%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV141^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:23 AM UTC 2026
% Result : Theorem 1.44s 1.49s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 279 ( 16 unt; 0 typ; 13 def)
% Number of atoms : 2843 ( 271 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 8846 ( 413 ~; 501 |; 459 &;5527 @)
% ( 13 <=>; 712 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 692 ( 692 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 46 usr; 40 con; 0-2 aty)
% (1221 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1474 (1324 ^; 150 !; 0 ?;1474 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a > a > $o ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a > a > $o ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a > a > $o ).
thf(func_def_37,type,
sK18: a > a > $o ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a > a > $o ).
thf(func_def_43,type,
sK24: a > a > $o ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(f1906,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f93,f162,f193,f220,f345,f685,f1165,f1376,f1585,f1680,f1806,f1865,f1905]) ).
thf(f1905,plain,
( ~ spl0_3
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f1904]) ).
thf(f1904,plain,
( $false
| ~ spl0_3
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f1903]) ).
thf(f1903,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1902]) ).
thf(f1902,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_3
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1901]) ).
thf(f1901,plain,
( ( $true
= ( ~ ( ( sK3 @ sK32 @ sK33 )
| $true ) ) )
| ~ spl0_3
| ~ spl0_29 ),
inference(forward_demodulation,[status(thm)],[f1899,f1888]) ).
thf(f1888,plain,
( ( ( sK2 @ sK32 @ sK33 )
= $true )
| ~ spl0_29 ),
inference(binary_proxy_clausification,[status(thm)],[f1886]) ).
thf(f1886,plain,
( ( $false
= ( ( sK2 @ sK32 @ sK33 )
=> ( sK6 @ sK32 @ sK33 ) ) )
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1885]) ).
thf(f1885,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK32 @ Y0 )
=> ( sK6 @ sK32 @ Y0 ) )
@ sK33 )
= $false )
| ~ spl0_29 ),
inference(sigma_clausification,[status(thm)],[f1878]) ).
thf(f1878,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK32 @ Y0 )
=> ( sK6 @ sK32 @ Y0 ) ) )
= $false )
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1876]) ).
thf(f1876,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK32 ) )
| ~ spl0_29 ),
inference(sigma_clausification,[status(thm)],[f1805]) ).
thf(f1805,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_29 ),
inference(avatar_component_clause,[status(thm)],[f1804]) ).
thf(f1804,definition,
( spl0_29
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition]) ).
thf(f1899,plain,
( ( $true
= ( ~ ( ( sK3 @ sK32 @ sK33 )
| ( sK2 @ sK32 @ sK33 ) ) ) )
| ~ spl0_3
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1894]) ).
thf(f1894,plain,
( ( ( ( ( sK3 @ sK32 @ sK33 )
| ( sK2 @ sK32 @ sK33 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_29 ),
inference(superposition,[status(thm)],[f1417,f1890]) ).
thf(f1890,plain,
( ( $false
= ( sK6 @ sK32 @ sK33 ) )
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1889]) ).
thf(f1889,plain,
( ( $false
= ( $true
=> ( sK6 @ sK32 @ sK33 ) ) )
| ~ spl0_29 ),
inference(backward_demodulation,[status(thm)],[f1886,f1888]) ).
thf(f1417,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK3 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f1416]) ).
thf(f1416,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f1413]) ).
thf(f1413,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f1412]) ).
thf(f1412,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f1409]) ).
thf(f1409,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f1397]) ).
thf(f1397,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f1385]) ).
thf(f1385,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f1384]) ).
thf(f1384,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK6 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl0_3
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f1865,plain,
( ~ spl0_3
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f1864]) ).
thf(f1864,plain,
( $false
| ~ spl0_3
| ~ spl0_28 ),
inference(trivial_inequality_removal,[status(thm)],[f1860]) ).
thf(f1860,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_28 ),
inference(superposition,[status(thm)],[f1851,f1433]) ).
thf(f1433,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 @ X3 )
& ( sK6 @ X3 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f1432]) ).
thf(f1432,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ X2 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) )
@ X3 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f1419]) ).
thf(f1419,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X2 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f1418]) ).
thf(f1418,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f1415]) ).
thf(f1415,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f1414]) ).
thf(f1414,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f1411]) ).
thf(f1411,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f1410]) ).
thf(f1410,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f1397,f1409]) ).
thf(f1851,plain,
( ( ( ( ( sK6 @ sK29 @ sK30 )
& ( sK6 @ sK30 @ sK31 ) )
=> ( sK6 @ sK29 @ sK31 ) )
= $false )
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1850]) ).
thf(f1850,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK29 @ sK30 )
& ( sK6 @ sK30 @ Y0 ) )
=> ( sK6 @ sK29 @ Y0 ) )
@ sK31 )
= $false )
| ~ spl0_28 ),
inference(sigma_clausification,[status(thm)],[f1846]) ).
thf(f1846,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK29 @ sK30 )
& ( sK6 @ sK30 @ Y0 ) )
=> ( sK6 @ sK29 @ Y0 ) ) ) )
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1845]) ).
thf(f1845,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK29 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ sK29 @ Y1 ) ) )
@ sK30 )
= $false )
| ~ spl0_28 ),
inference(sigma_clausification,[status(thm)],[f1831]) ).
thf(f1831,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK29 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ sK29 @ Y1 ) ) ) )
= $false )
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1827]) ).
thf(f1827,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) )
@ sK29 )
= $false )
| ~ spl0_28 ),
inference(sigma_clausification,[status(thm)],[f1802]) ).
thf(f1802,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_28 ),
inference(avatar_component_clause,[status(thm)],[f1801]) ).
thf(f1801,definition,
( spl0_28
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition]) ).
thf(f1806,plain,
( spl0_28
| spl0_29
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f1797,f683,f91,f1804,f1801]) ).
thf(f91,definition,
( spl0_6
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f683,definition,
( spl0_14
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f1797,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f1789]) ).
thf(f1789,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(not_proxy_clausification,[status(thm)],[f1758]) ).
thf(f1758,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1757]) ).
thf(f1757,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f1741,f1683]) ).
thf(f1683,plain,
( ( ( sK6 @ sK19 @ sK20 )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1682]) ).
thf(f1682,plain,
( ( ( $true
=> ( sK6 @ sK19 @ sK20 ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1681]) ).
thf(f1681,plain,
( ( ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) ) )
=> ( sK6 @ sK19 @ sK20 ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f1473,f684]) ).
thf(f684,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f683]) ).
thf(f1473,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) ) )
=> ( sK6 @ sK19 @ sK20 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f1472]) ).
thf(f1472,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK19 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK19 @ Y0 ) ) ) )
=> ( sK6 @ sK19 @ Y0 ) )
@ sK20 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f1461]) ).
thf(f1461,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK19 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK19 @ Y0 ) ) ) )
=> ( sK6 @ sK19 @ Y0 ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f1459]) ).
thf(f1459,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f91]) ).
thf(f1741,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK19 @ sK20 ) )
= $true )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f1740]) ).
thf(f1740,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) )
@ X1 )
= $true )
| ~ spl0_14 ),
inference(pi_clausification,[status(thm)],[f684]) ).
thf(f1680,plain,
( ~ spl0_3
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f1679]) ).
thf(f1679,plain,
( $false
| ~ spl0_3
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f1678]) ).
thf(f1678,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f1677]) ).
thf(f1677,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f1676]) ).
thf(f1676,plain,
( ( ( ~ ( $true
| ( sK2 @ sK27 @ sK28 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f1675,f1661]) ).
thf(f1661,plain,
( ( ( sK3 @ sK27 @ sK28 )
= $true )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[status(thm)],[f1600]) ).
thf(f1600,plain,
( ( ( ( sK3 @ sK27 @ sK28 )
=> ( sK6 @ sK27 @ sK28 ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[status(thm)],[f1599]) ).
thf(f1599,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ sK27 @ Y0 )
=> ( sK6 @ sK27 @ Y0 ) )
@ sK28 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[status(thm)],[f1595]) ).
thf(f1595,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK27 @ Y0 )
=> ( sK6 @ sK27 @ Y0 ) ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[status(thm)],[f1591]) ).
thf(f1591,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK27 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[status(thm)],[f1584]) ).
thf(f1584,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f1583]) ).
thf(f1583,definition,
( spl0_21
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f1675,plain,
( ( ( ~ ( ( sK3 @ sK27 @ sK28 )
| ( sK2 @ sK27 @ sK28 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f1669]) ).
thf(f1669,plain,
( ( ( ( ( sK3 @ sK27 @ sK28 )
| ( sK2 @ sK27 @ sK28 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f1417,f1660]) ).
thf(f1660,plain,
( ( ( sK6 @ sK27 @ sK28 )
= $false )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[status(thm)],[f1600]) ).
thf(f1585,plain,
( spl0_21
| spl0_5
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f1579,f680,f91,f88,f1583]) ).
thf(f88,definition,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f680,definition,
( spl0_13
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f1579,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f1573]) ).
thf(f1573,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_13 ),
inference(not_proxy_clausification,[status(thm)],[f1526]) ).
thf(f1526,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1525]) ).
thf(f1525,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
=> $false ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f1520,f1476]) ).
thf(f1476,plain,
( ( ( sK6 @ sK19 @ sK20 )
= $false )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1475]) ).
thf(f1475,plain,
( ( ( $true
=> ( sK6 @ sK19 @ sK20 ) )
= $false )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1474]) ).
thf(f1474,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) )
| $true )
=> ( sK6 @ sK19 @ sK20 ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f1473,f681]) ).
thf(f681,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f680]) ).
thf(f1520,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK19 @ sK20 ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f1519]) ).
thf(f1519,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) )
@ X1 )
= $true )
| ~ spl0_13 ),
inference(pi_clausification,[status(thm)],[f681]) ).
thf(f1376,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f1375]) ).
thf(f1375,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1374]) ).
thf(f1374,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1373]) ).
thf(f1373,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f1366,f219]) ).
thf(f219,plain,
( ( $true
= ( sK2 @ sK11 @ sK12 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f218]) ).
thf(f218,definition,
( spl0_10
<=> ( $true
= ( sK2 @ sK11 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f1366,plain,
( ( $true
= ( ~ ( sK2 @ sK11 @ sK12 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1360]) ).
thf(f1360,plain,
( ( ( ( sK2 @ sK11 @ sK12 )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f1358,f1260]) ).
thf(f1260,plain,
( ( ( sK23 @ sK11 @ sK12 )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1259]) ).
thf(f1259,plain,
( ( ( $true
=> ( sK23 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f1251,f1258]) ).
thf(f1258,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y0 @ Y1 )
& ( sK23 @ Y1 @ Y2 ) )
=> ( sK23 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f1251]) ).
thf(f1251,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y0 @ Y1 )
& ( sK23 @ Y1 @ Y2 ) )
=> ( sK23 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) ) ) )
=> ( sK23 @ sK11 @ sK12 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1249]) ).
thf(f1249,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) )
@ sK23 )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f1193]) ).
thf(f1193,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f1181]) ).
thf(f1181,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(not_proxy_clausification,[status(thm)],[f1173]) ).
thf(f1173,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1172]) ).
thf(f1172,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f741,f1168]) ).
thf(f1168,plain,
( ( ( sK10 @ sK11 @ sK12 )
= $false )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1167]) ).
thf(f1167,plain,
( ( ( $true
=> ( sK10 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1166]) ).
thf(f1166,plain,
( ( ( ( ( sK3 @ sK11 @ sK12 )
| $true )
=> ( sK10 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_7
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f365,f219]) ).
thf(f365,plain,
( ( ( ( ( sK3 @ sK11 @ sK12 )
| ( sK2 @ sK11 @ sK12 ) )
=> ( sK10 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f364]) ).
thf(f364,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK11 @ Y0 )
| ( sK2 @ sK11 @ Y0 ) )
=> ( sK10 @ sK11 @ Y0 ) )
@ sK12 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f350]) ).
thf(f350,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK11 @ Y0 )
| ( sK2 @ sK11 @ Y0 ) )
=> ( sK10 @ sK11 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f348]) ).
thf(f348,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) )
@ sK11 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f188]) ).
thf(f188,definition,
( spl0_7
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f741,plain,
( ! [X2: a,X1: a] :
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X1 @ X2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ X1 @ X2 ) ) ) )
=> ( sK10 @ X1 @ X2 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f740]) ).
thf(f740,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) ) )
=> ( sK10 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f737]) ).
thf(f737,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) ) )
=> ( sK10 @ X1 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f736]) ).
thf(f736,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK10 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f735]) ).
thf(f735,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f734]) ).
thf(f734,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f722,f733]) ).
thf(f733,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f722]) ).
thf(f722,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f710]) ).
thf(f710,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
=> ( sK10 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f709]) ).
thf(f709,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl0_4
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1358,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK23 @ X1 @ X2 ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1357]) ).
thf(f1357,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK23 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(pi_clausification,[status(thm)],[f1356]) ).
thf(f1356,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK23 @ X1 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1355]) ).
thf(f1355,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(pi_clausification,[status(thm)],[f1298]) ).
thf(f1298,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f1258]) ).
thf(f1165,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f1164]) ).
thf(f1164,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1163]) ).
thf(f1163,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f1156,f932]) ).
thf(f932,plain,
( ( ( sK18 @ sK11 @ sK12 )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f931]) ).
thf(f931,plain,
( ( ( $true
=> ( sK18 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f921,f930]) ).
thf(f930,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK18 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y1 @ Y2 )
& ( sK18 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f921]) ).
thf(f921,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK18 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y1 @ Y2 )
& ( sK18 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK18 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f919]) ).
thf(f919,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) )
@ sK18 ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f787]) ).
thf(f787,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f777]) ).
thf(f777,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(not_proxy_clausification,[status(thm)],[f747]) ).
thf(f747,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f746]) ).
thf(f746,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f741,f368]) ).
thf(f368,plain,
( ( ( sK10 @ sK11 @ sK12 )
= $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f367]) ).
thf(f367,plain,
( ( ( $true
=> ( sK10 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f366]) ).
thf(f366,plain,
( ( $false
= ( ( $true
| ( sK2 @ sK11 @ sK12 ) )
=> ( sK10 @ sK11 @ sK12 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f365,f216]) ).
thf(f216,plain,
( ( $true
= ( sK3 @ sK11 @ sK12 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f215]) ).
thf(f215,definition,
( spl0_9
<=> ( $true
= ( sK3 @ sK11 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f1156,plain,
( ( ( sK18 @ sK11 @ sK12 )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1151]) ).
thf(f1151,plain,
( ( ( $true
=> ( sK18 @ sK11 @ sK12 ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f1147,f216]) ).
thf(f1147,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( sK18 @ X1 @ X2 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f1146]) ).
thf(f1146,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK18 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(pi_clausification,[status(thm)],[f1143]) ).
thf(f1143,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK18 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f1142]) ).
thf(f1142,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK18 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(pi_clausification,[status(thm)],[f1039]) ).
thf(f1039,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK18 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f930]) ).
thf(f685,plain,
( spl0_13
| spl0_14
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f678,f91,f683,f680]) ).
thf(f678,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f624]) ).
thf(f624,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) ) ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f615]) ).
thf(f615,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK20 ) ) ) )
=> ( sK6 @ sK19 @ sK20 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f614]) ).
thf(f614,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK19 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK19 @ Y0 ) ) ) )
=> ( sK6 @ sK19 @ Y0 ) )
@ sK20 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f602]) ).
thf(f602,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK19 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK19 @ Y0 ) ) ) )
=> ( sK6 @ sK19 @ Y0 ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f600]) ).
thf(f600,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f92]) ).
thf(f345,plain,
( ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f344]) ).
thf(f344,plain,
( $false
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f343]) ).
thf(f343,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f342]) ).
thf(f342,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f336,f246]) ).
thf(f246,plain,
( ( $true
= ( sK10 @ sK14 @ sK16 ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f242]) ).
thf(f242,plain,
( ( $true
= ( ( sK10 @ sK14 @ sK16 )
& ( sK10 @ sK16 @ sK13 ) ) )
| ~ spl0_8 ),
inference(not_proxy_clausification,[status(thm)],[f241]) ).
thf(f241,plain,
( ( ( ~ ( ( sK10 @ sK14 @ sK16 )
& ( sK10 @ sK16 @ sK13 ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f240]) ).
thf(f240,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK10 @ sK14 @ Y0 )
& ( sK10 @ Y0 @ sK13 ) )
@ sK16 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f236]) ).
thf(f236,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK10 @ sK14 @ Y0 )
& ( sK10 @ Y0 @ sK13 ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f235]) ).
thf(f235,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK14 @ Y0 )
& ( sK10 @ Y0 @ sK13 ) )
=> $false ) )
= $false )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f229,f232]) ).
thf(f232,plain,
( ( $false
= ( sK10 @ sK14 @ sK13 ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
( ( ( ( ( sK10 @ sK14 @ sK15 )
& ( sK10 @ sK15 @ sK13 ) )
=> ( sK10 @ sK14 @ sK13 ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f230]) ).
thf(f230,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ sK14 @ Y0 )
& ( sK10 @ Y0 @ sK13 ) )
=> ( sK10 @ sK14 @ sK13 ) )
@ sK15 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK14 @ Y0 )
& ( sK10 @ Y0 @ sK13 ) )
=> ( sK10 @ sK14 @ sK13 ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f228]) ).
thf(f228,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ Y1 )
& ( sK10 @ Y1 @ sK13 ) )
=> ( sK10 @ Y0 @ sK13 ) ) )
@ sK14 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f225]) ).
thf(f225,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ Y1 )
& ( sK10 @ Y1 @ sK13 ) )
=> ( sK10 @ Y0 @ sK13 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f223]) ).
thf(f223,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y2 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f192]) ).
thf(f192,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y2 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f191]) ).
thf(f191,definition,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y2 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f336,plain,
( ( $true
= ( ~ ( sK10 @ sK14 @ sK16 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f331]) ).
thf(f331,plain,
( ( ( ( sK10 @ sK14 @ sK16 )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f299,f232]) ).
thf(f299,plain,
( ! [X0: a] :
( ( ( sK10 @ X0 @ sK16 )
=> ( sK10 @ X0 @ sK13 ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f274]) ).
thf(f274,plain,
( ! [X0: a] :
( ( ( $true
& ( sK10 @ X0 @ sK16 ) )
=> ( sK10 @ X0 @ sK13 ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f258,f248]) ).
thf(f248,plain,
( ( ( sK10 @ sK16 @ sK13 )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f247]) ).
thf(f247,plain,
( ( ( $true
& ( sK10 @ sK16 @ sK13 ) )
= $true )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f242,f246]) ).
thf(f258,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK10 @ X2 @ X3 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X1 @ X3 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f257]) ).
thf(f257,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK10 @ X2 @ Y0 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X1 @ Y0 ) )
@ X3 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X2 @ Y0 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X1 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f255]) ).
thf(f255,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ Y1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f250]) ).
thf(f250,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ Y1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f249]) ).
thf(f249,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f211]) ).
thf(f211,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& $true )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f176,f209]) ).
thf(f209,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f174]) ).
thf(f174,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
=> ( sK10 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f173]) ).
thf(f173,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f220,plain,
( spl0_9
| spl0_10
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f213,f188,f218,f215]) ).
thf(f213,plain,
( ( $true
= ( sK3 @ sK11 @ sK12 ) )
| ( $true
= ( sK2 @ sK11 @ sK12 ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f204]) ).
thf(f204,plain,
( ( ( ( sK3 @ sK11 @ sK12 )
| ( sK2 @ sK11 @ sK12 ) )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f202]) ).
thf(f202,plain,
( ( ( ( ( sK3 @ sK11 @ sK12 )
| ( sK2 @ sK11 @ sK12 ) )
=> ( sK10 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f201]) ).
thf(f201,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK11 @ Y0 )
| ( sK2 @ sK11 @ Y0 ) )
=> ( sK10 @ sK11 @ Y0 ) )
@ sK12 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f198]) ).
thf(f198,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK11 @ Y0 )
| ( sK2 @ sK11 @ Y0 ) )
=> ( sK10 @ sK11 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f196]) ).
thf(f196,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) )
@ sK11 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f189]) ).
thf(f193,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f184,f32,f191,f188]) ).
thf(f184,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y2 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y2 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y2 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f179]) ).
thf(f179,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y2 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f168,f178]) ).
thf(f178,plain,
( ( $false
= ( sK10 @ sK4 @ sK5 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f177]) ).
thf(f177,plain,
( ( ( $true
=> ( sK10 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f174,f176]) ).
thf(f168,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f167]) ).
thf(f167,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
!= $false )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f18,f33]) ).
thf(f18,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X5 @ X7 )
& ( X4 @ X6 @ X5 ) )
=> ( X4 @ X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X9 @ X8 )
| ( X0 @ X9 @ X8 ) )
=> ( X4 @ X9 @ X8 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X10: a,X11: a] :
! [X12: a > a > $o] :
( ( ! [X13: a,X14: a] :
( ( ! [X15: a > a > $o] :
( ( ! [X16: a,X17: a,X18: a] :
( ( ( X15 @ X18 @ X17 )
& ( X15 @ X17 @ X16 ) )
=> ( X15 @ X18 @ X16 ) )
& ! [X19: a,X20: a] :
( ( X0 @ X20 @ X19 )
=> ( X15 @ X20 @ X19 ) ) )
=> ( X15 @ X14 @ X13 ) )
| ! [X21: a > a > $o] :
( ( ! [X22: a,X23: a] :
( ( X1 @ X23 @ X22 )
=> ( X21 @ X23 @ X22 ) )
& ! [X24: a,X25: a,X26: a] :
( ( ( X21 @ X25 @ X24 )
& ( X21 @ X26 @ X25 ) )
=> ( X21 @ X26 @ X24 ) ) )
=> ( X21 @ X14 @ X13 ) ) )
=> ( X12 @ X14 @ X13 ) )
& ! [X27: a,X28: a,X29: a] :
( ( ( X12 @ X29 @ X28 )
& ( X12 @ X28 @ X27 ) )
=> ( X12 @ X29 @ X27 ) ) )
=> ( X12 @ X10 @ X11 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X7: a,X10: a,X9: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) )
& ! [X10: a,X9: a] :
( ( X0 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X5 @ X6 ) )
| ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ! [X7: a,X10: a,X9: a] :
( ( ( X8 @ X10 @ X7 )
& ( X8 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X7 ) ) )
=> ( X8 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X7: a,X10: a,X9: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) )
& ! [X10: a,X9: a] :
( ( X0 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X5 @ X6 ) )
| ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ! [X7: a,X10: a,X9: a] :
( ( ( X8 @ X10 @ X7 )
& ( X8 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X7 ) ) )
=> ( X8 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Yfwa6cQPBu/DTF2THF_14272.p',cTHM250_pme) ).
thf(f162,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f161]) ).
thf(f161,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f160]) ).
thf(f160,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f159]) ).
thf(f159,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f153,f127]) ).
thf(f127,plain,
( ( $true
= ( sK6 @ sK8 @ sK9 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ( ( sK6 @ sK8 @ sK9 )
& ( sK6 @ sK7 @ sK8 ) )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( ( ( ( sK6 @ sK8 @ sK9 )
& ( sK6 @ sK7 @ sK8 ) )
=> ( sK6 @ sK7 @ sK9 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK8 @ Y0 )
& ( sK6 @ sK7 @ sK8 ) )
=> ( sK6 @ sK7 @ Y0 ) )
@ sK9 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK8 @ Y0 )
& ( sK6 @ sK7 @ sK8 ) )
=> ( sK6 @ sK7 @ Y0 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ sK7 @ Y0 ) )
=> ( sK6 @ sK7 @ Y1 ) ) )
@ sK8 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ sK7 @ Y0 ) )
=> ( sK6 @ sK7 @ Y1 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f103]) ).
thf(f103,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) )
@ sK7 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f153,plain,
( ( $true
= ( ~ ( sK6 @ sK8 @ sK9 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f151]) ).
thf(f151,plain,
( ( $true
= ( ( sK6 @ sK8 @ sK9 )
=> $false ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f135,f112]) ).
thf(f112,plain,
( ( $false
= ( sK6 @ sK7 @ sK9 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f135,plain,
( ! [X0: a] :
( $true
= ( ( sK6 @ sK8 @ X0 )
=> ( sK6 @ sK7 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f130]) ).
thf(f130,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK6 @ sK8 @ X0 ) )
=> ( sK6 @ sK7 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f62,f129]) ).
thf(f129,plain,
( ( ( sK6 @ sK7 @ sK8 )
= $true )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ( $true
& ( sK6 @ sK7 @ sK8 ) )
= $true )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f113,f127]) ).
thf(f62,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 @ X3 )
& ( sK6 @ X3 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ X2 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) )
@ X3 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X2 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f44,f54]) ).
thf(f54,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK6 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f93,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f84,f29,f91,f88]) ).
thf(f84,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f42,f46]) ).
thf(f46,plain,
( ( $false
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( $true
=> ( sK6 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f40,f44]) ).
thf(f42,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
!= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f18,f30]) ).
thf(f34,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f20,f32,f29]) ).
thf(f20,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV141^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:40:29 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEV141^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.42 % Domain : Set Theory (Relations)
% 0.16/0.42 % Problem : TPS problem THM250
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0537 [Bro09]
% 0.16/0.42 % : tps_0538 [Bro09]
% 0.16/0.42 % : tps_1172 [Bro09]
% 0.16/0.42 % : THM250 [TPS]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.56 v9.1.0, 0.62 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.71 v7.4.0, 0.56 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.16/0.42 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.42 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 1 ( 1 avg)
% 0.16/0.42 % Number of connectives : 70 ( 0 ~; 2 |; 8 &; 48 @)
% 0.16/0.42 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 3 ( 3 avg)
% 0.16/0.42 % Number of types : 2 ( 1 usr)
% 0.16/0.42 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.42 % Number of variables : 30 ( 4 ^; 26 !; 0 ?; 30 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 % : Polymorphic definitions expanded.
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(a_type,type,
% 0.16/0.42 a: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(cTHM250_pme,conjecture,
% 0.16/0.42 ! [R: a > a > $o,S: a > a > $o] :
% 0.16/0.42 ( ( ^ [Xx1: a,Xy1: a] :
% 0.16/0.42 ! [Xp1: a > a > $o] :
% 0.16/0.42 ( ( ! [Xx: a,Xy: a] :
% 0.16/0.42 ( ( ( R @ Xx @ Xy )
% 0.16/0.42 | ( S @ Xx @ Xy ) )
% 0.16/0.42 => ( Xp1 @ Xx @ Xy ) )
% 0.16/0.42 & ! [Xx: a,Xy: a,Xz: a] :
% 0.16/0.42 ( ( ( Xp1 @ Xx @ Xy )
% 0.16/0.42 & ( Xp1 @ Xy @ Xz ) )
% 0.16/0.42 => ( Xp1 @ Xx @ Xz ) ) )
% 0.16/0.42 => ( Xp1 @ Xx1 @ Xy1 ) ) )
% 0.16/0.42 = ( ^ [Xx1: a,Xy1: a] :
% 0.16/0.42 ! [Xp1: a > a > $o] :
% 0.16/0.42 ( ( ! [Xx: a,Xy: a] :
% 0.16/0.42 ( ( ! [Xp10: a > a > $o] :
% 0.16/0.42 ( ( ! [Xx0: a,Xy0: a] :
% 0.16/0.42 ( ( R @ Xx0 @ Xy0 )
% 0.16/0.42 => ( Xp10 @ Xx0 @ Xy0 ) )
% 0.16/0.42 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.16/0.42 ( ( ( Xp10 @ Xx0 @ Xy0 )
% 0.16/0.42 & ( Xp10 @ Xy0 @ Xz ) )
% 0.16/0.42 => ( Xp10 @ Xx0 @ Xz ) ) )
% 0.16/0.42 => ( Xp10 @ Xx @ Xy ) )
% 0.16/0.42 | ! [Xp10: a > a > $o] :
% 0.16/0.42 ( ( ! [Xx0: a,Xy0: a] :
% 0.16/0.42 ( ( S @ Xx0 @ Xy0 )
% 0.16/0.42 => ( Xp10 @ Xx0 @ Xy0 ) )
% 0.16/0.42 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.16/0.42 ( ( ( Xp10 @ Xx0 @ Xy0 )
% 0.16/0.42 & ( Xp10 @ Xy0 @ Xz ) )
% 0.16/0.42 => ( Xp10 @ Xx0 @ Xz ) ) )
% 0.16/0.42 => ( Xp10 @ Xx @ Xy ) ) )
% 0.16/0.42 => ( Xp1 @ Xx @ Xy ) )
% 0.16/0.42 & ! [Xx: a,Xy: a,Xz: a] :
% 0.16/0.42 ( ( ( Xp1 @ Xx @ Xy )
% 0.16/0.42 & ( Xp1 @ Xy @ Xz ) )
% 0.16/0.42 => ( Xp1 @ Xx @ Xz ) ) )
% 0.16/0.42 => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.34/1.16 ---- Embedded in THF ---
% 1.34/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.34/1.16 %%% Generated on Tue Feb 24 12:40:30 EST 2026
% 1.34/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.34/1.16 %%% Logic specification used:
% 1.34/1.16 %%% thf(spec, logic, $$dhol).
% 1.34/1.16
% 1.34/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Yfwa6cQPBu/DTF2DTF14272.p
% See solution above
% 1.34/1.16 ------------------------
% 1.34/1.17 ---- Cleaned THF ---
% 1.34/1.17 thf(a_type,type,
% 1.34/1.17 a: $tType ).
% 1.34/1.17
% 1.34/1.17 thf(cTHM250_pme,conjecture,
% 1.34/1.17 ! [R: a > a > $o,S: a > a > $o] :
% 1.34/1.17 ( ( ^ [Xx1: a,Xy1: a] :
% 1.34/1.17 ! [Xp1: a > a > $o] :
% 1.34/1.17 ( ( ! [Xx: a,Xy: a] :
% 1.34/1.17 ( ( ( R @ Xx @ Xy )
% 1.34/1.17 | ( S @ Xx @ Xy ) )
% 1.34/1.17 => ( Xp1 @ Xx @ Xy ) )
% 1.34/1.17 & ! [Xx: a,Xy: a,Xz: a] :
% 1.34/1.17 ( ( ( Xp1 @ Xx @ Xy )
% 1.34/1.17 & ( Xp1 @ Xy @ Xz ) )
% 1.34/1.17 => ( Xp1 @ Xx @ Xz ) ) )
% 1.34/1.17 => ( Xp1 @ Xx1 @ Xy1 ) ) )
% 1.34/1.17 = ( ^ [Xx1: a,Xy1: a] :
% 1.34/1.17 ! [Xp1: a > a > $o] :
% 1.34/1.17 ( ( ! [Xx: a,Xy: a] :
% 1.34/1.17 ( ( ! [Xp10: a > a > $o] :
% 1.34/1.17 ( ( ! [Xx0: a,Xy0: a] :
% 1.34/1.17 ( ( R @ Xx0 @ Xy0 )
% 1.34/1.17 => ( Xp10 @ Xx0 @ Xy0 ) )
% 1.34/1.17 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.34/1.17 ( ( ( Xp10 @ Xx0 @ Xy0 )
% 1.34/1.17 & ( Xp10 @ Xy0 @ Xz ) )
% 1.34/1.17 => ( Xp10 @ Xx0 @ Xz ) ) )
% 1.34/1.17 => ( Xp10 @ Xx @ Xy ) )
% 1.34/1.17 | ! [Xp10: a > a > $o] :
% 1.34/1.17 ( ( ! [Xx0: a,Xy0: a] :
% 1.34/1.17 ( ( S @ Xx0 @ Xy0 )
% 1.34/1.17 => ( Xp10 @ Xx0 @ Xy0 ) )
% 1.34/1.17 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.34/1.17 ( ( ( Xp10 @ Xx0 @ Xy0 )
% 1.34/1.17 & ( Xp10 @ Xy0 @ Xz ) )
% 1.34/1.17 => ( Xp10 @ Xx0 @ Xz ) ) )
% 1.34/1.17 => ( Xp10 @ Xx @ Xy ) ) )
% 1.34/1.17 => ( Xp1 @ Xx @ Xy ) )
% 1.34/1.17 & ! [Xx: a,Xy: a,Xz: a] :
% 1.34/1.17 ( ( ( Xp1 @ Xx @ Xy )
% 1.34/1.17 & ( Xp1 @ Xy @ Xz ) )
% 1.34/1.17 => ( Xp1 @ Xx @ Xz ) ) )
% 1.34/1.17 => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) ).
% 1.34/1.17 ------------------------
% 1.34/1.18 % (14369)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14272 for (3000ds/183Mi)
% 1.34/1.19 % (14371)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_14272 for (3000ds/27Mi)
% 1.34/1.19 % (14373)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_14272 for (3000ds/2Mi)
% 1.34/1.19 % (14374)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_14272 for (3000ds/275Mi)
% 1.34/1.19 % (14375)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14272 for (3000ds/18Mi)
% 1.34/1.19 % (14370)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_14272 for (3000ds/4Mi)
% 1.34/1.19 % (14373)Instruction limit reached!
% 1.34/1.19 % (14373)------------------------------
% 1.34/1.19 % (14373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.19 % (14373)Termination reason: Unknown
% 1.34/1.19 % (14373)Termination phase: Property scanning
% 1.34/1.19
% 1.34/1.19 % (14373)Memory used [KB]: 1023
% 1.34/1.19 % (14373)Time elapsed: 0.003 s
% 1.34/1.19 % (14373)Instructions burned: 3 (million)
% 1.34/1.19 % (14373)------------------------------
% 1.34/1.19 % (14373)------------------------------
% 1.34/1.19 % (14370)Instruction limit reached!
% 1.34/1.19 % (14370)------------------------------
% 1.34/1.19 % (14370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.19 % (14370)Termination reason: Unknown
% 1.34/1.19 % (14370)Termination phase: Preprocessing 3
% 1.34/1.19
% 1.34/1.19 % (14370)Memory used [KB]: 1023
% 1.34/1.19 % (14370)Time elapsed: 0.003 s
% 1.34/1.19 % (14370)Instructions burned: 4 (million)
% 1.34/1.19 % (14370)------------------------------
% 1.34/1.19 % (14370)------------------------------
% 1.34/1.19 % (14372)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14272 for (3000ds/2Mi)
% 1.34/1.19 % (14372)Instruction limit reached!
% 1.34/1.19 % (14372)------------------------------
% 1.34/1.19 % (14372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.19 % (14372)Termination reason: Unknown
% 1.34/1.19 % (14372)Termination phase: Preprocessing 1
% 1.34/1.19
% 1.34/1.19 % (14372)Memory used [KB]: 1023
% 1.34/1.19 % (14372)Time elapsed: 0.003 s
% 1.34/1.19 % (14372)Instructions burned: 3 (million)
% 1.34/1.19 % (14372)------------------------------
% 1.34/1.19 % (14372)------------------------------
% 1.34/1.19 % (14375)Instruction limit reached!
% 1.34/1.19 % (14375)------------------------------
% 1.34/1.19 % (14375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.19 % (14375)Termination reason: Unknown
% 1.34/1.19 % (14375)Termination phase: Saturation
% 1.34/1.19
% 1.34/1.19 % (14375)Memory used [KB]: 5500
% 1.34/1.19 % (14375)Time elapsed: 0.010 s
% 1.34/1.19 % (14375)Instructions burned: 19 (million)
% 1.34/1.19 % (14375)------------------------------
% 1.34/1.19 % (14375)------------------------------
% 1.44/1.20 % (14371)Instruction limit reached!
% 1.44/1.20 % (14371)------------------------------
% 1.44/1.20 % (14371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.20 % (14371)Termination reason: Unknown
% 1.44/1.20 % (14371)Termination phase: Saturation
% 1.44/1.20
% 1.44/1.20 % (14371)Memory used [KB]: 5628
% 1.44/1.20 % (14371)Time elapsed: 0.014 s
% 1.44/1.20 % (14371)Instructions burned: 27 (million)
% 1.44/1.20 % (14371)------------------------------
% 1.44/1.20 % (14371)------------------------------
% 1.44/1.20 % (14377)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_14272 for (2999ds/37Mi)
% 1.44/1.20 % (14376)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/3Mi)
% 1.44/1.20 % (14376)Instruction limit reached!
% 1.44/1.20 % (14376)------------------------------
% 1.44/1.20 % (14376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.20 % (14376)Termination reason: Unknown
% 1.44/1.20 % (14376)Termination phase: Property scanning
% 1.44/1.20
% 1.44/1.20 % (14376)Memory used [KB]: 1023
% 1.44/1.20 % (14376)Time elapsed: 0.003 s
% 1.44/1.20 % (14376)Instructions burned: 3 (million)
% 1.44/1.20 % (14376)------------------------------
% 1.44/1.20 % (14376)------------------------------
% 1.44/1.21 % (14378)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_14272 for (2999ds/15Mi)
% 1.44/1.21 % (14379)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_14272 for (2999ds/3Mi)
% 1.44/1.21 % (14379)Instruction limit reached!
% 1.44/1.21 % (14379)------------------------------
% 1.44/1.21 % (14379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.21 % (14379)Termination reason: Unknown
% 1.44/1.21 % (14379)Termination phase: Preprocessing 3
% 1.44/1.21
% 1.44/1.21 % (14379)Memory used [KB]: 1023
% 1.44/1.21 % (14379)Time elapsed: 0.003 s
% 1.44/1.21 % (14379)Instructions burned: 3 (million)
% 1.44/1.21 % (14379)------------------------------
% 1.44/1.21 % (14379)------------------------------
% 1.44/1.21 % (14380)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_14272 for (2999ds/1041Mi)
% 1.44/1.22 % (14378)Instruction limit reached!
% 1.44/1.22 % (14378)------------------------------
% 1.44/1.22 % (14378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.22 % (14378)Termination reason: Unknown
% 1.44/1.22 % (14378)Termination phase: Saturation
% 1.44/1.22
% 1.44/1.22 % (14378)Memory used [KB]: 5628
% 1.44/1.22 % (14378)Time elapsed: 0.010 s
% 1.44/1.22 % (14378)Instructions burned: 16 (million)
% 1.44/1.22 % (14378)------------------------------
% 1.44/1.22 % (14378)------------------------------
% 1.44/1.22 % (14377)Instruction limit reached!
% 1.44/1.22 % (14377)------------------------------
% 1.44/1.22 % (14377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.22 % (14377)Termination reason: Unknown
% 1.44/1.22 % (14377)Termination phase: Saturation
% 1.44/1.22
% 1.44/1.22 % (14377)Memory used [KB]: 5628
% 1.44/1.22 % (14377)Time elapsed: 0.019 s
% 1.44/1.22 % (14377)Instructions burned: 38 (million)
% 1.44/1.22 % (14377)------------------------------
% 1.44/1.22 % (14377)------------------------------
% 1.44/1.22 % (14381)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/7Mi)
% 1.44/1.23 % (14381)Instruction limit reached!
% 1.44/1.23 % (14381)------------------------------
% 1.44/1.23 % (14381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.23 % (14381)Termination reason: Unknown
% 1.44/1.23 % (14381)Termination phase: Saturation
% 1.44/1.23
% 1.44/1.23 % (14381)Memory used [KB]: 1023
% 1.44/1.23 % (14381)Time elapsed: 0.006 s
% 1.44/1.23 % (14381)Instructions burned: 8 (million)
% 1.44/1.23 % (14381)------------------------------
% 1.44/1.23 % (14381)------------------------------
% 1.44/1.23 % (14382)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/16Mi)
% 1.44/1.23 % (14369)Instruction limit reached!
% 1.44/1.23 % (14369)------------------------------
% 1.44/1.23 % (14369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.23 % (14369)Termination reason: Unknown
% 1.44/1.23 % (14369)Termination phase: Saturation
% 1.44/1.23
% 1.44/1.23 % (14369)Memory used [KB]: 6396
% 1.44/1.23 % (14369)Time elapsed: 0.053 s
% 1.44/1.23 % (14369)Instructions burned: 185 (million)
% 1.44/1.23 % (14369)------------------------------
% 1.44/1.23 % (14369)------------------------------
% 1.44/1.24 % (14383)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_14272 for (2999ds/3Mi)
% 1.44/1.24 % (14384)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_14272 for (2999ds/3Mi)
% 1.44/1.24 % (14383)Instruction limit reached!
% 1.44/1.24 % (14383)------------------------------
% 1.44/1.24 % (14383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.24 % (14383)Termination reason: Unknown
% 1.44/1.24 % (14383)Termination phase: Preprocessing 3
% 1.44/1.24
% 1.44/1.24 % (14383)Memory used [KB]: 1023
% 1.44/1.24 % (14383)Time elapsed: 0.003 s
% 1.44/1.24 % (14383)Instructions burned: 3 (million)
% 1.44/1.24 % (14383)------------------------------
% 1.44/1.24 % (14383)------------------------------
% 1.44/1.24 % (14384)Instruction limit reached!
% 1.44/1.24 % (14384)------------------------------
% 1.44/1.24 % (14384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.24 % (14384)Termination reason: Unknown
% 1.44/1.24 % (14384)Termination phase: Preprocessing 3
% 1.44/1.24
% 1.44/1.24 % (14384)Memory used [KB]: 1023
% 1.44/1.24 % (14384)Time elapsed: 0.003 s
% 1.44/1.24 % (14384)Instructions burned: 4 (million)
% 1.44/1.24 % (14384)------------------------------
% 1.44/1.24 % (14384)------------------------------
% 1.44/1.24 % (14382)Instruction limit reached!
% 1.44/1.24 % (14382)------------------------------
% 1.44/1.24 % (14382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.24 % (14382)Termination reason: Unknown
% 1.44/1.24 % (14382)Termination phase: Saturation
% 1.44/1.24
% 1.44/1.24 % (14382)Memory used [KB]: 5756
% 1.44/1.24 % (14382)Time elapsed: 0.010 s
% 1.44/1.24 % (14382)Instructions burned: 17 (million)
% 1.44/1.24 % (14382)------------------------------
% 1.44/1.24 % (14382)------------------------------
% 1.44/1.24 % (14386)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/3Mi)
% 1.44/1.24 % (14385)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/7Mi)
% 1.44/1.24 % (14386)Instruction limit reached!
% 1.44/1.24 % (14386)------------------------------
% 1.44/1.24 % (14386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.24 % (14386)Termination reason: Unknown
% 1.44/1.24 % (14386)Termination phase: Saturation
% 1.44/1.24
% 1.44/1.24 % (14386)Memory used [KB]: 5500
% 1.44/1.24 % (14386)Time elapsed: 0.003 s
% 1.44/1.24 % (14386)Instructions burned: 5 (million)
% 1.44/1.24 % (14386)------------------------------
% 1.44/1.24 % (14386)------------------------------
% 1.44/1.25 % (14385)Instruction limit reached!
% 1.44/1.25 % (14385)------------------------------
% 1.44/1.25 % (14385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.25 % (14385)Termination reason: Unknown
% 1.44/1.25 % (14385)Termination phase: Saturation
% 1.44/1.25
% 1.44/1.25 % (14385)Memory used [KB]: 5500
% 1.44/1.25 % (14385)Time elapsed: 0.005 s
% 1.44/1.25 % (14385)Instructions burned: 7 (million)
% 1.44/1.25 % (14385)------------------------------
% 1.44/1.25 % (14385)------------------------------
% 1.44/1.25 % (14390)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/6Mi)
% 1.44/1.25 % (14388)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/18Mi)
% 1.44/1.25 % (14387)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/4Mi)
% 1.44/1.25 % (14389)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/710Mi)
% 1.44/1.26 % (14390)Instruction limit reached!
% 1.44/1.26 % (14390)------------------------------
% 1.44/1.26 % (14390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.26 % (14390)Termination reason: Unknown
% 1.44/1.26 % (14390)Termination phase: Saturation
% 1.44/1.26
% 1.44/1.26 % (14390)Memory used [KB]: 5500
% 1.44/1.26 % (14390)Time elapsed: 0.004 s
% 1.44/1.26 % (14390)Instructions burned: 9 (million)
% 1.44/1.26 % (14390)------------------------------
% 1.44/1.26 % (14390)------------------------------
% 1.44/1.26 % (14387)Instruction limit reached!
% 1.44/1.26 % (14387)------------------------------
% 1.44/1.26 % (14387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.26 % (14387)Termination reason: Unknown
% 1.44/1.26 % (14387)Termination phase: Saturation
% 1.44/1.26
% 1.44/1.26 % (14387)Memory used [KB]: 1023
% 1.44/1.26 % (14387)Time elapsed: 0.004 s
% 1.44/1.26 % (14387)Instructions burned: 5 (million)
% 1.44/1.26 % (14387)------------------------------
% 1.44/1.26 % (14387)------------------------------
% 1.44/1.26 % (14388)Instruction limit reached!
% 1.44/1.26 % (14388)------------------------------
% 1.44/1.26 % (14388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.26 % (14388)Termination reason: Unknown
% 1.44/1.26 % (14388)Termination phase: Saturation
% 1.44/1.26
% 1.44/1.26 % (14388)Memory used [KB]: 5500
% 1.44/1.26 % (14388)Time elapsed: 0.010 s
% 1.44/1.26 % (14388)Instructions burned: 18 (million)
% 1.44/1.26 % (14388)------------------------------
% 1.44/1.26 % (14388)------------------------------
% 1.44/1.26 % (14391)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_14272 for (2999ds/902Mi)
% 1.44/1.27 % (14392)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_14272 for (2999ds/21Mi)
% 1.44/1.28 % (14392)Instruction limit reached!
% 1.44/1.28 % (14392)------------------------------
% 1.44/1.28 % (14392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.28 % (14392)Termination reason: Unknown
% 1.44/1.28 % (14392)Termination phase: Saturation
% 1.44/1.28
% 1.44/1.28 % (14392)Memory used [KB]: 5628
% 1.44/1.28 % (14392)Time elapsed: 0.032 s
% 1.44/1.28 % (14392)Instructions burned: 21 (million)
% 1.44/1.28 % (14392)------------------------------
% 1.44/1.28 % (14392)------------------------------
% 1.44/1.28 % (14394)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_14272 for (2999ds/6Mi)
% 1.44/1.28 % (14393)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/5Mi)
% 1.44/1.28 % (14393)Instruction limit reached!
% 1.44/1.28 % (14393)------------------------------
% 1.44/1.28 % (14393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.28 % (14393)Termination reason: Unknown
% 1.44/1.28 % (14393)Termination phase: Saturation
% 1.44/1.28
% 1.44/1.28 % (14393)Memory used [KB]: 5500
% 1.44/1.28 % (14393)Time elapsed: 0.027 s
% 1.44/1.28 % (14393)Instructions burned: 5 (million)
% 1.44/1.28 % (14393)------------------------------
% 1.44/1.28 % (14393)------------------------------
% 1.44/1.28 % (14394)Instruction limit reached!
% 1.44/1.28 % (14394)------------------------------
% 1.44/1.28 % (14394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.28 % (14394)Termination reason: Unknown
% 1.44/1.28 % (14394)Termination phase: Saturation
% 1.44/1.28
% 1.44/1.28 % (14394)Memory used [KB]: 5500
% 1.44/1.28 % (14394)Time elapsed: 0.004 s
% 1.44/1.28 % (14394)Instructions burned: 6 (million)
% 1.44/1.28 % (14394)------------------------------
% 1.44/1.28 % (14394)------------------------------
% 1.44/1.29 % (14396)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_14272 for (2998ds/779Mi)
% 1.44/1.29 % (14395)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14272 for (2999ds/377Mi)
% 1.44/1.30 % (14397)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_14272 for (2998ds/19Mi)
% 1.44/1.30 % (14397)Instruction limit reached!
% 1.44/1.30 % (14397)------------------------------
% 1.44/1.30 % (14397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.30 % (14397)Termination reason: Unknown
% 1.44/1.30 % (14397)Termination phase: Saturation
% 1.44/1.30
% 1.44/1.30 % (14397)Memory used [KB]: 5500
% 1.44/1.30 % (14397)Time elapsed: 0.011 s
% 1.44/1.30 % (14397)Instructions burned: 21 (million)
% 1.44/1.30 % (14397)------------------------------
% 1.44/1.30 % (14397)------------------------------
% 1.44/1.32 % (14398)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14272 for (2998ds/879Mi)
% 1.44/1.34 % (14374)Instruction limit reached!
% 1.44/1.34 % (14374)------------------------------
% 1.44/1.34 % (14374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.34 % (14374)Termination reason: Unknown
% 1.44/1.34 % (14374)Termination phase: Saturation
% 1.44/1.34
% 1.44/1.34 % (14374)Memory used [KB]: 6780
% 1.44/1.34 % (14374)Time elapsed: 0.157 s
% 1.44/1.34 % (14374)Instructions burned: 275 (million)
% 1.44/1.34 % (14374)------------------------------
% 1.44/1.34 % (14374)------------------------------
% 1.44/1.36 % (14399)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14272 for (2998ds/17Mi)
% 1.44/1.37 % (14399)Instruction limit reached!
% 1.44/1.37 % (14399)------------------------------
% 1.44/1.37 % (14399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.37 % (14399)Termination reason: Unknown
% 1.44/1.37 % (14399)Termination phase: Saturation
% 1.44/1.37
% 1.44/1.37 % (14399)Memory used [KB]: 5628
% 1.44/1.37 % (14399)Time elapsed: 0.013 s
% 1.44/1.37 % (14399)Instructions burned: 18 (million)
% 1.44/1.37 % (14399)------------------------------
% 1.44/1.37 % (14399)------------------------------
% 1.44/1.39 % (14400)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14272 for (2997ds/3Mi)
% 1.44/1.40 % (14400)Instruction limit reached!
% 1.44/1.40 % (14400)------------------------------
% 1.44/1.40 % (14400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.40 % (14400)Termination reason: Unknown
% 1.44/1.40 % (14400)Termination phase: Property scanning
% 1.44/1.40
% 1.44/1.40 % (14400)Memory used [KB]: 1023
% 1.44/1.40 % (14400)Time elapsed: 0.004 s
% 1.44/1.40 % (14400)Instructions burned: 3 (million)
% 1.44/1.40 % (14400)------------------------------
% 1.44/1.40 % (14400)------------------------------
% 1.44/1.42 % (14401)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14272 for (2997ds/30Mi)
% 1.44/1.42 % (14401)Refutation not found, incomplete strategy
% 1.44/1.42 % (14401)------------------------------
% 1.44/1.42 % (14401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.42 % (14401)Termination reason: Refutation not found, incomplete strategy
% 1.44/1.42
% 1.44/1.42
% 1.44/1.42 % (14401)Memory used [KB]: 5500
% 1.44/1.42 % (14401)Time elapsed: 0.006 s
% 1.44/1.42 % (14401)Instructions burned: 14 (million)
% 1.44/1.42 % (14401)------------------------------
% 1.44/1.42 % (14401)------------------------------
% 1.44/1.43 % (14402)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14272 for (2997ds/127Mi)
% 1.44/1.46 % (14395)Instruction limit reached!
% 1.44/1.46 % (14395)------------------------------
% 1.44/1.46 % (14395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.46 % (14395)Termination reason: Unknown
% 1.44/1.46 % (14395)Termination phase: Saturation
% 1.44/1.46
% 1.44/1.46 % (14395)Memory used [KB]: 7291
% 1.44/1.46 % (14395)Time elapsed: 0.166 s
% 1.44/1.46 % (14395)Instructions burned: 377 (million)
% 1.44/1.46 % (14395)------------------------------
% 1.44/1.46 % (14395)------------------------------
% 1.44/1.47 % (14402)Instruction limit reached!
% 1.44/1.47 % (14402)------------------------------
% 1.44/1.47 % (14402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.47 % (14402)Termination reason: Unknown
% 1.44/1.47 % (14402)Termination phase: Saturation
% 1.44/1.47
% 1.44/1.47 % (14402)Memory used [KB]: 6012
% 1.44/1.47 % (14402)Time elapsed: 0.037 s
% 1.44/1.47 % (14402)Instructions burned: 128 (million)
% 1.44/1.47 % (14402)------------------------------
% 1.44/1.47 % (14402)------------------------------
% 1.44/1.47 % (14380)First to succeed.
% 1.44/1.47 % (14403)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14272 for (2997ds/100Mi)
% 1.44/1.48 % (14404)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_14272 for (2996ds/3Mi)
% 1.44/1.48 % (14404)Instruction limit reached!
% 1.44/1.48 % (14404)------------------------------
% 1.44/1.48 % (14404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.48 % (14404)Termination reason: Unknown
% 1.44/1.48 % (14404)Termination phase: Property scanning
% 1.44/1.48
% 1.44/1.48 % (14404)Memory used [KB]: 1023
% 1.44/1.48 % (14404)Time elapsed: 0.003 s
% 1.44/1.48 % (14404)Instructions burned: 4 (million)
% 1.44/1.48 % (14404)------------------------------
% 1.44/1.48 % (14404)------------------------------
% 1.44/1.49 % (14380)Refutation found. Thanks to Tanya!
% 1.44/1.49 % SZS status Theorem for DTF2THF_14272
% 1.44/1.49 % SZS output start Proof for DTF2THF_14272
% 1.44/1.49 thf(type_def_5, type, a: $tType).
% 1.44/1.49 thf(func_def_0, type, a: $tType).
% 1.44/1.49 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.44/1.49 thf(func_def_21, type, sK2: a > a > $o).
% 1.44/1.49 thf(func_def_22, type, sK3: a > a > $o).
% 1.44/1.49 thf(func_def_23, type, sK4: a).
% 1.44/1.49 thf(func_def_24, type, sK5: a).
% 1.44/1.49 thf(func_def_25, type, sK6: a > a > $o).
% 1.44/1.49 thf(func_def_26, type, sK7: a).
% 1.44/1.49 thf(func_def_27, type, sK8: a).
% 1.44/1.49 thf(func_def_28, type, sK9: a).
% 1.44/1.49 thf(func_def_29, type, sK10: a > a > $o).
% 1.44/1.49 thf(func_def_30, type, sK11: a).
% 1.44/1.49 thf(func_def_31, type, sK12: a).
% 1.44/1.49 thf(func_def_32, type, sK13: a).
% 1.44/1.49 thf(func_def_33, type, sK14: a).
% 1.44/1.49 thf(func_def_34, type, sK15: a).
% 1.44/1.49 thf(func_def_35, type, sK16: a).
% 1.44/1.49 thf(func_def_36, type, sK17: a > a > $o).
% 1.44/1.49 thf(func_def_37, type, sK18: a > a > $o).
% 1.44/1.49 thf(func_def_38, type, sK19: a).
% 1.44/1.49 thf(func_def_39, type, sK20: a).
% 1.44/1.49 thf(func_def_40, type, sK21: a).
% 1.44/1.49 thf(func_def_41, type, sK22: a).
% 1.44/1.49 thf(func_def_42, type, sK23: a > a > $o).
% 1.44/1.49 thf(func_def_43, type, sK24: a > a > $o).
% 1.44/1.49 thf(func_def_44, type, sK25: a).
% 1.44/1.49 thf(func_def_45, type, sK26: a).
% 1.44/1.49 thf(func_def_46, type, sK27: a).
% 1.44/1.49 thf(func_def_47, type, sK28: a).
% 1.44/1.49 thf(func_def_48, type, sK29: a).
% 1.44/1.49 thf(func_def_49, type, sK30: a).
% 1.44/1.49 thf(func_def_50, type, sK31: a).
% 1.44/1.49 thf(func_def_51, type, sK32: a).
% 1.44/1.49 thf(func_def_52, type, sK33: a).
% 1.44/1.49 thf(f1906,plain,(
% 1.44/1.49 $false),
% 1.44/1.49 inference(avatar_sat_refutation,[status(thm)],[f34,f93,f162,f193,f220,f345,f685,f1165,f1376,f1585,f1680,f1806,f1865,f1905])).
% 1.44/1.49 thf(f1905,plain,(
% 1.44/1.49 ~spl0_3 | ~spl0_29),
% 1.44/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1904])).
% 1.44/1.49 thf(f1904,plain,(
% 1.44/1.49 $false | (~spl0_3 | ~spl0_29)),
% 1.44/1.49 inference(trivial_inequality_removal,[status(thm)],[f1903])).
% 1.44/1.49 thf(f1903,plain,(
% 1.44/1.49 ($true = $false) | (~spl0_3 | ~spl0_29)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1902])).
% 1.44/1.49 thf(f1902,plain,(
% 1.44/1.49 ((~ $true) = $true) | (~spl0_3 | ~spl0_29)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1901])).
% 1.44/1.49 thf(f1901,plain,(
% 1.44/1.49 ($true = (~ ((sK3 @ sK32 @ sK33) | $true))) | (~spl0_3 | ~spl0_29)),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f1899,f1888])).
% 1.44/1.49 thf(f1888,plain,(
% 1.44/1.49 ((sK2 @ sK32 @ sK33) = $true) | ~spl0_29),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1886])).
% 1.44/1.49 thf(f1886,plain,(
% 1.44/1.49 ($false = ((sK2 @ sK32 @ sK33) => (sK6 @ sK32 @ sK33))) | ~spl0_29),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1885])).
% 1.44/1.49 thf(f1885,plain,(
% 1.44/1.49 (((^[Y0 : a]: ((sK2 @ sK32 @ Y0) => (sK6 @ sK32 @ Y0))) @ sK33) = $false) | ~spl0_29),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1878])).
% 1.44/1.49 thf(f1878,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK32 @ Y0) => (sK6 @ sK32 @ Y0)))) = $false) | ~spl0_29),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1876])).
% 1.44/1.49 thf(f1876,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))) @ sK32)) | ~spl0_29),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1805])).
% 1.44/1.49 thf(f1805,plain,(
% 1.44/1.49 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))))) | ~spl0_29),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f1804])).
% 1.44/1.49 thf(f1804,definition,(
% 1.44/1.49 spl0_29 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))))),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition])).
% 1.44/1.49 thf(f1899,plain,(
% 1.44/1.49 ($true = (~ ((sK3 @ sK32 @ sK33) | (sK2 @ sK32 @ sK33)))) | (~spl0_3 | ~spl0_29)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1894])).
% 1.44/1.49 thf(f1894,plain,(
% 1.44/1.49 ((((sK3 @ sK32 @ sK33) | (sK2 @ sK32 @ sK33)) => $false) = $true) | (~spl0_3 | ~spl0_29)),
% 1.44/1.49 inference(superposition,[status(thm)],[f1417,f1890])).
% 1.44/1.49 thf(f1890,plain,(
% 1.44/1.49 ($false = (sK6 @ sK32 @ sK33)) | ~spl0_29),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1889])).
% 1.44/1.49 thf(f1889,plain,(
% 1.44/1.49 ($false = ($true => (sK6 @ sK32 @ sK33))) | ~spl0_29),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f1886,f1888])).
% 1.44/1.49 thf(f1417,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (((((sK3 @ X1 @ X2) | (sK2 @ X1 @ X2)) => (sK6 @ X1 @ X2)) = $true)) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1416])).
% 1.44/1.49 thf(f1416,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK3 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK6 @ X1 @ Y0))) @ X2))) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1413])).
% 1.44/1.49 thf(f1413,plain,(
% 1.44/1.49 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK3 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK6 @ X1 @ Y0)))) = $true)) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1412])).
% 1.44/1.49 thf(f1412,plain,(
% 1.44/1.49 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1409])).
% 1.44/1.49 thf(f1409,plain,(
% 1.44/1.49 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))) | ~spl0_3),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1397])).
% 1.44/1.49 thf(f1397,plain,(
% 1.44/1.49 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))))) | ~spl0_3),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1385])).
% 1.44/1.49 thf(f1385,plain,(
% 1.44/1.49 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))) => (sK6 @ sK4 @ sK5)) = $false) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1384])).
% 1.44/1.49 thf(f1384,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK4 @ sK5))) @ sK6)) | ~spl0_3),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f30])).
% 1.44/1.49 thf(f30,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $false) | ~spl0_3),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.44/1.49 thf(f29,definition,(
% 1.44/1.49 spl0_3 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $false)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.44/1.49 thf(f1865,plain,(
% 1.44/1.49 ~spl0_3 | ~spl0_28),
% 1.44/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1864])).
% 1.44/1.49 thf(f1864,plain,(
% 1.44/1.49 $false | (~spl0_3 | ~spl0_28)),
% 1.44/1.49 inference(trivial_inequality_removal,[status(thm)],[f1860])).
% 1.44/1.49 thf(f1860,plain,(
% 1.44/1.49 ($true = $false) | (~spl0_3 | ~spl0_28)),
% 1.44/1.49 inference(superposition,[status(thm)],[f1851,f1433])).
% 1.44/1.49 thf(f1433,plain,(
% 1.44/1.49 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK6 @ X2 @ X3) & (sK6 @ X3 @ X1)) => (sK6 @ X2 @ X1)))) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1432])).
% 1.44/1.49 thf(f1432,plain,(
% 1.44/1.49 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK6 @ X2 @ Y0) & (sK6 @ Y0 @ X1)) => (sK6 @ X2 @ X1))) @ X3))) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1419])).
% 1.44/1.49 thf(f1419,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X2 @ Y0) & (sK6 @ Y0 @ X1)) => (sK6 @ X2 @ X1)))) = $true)) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1418])).
% 1.44/1.49 thf(f1418,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ X1)) => (sK6 @ Y0 @ X1))))) @ X2) = $true)) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1415])).
% 1.44/1.49 thf(f1415,plain,(
% 1.44/1.49 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ X1)) => (sK6 @ Y0 @ X1)))))))) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1414])).
% 1.44/1.49 thf(f1414,plain,(
% 1.44/1.49 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))) @ X1) = $true)) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1411])).
% 1.44/1.49 thf(f1411,plain,(
% 1.44/1.49 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))) | ~spl0_3),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1410])).
% 1.44/1.49 thf(f1410,plain,(
% 1.44/1.49 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))) = $true) | ~spl0_3),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f1397,f1409])).
% 1.44/1.49 thf(f1851,plain,(
% 1.44/1.49 ((((sK6 @ sK29 @ sK30) & (sK6 @ sK30 @ sK31)) => (sK6 @ sK29 @ sK31)) = $false) | ~spl0_28),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1850])).
% 1.44/1.49 thf(f1850,plain,(
% 1.44/1.49 (((^[Y0 : a]: (((sK6 @ sK29 @ sK30) & (sK6 @ sK30 @ Y0)) => (sK6 @ sK29 @ Y0))) @ sK31) = $false) | ~spl0_28),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1846])).
% 1.44/1.49 thf(f1846,plain,(
% 1.44/1.49 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK29 @ sK30) & (sK6 @ sK30 @ Y0)) => (sK6 @ sK29 @ Y0))))) | ~spl0_28),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1845])).
% 1.44/1.49 thf(f1845,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ sK29 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ sK29 @ Y1))))) @ sK30) = $false) | ~spl0_28),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1831])).
% 1.44/1.49 thf(f1831,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ sK29 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ sK29 @ Y1)))))) = $false) | ~spl0_28),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1827])).
% 1.44/1.49 thf(f1827,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2))))))) @ sK29) = $false) | ~spl0_28),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1802])).
% 1.44/1.49 thf(f1802,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) = $false) | ~spl0_28),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f1801])).
% 1.44/1.49 thf(f1801,definition,(
% 1.44/1.49 spl0_28 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) = $false)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition])).
% 1.44/1.49 thf(f1806,plain,(
% 1.44/1.49 spl0_28 | spl0_29 | ~spl0_6 | ~spl0_14),
% 1.44/1.49 inference(avatar_split_clause,[status(thm)],[f1797,f683,f91,f1804,f1801])).
% 1.44/1.49 thf(f91,definition,(
% 1.44/1.49 spl0_6 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK6 @ Y0 @ Y1)))))) = $false)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.44/1.49 thf(f683,definition,(
% 1.44/1.49 spl0_14 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK19 @ sK20)))))),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.44/1.49 thf(f1797,plain,(
% 1.44/1.49 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) = $false) | (~spl0_6 | ~spl0_14)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1789])).
% 1.44/1.49 thf(f1789,plain,(
% 1.44/1.49 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))))) = $false) | (~spl0_6 | ~spl0_14)),
% 1.44/1.49 inference(not_proxy_clausification,[status(thm)],[f1758])).
% 1.44/1.49 thf(f1758,plain,(
% 1.44/1.49 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))))) = $true) | (~spl0_6 | ~spl0_14)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1757])).
% 1.44/1.49 thf(f1757,plain,(
% 1.44/1.49 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))))) => $false)) | (~spl0_6 | ~spl0_14)),
% 1.44/1.49 inference(superposition,[status(thm)],[f1741,f1683])).
% 1.44/1.49 thf(f1683,plain,(
% 1.44/1.49 ((sK6 @ sK19 @ sK20) = $false) | (~spl0_6 | ~spl0_14)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1682])).
% 1.44/1.49 thf(f1682,plain,(
% 1.44/1.49 (($true => (sK6 @ sK19 @ sK20)) = $false) | (~spl0_6 | ~spl0_14)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1681])).
% 1.44/1.49 thf(f1681,plain,(
% 1.44/1.49 ((($true | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK19 @ sK20))))) => (sK6 @ sK19 @ sK20)) = $false) | (~spl0_6 | ~spl0_14)),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f1473,f684])).
% 1.44/1.49 thf(f684,plain,(
% 1.44/1.49 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK19 @ sK20))))) | ~spl0_14),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f683])).
% 1.44/1.49 thf(f1473,plain,(
% 1.44/1.49 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK19 @ sK20)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK19 @ sK20))))) => (sK6 @ sK19 @ sK20)) = $false) | ~spl0_6),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1472])).
% 1.44/1.49 thf(f1472,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK19 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ sK19 @ Y0))))) => (sK6 @ sK19 @ Y0))) @ sK20)) | ~spl0_6),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1461])).
% 1.44/1.49 thf(f1461,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK19 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ sK19 @ Y0))))) => (sK6 @ sK19 @ Y0)))) = $false) | ~spl0_6),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1459])).
% 1.44/1.49 thf(f1459,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK6 @ Y0 @ Y1))))) @ sK19) = $false) | ~spl0_6),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f92])).
% 1.44/1.49 thf(f92,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK6 @ Y0 @ Y1)))))) = $false) | ~spl0_6),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f91])).
% 1.44/1.49 thf(f1741,plain,(
% 1.44/1.49 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y1) & (X1 @ Y1 @ Y2)) => (X1 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK19 @ sK20)) = $true)) ) | ~spl0_14),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1740])).
% 1.44/1.49 thf(f1740,plain,(
% 1.44/1.49 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK19 @ sK20))) @ X1) = $true)) ) | ~spl0_14),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f684])).
% 1.44/1.49 thf(f1680,plain,(
% 1.44/1.49 ~spl0_3 | ~spl0_21),
% 1.44/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1679])).
% 1.44/1.49 thf(f1679,plain,(
% 1.44/1.49 $false | (~spl0_3 | ~spl0_21)),
% 1.44/1.49 inference(trivial_inequality_removal,[status(thm)],[f1678])).
% 1.44/1.49 thf(f1678,plain,(
% 1.44/1.49 ($true = $false) | (~spl0_3 | ~spl0_21)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1677])).
% 1.44/1.49 thf(f1677,plain,(
% 1.44/1.49 ((~ $true) = $true) | (~spl0_3 | ~spl0_21)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1676])).
% 1.44/1.49 thf(f1676,plain,(
% 1.44/1.49 ((~ ($true | (sK2 @ sK27 @ sK28))) = $true) | (~spl0_3 | ~spl0_21)),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f1675,f1661])).
% 1.44/1.49 thf(f1661,plain,(
% 1.44/1.49 ((sK3 @ sK27 @ sK28) = $true) | ~spl0_21),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1600])).
% 1.44/1.49 thf(f1600,plain,(
% 1.44/1.49 (((sK3 @ sK27 @ sK28) => (sK6 @ sK27 @ sK28)) = $false) | ~spl0_21),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1599])).
% 1.44/1.49 thf(f1599,plain,(
% 1.44/1.49 (((^[Y0 : a]: ((sK3 @ sK27 @ Y0) => (sK6 @ sK27 @ Y0))) @ sK28) = $false) | ~spl0_21),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1595])).
% 1.44/1.49 thf(f1595,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK27 @ Y0) => (sK6 @ sK27 @ Y0)))) = $false) | ~spl0_21),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1591])).
% 1.44/1.49 thf(f1591,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))) @ sK27) = $false) | ~spl0_21),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1584])).
% 1.44/1.49 thf(f1584,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) = $false) | ~spl0_21),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f1583])).
% 1.44/1.49 thf(f1583,definition,(
% 1.44/1.49 spl0_21 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) = $false)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 1.44/1.49 thf(f1675,plain,(
% 1.44/1.49 ((~ ((sK3 @ sK27 @ sK28) | (sK2 @ sK27 @ sK28))) = $true) | (~spl0_3 | ~spl0_21)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1669])).
% 1.44/1.49 thf(f1669,plain,(
% 1.44/1.49 ((((sK3 @ sK27 @ sK28) | (sK2 @ sK27 @ sK28)) => $false) = $true) | (~spl0_3 | ~spl0_21)),
% 1.44/1.49 inference(superposition,[status(thm)],[f1417,f1660])).
% 1.44/1.49 thf(f1660,plain,(
% 1.44/1.49 ((sK6 @ sK27 @ sK28) = $false) | ~spl0_21),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1600])).
% 1.44/1.49 thf(f1585,plain,(
% 1.44/1.49 spl0_21 | spl0_5 | ~spl0_6 | ~spl0_13),
% 1.44/1.49 inference(avatar_split_clause,[status(thm)],[f1579,f680,f91,f88,f1583])).
% 1.44/1.49 thf(f88,definition,(
% 1.44/1.49 spl0_5 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) = $false)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.44/1.49 thf(f680,definition,(
% 1.44/1.49 spl0_13 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK19 @ sK20)))) = $true)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.44/1.49 thf(f1579,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) = $false) | (~spl0_6 | ~spl0_13)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1573])).
% 1.44/1.49 thf(f1573,plain,(
% 1.44/1.49 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2))))))))) = $false) | (~spl0_6 | ~spl0_13)),
% 1.44/1.49 inference(not_proxy_clausification,[status(thm)],[f1526])).
% 1.44/1.49 thf(f1526,plain,(
% 1.44/1.49 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))))) = $true) | (~spl0_6 | ~spl0_13)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1525])).
% 1.44/1.49 thf(f1525,plain,(
% 1.44/1.49 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2))))))))) => $false)) | (~spl0_6 | ~spl0_13)),
% 1.44/1.49 inference(superposition,[status(thm)],[f1520,f1476])).
% 1.44/1.49 thf(f1476,plain,(
% 1.44/1.49 ((sK6 @ sK19 @ sK20) = $false) | (~spl0_6 | ~spl0_13)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1475])).
% 1.44/1.49 thf(f1475,plain,(
% 1.44/1.49 (($true => (sK6 @ sK19 @ sK20)) = $false) | (~spl0_6 | ~spl0_13)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1474])).
% 1.44/1.49 thf(f1474,plain,(
% 1.44/1.49 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK19 @ sK20)))) | $true) => (sK6 @ sK19 @ sK20))) | (~spl0_6 | ~spl0_13)),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f1473,f681])).
% 1.44/1.49 thf(f681,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK19 @ sK20)))) = $true) | ~spl0_13),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f680])).
% 1.44/1.49 thf(f1520,plain,(
% 1.44/1.49 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y2) & (X1 @ Y0 @ Y1)) => (X1 @ Y0 @ Y2))))))))) => (X1 @ sK19 @ sK20)))) ) | ~spl0_13),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1519])).
% 1.44/1.49 thf(f1519,plain,(
% 1.44/1.49 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK19 @ sK20))) @ X1) = $true)) ) | ~spl0_13),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f681])).
% 1.44/1.49 thf(f1376,plain,(
% 1.44/1.49 ~spl0_4 | ~spl0_7 | ~spl0_10),
% 1.44/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1375])).
% 1.44/1.49 thf(f1375,plain,(
% 1.44/1.49 $false | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(trivial_inequality_removal,[status(thm)],[f1374])).
% 1.44/1.49 thf(f1374,plain,(
% 1.44/1.49 ($true = $false) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1373])).
% 1.44/1.49 thf(f1373,plain,(
% 1.44/1.49 ((~ $true) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f1366,f219])).
% 1.44/1.49 thf(f219,plain,(
% 1.44/1.49 ($true = (sK2 @ sK11 @ sK12)) | ~spl0_10),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f218])).
% 1.44/1.49 thf(f218,definition,(
% 1.44/1.49 spl0_10 <=> ($true = (sK2 @ sK11 @ sK12))),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.44/1.49 thf(f1366,plain,(
% 1.44/1.49 ($true = (~ (sK2 @ sK11 @ sK12))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1360])).
% 1.44/1.49 thf(f1360,plain,(
% 1.44/1.49 (((sK2 @ sK11 @ sK12) => $false) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(superposition,[status(thm)],[f1358,f1260])).
% 1.44/1.49 thf(f1260,plain,(
% 1.44/1.49 ((sK23 @ sK11 @ sK12) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1259])).
% 1.44/1.49 thf(f1259,plain,(
% 1.44/1.49 (($true => (sK23 @ sK11 @ sK12)) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f1251,f1258])).
% 1.44/1.49 thf(f1258,plain,(
% 1.44/1.49 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y0 @ Y1) & (sK23 @ Y1 @ Y2)) => (sK23 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1))))))) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1251])).
% 1.44/1.49 thf(f1251,plain,(
% 1.44/1.49 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y0 @ Y1) & (sK23 @ Y1 @ Y2)) => (sK23 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1))))))) => (sK23 @ sK11 @ sK12))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1249])).
% 1.44/1.49 thf(f1249,plain,(
% 1.44/1.49 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK11 @ sK12))) @ sK23) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f1193])).
% 1.44/1.49 thf(f1193,plain,(
% 1.44/1.49 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK11 @ sK12))))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1181])).
% 1.44/1.49 thf(f1181,plain,(
% 1.44/1.49 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK11 @ sK12)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK11 @ sK12))))) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(not_proxy_clausification,[status(thm)],[f1173])).
% 1.44/1.49 thf(f1173,plain,(
% 1.44/1.49 ((~ ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK11 @ sK12)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK11 @ sK12)))))) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1172])).
% 1.44/1.49 thf(f1172,plain,(
% 1.44/1.49 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK11 @ sK12)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK11 @ sK12))))) => $false) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(superposition,[status(thm)],[f741,f1168])).
% 1.44/1.49 thf(f1168,plain,(
% 1.44/1.49 ((sK10 @ sK11 @ sK12) = $false) | (~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1167])).
% 1.44/1.49 thf(f1167,plain,(
% 1.44/1.49 (($true => (sK10 @ sK11 @ sK12)) = $false) | (~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1166])).
% 1.44/1.49 thf(f1166,plain,(
% 1.44/1.49 ((((sK3 @ sK11 @ sK12) | $true) => (sK10 @ sK11 @ sK12)) = $false) | (~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f365,f219])).
% 1.44/1.49 thf(f365,plain,(
% 1.44/1.49 ((((sK3 @ sK11 @ sK12) | (sK2 @ sK11 @ sK12)) => (sK10 @ sK11 @ sK12)) = $false) | ~spl0_7),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f364])).
% 1.44/1.49 thf(f364,plain,(
% 1.44/1.49 (((^[Y0 : a]: (((sK3 @ sK11 @ Y0) | (sK2 @ sK11 @ Y0)) => (sK10 @ sK11 @ Y0))) @ sK12) = $false) | ~spl0_7),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f350])).
% 1.44/1.49 thf(f350,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK11 @ Y0) | (sK2 @ sK11 @ Y0)) => (sK10 @ sK11 @ Y0)))) = $false) | ~spl0_7),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f348])).
% 1.44/1.49 thf(f348,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y1))))) @ sK11) = $false) | ~spl0_7),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f189])).
% 1.44/1.49 thf(f189,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y1)))))) = $false) | ~spl0_7),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f188])).
% 1.44/1.49 thf(f188,definition,(
% 1.44/1.49 spl0_7 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y1)))))) = $false)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.44/1.49 thf(f741,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X1 @ X2)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ X1 @ X2))))) => (sK10 @ X1 @ X2)) = $true)) ) | ~spl0_4),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f740])).
% 1.44/1.49 thf(f740,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ X1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ X1 @ Y0))))) => (sK10 @ X1 @ Y0))) @ X2))) ) | ~spl0_4),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f737])).
% 1.44/1.49 thf(f737,plain,(
% 1.44/1.49 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ X1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ X1 @ Y0))))) => (sK10 @ X1 @ Y0)))))) ) | ~spl0_4),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f736])).
% 1.44/1.49 thf(f736,plain,(
% 1.44/1.49 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK10 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_4),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f735])).
% 1.44/1.49 thf(f735,plain,(
% 1.44/1.49 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK10 @ Y0 @ Y1))))))) | ~spl0_4),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f734])).
% 1.44/1.49 thf(f734,plain,(
% 1.44/1.49 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK10 @ Y0 @ Y1)))))))) | ~spl0_4),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f722,f733])).
% 1.44/1.49 thf(f733,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y2)))))))) = $true) | ~spl0_4),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f722])).
% 1.44/1.49 thf(f722,plain,(
% 1.44/1.49 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK10 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f710])).
% 1.44/1.49 thf(f710,plain,(
% 1.44/1.49 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK10 @ Y0 @ Y1))))))) => (sK10 @ sK4 @ sK5)) = $false) | ~spl0_4),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f709])).
% 1.44/1.49 thf(f709,plain,(
% 1.44/1.49 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))) @ sK10) = $false) | ~spl0_4),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f33])).
% 1.44/1.49 thf(f33,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))) = $false) | ~spl0_4),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.44/1.49 thf(f32,definition,(
% 1.44/1.49 spl0_4 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))) = $false)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.44/1.49 thf(f1358,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1 @ X2) => (sK23 @ X1 @ X2)) = $true)) ) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1357])).
% 1.44/1.49 thf(f1357,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK2 @ X1 @ Y0) => (sK23 @ X1 @ Y0))) @ X2) = $true)) ) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1356])).
% 1.44/1.49 thf(f1356,plain,(
% 1.44/1.49 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ X1 @ Y0) => (sK23 @ X1 @ Y0)))))) ) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1355])).
% 1.44/1.49 thf(f1355,plain,(
% 1.44/1.49 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1))))) @ X1) = $true)) ) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1298])).
% 1.44/1.49 thf(f1298,plain,(
% 1.44/1.49 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1))))))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f1258])).
% 1.44/1.49 thf(f1165,plain,(
% 1.44/1.49 ~spl0_4 | ~spl0_7 | ~spl0_9),
% 1.44/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1164])).
% 1.44/1.49 thf(f1164,plain,(
% 1.44/1.49 $false | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(trivial_inequality_removal,[status(thm)],[f1163])).
% 1.44/1.49 thf(f1163,plain,(
% 1.44/1.49 ($true = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f1156,f932])).
% 1.44/1.49 thf(f932,plain,(
% 1.44/1.49 ((sK18 @ sK11 @ sK12) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f931])).
% 1.44/1.49 thf(f931,plain,(
% 1.44/1.49 (($true => (sK18 @ sK11 @ sK12)) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f921,f930])).
% 1.44/1.49 thf(f930,plain,(
% 1.44/1.49 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y2)))))))))) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f921])).
% 1.44/1.49 thf(f921,plain,(
% 1.44/1.49 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y2))))))))) => (sK18 @ sK11 @ sK12)) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f919])).
% 1.44/1.49 thf(f919,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK11 @ sK12))) @ sK18)) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f787])).
% 1.44/1.49 thf(f787,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK11 @ sK12)))) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f777])).
% 1.44/1.49 thf(f777,plain,(
% 1.44/1.49 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK11 @ sK12)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK11 @ sK12))))) = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(not_proxy_clausification,[status(thm)],[f747])).
% 1.44/1.49 thf(f747,plain,(
% 1.44/1.49 ((~ ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK11 @ sK12)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK11 @ sK12)))))) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f746])).
% 1.44/1.49 thf(f746,plain,(
% 1.44/1.49 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK11 @ sK12)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK11 @ sK12))))) => $false) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(superposition,[status(thm)],[f741,f368])).
% 1.44/1.49 thf(f368,plain,(
% 1.44/1.49 ((sK10 @ sK11 @ sK12) = $false) | (~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f367])).
% 1.44/1.49 thf(f367,plain,(
% 1.44/1.49 (($true => (sK10 @ sK11 @ sK12)) = $false) | (~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f366])).
% 1.44/1.49 thf(f366,plain,(
% 1.44/1.49 ($false = (($true | (sK2 @ sK11 @ sK12)) => (sK10 @ sK11 @ sK12))) | (~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f365,f216])).
% 1.44/1.49 thf(f216,plain,(
% 1.44/1.49 ($true = (sK3 @ sK11 @ sK12)) | ~spl0_9),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f215])).
% 1.44/1.49 thf(f215,definition,(
% 1.44/1.49 spl0_9 <=> ($true = (sK3 @ sK11 @ sK12))),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.44/1.49 thf(f1156,plain,(
% 1.44/1.49 ((sK18 @ sK11 @ sK12) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f1151])).
% 1.44/1.49 thf(f1151,plain,(
% 1.44/1.49 (($true => (sK18 @ sK11 @ sK12)) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(superposition,[status(thm)],[f1147,f216])).
% 1.44/1.49 thf(f1147,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X1 @ X2) => (sK18 @ X1 @ X2)))) ) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1146])).
% 1.44/1.49 thf(f1146,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK18 @ X1 @ Y0))) @ X2))) ) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1143])).
% 1.44/1.49 thf(f1143,plain,(
% 1.44/1.49 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK18 @ X1 @ Y0)))) = $true)) ) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f1142])).
% 1.44/1.49 thf(f1142,plain,(
% 1.44/1.49 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1))))) @ X1))) ) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f1039])).
% 1.44/1.49 thf(f1039,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f930])).
% 1.44/1.49 thf(f685,plain,(
% 1.44/1.49 spl0_13 | spl0_14 | ~spl0_6),
% 1.44/1.49 inference(avatar_split_clause,[status(thm)],[f678,f91,f683,f680])).
% 1.44/1.49 thf(f678,plain,(
% 1.44/1.49 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK19 @ sK20))))) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK19 @ sK20)))) = $true) | ~spl0_6),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f624])).
% 1.44/1.49 thf(f624,plain,(
% 1.44/1.49 ($true = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK19 @ sK20)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK19 @ sK20)))))) | ~spl0_6),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f615])).
% 1.44/1.49 thf(f615,plain,(
% 1.44/1.49 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK19 @ sK20)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK19 @ sK20))))) => (sK6 @ sK19 @ sK20)) = $false) | ~spl0_6),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f614])).
% 1.44/1.49 thf(f614,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK19 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ sK19 @ Y0))))) => (sK6 @ sK19 @ Y0))) @ sK20)) | ~spl0_6),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f602])).
% 1.44/1.49 thf(f602,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK19 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ sK19 @ Y0))))) => (sK6 @ sK19 @ Y0)))) = $false) | ~spl0_6),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f600])).
% 1.44/1.49 thf(f600,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK6 @ Y0 @ Y1))))) @ sK19) = $false) | ~spl0_6),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f92])).
% 1.44/1.49 thf(f345,plain,(
% 1.44/1.49 ~spl0_4 | ~spl0_8),
% 1.44/1.49 inference(avatar_contradiction_clause,[status(thm)],[f344])).
% 1.44/1.49 thf(f344,plain,(
% 1.44/1.49 $false | (~spl0_4 | ~spl0_8)),
% 1.44/1.49 inference(trivial_inequality_removal,[status(thm)],[f343])).
% 1.44/1.49 thf(f343,plain,(
% 1.44/1.49 ($true = $false) | (~spl0_4 | ~spl0_8)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f342])).
% 1.44/1.49 thf(f342,plain,(
% 1.44/1.49 ((~ $true) = $true) | (~spl0_4 | ~spl0_8)),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f336,f246])).
% 1.44/1.49 thf(f246,plain,(
% 1.44/1.49 ($true = (sK10 @ sK14 @ sK16)) | ~spl0_8),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f242])).
% 1.44/1.49 thf(f242,plain,(
% 1.44/1.49 ($true = ((sK10 @ sK14 @ sK16) & (sK10 @ sK16 @ sK13))) | ~spl0_8),
% 1.44/1.49 inference(not_proxy_clausification,[status(thm)],[f241])).
% 1.44/1.49 thf(f241,plain,(
% 1.44/1.49 ((~ ((sK10 @ sK14 @ sK16) & (sK10 @ sK16 @ sK13))) = $false) | ~spl0_8),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f240])).
% 1.44/1.49 thf(f240,plain,(
% 1.44/1.49 (((^[Y0 : a]: (~ ((sK10 @ sK14 @ Y0) & (sK10 @ Y0 @ sK13)))) @ sK16) = $false) | ~spl0_8),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f236])).
% 1.44/1.49 thf(f236,plain,(
% 1.44/1.49 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK10 @ sK14 @ Y0) & (sK10 @ Y0 @ sK13)))))) | ~spl0_8),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f235])).
% 1.44/1.49 thf(f235,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (((sK10 @ sK14 @ Y0) & (sK10 @ Y0 @ sK13)) => $false))) = $false) | ~spl0_8),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f229,f232])).
% 1.44/1.49 thf(f232,plain,(
% 1.44/1.49 ($false = (sK10 @ sK14 @ sK13)) | ~spl0_8),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f231])).
% 1.44/1.49 thf(f231,plain,(
% 1.44/1.49 ((((sK10 @ sK14 @ sK15) & (sK10 @ sK15 @ sK13)) => (sK10 @ sK14 @ sK13)) = $false) | ~spl0_8),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f230])).
% 1.44/1.49 thf(f230,plain,(
% 1.44/1.49 (((^[Y0 : a]: (((sK10 @ sK14 @ Y0) & (sK10 @ Y0 @ sK13)) => (sK10 @ sK14 @ sK13))) @ sK15) = $false) | ~spl0_8),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f229])).
% 1.44/1.49 thf(f229,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (((sK10 @ sK14 @ Y0) & (sK10 @ Y0 @ sK13)) => (sK10 @ sK14 @ sK13)))) = $false) | ~spl0_8),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f228])).
% 1.44/1.49 thf(f228,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0 @ Y1) & (sK10 @ Y1 @ sK13)) => (sK10 @ Y0 @ sK13))))) @ sK14) = $false) | ~spl0_8),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f225])).
% 1.44/1.49 thf(f225,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0 @ Y1) & (sK10 @ Y1 @ sK13)) => (sK10 @ Y0 @ sK13)))))) = $false) | ~spl0_8),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f223])).
% 1.44/1.49 thf(f223,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y2 @ Y0)) => (sK10 @ Y1 @ Y0))))))) @ sK13) = $false) | ~spl0_8),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f192])).
% 1.44/1.49 thf(f192,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y2 @ Y0)) => (sK10 @ Y1 @ Y0)))))))) = $false) | ~spl0_8),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f191])).
% 1.44/1.49 thf(f191,definition,(
% 1.44/1.49 spl0_8 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y2 @ Y0)) => (sK10 @ Y1 @ Y0)))))))) = $false)),
% 1.44/1.49 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.44/1.49 thf(f336,plain,(
% 1.44/1.49 ($true = (~ (sK10 @ sK14 @ sK16))) | (~spl0_4 | ~spl0_8)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f331])).
% 1.44/1.49 thf(f331,plain,(
% 1.44/1.49 (((sK10 @ sK14 @ sK16) => $false) = $true) | (~spl0_4 | ~spl0_8)),
% 1.44/1.49 inference(superposition,[status(thm)],[f299,f232])).
% 1.44/1.49 thf(f299,plain,(
% 1.44/1.49 ( ! [X0 : a] : ((((sK10 @ X0 @ sK16) => (sK10 @ X0 @ sK13)) = $true)) ) | (~spl0_4 | ~spl0_8)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f274])).
% 1.44/1.49 thf(f274,plain,(
% 1.44/1.49 ( ! [X0 : a] : (((($true & (sK10 @ X0 @ sK16)) => (sK10 @ X0 @ sK13)) = $true)) ) | (~spl0_4 | ~spl0_8)),
% 1.44/1.49 inference(superposition,[status(thm)],[f258,f248])).
% 1.44/1.49 thf(f248,plain,(
% 1.44/1.49 ((sK10 @ sK16 @ sK13) = $true) | ~spl0_8),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f247])).
% 1.44/1.49 thf(f247,plain,(
% 1.44/1.49 (($true & (sK10 @ sK16 @ sK13)) = $true) | ~spl0_8),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f242,f246])).
% 1.44/1.49 thf(f258,plain,(
% 1.44/1.49 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK10 @ X2 @ X3) & (sK10 @ X1 @ X2)) => (sK10 @ X1 @ X3)) = $true)) ) | ~spl0_4),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f257])).
% 1.44/1.49 thf(f257,plain,(
% 1.44/1.49 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK10 @ X2 @ Y0) & (sK10 @ X1 @ X2)) => (sK10 @ X1 @ Y0))) @ X3))) ) | ~spl0_4),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f256])).
% 1.44/1.49 thf(f256,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK10 @ X2 @ Y0) & (sK10 @ X1 @ X2)) => (sK10 @ X1 @ Y0)))))) ) | ~spl0_4),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f255])).
% 1.44/1.49 thf(f255,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0 @ Y1) & (sK10 @ X1 @ Y0)) => (sK10 @ X1 @ Y1))))) @ X2))) ) | ~spl0_4),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f250])).
% 1.44/1.49 thf(f250,plain,(
% 1.44/1.49 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0 @ Y1) & (sK10 @ X1 @ Y0)) => (sK10 @ X1 @ Y1)))))) = $true)) ) | ~spl0_4),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f249])).
% 1.44/1.49 thf(f249,plain,(
% 1.44/1.49 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y2))))))) @ X1) = $true)) ) | ~spl0_4),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f212])).
% 1.44/1.49 thf(f212,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y2)))))))) = $true) | ~spl0_4),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f211])).
% 1.44/1.49 thf(f211,plain,(
% 1.44/1.49 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y2)))))))) & $true) = $true) | ~spl0_4),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f176,f209])).
% 1.44/1.49 thf(f209,plain,(
% 1.44/1.49 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK10 @ Y0 @ Y1))))))) | ~spl0_4),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f176])).
% 1.44/1.49 thf(f176,plain,(
% 1.44/1.49 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK10 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f174])).
% 1.44/1.49 thf(f174,plain,(
% 1.44/1.49 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK10 @ Y0 @ Y1))))))) => (sK10 @ sK4 @ sK5)) = $false) | ~spl0_4),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f173])).
% 1.44/1.49 thf(f173,plain,(
% 1.44/1.49 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))) @ sK10) = $false) | ~spl0_4),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f33])).
% 1.44/1.49 thf(f220,plain,(
% 1.44/1.49 spl0_9 | spl0_10 | ~spl0_7),
% 1.44/1.49 inference(avatar_split_clause,[status(thm)],[f213,f188,f218,f215])).
% 1.44/1.49 thf(f213,plain,(
% 1.44/1.49 ($true = (sK3 @ sK11 @ sK12)) | ($true = (sK2 @ sK11 @ sK12)) | ~spl0_7),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f204])).
% 1.44/1.49 thf(f204,plain,(
% 1.44/1.49 (((sK3 @ sK11 @ sK12) | (sK2 @ sK11 @ sK12)) = $true) | ~spl0_7),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f202])).
% 1.44/1.49 thf(f202,plain,(
% 1.44/1.49 ((((sK3 @ sK11 @ sK12) | (sK2 @ sK11 @ sK12)) => (sK10 @ sK11 @ sK12)) = $false) | ~spl0_7),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f201])).
% 1.44/1.49 thf(f201,plain,(
% 1.44/1.49 (((^[Y0 : a]: (((sK3 @ sK11 @ Y0) | (sK2 @ sK11 @ Y0)) => (sK10 @ sK11 @ Y0))) @ sK12) = $false) | ~spl0_7),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f198])).
% 1.44/1.49 thf(f198,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK11 @ Y0) | (sK2 @ sK11 @ Y0)) => (sK10 @ sK11 @ Y0)))) = $false) | ~spl0_7),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f196])).
% 1.44/1.49 thf(f196,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y1))))) @ sK11) = $false) | ~spl0_7),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f189])).
% 1.44/1.49 thf(f193,plain,(
% 1.44/1.49 spl0_7 | spl0_8 | ~spl0_4),
% 1.44/1.49 inference(avatar_split_clause,[status(thm)],[f184,f32,f191,f188])).
% 1.44/1.49 thf(f184,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y1)))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y2 @ Y0)) => (sK10 @ Y1 @ Y0)))))))) = $false) | ~spl0_4),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f181])).
% 1.44/1.49 thf(f181,plain,(
% 1.44/1.49 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y2 @ Y0)) => (sK10 @ Y1 @ Y0))))))))) = $false) | ~spl0_4),
% 1.44/1.49 inference(not_proxy_clausification,[status(thm)],[f180])).
% 1.44/1.49 thf(f180,plain,(
% 1.44/1.49 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y2 @ Y0)) => (sK10 @ Y1 @ Y0))))))))))) | ~spl0_4),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f179])).
% 1.44/1.49 thf(f179,plain,(
% 1.44/1.49 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK10 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK10 @ Y1 @ Y2) & (sK10 @ Y2 @ Y0)) => (sK10 @ Y1 @ Y0))))))))) => $false) = $true) | ~spl0_4),
% 1.44/1.49 inference(superposition,[status(thm)],[f168,f178])).
% 1.44/1.49 thf(f178,plain,(
% 1.44/1.49 ($false = (sK10 @ sK4 @ sK5)) | ~spl0_4),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f177])).
% 1.44/1.49 thf(f177,plain,(
% 1.44/1.49 (($true => (sK10 @ sK4 @ sK5)) = $false) | ~spl0_4),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f174,f176])).
% 1.44/1.49 thf(f168,plain,(
% 1.44/1.49 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y2) & (X1 @ Y2 @ Y0)) => (X1 @ Y1 @ Y0))))))))) => (X1 @ sK4 @ sK5)) = $true)) ) | ~spl0_4),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f167])).
% 1.44/1.49 thf(f167,plain,(
% 1.44/1.49 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK4 @ sK5))) @ X1))) ) | ~spl0_4),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f166])).
% 1.44/1.49 thf(f166,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) != $false) | ~spl0_4),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f18,f33])).
% 1.44/1.49 thf(f18,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) != (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))))),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.44/1.49 thf(f17,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y2 @ Y3))))) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ Y0))))) @ sK5) != ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK4 @ Y0))))) @ sK5))),
% 1.44/1.49 inference(negative_extensionality,[status(thm)],[f16])).
% 1.44/1.49 thf(f16,plain,(
% 1.44/1.49 ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y2 @ Y3))))) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ Y0))))) != (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK4 @ Y0))))))),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.44/1.49 thf(f15,plain,(
% 1.44/1.49 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))) @ sK4) != ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y3 @ Y4))))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) @ sK4))),
% 1.44/1.49 inference(negative_extensionality,[status(thm)],[f14])).
% 1.44/1.49 thf(f14,plain,(
% 1.44/1.49 ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y3 @ Y4))))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))))),
% 1.44/1.49 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 1.44/1.49 thf(f13,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y3 @ Y4))))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))))))))),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.44/1.49 thf(f12,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a > a > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK2 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y9) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y4 @ Y5))))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))))) @ sK3))),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f11])).
% 1.44/1.49 thf(f11,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK2 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y9) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y4 @ Y5))))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))))))))) = $false)),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.44/1.49 thf(f10,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y8 @ Y10)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y1 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y10) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y10))))))))) => (Y7 @ Y5 @ Y6))))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))))))) @ sK2))),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f7])).
% 1.44/1.49 thf(f7,plain,(
% 1.44/1.49 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y8 @ Y10)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y1 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y10) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y10))))))))) => (Y7 @ Y5 @ Y6))))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))))))))))))),
% 1.44/1.49 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.44/1.49 thf(f6,plain,(
% 1.44/1.49 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y8 @ Y10)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y1 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y10) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y10))))))))) => (Y7 @ Y5 @ Y6))))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))))))))))),
% 1.44/1.49 inference(cnf_transformation,[status(thm)],[f5])).
% 1.44/1.49 thf(f5,plain,(
% 1.44/1.49 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y8 @ Y10)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y1 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y10) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y10))))))))) => (Y7 @ Y5 @ Y6))))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))))))))))),
% 1.44/1.49 inference(fool_elimination,[status(thm)],[f4])).
% 1.44/1.49 thf(f4,plain,(
% 1.44/1.49 ~! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a,X7 : a] : (((X4 @ X5 @ X7) & (X4 @ X6 @ X5)) => (X4 @ X6 @ X7)) & ! [X8 : a,X9 : a] : (((X1 @ X9 @ X8) | (X0 @ X9 @ X8)) => (X4 @ X9 @ X8))) => (X4 @ X2 @ X3)))) = (^[X10 : a, X11 : a] : (! [X12 : a > a > $o] : ((! [X13 : a,X14 : a] : ((! [X15 : a > a > $o] : ((! [X16 : a,X17 : a,X18 : a] : (((X15 @ X18 @ X17) & (X15 @ X17 @ X16)) => (X15 @ X18 @ X16)) & ! [X19 : a,X20 : a] : ((X0 @ X20 @ X19) => (X15 @ X20 @ X19))) => (X15 @ X14 @ X13)) | ! [X21 : a > a > $o] : ((! [X22 : a,X23 : a] : ((X1 @ X23 @ X22) => (X21 @ X23 @ X22)) & ! [X24 : a,X25 : a,X26 : a] : (((X21 @ X25 @ X24) & (X21 @ X26 @ X25)) => (X21 @ X26 @ X24))) => (X21 @ X14 @ X13))) => (X12 @ X14 @ X13)) & ! [X27 : a,X28 : a,X29 : a] : (((X12 @ X29 @ X28) & (X12 @ X28 @ X27)) => (X12 @ X29 @ X27))) => (X12 @ X10 @ X11)))))),
% 1.44/1.49 inference(rectify,[status(thm)],[f2])).
% 1.44/1.49 thf(f2,negated_conjecture,(
% 1.44/1.49 ~! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X6 : a,X5 : a] : (((X1 @ X5 @ X6) | (X0 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : ((! [X8 : a > a > $o] : ((! [X7 : a,X10 : a,X9 : a] : (((X8 @ X9 @ X10) & (X8 @ X10 @ X7)) => (X8 @ X9 @ X7)) & ! [X10 : a,X9 : a] : ((X0 @ X9 @ X10) => (X8 @ X9 @ X10))) => (X8 @ X5 @ X6)) | ! [X8 : a > a > $o] : ((! [X10 : a,X9 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & ! [X7 : a,X10 : a,X9 : a] : (((X8 @ X10 @ X7) & (X8 @ X9 @ X10)) => (X8 @ X9 @ X7))) => (X8 @ X5 @ X6))) => (X4 @ X5 @ X6)) & ! [X7 : a,X6 : a,X5 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)))))),
% 1.44/1.49 inference(negated_conjecture,[status(cth)],[f1])).
% 1.44/1.49 thf(f1,conjecture,(
% 1.44/1.49 ! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X6 : a,X5 : a] : (((X1 @ X5 @ X6) | (X0 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : ((! [X8 : a > a > $o] : ((! [X7 : a,X10 : a,X9 : a] : (((X8 @ X9 @ X10) & (X8 @ X10 @ X7)) => (X8 @ X9 @ X7)) & ! [X10 : a,X9 : a] : ((X0 @ X9 @ X10) => (X8 @ X9 @ X10))) => (X8 @ X5 @ X6)) | ! [X8 : a > a > $o] : ((! [X10 : a,X9 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & ! [X7 : a,X10 : a,X9 : a] : (((X8 @ X10 @ X7) & (X8 @ X9 @ X10)) => (X8 @ X9 @ X7))) => (X8 @ X5 @ X6))) => (X4 @ X5 @ X6)) & ! [X7 : a,X6 : a,X5 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)))))),
% 1.44/1.49 file('/export/starexec/sandbox/tmp/tmp.Yfwa6cQPBu/DTF2THF_14272.p',cTHM250_pme)).
% 1.44/1.49 thf(f162,plain,(
% 1.44/1.49 ~spl0_3 | ~spl0_5),
% 1.44/1.49 inference(avatar_contradiction_clause,[status(thm)],[f161])).
% 1.44/1.49 thf(f161,plain,(
% 1.44/1.49 $false | (~spl0_3 | ~spl0_5)),
% 1.44/1.49 inference(trivial_inequality_removal,[status(thm)],[f160])).
% 1.44/1.49 thf(f160,plain,(
% 1.44/1.49 ($true = $false) | (~spl0_3 | ~spl0_5)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f159])).
% 1.44/1.49 thf(f159,plain,(
% 1.44/1.49 ((~ $true) = $true) | (~spl0_3 | ~spl0_5)),
% 1.44/1.49 inference(forward_demodulation,[status(thm)],[f153,f127])).
% 1.44/1.49 thf(f127,plain,(
% 1.44/1.49 ($true = (sK6 @ sK8 @ sK9)) | ~spl0_5),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.44/1.49 thf(f113,plain,(
% 1.44/1.49 (((sK6 @ sK8 @ sK9) & (sK6 @ sK7 @ sK8)) = $true) | ~spl0_5),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.44/1.49 thf(f111,plain,(
% 1.44/1.49 ((((sK6 @ sK8 @ sK9) & (sK6 @ sK7 @ sK8)) => (sK6 @ sK7 @ sK9)) = $false) | ~spl0_5),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f110])).
% 1.44/1.49 thf(f110,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a]: (((sK6 @ sK8 @ Y0) & (sK6 @ sK7 @ sK8)) => (sK6 @ sK7 @ Y0))) @ sK9)) | ~spl0_5),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f109])).
% 1.44/1.49 thf(f109,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (((sK6 @ sK8 @ Y0) & (sK6 @ sK7 @ sK8)) => (sK6 @ sK7 @ Y0)))) = $false) | ~spl0_5),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.44/1.49 thf(f108,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ sK7 @ Y0)) => (sK6 @ sK7 @ Y1))))) @ sK8) = $false) | ~spl0_5),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f105])).
% 1.44/1.49 thf(f105,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ sK7 @ Y0)) => (sK6 @ sK7 @ Y1)))))) = $false) | ~spl0_5),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f103])).
% 1.44/1.49 thf(f103,plain,(
% 1.44/1.49 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2))))))) @ sK7) = $false) | ~spl0_5),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f89])).
% 1.44/1.49 thf(f89,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) = $false) | ~spl0_5),
% 1.44/1.49 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.44/1.49 thf(f153,plain,(
% 1.44/1.49 ($true = (~ (sK6 @ sK8 @ sK9))) | (~spl0_3 | ~spl0_5)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f151])).
% 1.44/1.49 thf(f151,plain,(
% 1.44/1.49 ($true = ((sK6 @ sK8 @ sK9) => $false)) | (~spl0_3 | ~spl0_5)),
% 1.44/1.49 inference(superposition,[status(thm)],[f135,f112])).
% 1.44/1.49 thf(f112,plain,(
% 1.44/1.49 ($false = (sK6 @ sK7 @ sK9)) | ~spl0_5),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.44/1.49 thf(f135,plain,(
% 1.44/1.49 ( ! [X0 : a] : (($true = ((sK6 @ sK8 @ X0) => (sK6 @ sK7 @ X0)))) ) | (~spl0_3 | ~spl0_5)),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f130])).
% 1.44/1.49 thf(f130,plain,(
% 1.44/1.49 ( ! [X0 : a] : (($true = (($true & (sK6 @ sK8 @ X0)) => (sK6 @ sK7 @ X0)))) ) | (~spl0_3 | ~spl0_5)),
% 1.44/1.49 inference(superposition,[status(thm)],[f62,f129])).
% 1.44/1.49 thf(f129,plain,(
% 1.44/1.49 ((sK6 @ sK7 @ sK8) = $true) | ~spl0_5),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f128])).
% 1.44/1.49 thf(f128,plain,(
% 1.44/1.49 (($true & (sK6 @ sK7 @ sK8)) = $true) | ~spl0_5),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f113,f127])).
% 1.44/1.49 thf(f62,plain,(
% 1.44/1.49 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK6 @ X2 @ X3) & (sK6 @ X3 @ X1)) => (sK6 @ X2 @ X1)))) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.44/1.49 thf(f61,plain,(
% 1.44/1.49 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK6 @ X2 @ Y0) & (sK6 @ Y0 @ X1)) => (sK6 @ X2 @ X1))) @ X3))) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f60])).
% 1.44/1.49 thf(f60,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X2 @ Y0) & (sK6 @ Y0 @ X1)) => (sK6 @ X2 @ X1)))) = $true)) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.44/1.49 thf(f59,plain,(
% 1.44/1.49 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ X1)) => (sK6 @ Y0 @ X1))))) @ X2) = $true)) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f58])).
% 1.44/1.49 thf(f58,plain,(
% 1.44/1.49 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ X1)) => (sK6 @ Y0 @ X1)))))))) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.44/1.49 thf(f57,plain,(
% 1.44/1.49 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))) @ X1) = $true)) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f56])).
% 1.44/1.49 thf(f56,plain,(
% 1.44/1.49 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))) | ~spl0_3),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f55])).
% 1.44/1.49 thf(f55,plain,(
% 1.44/1.49 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))) = $true) | ~spl0_3),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f44,f54])).
% 1.44/1.49 thf(f54,plain,(
% 1.44/1.49 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))) | ~spl0_3),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.44/1.49 thf(f44,plain,(
% 1.44/1.49 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))))) | ~spl0_3),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.44/1.49 thf(f40,plain,(
% 1.44/1.49 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))) => (sK6 @ sK4 @ sK5)) = $false) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.44/1.49 thf(f39,plain,(
% 1.44/1.49 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK4 @ sK5))) @ sK6)) | ~spl0_3),
% 1.44/1.49 inference(sigma_clausification,[status(thm)],[f30])).
% 1.44/1.49 thf(f93,plain,(
% 1.44/1.49 spl0_5 | spl0_6 | ~spl0_3),
% 1.44/1.49 inference(avatar_split_clause,[status(thm)],[f84,f29,f91,f88])).
% 1.44/1.49 thf(f84,plain,(
% 1.44/1.49 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK6 @ Y0 @ Y1)))))) = $false) | ~spl0_3),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.44/1.49 thf(f72,plain,(
% 1.44/1.49 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK6 @ Y0 @ Y1))))))) = $false) | ~spl0_3),
% 1.44/1.49 inference(not_proxy_clausification,[status(thm)],[f49])).
% 1.44/1.49 thf(f49,plain,(
% 1.44/1.49 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK6 @ Y0 @ Y1))))))))) | ~spl0_3),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f48])).
% 1.44/1.49 thf(f48,plain,(
% 1.44/1.49 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (sK6 @ Y0 @ Y1))))))) => $false) = $true) | ~spl0_3),
% 1.44/1.49 inference(superposition,[status(thm)],[f42,f46])).
% 1.44/1.49 thf(f46,plain,(
% 1.44/1.49 ($false = (sK6 @ sK4 @ sK5)) | ~spl0_3),
% 1.44/1.49 inference(boolean_simplification,[status(thm)],[f45])).
% 1.44/1.49 thf(f45,plain,(
% 1.44/1.49 (($true => (sK6 @ sK4 @ sK5)) = $false) | ~spl0_3),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f40,f44])).
% 1.44/1.49 thf(f42,plain,(
% 1.44/1.49 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y2) & (X1 @ Y0 @ Y1)) => (X1 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK4 @ sK5)))) ) | ~spl0_3),
% 1.44/1.49 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.44/1.49 thf(f41,plain,(
% 1.44/1.49 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))) @ X1))) ) | ~spl0_3),
% 1.44/1.49 inference(pi_clausification,[status(thm)],[f35])).
% 1.44/1.49 thf(f35,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))) != $false) | ~spl0_3),
% 1.44/1.49 inference(backward_demodulation,[status(thm)],[f18,f30])).
% 1.44/1.49 thf(f34,plain,(
% 1.44/1.49 spl0_3 | spl0_4),
% 1.44/1.49 inference(avatar_split_clause,[status(thm)],[f20,f32,f29])).
% 1.44/1.49 thf(f20,plain,(
% 1.44/1.49 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))) = $false) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $false)),
% 1.44/1.49 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.44/1.49 % SZS output end Proof for DTF2THF_14272
% 1.44/1.49 % (14380)------------------------------
% 1.44/1.49 % (14380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.49 % (14380)Termination reason: Refutation
% 1.44/1.49
% 1.44/1.49 % (14380)Memory used [KB]: 6780
% 1.44/1.49 % (14380)Time elapsed: 0.276 s
% 1.44/1.49 % (14380)Instructions burned: 487 (million)
% 1.44/1.49 % (14380)------------------------------
% 1.44/1.49 % (14380)------------------------------
% 1.44/1.49 % (14368)Success in time 0.325 s
%------------------------------------------------------------------------------