%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO246^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 09:53:45 AM UTC 2026
% Result : Theorem 1.72s 1.46s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 114 ( 7 unt; 0 typ; 8 def)
% Number of atoms : 1022 ( 245 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 1436 ( 158 ~; 246 |; 100 &; 759 @)
% ( 8 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 702 ( 702 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 21 usr; 13 con; 0-3 aty)
% ( 35 !!; 45 ??; 0 @@+; 0 @@-)
% Number of variables : 272 ( 113 ^; 113 !; 46 ?; 272 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_12,type,
sK0: ( ( ( a > $o ) > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_13,type,
sK1: ( ( ( a > $o ) > $o ) > $o ) > ( a > $o ) > $o ).
thf(func_def_14,type,
sK2: ( ( a > $o ) > $o ) > $o ).
thf(func_def_15,type,
sK3: ( a > $o ) > $o ).
thf(func_def_16,type,
sK4: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_18,type,
ph6:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK7: a ).
thf(func_def_22,type,
sK8: ( a > $o ) > $o ).
thf(func_def_23,type,
sK9: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(func_def_24,type,
sK10: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_25,type,
sK11: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_26,type,
sK12: a > $o ).
thf(func_def_27,type,
sK13: a > $o ).
thf(f1023,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f105,f109,f113,f114,f121,f126,f130,f131,f325,f874,f980,f1022]) ).
thf(f1022,plain,
( ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f1021]) ).
thf(f1021,plain,
( $false
| ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1017]) ).
thf(f1017,plain,
( ( $false = $true )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_7 ),
inference(superposition,[status(thm)],[f1016,f125]) ).
thf(f125,plain,
( ( ( sK2 @ sK8 )
= $true )
| ~ spl5_7 ),
inference(avatar_component_clause,[status(thm)],[f123]) ).
thf(f123,definition,
( spl5_7
<=> ( ( sK2 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition]) ).
thf(f1016,plain,
( ( ( sK2 @ sK8 )
= $false )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1013]) ).
thf(f1013,plain,
( ( $false = $true )
| ( ( sK2 @ sK8 )
= $false )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_7 ),
inference(superposition,[status(thm)],[f1011,f112]) ).
thf(f112,plain,
( ! [X2: ( a > $o ) > $o] :
( ( ( sK10 @ X2 @ sK7 )
= $true )
| ( ( sK2 @ X2 )
= $false ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f111]) ).
thf(f111,definition,
( spl5_4
<=> ! [X2: ( a > $o ) > $o] :
( ( ( sK10 @ X2 @ sK7 )
= $true )
| ( ( sK2 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f1011,plain,
( ( ( sK10 @ sK8 @ sK7 )
= $false )
| ~ spl5_1
| ~ spl5_5
| ~ spl5_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1010]) ).
thf(f1010,plain,
( ( $false = $true )
| ( ( sK10 @ sK8 @ sK7 )
= $false )
| ~ spl5_1
| ~ spl5_5
| ~ spl5_7 ),
inference(forward_demodulation,[status(thm)],[f1007,f125]) ).
thf(f1007,plain,
( ( ( sK2 @ sK8 )
= $false )
| ( ( sK10 @ sK8 @ sK7 )
= $false )
| ~ spl5_1
| ~ spl5_5 ),
inference(trivial_inequality_removal,[status(thm)],[f987]) ).
thf(f987,plain,
( ( ( sK10 @ sK8 @ sK7 )
= $false )
| ( $false = $true )
| ( ( sK2 @ sK8 )
= $false )
| ~ spl5_1
| ~ spl5_5 ),
inference(superposition,[status(thm)],[f117,f101]) ).
thf(f101,plain,
( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( ( sK2 @ X2 )
= $false ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f100,definition,
( spl5_1
<=> ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( ( sK2 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f117,plain,
( ! [X2: a > $o] :
( ( ( sK8 @ X2 )
= $false )
| ( ( X2 @ sK7 )
= $false ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f116,definition,
( spl5_5
<=> ! [X2: a > $o] :
( ( ( X2 @ sK7 )
= $false )
| ( ( sK8 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f980,plain,
( ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f979]) ).
thf(f979,plain,
( $false
| ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f975]) ).
thf(f975,plain,
( ( $false = $true )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_8 ),
inference(superposition,[status(thm)],[f970,f129]) ).
thf(f129,plain,
( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( $true
= ( sK2 @ ( sK9 @ X1 ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[status(thm)],[f128]) ).
thf(f128,definition,
( spl5_8
<=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( $true
= ( sK2 @ ( sK9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition]) ).
thf(f970,plain,
( ( ( sK2 @ ( sK9 @ sK10 ) )
= $false )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f968]) ).
thf(f968,plain,
( ( $false = $true )
| ( ( sK2 @ ( sK9 @ sK10 ) )
= $false )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_8 ),
inference(superposition,[status(thm)],[f112,f910]) ).
thf(f910,plain,
( ( $false
= ( sK10 @ ( sK9 @ sK10 ) @ sK7 ) )
| ~ spl5_1
| ~ spl5_6
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f909]) ).
thf(f909,plain,
( ( $false
= ( sK10 @ ( sK9 @ sK10 ) @ sK7 ) )
| ( $false = $true )
| ~ spl5_1
| ~ spl5_6
| ~ spl5_8 ),
inference(forward_demodulation,[status(thm)],[f907,f129]) ).
thf(f907,plain,
( ( ( sK2 @ ( sK9 @ sK10 ) )
= $false )
| ( $false
= ( sK10 @ ( sK9 @ sK10 ) @ sK7 ) )
| ~ spl5_1
| ~ spl5_6 ),
inference(trivial_inequality_removal,[status(thm)],[f882]) ).
thf(f882,plain,
( ( ( sK2 @ ( sK9 @ sK10 ) )
= $false )
| ( $false = $true )
| ( $false
= ( sK10 @ ( sK9 @ sK10 ) @ sK7 ) )
| ~ spl5_1
| ~ spl5_6 ),
inference(superposition,[status(thm)],[f101,f120]) ).
thf(f120,plain,
( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( $false
= ( X1 @ ( sK9 @ X1 ) @ sK7 ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f119,definition,
( spl5_6
<=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( $false
= ( X1 @ ( sK9 @ X1 ) @ sK7 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f874,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f873]) ).
thf(f873,plain,
( $false
| ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f870]) ).
thf(f870,plain,
( ( $false = $true )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_8 ),
inference(superposition,[status(thm)],[f129,f840]) ).
thf(f840,plain,
( ( ( sK2 @ ( sK9 @ sK11 ) )
= $false )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f838]) ).
thf(f838,plain,
( ( $false = $true )
| ( ( sK2 @ ( sK9 @ sK11 ) )
= $false )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_8 ),
inference(superposition,[status(thm)],[f104,f724]) ).
thf(f724,plain,
( ( ( sK11 @ ( sK9 @ sK11 ) @ sK7 )
= $false )
| ~ spl5_3
| ~ spl5_6
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f723]) ).
thf(f723,plain,
( ( $false = $true )
| ( ( sK11 @ ( sK9 @ sK11 ) @ sK7 )
= $false )
| ~ spl5_3
| ~ spl5_6
| ~ spl5_8 ),
inference(forward_demodulation,[status(thm)],[f722,f129]) ).
thf(f722,plain,
( ( ( sK11 @ ( sK9 @ sK11 ) @ sK7 )
= $false )
| ( ( sK2 @ ( sK9 @ sK11 ) )
= $false )
| ~ spl5_3
| ~ spl5_6 ),
inference(trivial_inequality_removal,[status(thm)],[f714]) ).
thf(f714,plain,
( ( $false = $true )
| ( ( sK2 @ ( sK9 @ sK11 ) )
= $false )
| ( ( sK11 @ ( sK9 @ sK11 ) @ sK7 )
= $false )
| ~ spl5_3
| ~ spl5_6 ),
inference(superposition,[status(thm)],[f108,f120]) ).
thf(f108,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( sK11 @ X1 ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl5_3
<=> ! [X1: ( a > $o ) > $o] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( X1 @ ( sK11 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f104,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( sK11 @ X1 @ sK7 )
= $true )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f103,definition,
( spl5_2
<=> ! [X1: ( a > $o ) > $o] :
( ( ( sK11 @ X1 @ sK7 )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f325,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f324]) ).
thf(f324,plain,
( $false
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_7 ),
inference(trivial_inequality_removal,[status(thm)],[f320]) ).
thf(f320,plain,
( ( $false = $true )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_7 ),
inference(superposition,[status(thm)],[f304,f125]) ).
thf(f304,plain,
( ( ( sK2 @ sK8 )
= $false )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_7 ),
inference(trivial_inequality_removal,[status(thm)],[f301]) ).
thf(f301,plain,
( ( ( sK2 @ sK8 )
= $false )
| ( $false = $true )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_7 ),
inference(superposition,[status(thm)],[f238,f104]) ).
thf(f238,plain,
( ( ( sK11 @ sK8 @ sK7 )
= $false )
| ~ spl5_3
| ~ spl5_5
| ~ spl5_7 ),
inference(trivial_inequality_removal,[status(thm)],[f237]) ).
thf(f237,plain,
( ( ( sK11 @ sK8 @ sK7 )
= $false )
| ( $false = $true )
| ~ spl5_3
| ~ spl5_5
| ~ spl5_7 ),
inference(forward_demodulation,[status(thm)],[f233,f125]) ).
thf(f233,plain,
( ( ( sK11 @ sK8 @ sK7 )
= $false )
| ( ( sK2 @ sK8 )
= $false )
| ~ spl5_3
| ~ spl5_5 ),
inference(trivial_inequality_removal,[status(thm)],[f228]) ).
thf(f228,plain,
( ( $false = $true )
| ( ( sK2 @ sK8 )
= $false )
| ( ( sK11 @ sK8 @ sK7 )
= $false )
| ~ spl5_3
| ~ spl5_5 ),
inference(superposition,[status(thm)],[f117,f108]) ).
thf(f131,plain,
( spl5_7
| spl5_8 ),
inference(avatar_split_clause,[status(thm)],[f73,f128,f123]) ).
thf(f73,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK2 @ sK8 )
= $true )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK2 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ( sK2 @ ( sK9 @ X1 ) )
=> ( ( X1 @ ( sK9 @ X1 ) @ sK7 )
& ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) ) ) )
= $false )
| ( $false
= ( ( sK2 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK2 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) )
| ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ( X1 @ Y0 @ sK7 )
& ( Y0 @ ( X1 @ Y0 ) ) ) )
@ ( sK9 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ( X1 @ Y0 @ sK7 )
& ( Y0 @ ( X1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( sK2 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK2 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) )
| ( ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( $false
= ( ( sK2 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK7 ) ) ) )
@ sK8 )
= $false )
| ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK7 ) ) ) ) ) )
| ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
!= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK7 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK2 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) )
@ sK7 )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) )
@ sK7 ) ),
inference(negative_extensionality,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK2 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X2: ( a > $o ) > $o] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X2 @ ( sK0 @ X0 @ X2 ) )
= $true ) )
| ( ! [X4: a > $o] :
( ( sK1 @ X0 @ X4 )
!= $true )
& ( ( X0 @ ( sK1 @ X0 ) )
= $true ) ) )
& ( ( sK2 @ sK3 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK2 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) ) )
& ! [X7: ( a > $o ) > $o] :
( ( $true
= ( X7 @ ( sK4 @ X7 ) ) )
| ( $true
!= ( sK2 @ X7 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X0: ( ( a > $o ) > $o ) > $o] :
( ? [X1: ( ( a > $o ) > $o ) > a > $o] :
! [X2: ( a > $o ) > $o] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X2 @ ( X1 @ X2 ) )
= $true ) )
=> ! [X2: ( a > $o ) > $o] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X2 @ ( sK0 @ X0 @ X2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: ( ( a > $o ) > $o ) > $o] :
( ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( $true
!= ( X3 @ X4 ) )
& ( ( X0 @ X3 )
= $true ) )
=> ( ! [X4: a > $o] :
( ( sK1 @ X0 @ X4 )
!= $true )
& ( ( X0 @ ( sK1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: ( ( a > $o ) > $o ) > $o] :
( ? [X6: ( a > $o ) > $o] :
( ( X5 @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X5 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X5 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ! [X7: ( a > $o ) > $o] :
( ? [X8: a > $o] :
( ( X7 @ X8 )
= $true )
| ( ( X5 @ X7 )
!= $true ) ) )
=> ( ? [X6: ( a > $o ) > $o] :
( ( sK2 @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK2 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) ) )
& ! [X7: ( a > $o ) > $o] :
( ? [X8: a > $o] :
( ( X7 @ X8 )
= $true )
| ( $true
!= ( sK2 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: ( a > $o ) > $o] :
( ( sK2 @ X6 )
= $true )
=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X7: ( a > $o ) > $o] :
( ? [X8: a > $o] :
( ( X7 @ X8 )
= $true )
=> ( $true
= ( X7 @ ( sK4 @ X7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ? [X1: ( ( a > $o ) > $o ) > a > $o] :
! [X2: ( a > $o ) > $o] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X2 @ ( X1 @ X2 ) )
= $true ) )
| ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( $true
!= ( X3 @ X4 ) )
& ( ( X0 @ X3 )
= $true ) ) )
& ? [X5: ( ( a > $o ) > $o ) > $o] :
( ? [X6: ( a > $o ) > $o] :
( ( X5 @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X5 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X5 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ! [X7: ( a > $o ) > $o] :
( ? [X8: a > $o] :
( ( X7 @ X8 )
= $true )
| ( ( X5 @ X7 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X4: ( a > $o ) > $o] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X4 @ ( X3 @ X4 ) )
= $true ) )
| ? [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X1 )
= $true ) ) )
& ? [X5: ( ( a > $o ) > $o ) > $o] :
( ? [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
= $true )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X5 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X5 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ! [X6: ( a > $o ) > $o] :
( ? [X7: a > $o] :
( $true
= ( X6 @ X7 ) )
| ( ( X5 @ X6 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X5: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X5 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X5 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ? [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
= $true )
& ! [X6: ( a > $o ) > $o] :
( ? [X7: a > $o] :
( $true
= ( X6 @ X7 ) )
| ( ( X5 @ X6 )
!= $true ) ) )
& ! [X0: ( ( a > $o ) > $o ) > $o] :
( ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X4: ( a > $o ) > $o] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X4 @ ( X3 @ X4 ) )
= $true ) )
| ? [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X1: ( a > $o ) > $o] :
( ( ( X0 @ X1 )
= $true )
=> ? [X2: a > $o] :
( ( X1 @ X2 )
= $true ) )
=> ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X4: ( a > $o ) > $o] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X4 @ ( X3 @ X4 ) )
= $true ) ) )
=> ! [X5: ( ( a > $o ) > $o ) > $o] :
( ( ? [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
= $true )
& ! [X6: ( a > $o ) > $o] :
( ( ( X5 @ X6 )
= $true )
=> ? [X7: a > $o] :
( $true
= ( X6 @ X7 ) ) ) )
=> ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X5 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X5 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ? [X2: a > $o] : ( X1 @ X2 ) )
=> ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X4: ( a > $o ) > $o] :
( ( X0 @ X4 )
=> ( X4 @ ( X3 @ X4 ) ) ) )
=> ! [X5: ( ( a > $o ) > $o ) > $o] :
( ( ! [X6: ( a > $o ) > $o] :
( ( X5 @ X6 )
=> ? [X7: a > $o] : ( X6 @ X7 ) )
& ? [X8: ( a > $o ) > $o] : ( X5 @ X8 ) )
=> ( ( ^ [X9: a] :
? [X10: ( ( a > $o ) > $o ) > a > $o] :
! [X11: ( a > $o ) > $o] :
( ( X5 @ X11 )
=> ( ( X11 @ ( X10 @ X11 ) )
& ( X10 @ X11 @ X9 ) ) ) )
= ( ^ [X12: a] :
! [X13: ( a > $o ) > $o] :
( ( X5 @ X13 )
=> ? [X14: a > $o] :
( ( X14 @ X12 )
& ( X13 @ X14 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ? [X2: a > $o] : ( X1 @ X2 ) )
=> ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ( X1 @ ( X3 @ X1 ) ) ) )
=> ! [X4: ( ( a > $o ) > $o ) > $o] :
( ( ! [X1: ( a > $o ) > $o] :
( ( X4 @ X1 )
=> ? [X5: a > $o] : ( X1 @ X5 ) )
& ? [X1: ( a > $o ) > $o] : ( X4 @ X1 ) )
=> ( ( ^ [X6: a] :
? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X7: ( a > $o ) > $o] :
( ( X4 @ X7 )
=> ( ( X7 @ ( X3 @ X7 ) )
& ( X3 @ X7 @ X6 ) ) ) )
= ( ^ [X6: a] :
! [X7: ( a > $o ) > $o] :
( ( X4 @ X7 )
=> ? [X8: a > $o] :
( ( X8 @ X6 )
& ( X7 @ X8 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ? [X2: a > $o] : ( X1 @ X2 ) )
=> ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ( X1 @ ( X3 @ X1 ) ) ) )
=> ! [X4: ( ( a > $o ) > $o ) > $o] :
( ( ! [X1: ( a > $o ) > $o] :
( ( X4 @ X1 )
=> ? [X5: a > $o] : ( X1 @ X5 ) )
& ? [X1: ( a > $o ) > $o] : ( X4 @ X1 ) )
=> ( ( ^ [X6: a] :
? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X7: ( a > $o ) > $o] :
( ( X4 @ X7 )
=> ( ( X7 @ ( X3 @ X7 ) )
& ( X3 @ X7 @ X6 ) ) ) )
= ( ^ [X6: a] :
! [X7: ( a > $o ) > $o] :
( ( X4 @ X7 )
=> ? [X8: a > $o] :
( ( X8 @ X6 )
& ( X7 @ X8 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pA5XUtVn1P/DTF2THF_13344.p',cTHM535) ).
thf(f130,plain,
( spl5_8
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f76,f116,f128]) ).
thf(f76,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK2 @ ( sK9 @ X1 ) ) )
| ( ( X2 @ sK7 )
= $false )
| ( ( sK8 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK2 @ ( sK9 @ X1 ) ) )
| ( ( ( sK8 @ X2 )
& ( X2 @ sK7 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK2 @ ( sK9 @ X1 ) ) )
| ( ( ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f126,plain,
( spl5_7
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f79,f119,f123]) ).
thf(f79,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK2 @ sK8 )
= $true )
| ( $false
= ( X1 @ ( sK9 @ X1 ) @ sK7 ) )
| ( ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK2 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) )
| ( ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( $false
= ( X1 @ ( sK9 @ X1 ) @ sK7 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ( X1 @ ( sK9 @ X1 ) @ sK7 )
& ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) ) )
= $false )
| ( $false
= ( ( sK2 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f121,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f82,f119,f116]) ).
thf(f82,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( X2 @ sK7 )
= $false )
| ( ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( ( sK8 @ X2 )
= $false )
| ( $false
= ( X1 @ ( sK9 @ X1 ) @ sK7 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ( sK8 @ X2 )
& ( X2 @ sK7 ) )
= $false )
| ( $false
= ( X1 @ ( sK9 @ X1 ) @ sK7 ) )
| ( ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( X1 @ ( sK9 @ X1 ) @ sK7 ) )
| ( ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( ( ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( X1 @ ( sK9 @ X1 ) @ sK7 ) )
| ( ( sK9 @ X1 @ ( X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK7 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f114,plain,
( spl5_4
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f96,f107,f111]) ).
thf(f96,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( X1 @ ( sK11 @ X1 ) )
= $true )
| ( ( sK2 @ X2 )
= $false )
| ( ( sK10 @ X2 @ sK7 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK2 @ X2 )
= $false )
| ( ( ( X1 @ ( sK11 @ X1 ) )
& ( sK11 @ X1 @ sK7 ) )
= $true )
| ( $false
= ( sK2 @ X1 ) )
| ( ( sK10 @ X2 @ sK7 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) )
= $true )
| ( ( ( X1 @ ( sK11 @ X1 ) )
& ( sK11 @ X1 @ sK7 ) )
= $true )
| ( ( sK2 @ X2 )
= $false )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK2 @ X2 )
= $false )
| ( $false
= ( sK2 @ X1 ) )
| ( ( ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK7 ) )
@ ( sK11 @ X1 ) )
= $true )
| ( ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK2 @ X2 )
= $false )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK7 ) ) )
= $true )
| ( $false
= ( sK2 @ X1 ) )
| ( ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ( sK2 @ X2 )
=> ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) ) ) )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK7 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) )
@ X2 )
= $true )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK7 ) ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: ( a > $o ) > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
= $true )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK7 ) ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: ( a > $o ) > $o] :
( ( ( ( sK2 @ X1 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK7 ) ) ) )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: ( a > $o ) > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK7 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK7 ) ) ) ) )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
@ sK10 )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK7 ) ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK2 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK2 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK7 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f113,plain,
( spl5_2
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f95,f111,f103]) ).
thf(f95,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK10 @ X2 @ sK7 )
= $true )
| ( $false
= ( sK2 @ X1 ) )
| ( ( sK11 @ X1 @ sK7 )
= $true )
| ( ( sK2 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f109,plain,
( spl5_3
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f98,f100,f107]) ).
thf(f98,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK2 @ X2 )
= $false )
| ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( $false
= ( sK2 @ X1 ) )
| ( ( X1 @ ( sK11 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( ( ( X1 @ ( sK11 @ X1 ) )
& ( sK11 @ X1 @ sK7 ) )
= $true )
| ( ( sK2 @ X2 )
= $false )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f105,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f97,f103,f100]) ).
thf(f97,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK11 @ X1 @ sK7 )
= $true )
| ( $false
= ( sK2 @ X1 ) )
| ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( ( sK2 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO246^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:27:35 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO246^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_1022 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 1.00 v6.1.0, 0.86 v5.5.0, 1.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 27 ( 0 ~; 0 |; 3 &; 16 @)
% 0.19/0.46 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.46 % Number of variables : 15 ( 2 ^; 7 !; 6 ?; 15 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM535,conjecture,
% 0.19/0.46 ( ! [Xs: ( ( a > $o ) > $o ) > $o] :
% 0.19/0.46 ( ! [X: ( a > $o ) > $o] :
% 0.19/0.46 ( ( Xs @ X )
% 0.19/0.46 => ? [Xt: a > $o] : ( X @ Xt ) )
% 0.19/0.46 => ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
% 0.19/0.46 ! [X: ( a > $o ) > $o] :
% 0.19/0.46 ( ( Xs @ X )
% 0.19/0.46 => ( X @ ( Xf @ X ) ) ) )
% 0.19/0.46 => ! [A: ( ( a > $o ) > $o ) > $o] :
% 0.19/0.46 ( ( ? [X: ( a > $o ) > $o] : ( A @ X )
% 0.19/0.46 & ! [X: ( a > $o ) > $o] :
% 0.19/0.46 ( ( A @ X )
% 0.19/0.46 => ? [Xu: a > $o] : ( X @ Xu ) ) )
% 0.19/0.46 => ( ( ^ [Xx: a] :
% 0.19/0.46 ! [Xa: ( a > $o ) > $o] :
% 0.19/0.46 ( ( A @ Xa )
% 0.19/0.46 => ? [Xb: a > $o] :
% 0.19/0.46 ( ( Xa @ Xb )
% 0.19/0.46 & ( Xb @ Xx ) ) ) )
% 0.19/0.46 = ( ^ [Xx: a] :
% 0.19/0.46 ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
% 0.19/0.46 ! [Xa: ( a > $o ) > $o] :
% 0.19/0.46 ( ( A @ Xa )
% 0.19/0.46 => ( ( Xa @ ( Xf @ Xa ) )
% 0.19/0.46 & ( Xf @ Xa @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.65/1.32 ---- Embedded in THF ---
% 1.65/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.32 %%% Generated on Tue Feb 24 14:27:36 EST 2026
% 1.65/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.32 %%% Logic specification used:
% 1.65/1.32 %%% thf(spec, logic, $$dhol).
% 1.65/1.32
% 1.65/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pA5XUtVn1P/DTF2DTF13344.p
% See solution above
% 1.65/1.33 ------------------------
% 1.65/1.34 ---- Cleaned THF ---
% 1.65/1.34 thf(a_type,type,
% 1.65/1.34 a: $tType ).
% 1.65/1.34
% 1.65/1.34 thf(cTHM535,conjecture,
% 1.65/1.34 ( ! [Xs: ( ( a > $o ) > $o ) > $o] :
% 1.65/1.34 ( ! [X: ( a > $o ) > $o] :
% 1.65/1.34 ( ( Xs @ X )
% 1.65/1.34 => ? [Xt: a > $o] : ( X @ Xt ) )
% 1.65/1.34 => ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
% 1.65/1.34 ! [X: ( a > $o ) > $o] :
% 1.65/1.34 ( ( Xs @ X )
% 1.65/1.34 => ( X @ ( Xf @ X ) ) ) )
% 1.65/1.34 => ! [A: ( ( a > $o ) > $o ) > $o] :
% 1.65/1.34 ( ( ? [X: ( a > $o ) > $o] : ( A @ X )
% 1.65/1.34 & ! [X: ( a > $o ) > $o] :
% 1.65/1.34 ( ( A @ X )
% 1.65/1.34 => ? [Xu: a > $o] : ( X @ Xu ) ) )
% 1.65/1.34 => ( ( ^ [Xx: a] :
% 1.65/1.34 ! [Xa: ( a > $o ) > $o] :
% 1.65/1.34 ( ( A @ Xa )
% 1.65/1.34 => ? [Xb: a > $o] :
% 1.65/1.34 ( ( Xa @ Xb )
% 1.65/1.34 & ( Xb @ Xx ) ) ) )
% 1.65/1.34 = ( ^ [Xx: a] :
% 1.65/1.34 ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
% 1.65/1.34 ! [Xa: ( a > $o ) > $o] :
% 1.65/1.34 ( ( A @ Xa )
% 1.65/1.34 => ( ( Xa @ ( Xf @ Xa ) )
% 1.65/1.34 & ( Xf @ Xa @ Xx ) ) ) ) ) ) ) ).
% 1.65/1.34 ------------------------
% 1.65/1.36 % (13526)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/18Mi)
% 1.65/1.36 % (13520)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/183Mi)
% 1.65/1.36 % (13522)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_13344 for (2999ds/27Mi)
% 1.65/1.36 % (13523)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/2Mi)
% 1.65/1.36 % (13524)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_13344 for (2999ds/2Mi)
% 1.65/1.36 % (13525)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_13344 for (2999ds/275Mi)
% 1.65/1.36 % (13523)Instruction limit reached!
% 1.65/1.36 % (13523)------------------------------
% 1.65/1.36 % (13523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (13523)Termination reason: Unknown
% 1.65/1.36 % (13523)Termination phase: Property scanning
% 1.65/1.36
% 1.65/1.36 % (13524)Instruction limit reached!
% 1.65/1.36 % (13524)------------------------------
% 1.65/1.36 % (13524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (13524)Termination reason: Unknown
% 1.65/1.36 % (13524)Termination phase: Saturation
% 1.65/1.36
% 1.65/1.36 % (13524)Memory used [KB]: 895
% 1.65/1.36 % (13524)Time elapsed: 0.003 s
% 1.65/1.36 % (13524)Instructions burned: 2 (million)
% 1.65/1.36 % (13524)------------------------------
% 1.65/1.36 % (13524)------------------------------
% 1.65/1.36 % (13523)Memory used [KB]: 1023
% 1.65/1.36 % (13523)Time elapsed: 0.003 s
% 1.65/1.36 % (13523)Instructions burned: 2 (million)
% 1.65/1.36 % (13523)------------------------------
% 1.65/1.36 % (13523)------------------------------
% 1.65/1.37 % (13521)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_13344 for (2999ds/4Mi)
% 1.65/1.37 % (13526)Instruction limit reached!
% 1.65/1.37 % (13526)------------------------------
% 1.65/1.37 % (13526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (13526)Termination reason: Unknown
% 1.65/1.37 % (13526)Termination phase: Saturation
% 1.65/1.37
% 1.65/1.37 % (13526)Memory used [KB]: 5628
% 1.65/1.37 % (13526)Time elapsed: 0.008 s
% 1.65/1.37 % (13526)Instructions burned: 18 (million)
% 1.65/1.37 % (13526)------------------------------
% 1.65/1.37 % (13526)------------------------------
% 1.65/1.37 % (13521)Instruction limit reached!
% 1.65/1.37 % (13521)------------------------------
% 1.65/1.37 % (13521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (13521)Termination reason: Unknown
% 1.65/1.37 % (13521)Termination phase: Saturation
% 1.65/1.37
% 1.65/1.37 % (13521)Memory used [KB]: 5500
% 1.65/1.37 % (13521)Time elapsed: 0.005 s
% 1.65/1.37 % (13521)Instructions burned: 5 (million)
% 1.65/1.37 % (13521)------------------------------
% 1.65/1.37 % (13521)------------------------------
% 1.65/1.38 % (13529)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/3Mi)
% 1.65/1.38 % (13529)Instruction limit reached!
% 1.65/1.38 % (13529)------------------------------
% 1.65/1.38 % (13529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (13529)Termination reason: Unknown
% 1.65/1.38 % (13529)Termination phase: Saturation
% 1.65/1.38
% 1.65/1.38 % (13529)Memory used [KB]: 5500
% 1.65/1.38 % (13529)Time elapsed: 0.002 s
% 1.65/1.38 % (13529)Instructions burned: 3 (million)
% 1.65/1.38 % (13529)------------------------------
% 1.65/1.38 % (13529)------------------------------
% 1.65/1.38 % (13522)Instruction limit reached!
% 1.65/1.38 % (13522)------------------------------
% 1.65/1.38 % (13522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (13522)Termination reason: Unknown
% 1.65/1.38 % (13522)Termination phase: Saturation
% 1.65/1.38
% 1.65/1.38 % (13522)Memory used [KB]: 5628
% 1.65/1.38 % (13522)Time elapsed: 0.018 s
% 1.65/1.38 % (13522)Instructions burned: 27 (million)
% 1.65/1.38 % (13522)------------------------------
% 1.65/1.38 % (13522)------------------------------
% 1.65/1.38 % (13530)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_13344 for (2999ds/37Mi)
% 1.65/1.38 % (13531)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_13344 for (2999ds/15Mi)
% 1.65/1.39 % (13533)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_13344 for (2999ds/1041Mi)
% 1.65/1.39 % (13532)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_13344 for (2999ds/3Mi)
% 1.65/1.39 % (13532)Instruction limit reached!
% 1.65/1.39 % (13532)------------------------------
% 1.65/1.39 % (13532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (13532)Termination reason: Unknown
% 1.65/1.39 % (13532)Termination phase: Saturation
% 1.65/1.39
% 1.65/1.39 % (13532)Memory used [KB]: 5500
% 1.65/1.39 % (13532)Time elapsed: 0.004 s
% 1.65/1.39 % (13532)Instructions burned: 4 (million)
% 1.65/1.39 % (13532)------------------------------
% 1.65/1.39 % (13532)------------------------------
% 1.65/1.39 % (13531)Instruction limit reached!
% 1.65/1.39 % (13531)------------------------------
% 1.65/1.39 % (13531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (13531)Termination reason: Unknown
% 1.65/1.39 % (13531)Termination phase: Saturation
% 1.65/1.39
% 1.65/1.39 % (13531)Memory used [KB]: 5628
% 1.65/1.39 % (13531)Time elapsed: 0.010 s
% 1.65/1.39 % (13531)Instructions burned: 16 (million)
% 1.65/1.39 % (13531)------------------------------
% 1.65/1.39 % (13531)------------------------------
% 1.65/1.40 % (13534)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/7Mi)
% 1.72/1.40 % (13530)Instruction limit reached!
% 1.72/1.40 % (13530)------------------------------
% 1.72/1.40 % (13530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (13530)Termination reason: Unknown
% 1.72/1.40 % (13530)Termination phase: Saturation
% 1.72/1.40
% 1.72/1.40 % (13530)Memory used [KB]: 5884
% 1.72/1.40 % (13530)Time elapsed: 0.021 s
% 1.72/1.40 % (13530)Instructions burned: 37 (million)
% 1.72/1.40 % (13530)------------------------------
% 1.72/1.40 % (13530)------------------------------
% 1.72/1.40 % (13534)Instruction limit reached!
% 1.72/1.40 % (13534)------------------------------
% 1.72/1.40 % (13534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (13534)Termination reason: Unknown
% 1.72/1.40 % (13534)Termination phase: Saturation
% 1.72/1.40
% 1.72/1.40 % (13534)Memory used [KB]: 1023
% 1.72/1.40 % (13534)Time elapsed: 0.006 s
% 1.72/1.40 % (13534)Instructions burned: 8 (million)
% 1.72/1.40 % (13534)------------------------------
% 1.72/1.40 % (13534)------------------------------
% 1.72/1.41 % (13537)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_13344 for (2999ds/3Mi)
% 1.72/1.41 % (13537)Instruction limit reached!
% 1.72/1.41 % (13537)------------------------------
% 1.72/1.41 % (13537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (13537)Termination reason: Unknown
% 1.72/1.41 % (13537)Termination phase: Twee Goal Transformation
% 1.72/1.41
% 1.72/1.41 % (13537)Memory used [KB]: 1023
% 1.72/1.41 % (13537)Time elapsed: 0.003 s
% 1.72/1.41 % (13537)Instructions burned: 3 (million)
% 1.72/1.41 % (13537)------------------------------
% 1.72/1.41 % (13537)------------------------------
% 1.72/1.41 % (13536)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/16Mi)
% 1.72/1.42 % (13539)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_13344 for (2999ds/3Mi)
% 1.72/1.42 % (13539)Instruction limit reached!
% 1.72/1.42 % (13539)------------------------------
% 1.72/1.42 % (13539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (13539)Termination reason: Unknown
% 1.72/1.42 % (13539)Termination phase: Property scanning
% 1.72/1.42
% 1.72/1.42 % (13539)Memory used [KB]: 1023
% 1.72/1.42 % (13539)Time elapsed: 0.003 s
% 1.72/1.42 % (13539)Instructions burned: 3 (million)
% 1.72/1.42 % (13539)------------------------------
% 1.72/1.42 % (13539)------------------------------
% 1.72/1.42 % (13536)Instruction limit reached!
% 1.72/1.42 % (13536)------------------------------
% 1.72/1.42 % (13536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (13536)Termination reason: Unknown
% 1.72/1.42 % (13536)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (13536)Memory used [KB]: 5756
% 1.72/1.42 % (13536)Time elapsed: 0.011 s
% 1.72/1.42 % (13536)Instructions burned: 16 (million)
% 1.72/1.42 % (13536)------------------------------
% 1.72/1.42 % (13536)------------------------------
% 1.72/1.43 % (13541)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/3Mi)
% 1.72/1.43 % (13541)Instruction limit reached!
% 1.72/1.43 % (13541)------------------------------
% 1.72/1.43 % (13541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (13541)Termination reason: Unknown
% 1.72/1.43 % (13541)Termination phase: Saturation
% 1.72/1.43
% 1.72/1.43 % (13541)Memory used [KB]: 5500
% 1.72/1.43 % (13541)Time elapsed: 0.003 s
% 1.72/1.43 % (13541)Instructions burned: 3 (million)
% 1.72/1.43 % (13541)------------------------------
% 1.72/1.43 % (13541)------------------------------
% 1.72/1.43 % (13540)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/7Mi)
% 1.72/1.44 % (13543)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/18Mi)
% 1.72/1.44 % (13540)Instruction limit reached!
% 1.72/1.44 % (13540)------------------------------
% 1.72/1.44 % (13540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (13540)Termination reason: Unknown
% 1.72/1.44 % (13540)Termination phase: Saturation
% 1.72/1.44
% 1.72/1.44 % (13540)Memory used [KB]: 5500
% 1.72/1.44 % (13540)Time elapsed: 0.006 s
% 1.72/1.44 % (13540)Instructions burned: 7 (million)
% 1.72/1.44 % (13540)------------------------------
% 1.72/1.44 % (13540)------------------------------
% 1.72/1.44 % (13542)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/4Mi)
% 1.72/1.44 % (13542)Instruction limit reached!
% 1.72/1.44 % (13542)------------------------------
% 1.72/1.44 % (13542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (13542)Termination reason: Unknown
% 1.72/1.44 % (13542)Termination phase: Saturation
% 1.72/1.44
% 1.72/1.44 % (13542)Memory used [KB]: 5500
% 1.72/1.44 % (13542)Time elapsed: 0.004 s
% 1.72/1.44 % (13542)Instructions burned: 4 (million)
% 1.72/1.44 % (13542)------------------------------
% 1.72/1.44 % (13542)------------------------------
% 1.72/1.45 % (13543)Instruction limit reached!
% 1.72/1.45 % (13543)------------------------------
% 1.72/1.45 % (13543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (13543)Termination reason: Unknown
% 1.72/1.45 % (13543)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (13543)Memory used [KB]: 5628
% 1.72/1.45 % (13543)Time elapsed: 0.011 s
% 1.72/1.45 % (13543)Instructions burned: 19 (million)
% 1.72/1.45 % (13543)------------------------------
% 1.72/1.45 % (13543)------------------------------
% 1.72/1.45 % (13545)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/710Mi)
% 1.72/1.45 % (13520)Instruction limit reached!
% 1.72/1.45 % (13520)------------------------------
% 1.72/1.45 % (13520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (13520)Termination reason: Unknown
% 1.72/1.45 % (13520)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (13520)Memory used [KB]: 6780
% 1.72/1.45 % (13520)Time elapsed: 0.091 s
% 1.72/1.45 % (13520)Instructions burned: 183 (million)
% 1.72/1.45 % (13520)------------------------------
% 1.72/1.45 % (13520)------------------------------
% 1.72/1.45 % (13525)First to succeed.
% 1.72/1.46 % (13546)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13344 for (2999ds/6Mi)
% 1.72/1.46 % (13525)Refutation found. Thanks to Tanya!
% 1.72/1.46 % SZS status Theorem for DTF2THF_13344
% 1.72/1.46 % SZS output start Proof for DTF2THF_13344
% 1.72/1.46 thf(type_def_5, type, a: $tType).
% 1.72/1.46 thf(func_def_0, type, a: $tType).
% 1.72/1.46 thf(func_def_12, type, sK0: (((a > $o) > $o) > $o) > ((a > $o) > $o) > a > $o).
% 1.72/1.46 thf(func_def_13, type, sK1: (((a > $o) > $o) > $o) > (a > $o) > $o).
% 1.72/1.46 thf(func_def_14, type, sK2: ((a > $o) > $o) > $o).
% 1.72/1.46 thf(func_def_15, type, sK3: (a > $o) > $o).
% 1.72/1.46 thf(func_def_16, type, sK4: ((a > $o) > $o) > a > $o).
% 1.72/1.46 thf(func_def_18, type, ph6: !>[X0: $tType]:(X0)).
% 1.72/1.46 thf(func_def_21, type, sK7: a).
% 1.72/1.46 thf(func_def_22, type, sK8: (a > $o) > $o).
% 1.72/1.46 thf(func_def_23, type, sK9: (((a > $o) > $o) > a > $o) > (a > $o) > $o).
% 1.72/1.46 thf(func_def_24, type, sK10: ((a > $o) > $o) > a > $o).
% 1.72/1.46 thf(func_def_25, type, sK11: ((a > $o) > $o) > a > $o).
% 1.72/1.46 thf(func_def_26, type, sK12: a > $o).
% 1.72/1.46 thf(func_def_27, type, sK13: a > $o).
% 1.72/1.46 thf(f1023,plain,(
% 1.72/1.46 $false),
% 1.72/1.46 inference(avatar_sat_refutation,[status(thm)],[f105,f109,f113,f114,f121,f126,f130,f131,f325,f874,f980,f1022])).
% 1.72/1.46 thf(f1022,plain,(
% 1.72/1.46 ~spl5_1 | ~spl5_4 | ~spl5_5 | ~spl5_7),
% 1.72/1.46 inference(avatar_contradiction_clause,[status(thm)],[f1021])).
% 1.72/1.46 thf(f1021,plain,(
% 1.72/1.46 $false | (~spl5_1 | ~spl5_4 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f1017])).
% 1.72/1.46 thf(f1017,plain,(
% 1.72/1.46 ($false = $true) | (~spl5_1 | ~spl5_4 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(superposition,[status(thm)],[f1016,f125])).
% 1.72/1.46 thf(f125,plain,(
% 1.72/1.46 ((sK2 @ sK8) = $true) | ~spl5_7),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f123])).
% 1.72/1.46 thf(f123,definition,(
% 1.72/1.46 spl5_7 <=> ((sK2 @ sK8) = $true)),
% 1.72/1.46 introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition])).
% 1.72/1.46 thf(f1016,plain,(
% 1.72/1.46 ((sK2 @ sK8) = $false) | (~spl5_1 | ~spl5_4 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f1013])).
% 1.72/1.46 thf(f1013,plain,(
% 1.72/1.46 ($false = $true) | ((sK2 @ sK8) = $false) | (~spl5_1 | ~spl5_4 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(superposition,[status(thm)],[f1011,f112])).
% 1.72/1.46 thf(f112,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o] : (((sK10 @ X2 @ sK7) = $true) | ((sK2 @ X2) = $false)) ) | ~spl5_4),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f111])).
% 1.72/1.46 thf(f111,definition,(
% 1.72/1.46 spl5_4 <=> ! [X2 : (a > $o) > $o] : (((sK10 @ X2 @ sK7) = $true) | ((sK2 @ X2) = $false))),
% 1.72/1.46 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.72/1.46 thf(f1011,plain,(
% 1.72/1.46 ((sK10 @ sK8 @ sK7) = $false) | (~spl5_1 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f1010])).
% 1.72/1.46 thf(f1010,plain,(
% 1.72/1.46 ($false = $true) | ((sK10 @ sK8 @ sK7) = $false) | (~spl5_1 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(forward_demodulation,[status(thm)],[f1007,f125])).
% 1.72/1.46 thf(f1007,plain,(
% 1.72/1.46 ((sK2 @ sK8) = $false) | ((sK10 @ sK8 @ sK7) = $false) | (~spl5_1 | ~spl5_5)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f987])).
% 1.72/1.46 thf(f987,plain,(
% 1.72/1.46 ((sK10 @ sK8 @ sK7) = $false) | ($false = $true) | ((sK2 @ sK8) = $false) | (~spl5_1 | ~spl5_5)),
% 1.72/1.46 inference(superposition,[status(thm)],[f117,f101])).
% 1.72/1.46 thf(f101,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o] : (((X2 @ (sK10 @ X2)) = $true) | ((sK2 @ X2) = $false)) ) | ~spl5_1),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.72/1.46 thf(f100,definition,(
% 1.72/1.46 spl5_1 <=> ! [X2 : (a > $o) > $o] : (((X2 @ (sK10 @ X2)) = $true) | ((sK2 @ X2) = $false))),
% 1.72/1.46 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.72/1.46 thf(f117,plain,(
% 1.72/1.46 ( ! [X2 : a > $o] : (((sK8 @ X2) = $false) | ((X2 @ sK7) = $false)) ) | ~spl5_5),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.72/1.46 thf(f116,definition,(
% 1.72/1.46 spl5_5 <=> ! [X2 : a > $o] : (((X2 @ sK7) = $false) | ((sK8 @ X2) = $false))),
% 1.72/1.46 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.72/1.46 thf(f980,plain,(
% 1.72/1.46 ~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_8),
% 1.72/1.46 inference(avatar_contradiction_clause,[status(thm)],[f979])).
% 1.72/1.46 thf(f979,plain,(
% 1.72/1.46 $false | (~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f975])).
% 1.72/1.46 thf(f975,plain,(
% 1.72/1.46 ($false = $true) | (~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(superposition,[status(thm)],[f970,f129])).
% 1.72/1.46 thf(f129,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($true = (sK2 @ (sK9 @ X1)))) ) | ~spl5_8),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f128])).
% 1.72/1.46 thf(f128,definition,(
% 1.72/1.46 spl5_8 <=> ! [X1 : ((a > $o) > $o) > a > $o] : ($true = (sK2 @ (sK9 @ X1)))),
% 1.72/1.46 introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition])).
% 1.72/1.46 thf(f970,plain,(
% 1.72/1.46 ((sK2 @ (sK9 @ sK10)) = $false) | (~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f968])).
% 1.72/1.46 thf(f968,plain,(
% 1.72/1.46 ($false = $true) | ((sK2 @ (sK9 @ sK10)) = $false) | (~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(superposition,[status(thm)],[f112,f910])).
% 1.72/1.46 thf(f910,plain,(
% 1.72/1.46 ($false = (sK10 @ (sK9 @ sK10) @ sK7)) | (~spl5_1 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f909])).
% 1.72/1.46 thf(f909,plain,(
% 1.72/1.46 ($false = (sK10 @ (sK9 @ sK10) @ sK7)) | ($false = $true) | (~spl5_1 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(forward_demodulation,[status(thm)],[f907,f129])).
% 1.72/1.46 thf(f907,plain,(
% 1.72/1.46 ((sK2 @ (sK9 @ sK10)) = $false) | ($false = (sK10 @ (sK9 @ sK10) @ sK7)) | (~spl5_1 | ~spl5_6)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f882])).
% 1.72/1.46 thf(f882,plain,(
% 1.72/1.46 ((sK2 @ (sK9 @ sK10)) = $false) | ($false = $true) | ($false = (sK10 @ (sK9 @ sK10) @ sK7)) | (~spl5_1 | ~spl5_6)),
% 1.72/1.46 inference(superposition,[status(thm)],[f101,f120])).
% 1.72/1.46 thf(f120,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (((sK9 @ X1 @ (X1 @ (sK9 @ X1))) = $false) | ($false = (X1 @ (sK9 @ X1) @ sK7))) ) | ~spl5_6),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f119])).
% 1.72/1.46 thf(f119,definition,(
% 1.72/1.46 spl5_6 <=> ! [X1 : ((a > $o) > $o) > a > $o] : (((sK9 @ X1 @ (X1 @ (sK9 @ X1))) = $false) | ($false = (X1 @ (sK9 @ X1) @ sK7)))),
% 1.72/1.46 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 1.72/1.46 thf(f874,plain,(
% 1.72/1.46 ~spl5_2 | ~spl5_3 | ~spl5_6 | ~spl5_8),
% 1.72/1.46 inference(avatar_contradiction_clause,[status(thm)],[f873])).
% 1.72/1.46 thf(f873,plain,(
% 1.72/1.46 $false | (~spl5_2 | ~spl5_3 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f870])).
% 1.72/1.46 thf(f870,plain,(
% 1.72/1.46 ($false = $true) | (~spl5_2 | ~spl5_3 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(superposition,[status(thm)],[f129,f840])).
% 1.72/1.46 thf(f840,plain,(
% 1.72/1.46 ((sK2 @ (sK9 @ sK11)) = $false) | (~spl5_2 | ~spl5_3 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f838])).
% 1.72/1.46 thf(f838,plain,(
% 1.72/1.46 ($false = $true) | ((sK2 @ (sK9 @ sK11)) = $false) | (~spl5_2 | ~spl5_3 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(superposition,[status(thm)],[f104,f724])).
% 1.72/1.46 thf(f724,plain,(
% 1.72/1.46 ((sK11 @ (sK9 @ sK11) @ sK7) = $false) | (~spl5_3 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f723])).
% 1.72/1.46 thf(f723,plain,(
% 1.72/1.46 ($false = $true) | ((sK11 @ (sK9 @ sK11) @ sK7) = $false) | (~spl5_3 | ~spl5_6 | ~spl5_8)),
% 1.72/1.46 inference(forward_demodulation,[status(thm)],[f722,f129])).
% 1.72/1.46 thf(f722,plain,(
% 1.72/1.46 ((sK11 @ (sK9 @ sK11) @ sK7) = $false) | ((sK2 @ (sK9 @ sK11)) = $false) | (~spl5_3 | ~spl5_6)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f714])).
% 1.72/1.46 thf(f714,plain,(
% 1.72/1.46 ($false = $true) | ((sK2 @ (sK9 @ sK11)) = $false) | ((sK11 @ (sK9 @ sK11) @ sK7) = $false) | (~spl5_3 | ~spl5_6)),
% 1.72/1.46 inference(superposition,[status(thm)],[f108,f120])).
% 1.72/1.46 thf(f108,plain,(
% 1.72/1.46 ( ! [X1 : (a > $o) > $o] : (((X1 @ (sK11 @ X1)) = $true) | ($false = (sK2 @ X1))) ) | ~spl5_3),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.72/1.46 thf(f107,definition,(
% 1.72/1.46 spl5_3 <=> ! [X1 : (a > $o) > $o] : (($false = (sK2 @ X1)) | ((X1 @ (sK11 @ X1)) = $true))),
% 1.72/1.46 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.72/1.46 thf(f104,plain,(
% 1.72/1.46 ( ! [X1 : (a > $o) > $o] : (((sK11 @ X1 @ sK7) = $true) | ($false = (sK2 @ X1))) ) | ~spl5_2),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.72/1.46 thf(f103,definition,(
% 1.72/1.46 spl5_2 <=> ! [X1 : (a > $o) > $o] : (((sK11 @ X1 @ sK7) = $true) | ($false = (sK2 @ X1)))),
% 1.72/1.46 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.72/1.46 thf(f325,plain,(
% 1.72/1.46 ~spl5_2 | ~spl5_3 | ~spl5_5 | ~spl5_7),
% 1.72/1.46 inference(avatar_contradiction_clause,[status(thm)],[f324])).
% 1.72/1.46 thf(f324,plain,(
% 1.72/1.46 $false | (~spl5_2 | ~spl5_3 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f320])).
% 1.72/1.46 thf(f320,plain,(
% 1.72/1.46 ($false = $true) | (~spl5_2 | ~spl5_3 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(superposition,[status(thm)],[f304,f125])).
% 1.72/1.46 thf(f304,plain,(
% 1.72/1.46 ((sK2 @ sK8) = $false) | (~spl5_2 | ~spl5_3 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f301])).
% 1.72/1.46 thf(f301,plain,(
% 1.72/1.46 ((sK2 @ sK8) = $false) | ($false = $true) | (~spl5_2 | ~spl5_3 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(superposition,[status(thm)],[f238,f104])).
% 1.72/1.46 thf(f238,plain,(
% 1.72/1.46 ((sK11 @ sK8 @ sK7) = $false) | (~spl5_3 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f237])).
% 1.72/1.46 thf(f237,plain,(
% 1.72/1.46 ((sK11 @ sK8 @ sK7) = $false) | ($false = $true) | (~spl5_3 | ~spl5_5 | ~spl5_7)),
% 1.72/1.46 inference(forward_demodulation,[status(thm)],[f233,f125])).
% 1.72/1.46 thf(f233,plain,(
% 1.72/1.46 ((sK11 @ sK8 @ sK7) = $false) | ((sK2 @ sK8) = $false) | (~spl5_3 | ~spl5_5)),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f228])).
% 1.72/1.46 thf(f228,plain,(
% 1.72/1.46 ($false = $true) | ((sK2 @ sK8) = $false) | ((sK11 @ sK8 @ sK7) = $false) | (~spl5_3 | ~spl5_5)),
% 1.72/1.46 inference(superposition,[status(thm)],[f117,f108])).
% 1.72/1.46 thf(f131,plain,(
% 1.72/1.46 spl5_7 | spl5_8),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f73,f128,f123])).
% 1.72/1.46 thf(f73,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (((sK2 @ sK8) = $true) | ($true = (sK2 @ (sK9 @ X1)))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.72/1.46 thf(f71,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = ((sK2 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7)))))) | ($true = (sK2 @ (sK9 @ X1)))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.72/1.46 thf(f69,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : ((((sK2 @ (sK9 @ X1)) => ((X1 @ (sK9 @ X1) @ sK7) & (sK9 @ X1 @ (X1 @ (sK9 @ X1))))) = $false) | ($false = ((sK2 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7))))))) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.72/1.46 thf(f68,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = ((sK2 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7)))))) | (((^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => ((X1 @ Y0 @ sK7) & (Y0 @ (X1 @ Y0))))) @ (sK9 @ X1)) = $false)) )),
% 1.72/1.46 inference(sigma_clausification,[status(thm)],[f67])).
% 1.72/1.46 thf(f67,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => ((X1 @ Y0 @ sK7) & (Y0 @ (X1 @ Y0))))))) | ($false = ((sK2 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7))))))) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.72/1.46 thf(f66,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = ((sK2 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7)))))) | (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => ((Y0 @ Y1 @ sK7) & (Y1 @ (Y0 @ Y1))))))) @ X1) = $false)) )),
% 1.72/1.46 inference(pi_clausification,[status(thm)],[f65])).
% 1.72/1.46 thf(f65,plain,(
% 1.72/1.46 ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => ((Y0 @ Y1 @ sK7) & (Y1 @ (Y0 @ Y1)))))))) = $false) | ($false = ((sK2 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7))))))),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.72/1.46 thf(f64,plain,(
% 1.72/1.46 (((^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK7)))))) @ sK8) = $false) | ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => ((Y0 @ Y1 @ sK7) & (Y1 @ (Y0 @ Y1)))))))) = $false)),
% 1.72/1.46 inference(sigma_clausification,[status(thm)],[f63])).
% 1.72/1.46 thf(f63,plain,(
% 1.72/1.46 ($false = (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK7)))))))) | ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => ((Y0 @ Y1 @ sK7) & (Y1 @ (Y0 @ Y1)))))))) = $false)),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.72/1.46 thf(f61,plain,(
% 1.72/1.46 ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => ((Y0 @ Y1 @ sK7) & (Y1 @ (Y0 @ Y1)))))))) != (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK7))))))))),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.72/1.46 thf(f60,plain,(
% 1.72/1.46 (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK2 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2))))))))) @ sK7) != ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) @ sK7))),
% 1.72/1.46 inference(negative_extensionality,[status(thm)],[f16])).
% 1.72/1.46 thf(f16,plain,(
% 1.72/1.46 ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK2 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2))))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))))),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f14])).
% 1.72/1.46 thf(f14,plain,(
% 1.72/1.46 ! [X0 : ((a > $o) > $o) > $o] : (! [X2 : (a > $o) > $o] : (((X0 @ X2) != $true) | ((X2 @ (sK0 @ X0 @ X2)) = $true)) | (! [X4 : a > $o] : ((sK1 @ X0 @ X4) != $true) & ((X0 @ (sK1 @ X0)) = $true))) & (((sK2 @ sK3) = $true) & ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK2 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2))))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0))))))))) & ! [X7 : (a > $o) > $o] : (($true = (X7 @ (sK4 @ X7))) | ($true != (sK2 @ X7))))),
% 1.72/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f13,f12,f11,f10,f9])).
% 1.72/1.46 thf(f9,plain,(
% 1.72/1.46 ! [X0 : ((a > $o) > $o) > $o] : (? [X1 : ((a > $o) > $o) > a > $o] : ! [X2 : (a > $o) > $o] : (((X0 @ X2) != $true) | ((X2 @ (X1 @ X2)) = $true)) => ! [X2 : (a > $o) > $o] : (((X0 @ X2) != $true) | ((X2 @ (sK0 @ X0 @ X2)) = $true)))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f10,plain,(
% 1.72/1.46 ! [X0 : ((a > $o) > $o) > $o] : (? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : ($true != (X3 @ X4)) & ((X0 @ X3) = $true)) => (! [X4 : a > $o] : ((sK1 @ X0 @ X4) != $true) & ((X0 @ (sK1 @ X0)) = $true)))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f11,plain,(
% 1.72/1.46 ? [X5 : ((a > $o) > $o) > $o] : (? [X6 : (a > $o) > $o] : ((X5 @ X6) = $true) & ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2)))))))))) & ! [X7 : (a > $o) > $o] : (? [X8 : a > $o] : ((X7 @ X8) = $true) | ((X5 @ X7) != $true))) => (? [X6 : (a > $o) > $o] : ((sK2 @ X6) = $true) & ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK2 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2))))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0))))))))) & ! [X7 : (a > $o) > $o] : (? [X8 : a > $o] : ((X7 @ X8) = $true) | ($true != (sK2 @ X7))))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f12,plain,(
% 1.72/1.46 ? [X6 : (a > $o) > $o] : ((sK2 @ X6) = $true) => ((sK2 @ sK3) = $true)),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f13,plain,(
% 1.72/1.46 ! [X7 : (a > $o) > $o] : (? [X8 : a > $o] : ((X7 @ X8) = $true) => ($true = (X7 @ (sK4 @ X7))))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f8,plain,(
% 1.72/1.46 ! [X0 : ((a > $o) > $o) > $o] : (? [X1 : ((a > $o) > $o) > a > $o] : ! [X2 : (a > $o) > $o] : (((X0 @ X2) != $true) | ((X2 @ (X1 @ X2)) = $true)) | ? [X3 : (a > $o) > $o] : (! [X4 : a > $o] : ($true != (X3 @ X4)) & ((X0 @ X3) = $true))) & ? [X5 : ((a > $o) > $o) > $o] : (? [X6 : (a > $o) > $o] : ((X5 @ X6) = $true) & ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2)))))))))) & ! [X7 : (a > $o) > $o] : (? [X8 : a > $o] : ((X7 @ X8) = $true) | ((X5 @ X7) != $true)))),
% 1.72/1.46 inference(rectify,[status(thm)],[f7])).
% 1.72/1.46 thf(f7,plain,(
% 1.72/1.46 ! [X0 : ((a > $o) > $o) > $o] : (? [X3 : ((a > $o) > $o) > a > $o] : ! [X4 : (a > $o) > $o] : (((X0 @ X4) != $true) | ((X4 @ (X3 @ X4)) = $true)) | ? [X1 : (a > $o) > $o] : (! [X2 : a > $o] : ((X1 @ X2) != $true) & ((X0 @ X1) = $true))) & ? [X5 : ((a > $o) > $o) > $o] : (? [X8 : (a > $o) > $o] : ((X5 @ X8) = $true) & ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2)))))))))) & ! [X6 : (a > $o) > $o] : (? [X7 : a > $o] : ($true = (X6 @ X7)) | ((X5 @ X6) != $true)))),
% 1.72/1.46 inference(flattening,[status(thm)],[f6])).
% 1.72/1.46 thf(f6,plain,(
% 1.72/1.46 ? [X5 : ((a > $o) > $o) > $o] : (((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2)))))))))) & (? [X8 : (a > $o) > $o] : ((X5 @ X8) = $true) & ! [X6 : (a > $o) > $o] : (? [X7 : a > $o] : ($true = (X6 @ X7)) | ((X5 @ X6) != $true)))) & ! [X0 : ((a > $o) > $o) > $o] : (? [X3 : ((a > $o) > $o) > a > $o] : ! [X4 : (a > $o) > $o] : (((X0 @ X4) != $true) | ((X4 @ (X3 @ X4)) = $true)) | ? [X1 : (a > $o) > $o] : (! [X2 : a > $o] : ((X1 @ X2) != $true) & ((X0 @ X1) = $true)))),
% 1.72/1.46 inference(ennf_transformation,[status(thm)],[f5])).
% 1.72/1.46 thf(f5,plain,(
% 1.72/1.46 ~(! [X0 : ((a > $o) > $o) > $o] : (! [X1 : (a > $o) > $o] : (((X0 @ X1) = $true) => ? [X2 : a > $o] : ((X1 @ X2) = $true)) => ? [X3 : ((a > $o) > $o) > a > $o] : ! [X4 : (a > $o) > $o] : (((X0 @ X4) = $true) => ((X4 @ (X3 @ X4)) = $true))) => ! [X5 : ((a > $o) > $o) > $o] : ((? [X8 : (a > $o) > $o] : ((X5 @ X8) = $true) & ! [X6 : (a > $o) > $o] : (((X5 @ X6) = $true) => ? [X7 : a > $o] : ($true = (X6 @ X7)))) => ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X5 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) = (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X5 @ Y2) => ((Y1 @ Y2 @ Y0) & (Y2 @ (Y1 @ Y2))))))))))))),
% 1.72/1.46 inference(fool_elimination,[status(thm)],[f4])).
% 1.72/1.46 thf(f4,plain,(
% 1.72/1.46 ~(! [X0 : ((a > $o) > $o) > $o] : (! [X1 : (a > $o) > $o] : ((X0 @ X1) => ? [X2 : a > $o] : (X1 @ X2)) => ? [X3 : ((a > $o) > $o) > a > $o] : ! [X4 : (a > $o) > $o] : ((X0 @ X4) => (X4 @ (X3 @ X4)))) => ! [X5 : ((a > $o) > $o) > $o] : ((! [X6 : (a > $o) > $o] : ((X5 @ X6) => ? [X7 : a > $o] : (X6 @ X7)) & ? [X8 : (a > $o) > $o] : (X5 @ X8)) => ((^[X9 : a] : (? [X10 : ((a > $o) > $o) > a > $o] : ! [X11 : (a > $o) > $o] : ((X5 @ X11) => ((X11 @ (X10 @ X11)) & (X10 @ X11 @ X9))))) = (^[X12 : a] : (! [X13 : (a > $o) > $o] : ((X5 @ X13) => ? [X14 : a > $o] : ((X14 @ X12) & (X13 @ X14))))))))),
% 1.72/1.46 inference(rectify,[status(thm)],[f2])).
% 1.72/1.46 thf(f2,negated_conjecture,(
% 1.72/1.46 ~(! [X0 : ((a > $o) > $o) > $o] : (! [X1 : (a > $o) > $o] : ((X0 @ X1) => ? [X2 : a > $o] : (X1 @ X2)) => ? [X3 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : ((X0 @ X1) => (X1 @ (X3 @ X1)))) => ! [X4 : ((a > $o) > $o) > $o] : ((! [X1 : (a > $o) > $o] : ((X4 @ X1) => ? [X5 : a > $o] : (X1 @ X5)) & ? [X1 : (a > $o) > $o] : (X4 @ X1)) => ((^[X6 : a] : (? [X3 : ((a > $o) > $o) > a > $o] : ! [X7 : (a > $o) > $o] : ((X4 @ X7) => ((X7 @ (X3 @ X7)) & (X3 @ X7 @ X6))))) = (^[X6 : a] : (! [X7 : (a > $o) > $o] : ((X4 @ X7) => ? [X8 : a > $o] : ((X8 @ X6) & (X7 @ X8))))))))),
% 1.72/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.72/1.46 thf(f1,conjecture,(
% 1.72/1.46 ! [X0 : ((a > $o) > $o) > $o] : (! [X1 : (a > $o) > $o] : ((X0 @ X1) => ? [X2 : a > $o] : (X1 @ X2)) => ? [X3 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : ((X0 @ X1) => (X1 @ (X3 @ X1)))) => ! [X4 : ((a > $o) > $o) > $o] : ((! [X1 : (a > $o) > $o] : ((X4 @ X1) => ? [X5 : a > $o] : (X1 @ X5)) & ? [X1 : (a > $o) > $o] : (X4 @ X1)) => ((^[X6 : a] : (? [X3 : ((a > $o) > $o) > a > $o] : ! [X7 : (a > $o) > $o] : ((X4 @ X7) => ((X7 @ (X3 @ X7)) & (X3 @ X7 @ X6))))) = (^[X6 : a] : (! [X7 : (a > $o) > $o] : ((X4 @ X7) => ? [X8 : a > $o] : ((X8 @ X6) & (X7 @ X8)))))))),
% 1.72/1.46 file('/export/starexec/sandbox2/tmp/tmp.pA5XUtVn1P/DTF2THF_13344.p',cTHM535)).
% 1.72/1.46 thf(f130,plain,(
% 1.72/1.46 spl5_8 | spl5_5),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f76,f116,f128])).
% 1.72/1.46 thf(f76,plain,(
% 1.72/1.46 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($true = (sK2 @ (sK9 @ X1))) | ((X2 @ sK7) = $false) | ((sK8 @ X2) = $false)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.72/1.46 thf(f75,plain,(
% 1.72/1.46 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($true = (sK2 @ (sK9 @ X1))) | (((sK8 @ X2) & (X2 @ sK7)) = $false)) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.72/1.46 thf(f74,plain,(
% 1.72/1.46 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($true = (sK2 @ (sK9 @ X1))) | (((^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7))) @ X2) = $false)) )),
% 1.72/1.46 inference(pi_clausification,[status(thm)],[f72])).
% 1.72/1.46 thf(f72,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7))))) | ($true = (sK2 @ (sK9 @ X1)))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.72/1.46 thf(f126,plain,(
% 1.72/1.46 spl5_7 | spl5_6),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f79,f119,f123])).
% 1.72/1.46 thf(f79,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (((sK2 @ sK8) = $true) | ($false = (X1 @ (sK9 @ X1) @ sK7)) | ((sK9 @ X1 @ (X1 @ (sK9 @ X1))) = $false)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.72/1.46 thf(f77,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = ((sK2 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7)))))) | ((sK9 @ X1 @ (X1 @ (sK9 @ X1))) = $false) | ($false = (X1 @ (sK9 @ X1) @ sK7))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.72/1.46 thf(f70,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : ((((X1 @ (sK9 @ X1) @ sK7) & (sK9 @ X1 @ (X1 @ (sK9 @ X1)))) = $false) | ($false = ((sK2 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7))))))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.72/1.46 thf(f121,plain,(
% 1.72/1.46 spl5_5 | spl5_6),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f82,f119,f116])).
% 1.72/1.46 thf(f82,plain,(
% 1.72/1.46 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (((X2 @ sK7) = $false) | ((sK9 @ X1 @ (X1 @ (sK9 @ X1))) = $false) | ((sK8 @ X2) = $false) | ($false = (X1 @ (sK9 @ X1) @ sK7))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.72/1.46 thf(f81,plain,(
% 1.72/1.46 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : ((((sK8 @ X2) & (X2 @ sK7)) = $false) | ($false = (X1 @ (sK9 @ X1) @ sK7)) | ((sK9 @ X1 @ (X1 @ (sK9 @ X1))) = $false)) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.72/1.46 thf(f80,plain,(
% 1.72/1.46 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($false = (X1 @ (sK9 @ X1) @ sK7)) | ((sK9 @ X1 @ (X1 @ (sK9 @ X1))) = $false) | (((^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7))) @ X2) = $false)) )),
% 1.72/1.46 inference(pi_clausification,[status(thm)],[f78])).
% 1.72/1.46 thf(f78,plain,(
% 1.72/1.46 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = (X1 @ (sK9 @ X1) @ sK7)) | ((sK9 @ X1 @ (X1 @ (sK9 @ X1))) = $false) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK7)))))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.72/1.46 thf(f114,plain,(
% 1.72/1.46 spl5_4 | spl5_3),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f96,f107,f111])).
% 1.72/1.46 thf(f96,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (($false = (sK2 @ X1)) | ((X1 @ (sK11 @ X1)) = $true) | ((sK2 @ X2) = $false) | ((sK10 @ X2 @ sK7) = $true)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.72/1.46 thf(f94,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((sK2 @ X2) = $false) | (((X1 @ (sK11 @ X1)) & (sK11 @ X1 @ sK7)) = $true) | ($false = (sK2 @ X1)) | ((sK10 @ X2 @ sK7) = $true)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.72/1.46 thf(f92,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : ((((sK10 @ X2 @ sK7) & (X2 @ (sK10 @ X2))) = $true) | (((X1 @ (sK11 @ X1)) & (sK11 @ X1 @ sK7)) = $true) | ((sK2 @ X2) = $false) | ($false = (sK2 @ X1))) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.72/1.46 thf(f91,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((sK2 @ X2) = $false) | ($false = (sK2 @ X1)) | (((^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK7))) @ (sK11 @ X1)) = $true) | (((sK10 @ X2 @ sK7) & (X2 @ (sK10 @ X2))) = $true)) )),
% 1.72/1.46 inference(sigma_clausification,[status(thm)],[f90])).
% 1.72/1.46 thf(f90,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((sK2 @ X2) = $false) | ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK7)))) = $true) | ($false = (sK2 @ X1)) | (((sK10 @ X2 @ sK7) & (X2 @ (sK10 @ X2))) = $true)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.72/1.46 thf(f89,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (($false = (sK2 @ X1)) | ($true = ((sK2 @ X2) => ((sK10 @ X2 @ sK7) & (X2 @ (sK10 @ X2))))) | ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK7)))) = $true)) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.72/1.46 thf(f88,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : ((((^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => ((sK10 @ Y0 @ sK7) & (Y0 @ (sK10 @ Y0))))) @ X2) = $true) | ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK7)))) = $true) | ($false = (sK2 @ X1))) )),
% 1.72/1.46 inference(pi_clausification,[status(thm)],[f87])).
% 1.72/1.46 thf(f87,plain,(
% 1.72/1.46 ( ! [X1 : (a > $o) > $o] : (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => ((sK10 @ Y0 @ sK7) & (Y0 @ (sK10 @ Y0)))))) = $true) | ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK7)))) = $true) | ($false = (sK2 @ X1))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.72/1.46 thf(f86,plain,(
% 1.72/1.46 ( ! [X1 : (a > $o) > $o] : ((((sK2 @ X1) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((X1 @ Y0) & (Y0 @ sK7))))) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => ((sK10 @ Y0 @ sK7) & (Y0 @ (sK10 @ Y0)))))) = $true)) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.72/1.46 thf(f85,plain,(
% 1.72/1.46 ( ! [X1 : (a > $o) > $o] : (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => ((sK10 @ Y0 @ sK7) & (Y0 @ (sK10 @ Y0)))))) = $true) | (((^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK7)))))) @ X1) = $true)) )),
% 1.72/1.46 inference(pi_clausification,[status(thm)],[f84])).
% 1.72/1.46 thf(f84,plain,(
% 1.72/1.46 ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK7))))))) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => ((sK10 @ Y0 @ sK7) & (Y0 @ (sK10 @ Y0)))))) = $true)),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.72/1.46 thf(f83,plain,(
% 1.72/1.46 (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => ((Y0 @ Y1 @ sK7) & (Y1 @ (Y0 @ Y1))))))) @ sK10) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK7))))))) = $true)),
% 1.72/1.46 inference(sigma_clausification,[status(thm)],[f62])).
% 1.72/1.46 thf(f62,plain,(
% 1.72/1.46 ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK2 @ Y1) => ((Y0 @ Y1 @ sK7) & (Y1 @ (Y0 @ Y1)))))))) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK2 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK7))))))) = $true)),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.72/1.46 thf(f113,plain,(
% 1.72/1.46 spl5_2 | spl5_4),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f95,f111,f103])).
% 1.72/1.46 thf(f95,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((sK10 @ X2 @ sK7) = $true) | ($false = (sK2 @ X1)) | ((sK11 @ X1 @ sK7) = $true) | ((sK2 @ X2) = $false)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.72/1.46 thf(f109,plain,(
% 1.72/1.46 spl5_3 | spl5_1),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f98,f100,f107])).
% 1.72/1.46 thf(f98,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((sK2 @ X2) = $false) | ((X2 @ (sK10 @ X2)) = $true) | ($false = (sK2 @ X1)) | ((X1 @ (sK11 @ X1)) = $true)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.72/1.46 thf(f93,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((X2 @ (sK10 @ X2)) = $true) | (((X1 @ (sK11 @ X1)) & (sK11 @ X1 @ sK7)) = $true) | ((sK2 @ X2) = $false) | ($false = (sK2 @ X1))) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.72/1.46 thf(f105,plain,(
% 1.72/1.46 spl5_1 | spl5_2),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f97,f103,f100])).
% 1.72/1.46 thf(f97,plain,(
% 1.72/1.46 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((sK11 @ X1 @ sK7) = $true) | ($false = (sK2 @ X1)) | ((X2 @ (sK10 @ X2)) = $true) | ((sK2 @ X2) = $false)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.72/1.46 % SZS output end Proof for DTF2THF_13344
% 1.72/1.46 % (13525)------------------------------
% 1.72/1.46 % (13525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (13525)Termination reason: Refutation
% 1.72/1.46
% 1.72/1.46 % (13525)Memory used [KB]: 6012
% 1.72/1.46 % (13525)Time elapsed: 0.097 s
% 1.72/1.46 % (13525)Instructions burned: 166 (million)
% 1.72/1.46 % (13525)------------------------------
% 1.72/1.46 % (13525)------------------------------
% 1.72/1.46 % (13519)Success in time 0.105 s
%------------------------------------------------------------------------------