true) & ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7) != $true)) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6) != $true)) & ((((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6) = $true) & ! [X8 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X8) != $true) | ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X8) = $true))) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X6) = $true))) => ((($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3)) | ? [X7 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X7) = $true) & ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7) != $true)) | ($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))) & ((($true = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3)) & ! [X8 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X8) != $true) | ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X8) = $true))) | ($true = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))))),
% 1.58/1.38 introduced(definition,[],[choice_axiom])).
% 1.58/1.38 thf(f16,plain,(
% 1.58/1.38 ? [X7 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X7) = $true) & ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7) != $true)) => (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4) = $true) & ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK4) != $true))),
% 1.58/1.38 introduced(definition,[],[choice_axiom])).
% 1.58/1.38 thf(f17,plain,(
% 1.58/1.38 ? [X10 : $i] : (? [X11 : $i > $o] : (((X11 @ X10) = $true) & ! [X12 : $i] : (($true = (sK0 @ X11 @ X12)) | ($true != (X11 @ X12)))) & ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10) != $true)) => (? [X11 : $i > $o] : (($true = (X11 @ sK5)) & ! [X12 : $i] : (($true = (sK0 @ X11 @ X12)) | ($true != (X11 @ X12)))) & ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) != $true))),
% 1.58/1.38 introduced(definition,[],[choice_axiom])).
% 1.58/1.38 thf(f18,plain,(
% 1.58/1.38 ? [X11 : $i > $o] : (($true = (X11 @ sK5)) & ! [X12 : $i] : (($true = (sK0 @ X11 @ X12)) | ($true != (X11 @ X12)))) => (((sK6 @ sK5) = $true) & ! [X12 : $i] : (((sK0 @ sK6 @ X12) = $true) | ((sK6 @ X12) != $true)))),
% 1.58/1.38 introduced(definition,[],[choice_axiom])).
% 1.58/1.38 thf(f11,plain,(
% 1.58/1.38 ? [X0 : ($i > $o) > $i > $o] : (! [X1 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) = $true) & ! [X3 : $i > $o] : (? [X4 : $i] : (((X0 @ X3 @ X4) != $true) & ((X3 @ X4) = $true)) | ((X3 @ X2) != $true))) | ! [X5 : $i] : (($true != (X0 @ X1 @ X5)) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5) = $true))) & ? [X6 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6) != $true) | ? [X7 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X7) = $true) & ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7) != $true)) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6) != $true)) & ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6) = $true) & ! [X8 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X8) != $true) | ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X8) = $true))) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X6) = $true))) & (! [X9 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X9) != $true) | ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9) = $true)) | ? [X10 : $i] : (? [X11 : $i > $o] : (((X11 @ X10) = $true) & ! [X12 : $i] : (((X0 @ X11 @ X12) = $true) | ($true != (X11 @ X12)))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X10) != $true))))),
% 1.58/1.38 inference(rectify,[status(thm)],[f10])).
% 1.58/1.38 thf(f10,plain,(
% 1.58/1.38 ? [X0 : ($i > $o) > $i > $o] : (! [X5 : $i > $o] : (? [X6 : $i] : (((X5 @ X6) = $true) & ! [X7 : $i > $o] : (? [X8 : $i] : (((X0 @ X7 @ X8) != $true) & ((X7 @ X8) = $true)) | ((X7 @ X6) != $true))) | ! [X9 : $i] : (((X0 @ X5 @ X9) != $true) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9) = $true))) & ? [X10 : $i] : ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) != $true) | ? [X11 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X11) = $true) & ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11) != $true)) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) != $true)) & ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true) & ! [X11 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X11) != $true) | ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11) = $true))) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true))) & (! [X4 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X4) != $true) | ($true = (X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ? [X1 : $i] : (? [X2 : $i > $o] : (((X2 @ X1) = $true) & ! [X3 : $i] : (((X0 @ X2 @ X3) = $true) | ((X2 @ X3) != $true))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1) != $true))))),
% 1.58/1.38 inference(flattening,[status(thm)],[f9])).
% 1.58/1.38 thf(f9,plain,(
% 1.58/1.38 ? [X0 : ($i > $o) > $i > $o] : (! [X5 : $i > $o] : (? [X6 : $i] : (((X5 @ X6) = $true) & ! [X7 : $i > $o] : (? [X8 : $i] : (((X0 @ X7 @ X8) != $true) & ((X7 @ X8) = $true)) | ((X7 @ X6) != $true))) | ! [X9 : $i] : (((X0 @ X5 @ X9) != $true) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9) = $true))) & ? [X10 : $i] : (((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) != $true) | ? [X11 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X11) = $true) & ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11) != $true))) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) != $true)) & ((((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true) & ! [X11 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X11) != $true) | ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11) = $true))) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true))) & (! [X4 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X4) != $true) | ($true = (X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ? [X1 : $i] : (? [X2 : $i > $o] : (((X2 @ X1) = $true) & ! [X3 : $i] : (((X0 @ X2 @ X3) = $true) | ((X2 @ X3) != $true))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1) != $true))))),
% 1.58/1.38 inference(nnf_transformation,[status(thm)],[f8])).
% 1.58/1.38 thf(f8,plain,(
% 1.58/1.38 ? [X0 : ($i > $o) > $i > $o] : (! [X5 : $i > $o] : (? [X6 : $i] : (((X5 @ X6) = $true) & ! [X7 : $i > $o] : (? [X8 : $i] : (((X0 @ X7 @ X8) != $true) & ((X7 @ X8) = $true)) | ((X7 @ X6) != $true))) | ! [X9 : $i] : (((X0 @ X5 @ X9) != $true) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9) = $true))) & ? [X10 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true) <~> (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true) & ! [X11 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X11) != $true) | ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11) = $true)))) & (! [X4 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X4) != $true) | ($true = (X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ? [X1 : $i] : (? [X2 : $i > $o] : (((X2 @ X1) = $true) & ! [X3 : $i] : (((X0 @ X2 @ X3) = $true) | ((X2 @ X3) != $true))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1) != $true))))),
% 1.58/1.38 inference(flattening,[status(thm)],[f7])).
% 1.58/1.38 thf(f7,plain,(
% 1.58/1.38 ? [X0 : ($i > $o) > $i > $o] : (? [X10 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true) <~> (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true) & ! [X11 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X11) != $true) | ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11) = $true)))) & (! [X5 : $i > $o] : (? [X6 : $i] : (((X5 @ X6) = $true) & ! [X7 : $i > $o] : (? [X8 : $i] : (((X0 @ X7 @ X8) != $true) & ((X7 @ X8) = $true)) | ((X7 @ X6) != $true))) | ! [X9 : $i] : (((X0 @ X5 @ X9) != $true) | ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9) = $true))) & (! [X4 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X4) != $true) | ($true = (X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))) | ? [X1 : $i] : (? [X2 : $i > $o] : (((X2 @ X1) = $true) & ! [X3 : $i] : (((X0 @ X2 @ X3) = $true) | ((X2 @ X3) != $true))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1) != $true)))))),
% 1.58/1.38 inference(ennf_transformation,[status(thm)],[f6])).
% 1.58/1.38 thf(f6,plain,(
% 1.58/1.38 ~! [X0 : ($i > $o) > $i > $o] : ((! [X5 : $i > $o] : (! [X6 : $i] : (((X5 @ X6) = $true) => ? [X7 : $i > $o] : (! [X8 : $i] : (((X7 @ X8) = $true) => ((X0 @ X7 @ X8) = $true)) & ((X7 @ X6) = $true))) => ! [X9 : $i] : (((X0 @ X5 @ X9) = $true) => ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X9) = $true))) & (! [X1 : $i] : (? [X2 : $i > $o] : (((X2 @ X1) = $true) & ! [X3 : $i] : (((X2 @ X3) = $true) => ((X0 @ X2 @ X3) = $true))) => ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1) = $true)) => ! [X4 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X4) = $true) => ($true = (X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X4))))) => ! [X10 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true) <=> (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X10) = $true) & ! [X11 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X11) = $true) => ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X11) = $true)))))),
% 1.58/1.38 inference(rectify,[status(thm)],[f5])).
% 1.58/1.38 thf(f5,plain,(
% 1.58/1.38 ~! [X0 : ($i > $o) > $i > $o] : (((! [X1 : $i] : (? [X2 : $i > $o] : (((X2 @ X1) = $true) & ! [X3 : $i] : (((X2 @ X3) = $true) => ((X0 @ X2 @ X3) = $true))) => ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1) = $true)) => ! [X7 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X7) = $true) => ((X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X7) = $true))) & ! [X14 : $i > $o] : (! [X15 : $i] : (((X14 @ X15) = $true) => ? [X16 : $i > $o] : (! [X17 : $i] : (((X16 @ X17) = $true) => ((X0 @ X16 @ X17) = $true)) & ((X16 @ X15) = $true))) => ! [X18 : $i] : (((X0 @ X14 @ X18) = $true) => ($true = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X18))))) => ! [X22 : $i] : ((! [X23 : $i] : (((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X23) = $true) => ($true = (X0 @ (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X23))) & ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X22) = $true)) <=> ((X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (X0 @ Y1 @ Y2)))))))) @ X22) = $true)))),
% 1.58/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.58/1.38 thf(f4,plain,(
% 1.58/1.38 ~! [X0 : ($i > $o) > $i > $o] : (((! [X1 : $i] : (? [X2 : $i > $o] : (! [X3 : $i] : ((X2 @ X3) => (X0 @ X2 @ X3)) & (X2 @ X1)) => (X0 @ (^[X4 : $i] : (? [X5 : $i > $o] : ((X5 @ X4) & ! [X6 : $i] : ((X5 @ X6) => (X0 @ X5 @ X6))))) @ X1)) => ! [X7 : $i] : ((X0 @ (^[X8 : $i] : (? [X9 : $i > $o] : (! [X10 : $i] : ((X9 @ X10) => (X0 @ X9 @ X10)) & (X9 @ X8)))) @ X7) => (X0 @ (X0 @ (^[X11 : $i] : (? [X12 : $i > $o] : ((X12 @ X11) & ! [X13 : $i] : ((X12 @ X13) => (X0 @ X12 @ X13)))))) @ X7))) & ! [X14 : $i > $o] : (! [X15 : $i] : ((X14 @ X15) => ? [X16 : $i > $o] : (! [X17 : $i] : ((X16 @ X17) => (X0 @ X16 @ X17)) & (X16 @ X15))) => ! [X18 : $i] : ((X0 @ X14 @ X18) => (X0 @ (^[X19 : $i] : (? [X20 : $i > $o] : ((X20 @ X19) & ! [X21 : $i] : ((X20 @ X21) => (X0 @ X20 @ X21))))) @ X18)))) => ! [X22 : $i] : ((! [X23 : $i] : ((X0 @ (^[X24 : $i] : (? [X25 : $i > $o] : (! [X26 : $i] : ((X25 @ X26) => (X0 @ X25 @ X26)) & (X25 @ X24)))) @ X23) => (X0 @ (X0 @ (^[X27 : $i] : (? [X28 : $i > $o] : ((X28 @ X27) & ! [X29 : $i] : ((X28 @ X29) => (X0 @ X28 @ X29)))))) @ X23)) & (X0 @ (^[X30 : $i] : (? [X31 : $i > $o] : (! [X32 : $i] : ((X31 @ X32) => (X0 @ X31 @ X32)) & (X31 @ X30)))) @ X22)) <=> (X0 @ (^[X33 : $i] : (? [X34 : $i > $o] : (! [X35 : $i] : ((X34 @ X35) => (X0 @ X34 @ X35)) & (X34 @ X33)))) @ X22)))),
% 1.58/1.38 inference(rectify,[status(thm)],[f2])).
% 1.58/1.38 thf(f2,negated_conjecture,(
% 1.58/1.38 ~! [X0 : ($i > $o) > $i > $o] : (((! [X1 : $i] : (? [X3 : $i > $o] : (! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2)) & (X3 @ X1)) => (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1)) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))))) @ X1))) & ! [X1 : $i > $o] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : $i > $o] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))) => ! [X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2)))) => ! [X1 : $i] : ((! [X2 : $i] : ((X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : (! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5)) & (X3 @ X4)))) @ X2) => (X0 @ (X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5)))))) @ X2)) & (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1)) <=> (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1)))),
% 1.58/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.58/1.38 thf(f1,conjecture,(
% 1.58/1.38 ! [X0 : ($i > $o) > $i > $o] : (((! [X1 : $i] : (? [X3 : $i > $o] : (! [X2 : $i] : ((X3 @ X2) => (X0 @ X3 @ X2)) & (X3 @ X1)) => (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1)) => ! [X1 : $i] : ((X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)))))) @ X1))) & ! [X1 : $i > $o] : (! [X2 : $i] : ((X1 @ X2) => ? [X3 : $i > $o] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))) => ! [X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2)))) => ! [X1 : $i] : ((! [X2 : $i] : ((X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : (! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5)) & (X3 @ X4)))) @ X2) => (X0 @ (X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : ((X3 @ X4) & ! [X5 : $i] : ((X3 @ X5) => (X0 @ X3 @ X5)))))) @ X2)) & (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1)) <=> (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (! [X4 : $i] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2)))) @ X1)))),
% 1.58/1.38 file('/export/starexec/sandbox/tmp/tmp.7TYe0oTisK/DTF2THF_21112.p',cTHM2D_pme)).
% 1.58/1.38 thf(f267,plain,(
% 1.58/1.38 ((sK6 @ (sK1 @ sK6)) != $true) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(subsumption_resolution,[status(thm)],[f257,f48])).
% 1.58/1.38 thf(f257,plain,(
% 1.58/1.38 ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) = $true) | ((sK6 @ (sK1 @ sK6)) != $true) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(trivial_inequality_removal,[status(thm)],[f254])).
% 1.58/1.38 thf(f254,plain,(
% 1.58/1.38 ($true != $true) | ((sK6 @ (sK1 @ sK6)) != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) = $true) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(superposition,[status(thm)],[f186,f143])).
% 1.58/1.38 thf(f186,plain,(
% 1.58/1.38 ( ! [X0 : $i > $o,X1 : $i] : (((sK0 @ X0 @ X1) != $true) | ($true != (sK6 @ (sK1 @ X0))) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1) = $true)) ) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(trivial_inequality_removal,[status(thm)],[f181])).
% 1.58/1.38 thf(f181,plain,(
% 1.58/1.38 ( ! [X0 : $i > $o,X1 : $i] : (($true != $true) | ($true != (sK6 @ (sK1 @ X0))) | ((sK0 @ X0 @ X1) != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1) = $true)) ) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(superposition,[status(thm)],[f28,f166])).
% 1.58/1.38 thf(f166,plain,(
% 1.58/1.38 ((sK0 @ sK6 @ (sK2 @ sK6)) = $true) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.58/1.38 thf(f165,plain,(
% 1.58/1.38 ((sK0 @ sK6 @ (sK2 @ sK6)) = $true) | ($true != $true) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(superposition,[status(thm)],[f43,f162])).
% 1.58/1.38 thf(f162,plain,(
% 1.58/1.38 ($true = (sK6 @ (sK2 @ sK6))) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.58/1.38 thf(f158,plain,(
% 1.58/1.38 ($true != $true) | ($true = (sK6 @ (sK2 @ sK6))) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(superposition,[status(thm)],[f151,f150])).
% 1.58/1.38 thf(f151,plain,(
% 1.58/1.38 ( ! [X0 : $i > $o] : (((X0 @ (sK1 @ sK6)) != $true) | ((X0 @ (sK2 @ X0)) = $true)) ) | (~spl7_2 | ~spl7_3 | spl7_4)),
% 1.58/1.38 inference(subsumption_resolution,[status(thm)],[f147,f48])).
% 1.58/1.38 thf(f147,plain,(
% 1.58/1.38 ( ! [X0 : $i > $o] : (((X0 @ (sK1 @ sK6)) != $true) | ((X0 @ (sK2 @ X0)) = $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) = $true)) ) | (~spl7_2 | ~spl7_3)),
% 1.58/1.38 inference(trivial_inequality_removal,[status(thm)],[f145])).
% 1.58/1.38 thf(f145,plain,(
% 1.58/1.38 ( ! [X0 : $i > $o] : (((X0 @ (sK2 @ X0)) = $true) | ($true != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) = $true) | ((X0 @ (sK1 @ sK6)) != $true)) ) | (~spl7_2 | ~spl7_3)),
% 1.58/1.38 inference(superposition,[status(thm)],[f27,f143])).
% 1.58/1.38 thf(f27,plain,(
% 1.58/1.38 ( ! [X3 : $i > $o,X1 : $i > $o,X5 : $i] : (((sK0 @ X1 @ X5) != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5) = $true) | ((X3 @ (sK1 @ X1)) != $true) | ((X3 @ (sK2 @ X3)) = $true)) )),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 thf(f28,plain,(
% 1.58/1.38 ( ! [X3 : $i > $o,X1 : $i > $o,X5 : $i] : (((sK0 @ X3 @ (sK2 @ X3)) != $true) | ((sK0 @ X1 @ X5) != $true) | ((X3 @ (sK1 @ X1)) != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5) = $true)) )),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 thf(f141,plain,(
% 1.58/1.38 ~spl7_1),
% 1.58/1.38 inference(avatar_contradiction_clause,[status(thm)],[f140])).
% 1.58/1.38 thf(f140,plain,(
% 1.58/1.38 $false | ~spl7_1),
% 1.58/1.38 inference(subsumption_resolution,[status(thm)],[f139,f51])).
% 1.58/1.38 thf(f51,plain,(
% 1.58/1.38 ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK4) != $true)),
% 1.58/1.38 inference(subsumption_resolution,[status(thm)],[f30,f32])).
% 1.58/1.38 thf(f32,plain,(
% 1.58/1.38 ($true = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))),
% 1.58/1.38 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.58/1.38 thf(f24,plain,(
% 1.58/1.38 ($true = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3)) | ($true = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 thf(f30,plain,(
% 1.58/1.38 ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK4) != $true) | ($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))),
% 1.58/1.38 inference(duplicate_literal_removal,[status(thm)],[f25])).
% 1.58/1.38 thf(f25,plain,(
% 1.58/1.38 ($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3)) | ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK4) != $true) | ($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 thf(f139,plain,(
% 1.58/1.38 ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK4) = $true) | ~spl7_1),
% 1.58/1.38 inference(trivial_inequality_removal,[status(thm)],[f137])).
% 1.58/1.38 thf(f137,plain,(
% 1.58/1.38 ($true != $true) | ((sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ sK4) = $true) | ~spl7_1),
% 1.58/1.38 inference(superposition,[status(thm)],[f35,f50])).
% 1.58/1.38 thf(f50,plain,(
% 1.58/1.38 ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4) = $true)),
% 1.58/1.38 inference(subsumption_resolution,[status(thm)],[f31,f32])).
% 1.58/1.38 thf(f31,plain,(
% 1.58/1.38 ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4) = $true) | ($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))),
% 1.58/1.38 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.58/1.38 thf(f26,plain,(
% 1.58/1.38 ($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3)) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4) = $true) | ($true != (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK3))),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 thf(f35,plain,(
% 1.58/1.38 ( ! [X9 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X9) != $true) | ($true = (sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9))) ) | ~spl7_1),
% 1.58/1.38 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.58/1.38 thf(f34,definition,(
% 1.58/1.38 spl7_1 <=> ! [X9 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X9) != $true) | ($true = (sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9)))),
% 1.58/1.38 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 1.58/1.38 thf(f49,plain,(
% 1.58/1.38 spl7_1 | ~spl7_4),
% 1.58/1.38 inference(avatar_split_clause,[status(thm)],[f20,f46,f34])).
% 1.58/1.38 thf(f20,plain,(
% 1.58/1.38 ( ! [X9 : $i] : (($true = (sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9)) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK5) != $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X9) != $true)) )),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 thf(f44,plain,(
% 1.58/1.38 spl7_3 | spl7_1),
% 1.58/1.38 inference(avatar_split_clause,[status(thm)],[f21,f34,f42])).
% 1.58/1.38 thf(f21,plain,(
% 1.58/1.38 ( ! [X9 : $i,X12 : $i] : (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X9) != $true) | ((sK6 @ X12) != $true) | ($true = (sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9)) | ((sK0 @ sK6 @ X12) = $true)) )),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 thf(f40,plain,(
% 1.58/1.38 spl7_1 | spl7_2),
% 1.58/1.38 inference(avatar_split_clause,[status(thm)],[f22,f37,f34])).
% 1.58/1.38 thf(f22,plain,(
% 1.58/1.38 ( ! [X9 : $i] : (((sK6 @ sK5) = $true) | ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ X9) != $true) | ($true = (sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))) & (Y1 @ Y0)))))) @ X9))) )),
% 1.58/1.38 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.38 % SZS output end Proof for DTF2THF_21112
% 1.58/1.38 % (21263)------------------------------
% 1.58/1.38 % (21263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (21263)Termination reason: Refutation
% 1.58/1.38
% 1.58/1.38 % (21263)Memory used [KB]: 5884
% 1.58/1.38 % (21263)Time elapsed: 0.017 s
% 1.58/1.38 % (21263)Instructions burned: 38 (million)
% 1.58/1.38 % (21263)------------------------------
% 1.58/1.38 % (21263)------------------------------
% 1.58/1.38 % (21233)Success in time 0.114 s
%------------------------------------------------------------------------------