%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG273^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 08:37:48 AM UTC 2026
% Result : Theorem 2.60s 2.24s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 18
% Syntax : Number of formulae : 195 ( 40 unt; 0 typ; 10 def)
% Number of atoms : 1669 ( 725 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 4196 ( 187 ~; 328 |; 115 &;3031 @)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 28 usr; 22 con; 0-2 aty)
% ( 413 !!; 109 ??; 0 @@+; 0 @@-)
% Number of variables : 811 ( 630 ^; 177 !; 4 ?; 811 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(func_def_3,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_4,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_7,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_24,type,
sK1: g > g > g ).
thf(func_def_25,type,
sK2: g ).
thf(func_def_26,type,
sK3: g ).
thf(func_def_27,type,
sK4: g ).
thf(func_def_28,type,
sK5: g ).
thf(func_def_29,type,
sK6: g ).
thf(func_def_30,type,
sK7: g ).
thf(func_def_31,type,
sK8: g ).
thf(func_def_32,type,
sK9: g ).
thf(func_def_33,type,
sK10: g > g ).
thf(func_def_34,type,
sK11: g > g ).
thf(f968,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f99,f132,f155,f172,f184,f200,f206,f210,f298,f316,f329,f397,f416,f951,f967]) ).
thf(f967,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f966]) ).
thf(f966,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f962]) ).
thf(f962,plain,
( ( sK2 != sK2 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f98,f915]) ).
thf(f915,plain,
( ! [X0: g] :
( sK2
= ( sK1 @ ( sK11 @ X0 ) @ X0 ) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f623,f907]) ).
thf(f907,plain,
( ! [X0: g] :
( ( sK1 @ sK2 @ ( sK11 @ ( sK11 @ X0 ) ) )
= X0 )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f880,f183]) ).
thf(f183,plain,
( ! [X1: g] :
( ( sK1 @ X1 @ sK2 )
= X1 )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f182]) ).
thf(f182,definition,
( spl0_10
<=> ! [X1: g] :
( ( sK1 @ X1 @ sK2 )
= X1 ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f880,plain,
( ! [X0: g] :
( ( sK1 @ X0 @ sK2 )
= ( sK1 @ sK2 @ ( sK11 @ ( sK11 @ X0 ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f411,f154]) ).
thf(f154,plain,
( ! [X1: g] :
( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f153]) ).
thf(f153,definition,
( spl0_9
<=> ! [X1: g] :
( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f411,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK11 @ X0 ) @ X1 ) )
= ( sK1 @ sK2 @ X1 ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f123,f154]) ).
thf(f123,plain,
( ! [X2: g,X3: g,X1: g] :
( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f122,definition,
( spl0_7
<=> ! [X2: g,X1: g,X3: g] :
( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f623,plain,
( ! [X0: g] :
( ( sK1 @ X0 @ ( sK1 @ sK2 @ ( sK11 @ X0 ) ) )
= sK2 )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f408,f183]) ).
thf(f408,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ X1 @ ( sK11 @ ( sK1 @ X0 @ X1 ) ) ) )
= sK2 )
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f154,f123]) ).
thf(f98,plain,
( ! [X2: g] :
( ( sK1 @ X2 @ sK9 )
!= sK2 )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f97]) ).
thf(f97,definition,
( spl0_5
<=> ! [X2: g] :
( ( sK1 @ X2 @ sK9 )
!= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f951,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f950]) ).
thf(f950,plain,
( $false
| spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f941]) ).
thf(f941,plain,
( ( sK6 != sK6 )
| spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f87,f931]) ).
thf(f931,plain,
( ! [X0: g] :
( ( sK1 @ sK2 @ X0 )
= X0 )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f924,f183]) ).
thf(f924,plain,
( ! [X0: g] :
( ( sK1 @ X0 @ sK2 )
= ( sK1 @ sK2 @ X0 ) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f411,f915]) ).
thf(f87,plain,
( ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f85,definition,
( spl0_2
<=> ( sK6
= ( sK1 @ sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f416,plain,
( ~ spl0_1
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f415]) ).
thf(f415,plain,
( $false
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f414]) ).
thf(f414,plain,
( ( sK2 != sK2 )
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f83,f154]) ).
thf(f83,plain,
( ! [X1: g] :
( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f82]) ).
thf(f82,definition,
( spl0_1
<=> ! [X1: g] :
( ( sK1 @ sK5 @ X1 )
!= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f397,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f396]) ).
thf(f396,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f395]) ).
thf(f395,plain,
( ( sK2 != sK2 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f83,f282]) ).
thf(f282,plain,
( ! [X0: g] :
( sK2
= ( sK1 @ X0 @ ( sK10 @ X0 ) ) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f214,f120]) ).
thf(f120,plain,
( ! [X4: g] :
( ( sK1 @ ( sK10 @ X4 ) @ X4 )
= sK2 )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f119,definition,
( spl0_6
<=> ! [X4: g] :
( ( sK1 @ ( sK10 @ X4 ) @ X4 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f214,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ ( sK10 @ ( sK10 @ X0 ) ) @ X1 )
= ( sK1 @ X0 @ X1 ) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f208,f208]) ).
thf(f208,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ ( sK10 @ X0 ) @ ( sK1 @ X0 @ X1 ) )
= X1 )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f202,f138]) ).
thf(f138,plain,
( ! [X4: g] :
( ( sK1 @ sK2 @ X4 )
= X4 )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f137]) ).
thf(f137,definition,
( spl0_8
<=> ! [X4: g] :
( ( sK1 @ sK2 @ X4 )
= X4 ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f202,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ sK2 @ X1 )
= ( sK1 @ ( sK10 @ X0 ) @ ( sK1 @ X0 @ X1 ) ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f123,f120]) ).
thf(f329,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f328]) ).
thf(f328,plain,
( $false
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f325]) ).
thf(f325,plain,
( ( sK2 != sK2 )
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f98,f120]) ).
thf(f316,plain,
( spl0_4
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f315]) ).
thf(f315,plain,
( $false
| spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f314]) ).
thf(f314,plain,
( ( sK7 != sK7 )
| spl0_4
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f95,f183]) ).
thf(f95,plain,
( ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl0_4
<=> ( ( sK1 @ sK7 @ sK2 )
= sK7 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f298,plain,
( spl0_10
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f287,f137,f122,f119,f182]) ).
thf(f287,plain,
( ! [X0: g] :
( ( sK1 @ X0 @ sK2 )
= X0 )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f212,f214]) ).
thf(f212,plain,
( ! [X0: g] :
( ( sK1 @ ( sK10 @ ( sK10 @ X0 ) ) @ sK2 )
= X0 )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f208,f120]) ).
thf(f210,plain,
( spl0_2
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f209]) ).
thf(f209,plain,
( $false
| spl0_2
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f87,f138]) ).
thf(f206,plain,
( spl0_3
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f205]) ).
thf(f205,plain,
( $false
| spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f204]) ).
thf(f204,plain,
( ( ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| spl0_3
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f91,f123]) ).
thf(f91,plain,
( ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl0_3
<=> ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f200,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f199,f119,f182]) ).
thf(f199,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ ( sK10 @ X2 ) @ X2 )
= sK2 )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f198]) ).
thf(f198,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ sK2 )
= X1 )
| ( ( ( sK1 @ ( sK10 @ X2 ) @ X2 )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f197]) ).
thf(f197,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ X2 )
= sK2 )
@ ( sK10 @ X2 ) ) )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(sigma_clausification,[status(thm)],[f196]) ).
thf(f196,plain,
! [X2: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X2 )
= sK2 ) )
= $true )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f195]) ).
thf(f195,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ sK2 )
= X1 )
| ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
= $true )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
! [X1: g] :
( ( ( sK1 @ X1 @ sK2 )
= X1 )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
! [X1: g] :
( ( ( sK1 @ X1 @ sK2 )
= X1 )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f174]) ).
thf(f174,plain,
! [X1: g] :
( ( ( ( sK1 @ X1 @ sK2 )
= X1 )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f173]) ).
thf(f173,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true )
| ( ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
!= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
= ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [Y0: g] :
( ( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y3 @ Y2 ) @ Y1 )
= ( sK1 @ Y3 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= Y1 ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y3 @ Y2 ) @ Y1 )
= ( sK1 @ Y3 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y3 @ Y2 ) @ Y1 )
= ( sK1 @ Y3 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= Y1 ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y3 @ Y2 ) @ Y1 )
= ( sK1 @ Y3 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
= ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ?? @ g
@ ^ [Y7: g] :
( ( Y4 @ Y7 @ Y6 )
= Y5 ) ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g] :
( !! @ g
@ ^ [Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( !! @ g
@ ^ [Y7: g] :
( ( Y4 @ ( Y4 @ Y7 @ Y6 ) @ Y5 )
= ( Y4 @ Y7 @ ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
@ Y2 )
& ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ( Y4 @ Y5 @ Y6 )
= Y6 ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
= ( ^ [Y2: g > g > g,Y3: g] :
( ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ?? @ g
@ ^ [Y7: g] :
( ( Y4 @ Y6 @ Y7 )
= Y5 ) ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ( Y4 @ Y6 @ Y5 )
= Y6 ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g] :
( !! @ g
@ ^ [Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( !! @ g
@ ^ [Y7: g] :
( ( Y4 @ ( Y4 @ Y7 @ Y6 ) @ Y5 )
= ( Y4 @ Y7 @ ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
@ Y2 ) )
@ Y0
@ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f29,f34,f35]) ).
thf(f35,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f32,f27,f26,f28]) ).
thf(f28,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( cGRP_ASSOC
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_ASSOC_def) ).
thf(f26,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) )
= cGRP_RIGHT_UNIT ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( X0 @ X1 @ X4 )
= X1 ) )
= cGRP_RIGHT_UNIT ),
file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_RIGHT_UNIT_def) ).
thf(f27,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) )
= cGRP_RIGHT_INVERSE ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X1 @ X2 )
= X4 ) )
= cGRP_RIGHT_INVERSE ),
file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_RIGHT_INVERSE_def) ).
thf(f32,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( cGROUP3
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( cGROUP3
= ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X4 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGROUP3_def) ).
thf(f34,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f30,f28,f31]) ).
thf(f31,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( cGRP_LEFT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( cGRP_LEFT_UNIT
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( X0 @ X4 @ X1 )
= X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_LEFT_UNIT_def) ).
thf(f30,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X3 @ X2 )
= X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X2 @ X1 )
= X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_LEFT_INVERSE_def) ).
thf(f33,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( cGROUP2
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_LEFT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_INVERSE @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( cGROUP2
= ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_LEFT_UNIT @ X0 @ X4 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_INVERSE @ X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGROUP2_def) ).
thf(f29,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( cGROUP2 @ Y0 @ Y1 )
= ( cGROUP3 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( cGROUP2 @ Y0 @ Y1 )
= ( cGROUP3 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
~ ! [X0: g,X1: g > g > g] :
( ( cGROUP2 @ X1 @ X0 )
<=> ( cGROUP3 @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ! [X4: g,X0: g > g > g] :
( ( cGROUP2 @ X0 @ X4 )
<=> ( cGROUP3 @ X0 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
! [X4: g,X0: g > g > g] :
( ( cGROUP2 @ X0 @ X4 )
<=> ( cGROUP3 @ X0 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cEQUIV_02_03) ).
thf(f184,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f180,f182,f137]) ).
thf(f180,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ sK2 )
= X1 )
| ( ( sK1 @ sK2 @ X2 )
= X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
! [X2: g,X1: g] :
( ( ( ( sK1 @ sK2 @ X2 )
= X2 )
= $true )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ sK2 )
= X1 )
| ( ( ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $true )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f172,plain,
( spl0_6
| spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f171,f153,f119]) ).
thf(f171,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ ( sK10 @ X2 ) @ X2 )
= sK2 )
| ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
! [X2: g,X1: g] :
( ( ( ( sK1 @ ( sK10 @ X2 ) @ X2 )
= sK2 )
= $true )
| ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f169]) ).
thf(f169,plain,
! [X2: g,X1: g] :
( ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ X2 )
= sK2 )
@ ( sK10 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: g,X1: g] :
( ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X2 )
= sK2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) )
@ X2 )
= $true )
| ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
! [X1: g] :
( ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
! [X1: g] :
( ( ( ( sK1 @ X1 @ ( sK11 @ X1 ) )
= sK2 )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true )
| ( ( ( sK1 @ X1 @ ( sK11 @ X1 ) )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f144]) ).
thf(f144,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK2 )
@ ( sK11 @ X1 ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK2 ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) )
@ X1 )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f155,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f151,f153,f137]) ).
thf(f151,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK2 @ X2 )
= X2 )
| ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X2: g,X1: g] :
( ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) )
| ( ( ( sK1 @ sK2 @ X2 )
= X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f149]) ).
thf(f149,plain,
! [X2: g,X1: g] :
( ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) )
| ( ( ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
! [X1: g] :
( ( sK2
= ( sK1 @ X1 @ ( sK11 @ X1 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
! [X1: g] :
( ( ( ( sK1 @ X1 @ ( sK11 @ X1 ) )
= sK2 )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f145]) ).
thf(f132,plain,
( spl0_7
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f131,f122,f122]) ).
thf(f131,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK1 @ ( sK1 @ X6 @ X5 ) @ X4 )
= ( sK1 @ X6 @ ( sK1 @ X5 @ X4 ) ) )
| ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
| ( ( ( sK1 @ ( sK1 @ X6 @ X5 ) @ X4 )
= ( sK1 @ X6 @ ( sK1 @ X5 @ X4 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f129]) ).
thf(f129,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
| ( ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ X5 ) @ X4 )
= ( sK1 @ Y0 @ ( sK1 @ X5 @ X4 ) ) )
@ X6 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ X5 ) @ X4 )
= ( sK1 @ Y0 @ ( sK1 @ X5 @ X4 ) ) ) ) )
| ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f127]) ).
thf(f127,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ X4 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ X4 ) ) ) )
@ X5 ) )
| ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ X4 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ X4 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f125]) ).
thf(f125,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( sK1 @ ( sK1 @ X3 @ X2 ) @ X1 )
= ( sK1 @ X3 @ ( sK1 @ X2 @ X1 ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true )
| ( ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ X2 ) @ X1 )
= ( sK1 @ Y0 @ ( sK1 @ X2 @ X1 ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ X2 ) @ X1 )
= ( sK1 @ Y0 @ ( sK1 @ X2 @ X1 ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ X1 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ X1 ) ) ) )
@ X2 )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ X1 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ X1 ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f99,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f80,f97,f93,f89,f85,f82]) ).
thf(f80,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( ( sK1 @ X2 @ sK9 )
!= sK2 )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK1 @ X2 @ sK9 )
= sK2 ) )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( $false
= ( ( sK1 @ X2 @ sK9 )
= sK2 ) )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 ) ),
inference(equality_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( $false
= ( ( sK1 @ X2 @ sK9 )
= sK2 ) )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK9 )
= sK2 )
@ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK9 )
= sK2 ) )
= $false )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( $false
= ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) ) )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK9 )
= sK2 ) )
= $false )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) )
@ sK8 )
= $false )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) ) ),
inference(sigma_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK9 )
= sK2 ) )
= $false )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: g] :
( ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) )
@ sK9 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) ) ),
inference(sigma_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: g] :
( ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) )
@ sK4 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( sK1 @ sK5 @ X1 )
!= sK2 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: g] :
( ( ( ( sK1 @ sK5 @ X1 )
= sK2 )
= $false )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 )
@ X1 ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( ( sK1 @ sK7 @ sK2 )
!= sK7 )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( ( sK1 @ sK7 @ sK2 )
= sK7 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
!= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $false
= ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) ) )
| ( ( ( sK1 @ sK7 @ sK2 )
= sK7 )
= $false )
| ( sK6
!= ( sK1 @ sK2 @ sK6 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( $false
= ( ( sK1 @ ( sK1 @ sK8 @ sK4 ) @ sK3 )
= ( sK1 @ sK8 @ ( sK1 @ sK4 @ sK3 ) ) ) )
| ( ( ( sK1 @ sK7 @ sK2 )
= sK7 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) )
@ sK8 )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false )
| ( ( ( sK1 @ sK7 @ sK2 )
= sK7 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK7 @ sK2 )
= sK7 )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 )
@ sK7 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 )
@ sK6 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) )
@ sK3 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) )
@ sK5 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ Y0 @ sK4 ) @ sK3 )
= ( sK1 @ Y0 @ ( sK1 @ sK4 @ sK3 ) ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) )
@ sK4 ) ) ),
inference(sigma_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y0 ) @ sK3 )
= ( sK1 @ Y1 @ ( sK1 @ Y0 @ sK3 ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK2 @ Y0 )
= Y0 ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y2 @ Y1 ) @ Y0 )
= ( sK1 @ Y2 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG273^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.34 % Computer : n026.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Tue Feb 24 03:43:10 EST 2026
% 0.11/0.34 % CPUTime :
% 0.11/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.45 ---- Original DTF file ---
% 0.15/0.45 thf(spec,logic,$$dhol).
% 0.15/0.45 %------------------------------------------------------------------------------
% 0.15/0.45 % File : ALG273^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.15/0.45 % Domain : General Algebra
% 0.15/0.45 % Problem : TPS problem EQUIV-02-03
% 0.15/0.45 % Version : Especial.
% 0.15/0.45 % English :
% 0.15/0.45
% 0.15/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.45 % Source : [Bro09]
% 0.15/0.45 % Names : tps_0549 [Bro09]
% 0.15/0.45 % : EQUIV-02-03 [TPS]
% 0.15/0.45
% 0.15/0.45 % Status : Theorem
% 0.15/0.45 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.71 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.15/0.45 % Syntax : Number of formulae : 16 ( 7 unt; 8 typ; 7 def)
% 0.15/0.45 % Number of atoms : 27 ( 12 equ; 0 cnn)
% 0.15/0.45 % Maximal formula atoms : 2 ( 3 avg)
% 0.15/0.45 % Number of connectives : 35 ( 0 ~; 0 |; 4 &; 30 @)
% 0.15/0.45 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.15/0.45 % Maximal formula depth : 6 ( 2 avg)
% 0.15/0.45 % Number of types : 2 ( 1 usr)
% 0.15/0.45 % Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% 0.15/0.45 % Number of symbols : 8 ( 7 usr; 0 con; 1-2 aty)
% 0.15/0.45 % Number of variables : 24 ( 13 ^; 9 !; 2 ?; 24 :)
% 0.15/0.45 % SPC : TH0_THM_EQU_NAR
% 0.15/0.45
% 0.15/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.45 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.15/0.45 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.15/0.45 %------------------------------------------------------------------------------
% 0.15/0.45 thf(g_type,type,
% 0.15/0.45 g: $tType ).
% 0.15/0.45
% 0.15/0.45 thf(cGROUP2_type,type,
% 0.15/0.45 cGROUP2: ( g > g > g ) > g > $o ).
% 0.15/0.45
% 0.15/0.45 thf(cGROUP3_type,type,
% 0.15/0.45 cGROUP3: ( g > g > g ) > g > $o ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_ASSOC_type,type,
% 0.15/0.45 cGRP_ASSOC: ( g > g > g ) > $o ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_LEFT_INVERSE_type,type,
% 0.15/0.45 cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_LEFT_UNIT_type,type,
% 0.15/0.45 cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_RIGHT_INVERSE_type,type,
% 0.15/0.45 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_RIGHT_UNIT_type,type,
% 0.15/0.45 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_ASSOC_def,definition,
% 0.15/0.45 ( cGRP_ASSOC
% 0.15/0.45 = ( ^ [Xf: g > g > g] :
% 0.15/0.45 ! [Xa: g,Xb: g,Xc: g] :
% 0.15/0.45 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.15/0.45 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_LEFT_INVERSE_def,definition,
% 0.15/0.45 ( cGRP_LEFT_INVERSE
% 0.15/0.45 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.15/0.45 ! [Xa: g] :
% 0.15/0.45 ? [Xb: g] :
% 0.15/0.45 ( ( Xf @ Xb @ Xa )
% 0.15/0.45 = Xe ) ) ) ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_LEFT_UNIT_def,definition,
% 0.15/0.45 ( cGRP_LEFT_UNIT
% 0.15/0.45 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.15/0.45 ! [Xa: g] :
% 0.15/0.45 ( ( Xf @ Xe @ Xa )
% 0.15/0.45 = Xa ) ) ) ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_RIGHT_INVERSE_def,definition,
% 0.15/0.45 ( cGRP_RIGHT_INVERSE
% 0.15/0.45 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.15/0.45 ! [Xa: g] :
% 0.15/0.45 ? [Xb: g] :
% 0.15/0.45 ( ( Xf @ Xa @ Xb )
% 0.15/0.45 = Xe ) ) ) ).
% 0.15/0.45
% 0.15/0.45 thf(cGRP_RIGHT_UNIT_def,definition,
% 0.15/0.45 ( cGRP_RIGHT_UNIT
% 0.15/0.45 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.15/0.45 ! [Xa: g] :
% 0.15/0.45 ( ( Xf @ Xa @ Xe )
% 0.15/0.45 = Xa ) ) ) ).
% 0.15/0.45
% 0.15/0.45 thf(cGROUP2_def,definition,
% 0.15/0.45 ( cGROUP2
% 0.15/0.45 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.15/0.45 ( ( cGRP_ASSOC @ Xf )
% 0.15/0.45 & ( cGRP_LEFT_UNIT @ Xf @ Xe )
% 0.15/0.45 & ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 thf(cGROUP3_def,definition,
% 0.15/0.45 ( cGROUP3
% 0.15/0.45 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.15/0.45 ( ( cGRP_ASSOC @ Xf )
% 0.15/0.45 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 0.15/0.45 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.15/0.45
% 0.15/0.45 thf(cEQUIV_02_03,conjecture,
% 0.15/0.45 ! [Xf: g > g > g,Xe: g] :
% 0.15/0.45 ( ( cGROUP2 @ Xf @ Xe )
% 0.15/0.45 <=> ( cGROUP3 @ Xf @ Xe ) ) ).
% 0.15/0.45
% 0.15/0.45 %------------------------------------------------------------------------------
% 0.15/0.45 ------------------------
% 1.62/1.98 ---- Embedded in THF ---
% 1.62/1.98 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.98 %%% Generated on Tue Feb 24 03:43:11 EST 2026
% 1.62/1.98 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.98 %%% Logic specification used:
% 1.62/1.98 %%% thf(spec, logic, $$dhol).
% 1.62/1.98
% 1.62/1.98 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2DTF28610.p
% See solution above
% 1.62/1.98 ------------------------
% 1.62/1.99 ---- Cleaned THF ---
% 1.62/1.99 thf(g_type,type,
% 1.62/1.99 g: $tType ).
% 1.62/1.99
% 1.62/1.99 thf(cGROUP2_type,type,
% 1.62/1.99 cGROUP2: ( g > g > g ) > g > $o ).
% 1.62/1.99
% 1.62/1.99 thf(cGROUP3_type,type,
% 1.62/1.99 cGROUP3: ( g > g > g ) > g > $o ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_ASSOC_type,type,
% 1.62/1.99 cGRP_ASSOC: ( g > g > g ) > $o ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_LEFT_INVERSE_type,type,
% 1.62/1.99 cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_LEFT_UNIT_type,type,
% 1.62/1.99 cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_RIGHT_INVERSE_type,type,
% 1.62/1.99 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_RIGHT_UNIT_type,type,
% 1.62/1.99 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_ASSOC_def,definition,
% 1.62/1.99 ( cGRP_ASSOC
% 1.62/1.99 = ( ^ [Xf: g > g > g] :
% 1.62/1.99 ! [Xa: g,Xb: g,Xc: g] :
% 1.62/1.99 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 1.62/1.99 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_LEFT_INVERSE_def,definition,
% 1.62/1.99 ( cGRP_LEFT_INVERSE
% 1.62/1.99 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.62/1.99 ! [Xa: g] :
% 1.62/1.99 ? [Xb: g] :
% 1.62/1.99 ( ( Xf @ Xb @ Xa )
% 1.62/1.99 = Xe ) ) ) ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_LEFT_UNIT_def,definition,
% 1.62/1.99 ( cGRP_LEFT_UNIT
% 1.62/1.99 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.62/1.99 ! [Xa: g] :
% 1.62/1.99 ( ( Xf @ Xe @ Xa )
% 1.62/1.99 = Xa ) ) ) ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_RIGHT_INVERSE_def,definition,
% 1.62/1.99 ( cGRP_RIGHT_INVERSE
% 1.62/1.99 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.62/1.99 ! [Xa: g] :
% 1.62/1.99 ? [Xb: g] :
% 1.62/1.99 ( ( Xf @ Xa @ Xb )
% 1.62/1.99 = Xe ) ) ) ).
% 1.62/1.99
% 1.62/1.99 thf(cGRP_RIGHT_UNIT_def,definition,
% 1.62/1.99 ( cGRP_RIGHT_UNIT
% 1.62/1.99 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.62/1.99 ! [Xa: g] :
% 1.62/1.99 ( ( Xf @ Xa @ Xe )
% 1.62/1.99 = Xa ) ) ) ).
% 1.62/1.99
% 1.62/1.99 thf(cGROUP2_def,definition,
% 1.62/1.99 ( cGROUP2
% 1.62/1.99 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.62/1.99 ( ( cGRP_ASSOC @ Xf )
% 1.62/1.99 & ( cGRP_LEFT_UNIT @ Xf @ Xe )
% 1.62/1.99 & ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 1.62/1.99
% 1.62/1.99 thf(cGROUP3_def,definition,
% 1.62/1.99 ( cGROUP3
% 1.62/1.99 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.62/1.99 ( ( cGRP_ASSOC @ Xf )
% 1.62/1.99 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 1.62/1.99 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 1.62/1.99
% 1.62/1.99 thf(cEQUIV_02_03,conjecture,
% 1.62/1.99 ! [Xf: g > g > g,Xe: g] :
% 1.62/1.99 ( ( cGROUP2 @ Xf @ Xe )
% 1.62/1.99 <=> ( cGROUP3 @ Xf @ Xe ) ) ).
% 1.62/1.99 ------------------------
% 1.62/2.01 % (28710)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/2Mi)
% 1.62/2.01 % (28707)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/183Mi)
% 1.62/2.01 % (28713)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/18Mi)
% 1.62/2.01 % (28712)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_28610 for (2999ds/275Mi)
% 1.62/2.01 % (28709)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_28610 for (2999ds/27Mi)
% 1.62/2.01 % (28708)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_28610 for (2999ds/4Mi)
% 1.62/2.01 % (28708)Instruction limit reached!
% 1.62/2.01 % (28708)------------------------------
% 1.62/2.01 % (28708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/2.01 % (28708)Termination reason: Unknown
% 1.62/2.01 % (28708)Termination phase: Saturation
% 1.62/2.01
% 1.62/2.01 % (28708)Memory used [KB]: 5500
% 1.62/2.01 % (28708)Time elapsed: 0.003 s
% 1.62/2.01 % (28708)Instructions burned: 4 (million)
% 1.62/2.01 % (28708)------------------------------
% 1.62/2.01 % (28708)------------------------------
% 1.62/2.01 % (28710)Instruction limit reached!
% 1.62/2.01 % (28710)------------------------------
% 1.62/2.01 % (28710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/2.01 % (28710)Termination reason: Unknown
% 1.62/2.01 % (28710)Termination phase: shuffling
% 1.62/2.01
% 1.62/2.01 % (28710)Memory used [KB]: 895
% 1.62/2.01 % (28710)Time elapsed: 0.004 s
% 1.62/2.01 % (28710)Instructions burned: 2 (million)
% 1.62/2.01 % (28710)------------------------------
% 1.62/2.01 % (28710)------------------------------
% 1.62/2.01 % (28711)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_28610 for (2999ds/2Mi)
% 1.62/2.01 % (28711)Instruction limit reached!
% 1.62/2.01 % (28711)------------------------------
% 1.62/2.01 % (28711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/2.01 % (28711)Termination reason: Unknown
% 1.62/2.01 % (28711)Termination phase: Property scanning
% 1.62/2.01
% 1.62/2.01 % (28711)Memory used [KB]: 1023
% 1.62/2.01 % (28711)Time elapsed: 0.003 s
% 1.62/2.01 % (28711)Instructions burned: 2 (million)
% 1.62/2.01 % (28711)------------------------------
% 1.62/2.01 % (28711)------------------------------
% 1.62/2.02 % (28713)Instruction limit reached!
% 1.62/2.02 % (28713)------------------------------
% 1.62/2.02 % (28713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/2.02 % (28713)Termination reason: Unknown
% 1.62/2.02 % (28713)Termination phase: Saturation
% 1.62/2.02
% 1.62/2.02 % (28713)Memory used [KB]: 5628
% 1.62/2.02 % (28713)Time elapsed: 0.012 s
% 1.62/2.02 % (28713)Instructions burned: 18 (million)
% 1.62/2.02 % (28713)------------------------------
% 1.62/2.02 % (28713)------------------------------
% 1.62/2.02 % (28709)Instruction limit reached!
% 1.62/2.02 % (28709)------------------------------
% 1.62/2.02 % (28709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/2.02 % (28709)Termination reason: Unknown
% 1.62/2.02 % (28709)Termination phase: Saturation
% 1.62/2.02
% 1.62/2.02 % (28709)Memory used [KB]: 5628
% 1.62/2.02 % (28709)Time elapsed: 0.016 s
% 1.62/2.02 % (28709)Instructions burned: 27 (million)
% 1.62/2.02 % (28709)------------------------------
% 1.62/2.02 % (28709)------------------------------
% 1.90/2.03 % (28715)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_28610 for (2999ds/37Mi)
% 1.90/2.03 % (28714)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/3Mi)
% 1.90/2.03 % (28714)Instruction limit reached!
% 1.90/2.03 % (28714)------------------------------
% 1.90/2.03 % (28714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.03 % (28714)Termination reason: Unknown
% 1.90/2.03 % (28714)Termination phase: Saturation
% 1.90/2.03
% 1.90/2.03 % (28714)Memory used [KB]: 5500
% 1.90/2.03 % (28714)Time elapsed: 0.004 s
% 1.90/2.03 % (28714)Instructions burned: 4 (million)
% 1.90/2.03 % (28714)------------------------------
% 1.90/2.03 % (28714)------------------------------
% 1.90/2.03 % (28716)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_28610 for (2999ds/15Mi)
% 1.90/2.04 % (28717)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_28610 for (2999ds/3Mi)
% 1.90/2.04 % (28717)Instruction limit reached!
% 1.90/2.04 % (28717)------------------------------
% 1.90/2.04 % (28717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.04 % (28717)Termination reason: Unknown
% 1.90/2.04 % (28717)Termination phase: Saturation
% 1.90/2.04
% 1.90/2.04 % (28717)Memory used [KB]: 5500
% 1.90/2.04 % (28717)Time elapsed: 0.003 s
% 1.90/2.04 % (28717)Instructions burned: 4 (million)
% 1.90/2.04 % (28717)------------------------------
% 1.90/2.04 % (28717)------------------------------
% 1.90/2.04 % (28716)Instruction limit reached!
% 1.90/2.04 % (28716)------------------------------
% 1.90/2.04 % (28716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.04 % (28718)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_28610 for (2999ds/1041Mi)
% 1.90/2.04 % (28716)Termination reason: Unknown
% 1.90/2.04 % (28716)Termination phase: Saturation
% 1.90/2.04
% 1.90/2.04 % (28716)Memory used [KB]: 5628
% 1.90/2.04 % (28716)Time elapsed: 0.011 s
% 1.90/2.04 % (28716)Instructions burned: 16 (million)
% 1.90/2.04 % (28716)------------------------------
% 1.90/2.04 % (28716)------------------------------
% 1.90/2.05 % (28715)Instruction limit reached!
% 1.90/2.05 % (28715)------------------------------
% 1.90/2.05 % (28715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.05 % (28715)Termination reason: Unknown
% 1.90/2.05 % (28715)Termination phase: Saturation
% 1.90/2.05
% 1.90/2.05 % (28715)Memory used [KB]: 5756
% 1.90/2.05 % (28715)Time elapsed: 0.020 s
% 1.90/2.05 % (28715)Instructions burned: 37 (million)
% 1.90/2.05 % (28715)------------------------------
% 1.90/2.05 % (28715)------------------------------
% 1.90/2.05 % (28719)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/7Mi)
% 1.90/2.05 % (28719)Instruction limit reached!
% 1.90/2.05 % (28719)------------------------------
% 1.90/2.05 % (28719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.05 % (28719)Termination reason: Unknown
% 1.90/2.05 % (28719)Termination phase: Saturation
% 1.90/2.05
% 1.90/2.05 % (28719)Memory used [KB]: 1023
% 1.90/2.05 % (28719)Time elapsed: 0.006 s
% 1.90/2.05 % (28719)Instructions burned: 8 (million)
% 1.90/2.05 % (28719)------------------------------
% 1.90/2.05 % (28719)------------------------------
% 1.90/2.05 % (28720)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/16Mi)
% 1.90/2.06 % (28721)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_28610 for (2999ds/3Mi)
% 1.90/2.06 % (28721)Instruction limit reached!
% 1.90/2.06 % (28721)------------------------------
% 1.90/2.06 % (28721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.06 % (28721)Termination reason: Unknown
% 1.90/2.06 % (28721)Termination phase: Property scanning
% 1.90/2.06
% 1.90/2.06 % (28721)Memory used [KB]: 1023
% 1.90/2.06 % (28721)Time elapsed: 0.004 s
% 1.90/2.06 % (28721)Instructions burned: 3 (million)
% 1.90/2.06 % (28721)------------------------------
% 1.90/2.06 % (28721)------------------------------
% 1.90/2.06 % (28720)Instruction limit reached!
% 1.90/2.06 % (28720)------------------------------
% 1.90/2.06 % (28720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.06 % (28720)Termination reason: Unknown
% 1.90/2.06 % (28720)Termination phase: Saturation
% 1.90/2.06
% 1.90/2.06 % (28720)Memory used [KB]: 5756
% 1.90/2.06 % (28720)Time elapsed: 0.011 s
% 1.90/2.06 % (28720)Instructions burned: 16 (million)
% 1.90/2.06 % (28720)------------------------------
% 1.90/2.06 % (28720)------------------------------
% 1.90/2.06 % (28722)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_28610 for (2999ds/3Mi)
% 1.90/2.06 % (28722)Instruction limit reached!
% 1.90/2.06 % (28722)------------------------------
% 1.90/2.06 % (28722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.06 % (28722)Termination reason: Unknown
% 1.90/2.06 % (28722)Termination phase: Property scanning
% 1.90/2.06
% 1.90/2.06 % (28722)Memory used [KB]: 1023
% 1.90/2.06 % (28722)Time elapsed: 0.003 s
% 1.90/2.06 % (28722)Instructions burned: 3 (million)
% 1.90/2.06 % (28722)------------------------------
% 1.90/2.06 % (28722)------------------------------
% 1.90/2.07 % (28723)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/7Mi)
% 1.90/2.07 % (28723)Instruction limit reached!
% 1.90/2.07 % (28723)------------------------------
% 1.90/2.07 % (28723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.07 % (28723)Termination reason: Unknown
% 1.90/2.07 % (28723)Termination phase: Saturation
% 1.90/2.07
% 1.90/2.07 % (28723)Memory used [KB]: 5500
% 1.90/2.07 % (28723)Time elapsed: 0.005 s
% 1.90/2.07 % (28723)Instructions burned: 7 (million)
% 1.90/2.07 % (28723)------------------------------
% 1.90/2.07 % (28723)------------------------------
% 1.90/2.08 % (28725)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/4Mi)
% 1.90/2.08 % (28725)Instruction limit reached!
% 1.90/2.08 % (28725)------------------------------
% 1.90/2.08 % (28725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.08 % (28725)Termination reason: Unknown
% 1.90/2.08 % (28725)Termination phase: Saturation
% 1.90/2.08
% 1.90/2.08 % (28725)Memory used [KB]: 5500
% 1.90/2.08 % (28725)Time elapsed: 0.004 s
% 1.90/2.08 % (28725)Instructions burned: 4 (million)
% 1.90/2.08 % (28725)------------------------------
% 1.90/2.08 % (28725)------------------------------
% 1.90/2.08 % (28724)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/3Mi)
% 1.90/2.08 % (28726)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/18Mi)
% 1.90/2.08 % (28724)Instruction limit reached!
% 1.90/2.08 % (28724)------------------------------
% 1.90/2.08 % (28724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.08 % (28724)Termination reason: Unknown
% 1.90/2.08 % (28724)Termination phase: Saturation
% 1.90/2.08
% 1.90/2.08 % (28724)Memory used [KB]: 1023
% 1.90/2.08 % (28724)Time elapsed: 0.004 s
% 1.90/2.08 % (28724)Instructions burned: 4 (million)
% 1.90/2.08 % (28724)------------------------------
% 1.90/2.08 % (28724)------------------------------
% 1.90/2.09 % (28727)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/710Mi)
% 1.90/2.09 % (28726)Instruction limit reached!
% 1.90/2.09 % (28726)------------------------------
% 1.90/2.09 % (28726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.09 % (28726)Termination reason: Unknown
% 1.90/2.09 % (28726)Termination phase: Saturation
% 1.90/2.09
% 1.90/2.09 % (28726)Memory used [KB]: 5628
% 1.90/2.09 % (28726)Time elapsed: 0.011 s
% 1.90/2.09 % (28726)Instructions burned: 18 (million)
% 1.90/2.09 % (28726)------------------------------
% 1.90/2.09 % (28726)------------------------------
% 1.90/2.10 % (28728)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28610 for (2999ds/6Mi)
% 1.90/2.10 % (28728)Instruction limit reached!
% 1.90/2.10 % (28728)------------------------------
% 1.90/2.10 % (28728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.10 % (28728)Termination reason: Unknown
% 1.90/2.10 % (28728)Termination phase: Saturation
% 1.90/2.10
% 1.90/2.10 % (28728)Memory used [KB]: 5500
% 1.90/2.10 % (28728)Time elapsed: 0.005 s
% 1.90/2.10 % (28728)Instructions burned: 6 (million)
% 1.90/2.10 % (28728)------------------------------
% 1.90/2.10 % (28728)------------------------------
% 1.90/2.10 % (28729)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_28610 for (2999ds/902Mi)
% 1.90/2.10 % (28707)Instruction limit reached!
% 1.90/2.10 % (28707)------------------------------
% 1.90/2.10 % (28707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.10 % (28707)Termination reason: Unknown
% 1.90/2.10 % (28707)Termination phase: Saturation
% 1.90/2.10
% 1.90/2.10 % (28707)Memory used [KB]: 6652
% 1.90/2.10 % (28707)Time elapsed: 0.094 s
% 1.90/2.10 % (28707)Instructions burned: 183 (million)
% 1.90/2.10 % (28707)------------------------------
% 1.90/2.10 % (28707)------------------------------
% 1.90/2.10 % (28729)Refutation not found, incomplete strategy
% 1.90/2.10 % (28729)------------------------------
% 1.90/2.10 % (28729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.10 % (28729)Termination reason: Refutation not found, incomplete strategy
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 % (28729)Memory used [KB]: 5500
% 1.90/2.10 % (28729)Time elapsed: 0.005 s
% 1.90/2.10 % (28729)Instructions burned: 3 (million)
% 1.90/2.10 % (28729)------------------------------
% 1.90/2.10 % (28729)------------------------------
% 1.90/2.11 % (28730)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_28610 for (2999ds/21Mi)
% 1.90/2.11 % (28731)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28610 for (2998ds/5Mi)
% 1.90/2.12 % (28731)Instruction limit reached!
% 1.90/2.12 % (28731)------------------------------
% 1.90/2.12 % (28731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.12 % (28731)Termination reason: Unknown
% 1.90/2.12 % (28731)Termination phase: Saturation
% 1.90/2.12
% 1.90/2.12 % (28731)Memory used [KB]: 5500
% 1.90/2.12 % (28731)Time elapsed: 0.005 s
% 1.90/2.12 % (28731)Instructions burned: 5 (million)
% 1.90/2.12 % (28731)------------------------------
% 1.90/2.12 % (28731)------------------------------
% 1.90/2.12 % (28730)Instruction limit reached!
% 1.90/2.12 % (28730)------------------------------
% 1.90/2.12 % (28730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.12 % (28730)Termination reason: Unknown
% 1.90/2.12 % (28730)Termination phase: Saturation
% 1.90/2.12
% 1.90/2.12 % (28730)Memory used [KB]: 5628
% 1.90/2.12 % (28730)Time elapsed: 0.013 s
% 1.90/2.12 % (28730)Instructions burned: 21 (million)
% 1.90/2.12 % (28730)------------------------------
% 1.90/2.12 % (28730)------------------------------
% 1.90/2.12 % (28732)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_28610 for (2998ds/6Mi)
% 1.90/2.12 % (28732)Instruction limit reached!
% 1.90/2.12 % (28732)------------------------------
% 1.90/2.12 % (28732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/2.12 % (28732)Termination reason: Unknown
% 1.90/2.12 % (28732)Termination phase: Saturation
% 1.90/2.12
% 1.90/2.12 % (28732)Memory used [KB]: 5500
% 1.90/2.12 % (28732)Time elapsed: 0.005 s
% 1.90/2.12 % (28732)Instructions burned: 6 (million)
% 1.90/2.12 % (28732)------------------------------
% 1.90/2.12 % (28732)------------------------------
% 1.90/2.12 % (28733)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28610 for (2998ds/377Mi)
% 2.47/2.13 % (28734)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_28610 for (2998ds/779Mi)
% 2.47/2.13 % (28735)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_28610 for (2998ds/19Mi)
% 2.47/2.14 % (28736)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_28610 for (2998ds/879Mi)
% 2.47/2.14 % (28735)Instruction limit reached!
% 2.47/2.14 % (28735)------------------------------
% 2.47/2.14 % (28735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/2.14 % (28712)Instruction limit reached!
% 2.47/2.14 % (28712)------------------------------
% 2.47/2.14 % (28712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/2.14 % (28712)Termination reason: Unknown
% 2.47/2.14 % (28712)Termination phase: Saturation
% 2.47/2.14
% 2.47/2.14 % (28712)Memory used [KB]: 6524
% 2.47/2.14 % (28712)Time elapsed: 0.135 s
% 2.47/2.14 % (28712)Instructions burned: 275 (million)
% 2.47/2.14 % (28712)------------------------------
% 2.47/2.14 % (28712)------------------------------
% 2.47/2.14 % (28735)Termination reason: Unknown
% 2.47/2.14 % (28735)Termination phase: Saturation
% 2.47/2.14
% 2.47/2.14 % (28735)Memory used [KB]: 5628
% 2.47/2.14 % (28735)Time elapsed: 0.011 s
% 2.47/2.14 % (28735)Instructions burned: 20 (million)
% 2.47/2.14 % (28735)------------------------------
% 2.47/2.14 % (28735)------------------------------
% 2.47/2.16 % (28738)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28610 for (2998ds/3Mi)
% 2.47/2.16 % (28737)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_28610 for (2998ds/17Mi)
% 2.47/2.16 % (28738)Instruction limit reached!
% 2.47/2.16 % (28738)------------------------------
% 2.47/2.16 % (28738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/2.16 % (28738)Termination reason: Unknown
% 2.47/2.16 % (28738)Termination phase: Property scanning
% 2.47/2.16
% 2.47/2.16 % (28738)Memory used [KB]: 1023
% 2.47/2.16 % (28738)Time elapsed: 0.004 s
% 2.47/2.16 % (28738)Instructions burned: 4 (million)
% 2.47/2.16 % (28738)------------------------------
% 2.47/2.16 % (28738)------------------------------
% 2.47/2.17 % (28737)Instruction limit reached!
% 2.47/2.17 % (28737)------------------------------
% 2.47/2.17 % (28737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/2.17 % (28737)Termination reason: Unknown
% 2.47/2.17 % (28737)Termination phase: Saturation
% 2.47/2.17
% 2.47/2.17 % (28737)Memory used [KB]: 5628
% 2.47/2.17 % (28737)Time elapsed: 0.011 s
% 2.47/2.17 % (28737)Instructions burned: 18 (million)
% 2.47/2.17 % (28737)------------------------------
% 2.47/2.17 % (28737)------------------------------
% 2.47/2.18 % (28739)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_28610 for (2998ds/30Mi)
% 2.47/2.18 % (28739)Refutation not found, incomplete strategy
% 2.47/2.18 % (28739)------------------------------
% 2.47/2.18 % (28739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/2.18 % (28739)Termination reason: Refutation not found, incomplete strategy
% 2.47/2.18
% 2.47/2.18
% 2.47/2.18 % (28739)Memory used [KB]: 5500
% 2.47/2.18 % (28739)Time elapsed: 0.005 s
% 2.47/2.18 % (28739)Instructions burned: 5 (million)
% 2.47/2.18 % (28739)------------------------------
% 2.47/2.18 % (28739)------------------------------
% 2.47/2.19 % (28740)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_28610 for (2998ds/127Mi)
% 2.60/2.20 % (28741)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_28610 for (2998ds/100Mi)
% 2.60/2.22 % (28734)First to succeed.
% 2.60/2.24 % (28734)Refutation found. Thanks to Tanya!
% 2.60/2.24 % SZS status Theorem for DTF2THF_28610
% 2.60/2.24 % SZS output start Proof for DTF2THF_28610
% 2.60/2.24 thf(type_def_5, type, g: $tType).
% 2.60/2.24 thf(func_def_0, type, g: $tType).
% 2.60/2.24 thf(func_def_1, type, cGROUP2: (g > g > g) > g > $o).
% 2.60/2.24 thf(func_def_2, type, cGROUP3: (g > g > g) > g > $o).
% 2.60/2.24 thf(func_def_3, type, cGRP_ASSOC: (g > g > g) > $o).
% 2.60/2.24 thf(func_def_4, type, cGRP_LEFT_INVERSE: (g > g > g) > g > $o).
% 2.60/2.24 thf(func_def_5, type, cGRP_LEFT_UNIT: (g > g > g) > g > $o).
% 2.60/2.24 thf(func_def_6, type, cGRP_RIGHT_INVERSE: (g > g > g) > g > $o).
% 2.60/2.24 thf(func_def_7, type, cGRP_RIGHT_UNIT: (g > g > g) > g > $o).
% 2.60/2.24 thf(func_def_24, type, sK1: g > g > g).
% 2.60/2.24 thf(func_def_25, type, sK2: g).
% 2.60/2.24 thf(func_def_26, type, sK3: g).
% 2.60/2.24 thf(func_def_27, type, sK4: g).
% 2.60/2.24 thf(func_def_28, type, sK5: g).
% 2.60/2.24 thf(func_def_29, type, sK6: g).
% 2.60/2.24 thf(func_def_30, type, sK7: g).
% 2.60/2.24 thf(func_def_31, type, sK8: g).
% 2.60/2.24 thf(func_def_32, type, sK9: g).
% 2.60/2.24 thf(func_def_33, type, sK10: g > g).
% 2.60/2.24 thf(func_def_34, type, sK11: g > g).
% 2.60/2.24 thf(f968,plain,(
% 2.60/2.24 $false),
% 2.60/2.24 inference(avatar_sat_refutation,[status(thm)],[f99,f132,f155,f172,f184,f200,f206,f210,f298,f316,f329,f397,f416,f951,f967])).
% 2.60/2.24 thf(f967,plain,(
% 2.60/2.24 ~spl0_5 | ~spl0_7 | ~spl0_9 | ~spl0_10),
% 2.60/2.24 inference(avatar_contradiction_clause,[status(thm)],[f966])).
% 2.60/2.24 thf(f966,plain,(
% 2.60/2.24 $false | (~spl0_5 | ~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(trivial_inequality_removal,[status(thm)],[f962])).
% 2.60/2.24 thf(f962,plain,(
% 2.60/2.24 (sK2 != sK2) | (~spl0_5 | ~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(superposition,[status(thm)],[f98,f915])).
% 2.60/2.24 thf(f915,plain,(
% 2.60/2.24 ( ! [X0 : g] : ((sK2 = (sK1 @ (sK11 @ X0) @ X0))) ) | (~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(superposition,[status(thm)],[f623,f907])).
% 2.60/2.24 thf(f907,plain,(
% 2.60/2.24 ( ! [X0 : g] : (((sK1 @ sK2 @ (sK11 @ (sK11 @ X0))) = X0)) ) | (~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(forward_demodulation,[status(thm)],[f880,f183])).
% 2.60/2.24 thf(f183,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((sK1 @ X1 @ sK2) = X1)) ) | ~spl0_10),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f182])).
% 2.60/2.24 thf(f182,definition,(
% 2.60/2.24 spl0_10 <=> ! [X1 : g] : ((sK1 @ X1 @ sK2) = X1)),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 2.60/2.24 thf(f880,plain,(
% 2.60/2.24 ( ! [X0 : g] : (((sK1 @ X0 @ sK2) = (sK1 @ sK2 @ (sK11 @ (sK11 @ X0))))) ) | (~spl0_7 | ~spl0_9)),
% 2.60/2.24 inference(superposition,[status(thm)],[f411,f154])).
% 2.60/2.24 thf(f154,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((sK2 = (sK1 @ X1 @ (sK11 @ X1)))) ) | ~spl0_9),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f153])).
% 2.60/2.24 thf(f153,definition,(
% 2.60/2.24 spl0_9 <=> ! [X1 : g] : (sK2 = (sK1 @ X1 @ (sK11 @ X1)))),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 2.60/2.24 thf(f411,plain,(
% 2.60/2.24 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ (sK11 @ X0) @ X1)) = (sK1 @ sK2 @ X1))) ) | (~spl0_7 | ~spl0_9)),
% 2.60/2.24 inference(superposition,[status(thm)],[f123,f154])).
% 2.60/2.24 thf(f123,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1)))) ) | ~spl0_7),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f122])).
% 2.60/2.24 thf(f122,definition,(
% 2.60/2.24 spl0_7 <=> ! [X2 : g,X1 : g,X3 : g] : ((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1)))),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 2.60/2.24 thf(f623,plain,(
% 2.60/2.24 ( ! [X0 : g] : (((sK1 @ X0 @ (sK1 @ sK2 @ (sK11 @ X0))) = sK2)) ) | (~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(superposition,[status(thm)],[f408,f183])).
% 2.60/2.24 thf(f408,plain,(
% 2.60/2.24 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ X1 @ (sK11 @ (sK1 @ X0 @ X1)))) = sK2)) ) | (~spl0_7 | ~spl0_9)),
% 2.60/2.24 inference(superposition,[status(thm)],[f154,f123])).
% 2.60/2.24 thf(f98,plain,(
% 2.60/2.24 ( ! [X2 : g] : (((sK1 @ X2 @ sK9) != sK2)) ) | ~spl0_5),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f97])).
% 2.60/2.24 thf(f97,definition,(
% 2.60/2.24 spl0_5 <=> ! [X2 : g] : ((sK1 @ X2 @ sK9) != sK2)),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 2.60/2.24 thf(f951,plain,(
% 2.60/2.24 spl0_2 | ~spl0_7 | ~spl0_9 | ~spl0_10),
% 2.60/2.24 inference(avatar_contradiction_clause,[status(thm)],[f950])).
% 2.60/2.24 thf(f950,plain,(
% 2.60/2.24 $false | (spl0_2 | ~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(trivial_inequality_removal,[status(thm)],[f941])).
% 2.60/2.24 thf(f941,plain,(
% 2.60/2.24 (sK6 != sK6) | (spl0_2 | ~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(superposition,[status(thm)],[f87,f931])).
% 2.60/2.24 thf(f931,plain,(
% 2.60/2.24 ( ! [X0 : g] : (((sK1 @ sK2 @ X0) = X0)) ) | (~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(forward_demodulation,[status(thm)],[f924,f183])).
% 2.60/2.24 thf(f924,plain,(
% 2.60/2.24 ( ! [X0 : g] : (((sK1 @ X0 @ sK2) = (sK1 @ sK2 @ X0))) ) | (~spl0_7 | ~spl0_9 | ~spl0_10)),
% 2.60/2.24 inference(superposition,[status(thm)],[f411,f915])).
% 2.60/2.24 thf(f87,plain,(
% 2.60/2.24 (sK6 != (sK1 @ sK2 @ sK6)) | spl0_2),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f85])).
% 2.60/2.24 thf(f85,definition,(
% 2.60/2.24 spl0_2 <=> (sK6 = (sK1 @ sK2 @ sK6))),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 2.60/2.24 thf(f416,plain,(
% 2.60/2.24 ~spl0_1 | ~spl0_9),
% 2.60/2.24 inference(avatar_contradiction_clause,[status(thm)],[f415])).
% 2.60/2.24 thf(f415,plain,(
% 2.60/2.24 $false | (~spl0_1 | ~spl0_9)),
% 2.60/2.24 inference(trivial_inequality_removal,[status(thm)],[f414])).
% 2.60/2.24 thf(f414,plain,(
% 2.60/2.24 (sK2 != sK2) | (~spl0_1 | ~spl0_9)),
% 2.60/2.24 inference(superposition,[status(thm)],[f83,f154])).
% 2.60/2.24 thf(f83,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((sK1 @ sK5 @ X1) != sK2)) ) | ~spl0_1),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f82])).
% 2.60/2.24 thf(f82,definition,(
% 2.60/2.24 spl0_1 <=> ! [X1 : g] : ((sK1 @ sK5 @ X1) != sK2)),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 2.60/2.24 thf(f397,plain,(
% 2.60/2.24 ~spl0_1 | ~spl0_6 | ~spl0_7 | ~spl0_8),
% 2.60/2.24 inference(avatar_contradiction_clause,[status(thm)],[f396])).
% 2.60/2.24 thf(f396,plain,(
% 2.60/2.24 $false | (~spl0_1 | ~spl0_6 | ~spl0_7 | ~spl0_8)),
% 2.60/2.24 inference(trivial_inequality_removal,[status(thm)],[f395])).
% 2.60/2.24 thf(f395,plain,(
% 2.60/2.24 (sK2 != sK2) | (~spl0_1 | ~spl0_6 | ~spl0_7 | ~spl0_8)),
% 2.60/2.24 inference(superposition,[status(thm)],[f83,f282])).
% 2.60/2.24 thf(f282,plain,(
% 2.60/2.24 ( ! [X0 : g] : ((sK2 = (sK1 @ X0 @ (sK10 @ X0)))) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
% 2.60/2.24 inference(superposition,[status(thm)],[f214,f120])).
% 2.60/2.24 thf(f120,plain,(
% 2.60/2.24 ( ! [X4 : g] : (((sK1 @ (sK10 @ X4) @ X4) = sK2)) ) | ~spl0_6),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f119])).
% 2.60/2.24 thf(f119,definition,(
% 2.60/2.24 spl0_6 <=> ! [X4 : g] : ((sK1 @ (sK10 @ X4) @ X4) = sK2)),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 2.60/2.24 thf(f214,plain,(
% 2.60/2.24 ( ! [X0 : g,X1 : g] : (((sK1 @ (sK10 @ (sK10 @ X0)) @ X1) = (sK1 @ X0 @ X1))) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
% 2.60/2.24 inference(superposition,[status(thm)],[f208,f208])).
% 2.60/2.24 thf(f208,plain,(
% 2.60/2.24 ( ! [X0 : g,X1 : g] : (((sK1 @ (sK10 @ X0) @ (sK1 @ X0 @ X1)) = X1)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
% 2.60/2.24 inference(forward_demodulation,[status(thm)],[f202,f138])).
% 2.60/2.24 thf(f138,plain,(
% 2.60/2.24 ( ! [X4 : g] : (((sK1 @ sK2 @ X4) = X4)) ) | ~spl0_8),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f137])).
% 2.60/2.24 thf(f137,definition,(
% 2.60/2.24 spl0_8 <=> ! [X4 : g] : ((sK1 @ sK2 @ X4) = X4)),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 2.60/2.24 thf(f202,plain,(
% 2.60/2.24 ( ! [X0 : g,X1 : g] : (((sK1 @ sK2 @ X1) = (sK1 @ (sK10 @ X0) @ (sK1 @ X0 @ X1)))) ) | (~spl0_6 | ~spl0_7)),
% 2.60/2.24 inference(superposition,[status(thm)],[f123,f120])).
% 2.60/2.24 thf(f329,plain,(
% 2.60/2.24 ~spl0_5 | ~spl0_6),
% 2.60/2.24 inference(avatar_contradiction_clause,[status(thm)],[f328])).
% 2.60/2.24 thf(f328,plain,(
% 2.60/2.24 $false | (~spl0_5 | ~spl0_6)),
% 2.60/2.24 inference(trivial_inequality_removal,[status(thm)],[f325])).
% 2.60/2.24 thf(f325,plain,(
% 2.60/2.24 (sK2 != sK2) | (~spl0_5 | ~spl0_6)),
% 2.60/2.24 inference(superposition,[status(thm)],[f98,f120])).
% 2.60/2.24 thf(f316,plain,(
% 2.60/2.24 spl0_4 | ~spl0_10),
% 2.60/2.24 inference(avatar_contradiction_clause,[status(thm)],[f315])).
% 2.60/2.24 thf(f315,plain,(
% 2.60/2.24 $false | (spl0_4 | ~spl0_10)),
% 2.60/2.24 inference(trivial_inequality_removal,[status(thm)],[f314])).
% 2.60/2.24 thf(f314,plain,(
% 2.60/2.24 (sK7 != sK7) | (spl0_4 | ~spl0_10)),
% 2.60/2.24 inference(superposition,[status(thm)],[f95,f183])).
% 2.60/2.24 thf(f95,plain,(
% 2.60/2.24 ((sK1 @ sK7 @ sK2) != sK7) | spl0_4),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f93])).
% 2.60/2.24 thf(f93,definition,(
% 2.60/2.24 spl0_4 <=> ((sK1 @ sK7 @ sK2) = sK7)),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 2.60/2.24 thf(f298,plain,(
% 2.60/2.24 spl0_10 | ~spl0_6 | ~spl0_7 | ~spl0_8),
% 2.60/2.24 inference(avatar_split_clause,[status(thm)],[f287,f137,f122,f119,f182])).
% 2.60/2.24 thf(f287,plain,(
% 2.60/2.24 ( ! [X0 : g] : (((sK1 @ X0 @ sK2) = X0)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
% 2.60/2.24 inference(superposition,[status(thm)],[f212,f214])).
% 2.60/2.24 thf(f212,plain,(
% 2.60/2.24 ( ! [X0 : g] : (((sK1 @ (sK10 @ (sK10 @ X0)) @ sK2) = X0)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
% 2.60/2.24 inference(superposition,[status(thm)],[f208,f120])).
% 2.60/2.24 thf(f210,plain,(
% 2.60/2.24 spl0_2 | ~spl0_8),
% 2.60/2.24 inference(avatar_contradiction_clause,[status(thm)],[f209])).
% 2.60/2.24 thf(f209,plain,(
% 2.60/2.24 $false | (spl0_2 | ~spl0_8)),
% 2.60/2.24 inference(subsumption_resolution,[status(thm)],[f87,f138])).
% 2.60/2.24 thf(f206,plain,(
% 2.60/2.24 spl0_3 | ~spl0_7),
% 2.60/2.24 inference(avatar_contradiction_clause,[status(thm)],[f205])).
% 2.60/2.24 thf(f205,plain,(
% 2.60/2.24 $false | (spl0_3 | ~spl0_7)),
% 2.60/2.24 inference(trivial_inequality_removal,[status(thm)],[f204])).
% 2.60/2.24 thf(f204,plain,(
% 2.60/2.24 ((sK1 @ sK8 @ (sK1 @ sK4 @ sK3)) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | (spl0_3 | ~spl0_7)),
% 2.60/2.24 inference(superposition,[status(thm)],[f91,f123])).
% 2.60/2.24 thf(f91,plain,(
% 2.60/2.24 ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | spl0_3),
% 2.60/2.24 inference(avatar_component_clause,[status(thm)],[f89])).
% 2.60/2.24 thf(f89,definition,(
% 2.60/2.24 spl0_3 <=> ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) = (sK1 @ sK8 @ (sK1 @ sK4 @ sK3)))),
% 2.60/2.24 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 2.60/2.24 thf(f200,plain,(
% 2.60/2.24 spl0_10 | spl0_6),
% 2.60/2.24 inference(avatar_split_clause,[status(thm)],[f199,f119,f182])).
% 2.60/2.24 thf(f199,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ (sK10 @ X2) @ X2) = sK2) | ((sK1 @ X1 @ sK2) = X1)) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f198])).
% 2.60/2.24 thf(f198,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ sK2) = X1) | (((sK1 @ (sK10 @ X2) @ X2) = sK2) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f197])).
% 2.60/2.24 thf(f197,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ Y0 @ X2) = sK2)) @ (sK10 @ X2))) | ((sK1 @ X1 @ sK2) = X1)) )),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f196])).
% 2.60/2.24 thf(f196,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X2) = sK2))) = $true) | ((sK1 @ X1 @ sK2) = X1)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f195])).
% 2.60/2.24 thf(f195,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ sK2) = X1) | (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))) @ X2) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f186])).
% 2.60/2.24 thf(f186,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) = $true) | ((sK1 @ X1 @ sK2) = X1)) )),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f177])).
% 2.60/2.24 thf(f177,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((sK1 @ X1 @ sK2) = X1) | (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) = $true)) )),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 2.60/2.24 thf(f175,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((sK1 @ X1 @ sK2) = X1) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f174])).
% 2.60/2.24 thf(f174,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((((sK1 @ X1 @ sK2) = X1) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f173])).
% 2.60/2.24 thf(f173,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true) | (((^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)) @ X1) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f140])).
% 2.60/2.24 thf(f140,plain,(
% 2.60/2.24 ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 2.60/2.24 thf(f101,plain,(
% 2.60/2.24 (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 2.60/2.24 thf(f44,plain,(
% 2.60/2.24 ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 2.60/2.24 thf(f43,plain,(
% 2.60/2.24 ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) != (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))))),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 2.60/2.24 thf(f42,plain,(
% 2.60/2.24 ($false = ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0))))))))))))),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f41])).
% 2.60/2.24 thf(f41,plain,(
% 2.60/2.24 (((^[Y0 : g]: ((((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y3 @ Y2) @ Y1) = (sK1 @ Y3 @ (sK1 @ Y2 @ Y1)))))))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = Y1)))) = (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y3 @ Y2) @ Y1) = (sK1 @ Y3 @ (sK1 @ Y2 @ Y1)))))))))))) @ sK2) = $false)),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f40])).
% 2.60/2.24 thf(f40,plain,(
% 2.60/2.24 ($false = (!! @ g @ (^[Y0 : g]: ((((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y3 @ Y2) @ Y1) = (sK1 @ Y3 @ (sK1 @ Y2 @ Y1)))))))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = Y1)))) = (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y3 @ Y2) @ Y1) = (sK1 @ Y3 @ (sK1 @ Y2 @ Y1))))))))))))))),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f39])).
% 2.60/2.24 thf(f39,plain,(
% 2.60/2.24 (((^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2)))) = (((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))))))) @ sK1) = $false)),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f38])).
% 2.60/2.24 thf(f38,plain,(
% 2.60/2.24 ($false = (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2)))) = (((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2))))))))))))))))),
% 2.60/2.24 inference(not_proxy_clausification,[status(thm)],[f37])).
% 2.60/2.24 thf(f37,plain,(
% 2.60/2.24 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2)))) = (((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))))))))) = $true)),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f36])).
% 2.60/2.24 thf(f36,plain,(
% 2.60/2.24 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (((^[Y2 : g > g > g]: ((^[Y3 : g]: ((((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (?? @ g @ (^[Y7 : g]: ((Y4 @ Y7 @ Y6) = Y5)))))))) @ Y2 @ Y3) & ((^[Y4 : g > g > g]: (!! @ g @ (^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (!! @ g @ (^[Y7 : g]: ((Y4 @ (Y4 @ Y7 @ Y6) @ Y5) = (Y4 @ Y7 @ (Y4 @ Y6 @ Y5)))))))))) @ Y2)) & ((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: ((Y4 @ Y5 @ Y6) = Y6)))))) @ Y2 @ Y3))))) @ Y0 @ Y1) = ((^[Y2 : g > g > g]: ((^[Y3 : g]: ((((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (?? @ g @ (^[Y7 : g]: ((Y4 @ Y6 @ Y7) = Y5)))))))) @ Y2 @ Y3) & ((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: ((Y4 @ Y6 @ Y5) = Y6)))))) @ Y2 @ Y3)) & ((^[Y4 : g > g > g]: (!! @ g @ (^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (!! @ g @ (^[Y7 : g]: ((Y4 @ (Y4 @ Y7 @ Y6) @ Y5) = (Y4 @ Y7 @ (Y4 @ Y6 @ Y5)))))))))) @ Y2))))) @ Y0 @ Y1))))))) = $true)),
% 2.60/2.24 inference(definition_unfolding,[status(thm)],[f29,f34,f35])).
% 2.60/2.24 thf(f35,plain,(
% 2.60/2.24 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: ((Y2 @ Y4 @ Y5) = Y3)))))))) @ Y0 @ Y1) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y2 @ Y4 @ Y3) = Y4)))))) @ Y0 @ Y1)) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ Y5 @ (Y2 @ Y4 @ Y3)))))))))) @ Y0))))))),
% 2.60/2.24 inference(definition_unfolding,[status(thm)],[f32,f27,f26,f28])).
% 2.60/2.24 thf(f28,plain,(
% 2.60/2.24 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ Y3 @ (Y0 @ Y2 @ Y1)))))))))))),
% 2.60/2.24 inference(cnf_transformation,[status(thm)],[f23])).
% 2.60/2.24 thf(f23,plain,(
% 2.60/2.24 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ Y3 @ (Y0 @ Y2 @ Y1)))))))))))),
% 2.60/2.24 inference(fool_elimination,[status(thm)],[f1])).
% 2.60/2.24 thf(f1,axiom,(
% 2.60/2.24 (cGRP_ASSOC = (^[X0 : g > g > g] : (! [X1 : g,X2 : g,X3 : g] : ((X0 @ (X0 @ X1 @ X2) @ X3) = (X0 @ X1 @ (X0 @ X2 @ X3))))))),
% 2.60/2.24 file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_ASSOC_def)).
% 2.60/2.24 thf(f26,plain,(
% 2.60/2.24 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 2.60/2.24 inference(cnf_transformation,[status(thm)],[f16])).
% 2.60/2.24 thf(f16,plain,(
% 2.60/2.24 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 2.60/2.24 inference(fool_elimination,[status(thm)],[f15])).
% 2.60/2.24 thf(f15,plain,(
% 2.60/2.24 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ((X0 @ X2 @ X1) = X2))) = cGRP_RIGHT_UNIT)),
% 2.60/2.24 inference(rectify,[status(thm)],[f5])).
% 2.60/2.24 thf(f5,axiom,(
% 2.60/2.24 ((^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ((X0 @ X1 @ X4) = X1))) = cGRP_RIGHT_UNIT)),
% 2.60/2.24 file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_RIGHT_UNIT_def)).
% 2.60/2.24 thf(f27,plain,(
% 2.60/2.24 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 2.60/2.24 inference(cnf_transformation,[status(thm)],[f25])).
% 2.60/2.24 thf(f25,plain,(
% 2.60/2.24 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 2.60/2.24 inference(fool_elimination,[status(thm)],[f24])).
% 2.60/2.24 thf(f24,plain,(
% 2.60/2.24 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : ((X0 @ X2 @ X3) = X1))) = cGRP_RIGHT_INVERSE)),
% 2.60/2.24 inference(rectify,[status(thm)],[f4])).
% 2.60/2.24 thf(f4,axiom,(
% 2.60/2.24 ((^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : ((X0 @ X1 @ X2) = X4))) = cGRP_RIGHT_INVERSE)),
% 2.60/2.24 file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_RIGHT_INVERSE_def)).
% 2.60/2.24 thf(f32,plain,(
% 2.60/2.24 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_INVERSE @ Y0 @ Y1) & (cGRP_RIGHT_UNIT @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))),
% 2.60/2.24 inference(cnf_transformation,[status(thm)],[f14])).
% 2.60/2.24 thf(f14,plain,(
% 2.60/2.24 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_INVERSE @ Y0 @ Y1) & (cGRP_RIGHT_UNIT @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))),
% 2.60/2.24 inference(fool_elimination,[status(thm)],[f13])).
% 2.60/2.24 thf(f13,plain,(
% 2.60/2.24 (cGROUP3 = (^[X0 : g > g > g, X1 : g] : ((cGRP_ASSOC @ X0) & (cGRP_RIGHT_UNIT @ X0 @ X1) & (cGRP_RIGHT_INVERSE @ X0 @ X1))))),
% 2.60/2.24 inference(rectify,[status(thm)],[f7])).
% 2.60/2.24 thf(f7,axiom,(
% 2.60/2.24 (cGROUP3 = (^[X0 : g > g > g, X4 : g] : ((cGRP_ASSOC @ X0) & (cGRP_RIGHT_UNIT @ X0 @ X4) & (cGRP_RIGHT_INVERSE @ X0 @ X4))))),
% 2.60/2.24 file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGROUP3_def)).
% 2.60/2.24 thf(f34,plain,(
% 2.60/2.24 (cGROUP2 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: ((Y2 @ Y5 @ Y4) = Y3)))))))) @ Y0 @ Y1) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ Y5 @ (Y2 @ Y4 @ Y3)))))))))) @ Y0)) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y2 @ Y3 @ Y4) = Y4)))))) @ Y0 @ Y1))))))),
% 2.60/2.24 inference(definition_unfolding,[status(thm)],[f33,f30,f28,f31])).
% 2.60/2.24 thf(f31,plain,(
% 2.60/2.24 (cGRP_LEFT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2)))))))),
% 2.60/2.24 inference(cnf_transformation,[status(thm)],[f12])).
% 2.60/2.24 thf(f12,plain,(
% 2.60/2.24 (cGRP_LEFT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2)))))))),
% 2.60/2.24 inference(fool_elimination,[status(thm)],[f11])).
% 2.60/2.24 thf(f11,plain,(
% 2.60/2.24 (cGRP_LEFT_UNIT = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ((X0 @ X1 @ X2) = X2))))),
% 2.60/2.24 inference(rectify,[status(thm)],[f3])).
% 2.60/2.24 thf(f3,axiom,(
% 2.60/2.24 (cGRP_LEFT_UNIT = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ((X0 @ X4 @ X1) = X1))))),
% 2.60/2.24 file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_LEFT_UNIT_def)).
% 2.60/2.24 thf(f30,plain,(
% 2.60/2.24 (cGRP_LEFT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1)))))))))),
% 2.60/2.24 inference(cnf_transformation,[status(thm)],[f18])).
% 2.60/2.24 thf(f18,plain,(
% 2.60/2.24 (cGRP_LEFT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1)))))))))),
% 2.60/2.24 inference(fool_elimination,[status(thm)],[f17])).
% 2.60/2.24 thf(f17,plain,(
% 2.60/2.24 (cGRP_LEFT_INVERSE = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : ((X0 @ X3 @ X2) = X1))))),
% 2.60/2.24 inference(rectify,[status(thm)],[f2])).
% 2.60/2.24 thf(f2,axiom,(
% 2.60/2.24 (cGRP_LEFT_INVERSE = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : ((X0 @ X2 @ X1) = X4))))),
% 2.60/2.24 file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGRP_LEFT_INVERSE_def)).
% 2.60/2.24 thf(f33,plain,(
% 2.60/2.24 (cGROUP2 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_LEFT_INVERSE @ Y0 @ Y1) & (cGRP_ASSOC @ Y0)) & (cGRP_LEFT_UNIT @ Y0 @ Y1))))))),
% 2.60/2.24 inference(cnf_transformation,[status(thm)],[f20])).
% 2.60/2.24 thf(f20,plain,(
% 2.60/2.24 (cGROUP2 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_LEFT_INVERSE @ Y0 @ Y1) & (cGRP_ASSOC @ Y0)) & (cGRP_LEFT_UNIT @ Y0 @ Y1))))))),
% 2.60/2.24 inference(fool_elimination,[status(thm)],[f19])).
% 2.60/2.24 thf(f19,plain,(
% 2.60/2.24 (cGROUP2 = (^[X0 : g > g > g, X1 : g] : ((cGRP_LEFT_UNIT @ X0 @ X1) & (cGRP_ASSOC @ X0) & (cGRP_LEFT_INVERSE @ X0 @ X1))))),
% 2.60/2.24 inference(rectify,[status(thm)],[f6])).
% 2.60/2.24 thf(f6,axiom,(
% 2.60/2.24 (cGROUP2 = (^[X0 : g > g > g, X4 : g] : ((cGRP_LEFT_UNIT @ X0 @ X4) & (cGRP_ASSOC @ X0) & (cGRP_LEFT_INVERSE @ X0 @ X4))))),
% 2.60/2.24 file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cGROUP2_def)).
% 2.60/2.24 thf(f29,plain,(
% 2.60/2.24 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((cGROUP2 @ Y0 @ Y1) = (cGROUP3 @ Y0 @ Y1))))))) = $true)),
% 2.60/2.24 inference(cnf_transformation,[status(thm)],[f22])).
% 2.60/2.24 thf(f22,plain,(
% 2.60/2.24 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((cGROUP2 @ Y0 @ Y1) = (cGROUP3 @ Y0 @ Y1))))))) = $true)),
% 2.60/2.24 inference(fool_elimination,[status(thm)],[f21])).
% 2.60/2.24 thf(f21,plain,(
% 2.60/2.24 ~! [X0 : g,X1 : g > g > g] : ((cGROUP2 @ X1 @ X0) <=> (cGROUP3 @ X1 @ X0))),
% 2.60/2.24 inference(rectify,[status(thm)],[f9])).
% 2.60/2.24 thf(f9,negated_conjecture,(
% 2.60/2.24 ~! [X4 : g,X0 : g > g > g] : ((cGROUP2 @ X0 @ X4) <=> (cGROUP3 @ X0 @ X4))),
% 2.60/2.24 inference(negated_conjecture,[status(cth)],[f8])).
% 2.60/2.24 thf(f8,conjecture,(
% 2.60/2.24 ! [X4 : g,X0 : g > g > g] : ((cGROUP2 @ X0 @ X4) <=> (cGROUP3 @ X0 @ X4))),
% 2.60/2.24 file('/export/starexec/sandbox2/tmp/tmp.JdBYYt9Dqg/DTF2THF_28610.p',cEQUIV_02_03)).
% 2.60/2.24 thf(f184,plain,(
% 2.60/2.24 spl0_8 | spl0_10),
% 2.60/2.24 inference(avatar_split_clause,[status(thm)],[f180,f182,f137])).
% 2.60/2.24 thf(f180,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ sK2) = X1) | ((sK1 @ sK2 @ X2) = X2)) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f179])).
% 2.60/2.24 thf(f179,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : ((((sK1 @ sK2 @ X2) = X2) = $true) | ((sK1 @ X1 @ sK2) = X1)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f178])).
% 2.60/2.24 thf(f178,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ sK2) = X1) | (((^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)) @ X2) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f176])).
% 2.60/2.24 thf(f176,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $true) | ((sK1 @ X1 @ sK2) = X1)) )),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 2.60/2.24 thf(f172,plain,(
% 2.60/2.24 spl0_6 | spl0_9),
% 2.60/2.24 inference(avatar_split_clause,[status(thm)],[f171,f153,f119])).
% 2.60/2.24 thf(f171,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ (sK10 @ X2) @ X2) = sK2) | (sK2 = (sK1 @ X1 @ (sK11 @ X1)))) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f170])).
% 2.60/2.24 thf(f170,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : ((((sK1 @ (sK10 @ X2) @ X2) = sK2) = $true) | (sK2 = (sK1 @ X1 @ (sK11 @ X1)))) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f169])).
% 2.60/2.24 thf(f169,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : ((sK2 = (sK1 @ X1 @ (sK11 @ X1))) | ($true = ((^[Y0 : g]: ((sK1 @ Y0 @ X2) = sK2)) @ (sK10 @ X2)))) )),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f168])).
% 2.60/2.24 thf(f168,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : ((sK2 = (sK1 @ X1 @ (sK11 @ X1))) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X2) = sK2))) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f167])).
% 2.60/2.24 thf(f167,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))) @ X2) = $true) | (sK2 = (sK1 @ X1 @ (sK11 @ X1)))) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f158])).
% 2.60/2.24 thf(f158,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((sK2 = (sK1 @ X1 @ (sK11 @ X1))) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) = $true)) )),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 2.60/2.24 thf(f156,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) = $true) | (sK2 = (sK1 @ X1 @ (sK11 @ X1)))) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f147])).
% 2.60/2.24 thf(f147,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((((sK1 @ X1 @ (sK11 @ X1)) = sK2) = $true) | (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) = $true)) )),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f145])).
% 2.60/2.24 thf(f145,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true) | (((sK1 @ X1 @ (sK11 @ X1)) = sK2) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f144])).
% 2.60/2.24 thf(f144,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((((^[Y0 : g]: ((sK1 @ X1 @ Y0) = sK2)) @ (sK11 @ X1)) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f143])).
% 2.60/2.24 thf(f143,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = sK2))) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f142])).
% 2.60/2.24 thf(f142,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))) @ X1) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f141])).
% 2.60/2.24 thf(f141,plain,(
% 2.60/2.24 ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 2.60/2.24 thf(f155,plain,(
% 2.60/2.24 spl0_8 | spl0_9),
% 2.60/2.24 inference(avatar_split_clause,[status(thm)],[f151,f153,f137])).
% 2.60/2.24 thf(f151,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ sK2 @ X2) = X2) | (sK2 = (sK1 @ X1 @ (sK11 @ X1)))) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f150])).
% 2.60/2.24 thf(f150,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : ((sK2 = (sK1 @ X1 @ (sK11 @ X1))) | (((sK1 @ sK2 @ X2) = X2) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f149])).
% 2.60/2.24 thf(f149,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : ((sK2 = (sK1 @ X1 @ (sK11 @ X1))) | (((^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)) @ X2) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f148])).
% 2.60/2.24 thf(f148,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((sK2 = (sK1 @ X1 @ (sK11 @ X1))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $true)) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f146])).
% 2.60/2.24 thf(f146,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((((sK1 @ X1 @ (sK11 @ X1)) = sK2) = $true) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $true)) )),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f145])).
% 2.60/2.24 thf(f132,plain,(
% 2.60/2.24 spl0_7 | spl0_7),
% 2.60/2.24 inference(avatar_split_clause,[status(thm)],[f131,f122,f122])).
% 2.60/2.24 thf(f131,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : (((sK1 @ (sK1 @ X6 @ X5) @ X4) = (sK1 @ X6 @ (sK1 @ X5 @ X4))) | ((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1)))) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f130])).
% 2.60/2.24 thf(f130,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : (((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1))) | (((sK1 @ (sK1 @ X6 @ X5) @ X4) = (sK1 @ X6 @ (sK1 @ X5 @ X4))) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f129])).
% 2.60/2.24 thf(f129,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : (((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1))) | (((^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ X5) @ X4) = (sK1 @ Y0 @ (sK1 @ X5 @ X4)))) @ X6) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f128])).
% 2.60/2.24 thf(f128,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g,X4 : g,X5 : g] : (($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ X5) @ X4) = (sK1 @ Y0 @ (sK1 @ X5 @ X4)))))) | ((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1)))) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f127])).
% 2.60/2.24 thf(f127,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g,X4 : g,X5 : g] : (($true = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ X4) = (sK1 @ Y1 @ (sK1 @ Y0 @ X4)))))) @ X5)) | ((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1)))) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f126])).
% 2.60/2.24 thf(f126,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ X4) = (sK1 @ Y1 @ (sK1 @ Y0 @ X4))))))) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f125])).
% 2.60/2.24 thf(f125,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1))) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))) @ X4) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f111])).
% 2.60/2.24 thf(f111,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1))) | ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0))))))))))) )),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 2.60/2.24 thf(f110,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1))) | (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) = $true)) )),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 2.60/2.24 thf(f108,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1))) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f107])).
% 2.60/2.24 thf(f107,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ (sK1 @ X3 @ X2) @ X1) = (sK1 @ X3 @ (sK1 @ X2 @ X1))) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f106])).
% 2.60/2.24 thf(f106,plain,(
% 2.60/2.24 ( ! [X2 : g,X3 : g,X1 : g] : (((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true) | (((^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ X2) @ X1) = (sK1 @ Y0 @ (sK1 @ X2 @ X1)))) @ X3) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f105])).
% 2.60/2.24 thf(f105,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ X2) @ X1) = (sK1 @ Y0 @ (sK1 @ X2 @ X1))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f104])).
% 2.60/2.24 thf(f104,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ X1) = (sK1 @ Y1 @ (sK1 @ Y0 @ X1)))))) @ X2) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f103])).
% 2.60/2.24 thf(f103,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ X1) = (sK1 @ Y1 @ (sK1 @ Y0 @ X1))))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f102])).
% 2.60/2.24 thf(f102,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))) @ X1) = $true)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f100])).
% 2.60/2.24 thf(f100,plain,(
% 2.60/2.24 ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) | ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $true)),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 2.60/2.24 thf(f99,plain,(
% 2.60/2.24 spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_4 | spl0_5),
% 2.60/2.24 inference(avatar_split_clause,[status(thm)],[f80,f97,f93,f89,f85,f82])).
% 2.60/2.24 thf(f80,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | ((sK1 @ sK5 @ X1) != sK2) | ((sK1 @ X2 @ sK9) != sK2) | ((sK1 @ sK7 @ sK2) != sK7) | (sK6 != (sK1 @ sK2 @ sK6))) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f79])).
% 2.60/2.24 thf(f79,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (($false = ((sK1 @ X2 @ sK9) = sK2)) | ((sK1 @ sK5 @ X1) != sK2) | ((sK1 @ sK7 @ sK2) != sK7) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | (sK6 != (sK1 @ sK2 @ sK6))) )),
% 2.60/2.24 inference(duplicate_literal_removal,[status(thm)],[f78])).
% 2.60/2.24 thf(f78,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | ($false = ((sK1 @ X2 @ sK9) = sK2)) | ((sK1 @ sK5 @ X1) != sK2) | (sK6 != (sK1 @ sK2 @ sK6)) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | ((sK1 @ sK7 @ sK2) != sK7)) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f77])).
% 2.60/2.24 thf(f77,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (($false = ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) = (sK1 @ sK8 @ (sK1 @ sK4 @ sK3)))) | (sK6 != (sK1 @ sK2 @ sK6)) | ($false = ((sK1 @ X2 @ sK9) = sK2)) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | ((sK1 @ sK7 @ sK2) != sK7) | ((sK1 @ sK5 @ X1) != sK2)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f76])).
% 2.60/2.24 thf(f76,plain,(
% 2.60/2.24 ( ! [X2 : g,X1 : g] : (($false = ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) = (sK1 @ sK8 @ (sK1 @ sK4 @ sK3)))) | (sK6 != (sK1 @ sK2 @ sK6)) | ((sK1 @ sK5 @ X1) != sK2) | ((sK1 @ sK7 @ sK2) != sK7) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | (((^[Y0 : g]: ((sK1 @ Y0 @ sK9) = sK2)) @ X2) = $false)) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f75])).
% 2.60/2.24 thf(f75,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK9) = sK2))) = $false) | ((sK1 @ sK7 @ sK2) != sK7) | ($false = ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) = (sK1 @ sK8 @ (sK1 @ sK4 @ sK3)))) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | (sK6 != (sK1 @ sK2 @ sK6)) | ((sK1 @ sK5 @ X1) != sK2)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f74])).
% 2.60/2.24 thf(f74,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK9) = sK2))) = $false) | ((sK1 @ sK5 @ X1) != sK2) | (((^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3)))) @ sK8) = $false) | ((sK1 @ sK7 @ sK2) != sK7) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | (sK6 != (sK1 @ sK2 @ sK6))) )),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f73])).
% 2.60/2.24 thf(f73,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | (sK6 != (sK1 @ sK2 @ sK6)) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK9) = sK2))) = $false) | ((sK1 @ sK5 @ X1) != sK2) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | ((sK1 @ sK7 @ sK2) != sK7)) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f72])).
% 2.60/2.24 thf(f72,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((sK1 @ sK7 @ sK2) != sK7) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))) @ sK9) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ((sK1 @ sK5 @ X1) != sK2) | (sK6 != (sK1 @ sK2 @ sK6))) )),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f71])).
% 2.60/2.24 thf(f71,plain,(
% 2.60/2.24 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((sK1 @ sK7 @ sK2) != sK7) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ((sK1 @ sK5 @ X1) != sK2) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | (sK6 != (sK1 @ sK2 @ sK6))) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f70])).
% 2.60/2.24 thf(f70,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((sK1 @ sK5 @ X1) != sK2) | ((sK1 @ sK7 @ sK2) != sK7) | (sK6 != (sK1 @ sK2 @ sK6)) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | ($false = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3)))))) @ sK4)) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))))) )),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f69])).
% 2.60/2.24 thf(f69,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ((sK1 @ sK5 @ X1) != sK2) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((sK1 @ sK7 @ sK2) != sK7) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | (sK6 != (sK1 @ sK2 @ sK6))) )),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f68])).
% 2.60/2.24 thf(f68,plain,(
% 2.60/2.24 ( ! [X1 : g] : ((((sK1 @ sK5 @ X1) = sK2) = $false) | (sK6 != (sK1 @ sK2 @ sK6)) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ((sK1 @ sK7 @ sK2) != sK7) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3)))) )),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f67])).
% 2.60/2.24 thf(f67,plain,(
% 2.60/2.24 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ((sK1 @ sK7 @ sK2) != sK7) | ($false = ((^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2)) @ X1)) | (sK6 != (sK1 @ sK2 @ sK6)) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3)))) )),
% 2.60/2.24 inference(pi_clausification,[status(thm)],[f66])).
% 2.60/2.24 thf(f66,plain,(
% 2.60/2.24 ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | ((sK1 @ sK7 @ sK2) != sK7) | (sK6 != (sK1 @ sK2 @ sK6))),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f65])).
% 2.60/2.24 thf(f65,plain,(
% 2.60/2.24 (((sK1 @ sK7 @ sK2) = sK7) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) != (sK1 @ sK8 @ (sK1 @ sK4 @ sK3))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | (sK6 != (sK1 @ sK2 @ sK6)) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false)),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f64])).
% 2.60/2.24 thf(f64,plain,(
% 2.60/2.24 ($false = ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) = (sK1 @ sK8 @ (sK1 @ sK4 @ sK3)))) | (((sK1 @ sK7 @ sK2) = sK7) = $false) | (sK6 != (sK1 @ sK2 @ sK6)) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false)),
% 2.60/2.24 inference(equality_proxy_clausification,[status(thm)],[f63])).
% 2.60/2.24 thf(f63,plain,(
% 2.60/2.24 (((sK1 @ sK2 @ sK6) = sK6) = $false) | ($false = ((sK1 @ (sK1 @ sK8 @ sK4) @ sK3) = (sK1 @ sK8 @ (sK1 @ sK4 @ sK3)))) | (((sK1 @ sK7 @ sK2) = sK7) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false)),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f62])).
% 2.60/2.24 thf(f62,plain,(
% 2.60/2.24 (((^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3)))) @ sK8) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false) | (((sK1 @ sK7 @ sK2) = sK7) = $false)),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f61])).
% 2.60/2.24 thf(f61,plain,(
% 2.60/2.24 ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | (((sK1 @ sK7 @ sK2) = sK7) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))))),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f60])).
% 2.60/2.24 thf(f60,plain,(
% 2.60/2.24 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ($false = ((^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)) @ sK7)) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false)),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f59])).
% 2.60/2.24 thf(f59,plain,(
% 2.60/2.24 ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))))),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f58])).
% 2.60/2.24 thf(f58,plain,(
% 2.60/2.24 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | (((^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)) @ sK6) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false)),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f57])).
% 2.60/2.24 thf(f57,plain,(
% 2.60/2.24 ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))))),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f56])).
% 2.60/2.24 thf(f56,plain,(
% 2.60/2.24 ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))) @ sK3) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false)),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f55])).
% 2.60/2.24 thf(f55,plain,(
% 2.60/2.24 ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK2))) = $false)),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f54])).
% 2.60/2.24 thf(f54,plain,(
% 2.60/2.24 (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))) @ sK5) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false)),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f53])).
% 2.60/2.24 thf(f53,plain,(
% 2.60/2.24 ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $false)),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 2.60/2.24 thf(f52,plain,(
% 2.60/2.24 (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false)),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 2.60/2.24 thf(f51,plain,(
% 2.60/2.24 ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0))))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ Y0 @ sK4) @ sK3) = (sK1 @ Y0 @ (sK1 @ sK4 @ sK3))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false)),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f50])).
% 2.60/2.24 thf(f50,plain,(
% 2.60/2.24 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false) | ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0))))))))))) | ($false = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3)))))) @ sK4))),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f49])).
% 2.60/2.24 thf(f49,plain,(
% 2.60/2.24 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ Y1 @ Y0) @ sK3) = (sK1 @ Y1 @ (sK1 @ Y0 @ sK3))))))) = $false) | ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0))))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false)),
% 2.60/2.24 inference(beta_eta_normalization,[status(thm)],[f48])).
% 2.60/2.24 thf(f48,plain,(
% 2.60/2.24 ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0))))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))) @ sK3) = $false)),
% 2.60/2.24 inference(sigma_clausification,[status(thm)],[f47])).
% 2.60/2.24 thf(f47,plain,(
% 2.60/2.24 ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) | ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0))))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false)),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 2.60/2.24 thf(f46,plain,(
% 2.60/2.24 (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0))) = $false) | ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))))),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 2.60/2.24 thf(f45,plain,(
% 2.60/2.24 ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK2))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ sK2 @ Y0) = Y0)))) = $false) | ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y2 @ Y1) @ Y0) = (sK1 @ Y2 @ (sK1 @ Y1 @ Y0)))))))))))),
% 2.60/2.24 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 2.60/2.24 % SZS output end Proof for DTF2THF_28610
% 2.60/2.24 % (28734)------------------------------
% 2.60/2.24 % (28734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/2.24 % (28734)Termination reason: Refutation
% 2.60/2.24
% 2.60/2.24 % (28734)Memory used [KB]: 6140
% 2.60/2.24 % (28734)Time elapsed: 0.102 s
% 2.60/2.24 % (28734)Instructions burned: 185 (million)
% 2.60/2.24 % (28734)------------------------------
% 2.60/2.24 % (28734)------------------------------
% 2.60/2.24 % (28706)Success in time 0.236 s
%------------------------------------------------------------------------------