%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV119^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 09:40:19 AM UTC 2026
% Result : Theorem 1.35s 1.26s
% Output : Refutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of formulae : 218 ( 18 unt; 0 typ; 11 def)
% Number of atoms : 2084 ( 211 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 5445 ( 363 ~; 460 |; 226 &;3209 @)
% ( 11 <=>; 508 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 840 ( 840 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 28 con; 0-2 aty)
% ( 668 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 837 ( 760 ^; 77 !; 0 ?; 837 :)
% 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 > a > $o ) > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a ).
thf(func_def_26,type,
sK7: a > a > $o ).
thf(func_def_27,type,
sK8: a > a > $o ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a ).
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 ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a > a > $o ).
thf(func_def_41,type,
sK22: a > a > $o ).
thf(func_def_42,type,
sK23: a > a > $o ).
thf(func_def_43,type,
sK24: a > a > $o ).
thf(f781,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f29,f36,f62,f65,f78,f171,f174,f241,f333,f336,f440,f774,f777]) ).
thf(f777,plain,
( spl0_14
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f776,f60,f27,f468]) ).
thf(f468,definition,
( spl0_14
<=> ( ( sK2 @ sK20 @ sK19 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f27,definition,
( spl0_2
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f60,definition,
( spl0_6
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f776,plain,
( ( ( sK2 @ sK20 @ sK19 )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f775]) ).
thf(f775,plain,
( ( ( ( sK2 @ sK20 @ sK19 )
| $false )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f456,f703]) ).
thf(f703,plain,
( ( ( sK3 @ sK20 @ sK19 )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(not_proxy_clausification,[status(thm)],[f696]) ).
thf(f696,plain,
( ( ( ~ ( sK3 @ sK20 @ sK19 ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f692]) ).
thf(f692,plain,
( ( ( ( sK3 @ sK20 @ sK19 )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f689,f664]) ).
thf(f664,plain,
( ( ( sK23 @ sK20 @ sK19 )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f663]) ).
thf(f663,plain,
( ( $false
= ( $true
=> ( sK23 @ sK20 @ sK19 ) ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f645,f662]) ).
thf(f662,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) ) )
& ( sK4 @ sK23 ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f645]) ).
thf(f645,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) ) )
& ( sK4 @ sK23 ) )
=> ( sK23 @ sK20 @ sK19 ) ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f643]) ).
thf(f643,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK20 @ sK19 ) )
@ sK23 )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f636]) ).
thf(f636,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK20 @ sK19 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f635]) ).
thf(f635,plain,
( ( ( $false
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK20 @ sK19 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f624,f632]) ).
thf(f632,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK20 @ sK19 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f624]) ).
thf(f624,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK20 @ sK19 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK20 @ sK19 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(not_proxy_clausification,[status(thm)],[f512]) ).
thf(f512,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK20 @ sK19 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK20 @ sK19 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f511]) ).
thf(f511,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK20 @ sK19 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK20 @ sK19 ) ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f498,f455]) ).
thf(f455,plain,
( ( ( sK7 @ sK20 @ sK19 )
= $false )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f447]) ).
thf(f447,plain,
( ( ( ( ( sK2 @ sK20 @ sK19 )
| ( sK3 @ sK20 @ sK19 ) )
=> ( sK7 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f446]) ).
thf(f446,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) )
=> ( sK7 @ Y0 @ sK19 ) )
@ sK20 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f443]) ).
thf(f443,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) )
=> ( sK7 @ Y0 @ sK19 ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f442]) ).
thf(f442,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK19 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f498,plain,
( ! [X2: a,X1: a] :
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X2 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ X2 @ X1 ) ) ) )
=> ( sK7 @ X2 @ X1 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f497]) ).
thf(f497,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK7 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK7 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f495]) ).
thf(f495,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f490]) ).
thf(f490,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f489]) ).
thf(f489,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f477,f487]) ).
thf(f487,plain,
( ( ( sK4 @ sK7 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f477]) ).
thf(f477,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f465]) ).
thf(f465,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) )
=> ( sK7 @ sK5 @ sK6 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f464]) ).
thf(f464,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f689,plain,
( ! [X2: a,X1: a] :
( ( ( sK3 @ X1 @ X2 )
=> ( sK23 @ X1 @ X2 ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f688]) ).
thf(f688,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK23 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f685]) ).
thf(f685,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK23 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f684]) ).
thf(f684,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f668]) ).
thf(f668,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f667]) ).
thf(f667,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK23 @ Y0 @ Y1 ) ) ) )
& $true )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f662,f665]) ).
thf(f665,plain,
( ( ( sK4 @ sK23 )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f662]) ).
thf(f456,plain,
( ( ( ( sK2 @ sK20 @ sK19 )
| ( sK3 @ sK20 @ sK19 ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f447]) ).
thf(f774,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f773]) ).
thf(f773,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f772]) ).
thf(f772,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f771]) ).
thf(f771,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f764,f469]) ).
thf(f469,plain,
( ( ( sK2 @ sK20 @ sK19 )
= $true )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f468]) ).
thf(f764,plain,
( ( ( ~ ( sK2 @ sK20 @ sK19 ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f761]) ).
thf(f761,plain,
( ( ( ( sK2 @ sK20 @ sK19 )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f755,f709]) ).
thf(f709,plain,
( ( $false
= ( sK24 @ sK20 @ sK19 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f708]) ).
thf(f708,plain,
( ( ( $true
=> ( sK24 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f699,f707]) ).
thf(f707,plain,
( ( ( ( sK4 @ sK24 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK24 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f699]) ).
thf(f699,plain,
( ( ( ( ( sK4 @ sK24 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK24 @ Y1 @ Y0 ) ) ) ) )
=> ( sK24 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f697]) ).
thf(f697,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK20 @ sK19 ) )
@ sK24 )
= $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f632]) ).
thf(f755,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X2 @ X1 )
=> ( sK24 @ X2 @ X1 ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f754]) ).
thf(f754,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK24 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f749]) ).
thf(f749,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK24 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f746]) ).
thf(f746,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK24 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f728]) ).
thf(f728,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK24 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f727]) ).
thf(f727,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK24 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f707,f724]) ).
thf(f724,plain,
( ( ( sK4 @ sK24 )
= $true )
| ~ spl0_2
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f707]) ).
thf(f440,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f439]) ).
thf(f439,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f438]) ).
thf(f438,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f437]) ).
thf(f437,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f436]) ).
thf(f436,plain,
( ( ( ~ ( ( sK2 @ sK17 @ sK18 )
| $true ) )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f435,f431]) ).
thf(f431,plain,
( ( ( sK3 @ sK17 @ sK18 )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f429]) ).
thf(f429,plain,
( ( ( ( sK3 @ sK17 @ sK18 )
=> ( sK8 @ sK17 @ sK18 ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f428]) ).
thf(f428,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ sK17 @ Y0 )
=> ( sK8 @ sK17 @ Y0 ) )
@ sK18 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f425]) ).
thf(f425,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK17 @ Y0 )
=> ( sK8 @ sK17 @ Y0 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f423]) ).
thf(f423,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) )
@ sK17 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f420]) ).
thf(f420,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[status(thm)],[f380]) ).
thf(f380,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f379]) ).
thf(f379,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f376,f341]) ).
thf(f341,plain,
( ( $false
= ( sK8 @ sK10 @ sK9 ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f340]) ).
thf(f340,plain,
( ( ( $true
=> ( sK8 @ sK10 @ sK9 ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f339]) ).
thf(f339,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
| $true )
=> ( sK8 @ sK10 @ sK9 ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f255,f170]) ).
thf(f170,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f169]) ).
thf(f169,definition,
( spl0_8
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f255,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK10 @ sK9 ) ) ) )
=> ( sK8 @ sK10 @ sK9 ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f254]) ).
thf(f254,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK9 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ sK9 ) ) ) )
=> ( sK8 @ Y0 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f246]) ).
thf(f246,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK9 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ sK9 ) ) ) )
=> ( sK8 @ Y0 @ sK9 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f244]) ).
thf(f244,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) )
@ sK9 ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f195]) ).
thf(f195,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f193]) ).
thf(f193,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& $true ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f188,f191]) ).
thf(f191,plain,
( ( $true
= ( sK4 @ sK8 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK8 ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK8 ) )
=> ( sK8 @ sK5 @ sK6 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f178]) ).
thf(f178,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK8 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl0_1
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f188,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK8 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f187]) ).
thf(f187,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK8 ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f90,f181]) ).
thf(f181,plain,
( ( ( sK8 @ sK5 @ sK6 )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f179]) ).
thf(f90,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ X1 ) )
=> ( X1 @ sK5 @ sK6 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl0_4
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f376,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
=> ( sK8 @ sK10 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f373]) ).
thf(f373,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
& $true )
=> ( sK8 @ sK10 @ sK9 ) )
= $true )
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f362,f191]) ).
thf(f362,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( sK4 @ X1 ) )
=> ( X1 @ sK10 @ sK9 ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f361]) ).
thf(f361,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK10 @ sK9 ) )
@ X1 )
= $true )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f170]) ).
thf(f435,plain,
( ( ( ~ ( ( sK2 @ sK17 @ sK18 )
| ( sK3 @ sK17 @ sK18 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f434]) ).
thf(f434,plain,
( ( $true
= ( ( ( sK2 @ sK17 @ sK18 )
| ( sK3 @ sK17 @ sK18 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f206,f433]) ).
thf(f433,plain,
( ( ( sK8 @ sK17 @ sK18 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f432]) ).
thf(f432,plain,
( ( $false
= ( $true
=> ( sK8 @ sK17 @ sK18 ) ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f429,f431]) ).
thf(f206,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK2 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
=> ( sK8 @ X2 @ X1 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f205]) ).
thf(f205,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK8 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f198]) ).
thf(f198,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK8 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f197]) ).
thf(f197,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK8 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f196]) ).
thf(f196,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f194]) ).
thf(f194,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f182,f191]) ).
thf(f336,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f335]) ).
thf(f335,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f334]) ).
thf(f334,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f237,f258]) ).
thf(f258,plain,
( ( $false
= ( sK8 @ sK10 @ sK9 ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( ( $true
=> ( sK8 @ sK10 @ sK9 ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f256]) ).
thf(f256,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK10 @ sK9 ) ) ) )
=> ( sK8 @ sK10 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f255,f167]) ).
thf(f167,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f166]) ).
thf(f166,definition,
( spl0_7
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f237,plain,
( ( $true
= ( sK8 @ sK10 @ sK9 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f236]) ).
thf(f236,definition,
( spl0_9
<=> ( $true
= ( sK8 @ sK10 @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f333,plain,
( ~ spl0_1
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f332]) ).
thf(f332,plain,
( $false
| ~ spl0_1
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f331]) ).
thf(f331,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f330]) ).
thf(f330,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f329]) ).
thf(f329,plain,
( ( ( ~ ( $true
| ( sK3 @ sK12 @ sK11 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f328,f319]) ).
thf(f319,plain,
( ( ( sK2 @ sK12 @ sK11 )
= $true )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f305]) ).
thf(f305,plain,
( ( ( ( sK2 @ sK12 @ sK11 )
=> ( sK8 @ sK12 @ sK11 ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f304]) ).
thf(f304,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK11 )
=> ( sK8 @ Y0 @ sK11 ) )
@ sK12 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f251]) ).
thf(f251,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK11 )
=> ( sK8 @ Y0 @ sK11 ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f249]) ).
thf(f249,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK8 @ Y1 @ Y0 ) ) )
@ sK11 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f240]) ).
thf(f240,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f239]) ).
thf(f239,definition,
( spl0_10
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f328,plain,
( ( ( ~ ( ( sK2 @ sK12 @ sK11 )
| ( sK3 @ sK12 @ sK11 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f327]) ).
thf(f327,plain,
( ( ( ( ( sK2 @ sK12 @ sK11 )
| ( sK3 @ sK12 @ sK11 ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f206,f321]) ).
thf(f321,plain,
( ( ( sK8 @ sK12 @ sK11 )
= $false )
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f320]) ).
thf(f320,plain,
( ( ( $true
=> ( sK8 @ sK12 @ sK11 ) )
= $false )
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f305,f319]) ).
thf(f241,plain,
( spl0_9
| spl0_10
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f234,f166,f24,f239,f236]) ).
thf(f234,plain,
( ( $true
= ( sK8 @ sK10 @ sK9 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f201]) ).
thf(f201,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ sK10 @ sK9 ) )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK8 @ Y1 @ Y0 ) ) ) ) )
=> ( sK8 @ sK10 @ sK9 ) )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f177,f191]) ).
thf(f177,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( sK4 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK10 @ sK9 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f176]) ).
thf(f176,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f167]) ).
thf(f174,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f173]) ).
thf(f173,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f35,f28]) ).
thf(f171,plain,
( spl0_7
| spl0_8
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f164,f34,f24,f169,f166]) ).
thf(f164,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK10 @ sK9 ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK10 @ sK9 ) ) ) )
=> ( sK8 @ sK10 @ sK9 ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK9 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ sK9 ) ) ) )
=> ( sK8 @ Y0 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK9 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ sK9 ) ) ) )
=> ( sK8 @ Y0 @ sK9 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) )
@ sK9 ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& $true ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f94,f100]) ).
thf(f100,plain,
( ( $true
= ( sK4 @ sK8 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( ( $true
& ( sK4 @ sK8 ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f84,f98]) ).
thf(f98,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK8 ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK8 ) )
=> ( sK8 @ sK5 @ sK6 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK8 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f94,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK8 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK8 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK8 ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f90,f83]) ).
thf(f83,plain,
( ( ( sK8 @ sK5 @ sK6 )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f78,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( $false
=> ( sK7 @ sK5 @ sK6 ) )
= $false )
| ~ spl0_2
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& $false )
=> ( sK7 @ sK5 @ sK6 ) )
= $false )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f73,f58]) ).
thf(f58,plain,
( ( $false
= ( sK4 @ sK7 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl0_5
<=> ( $false
= ( sK4 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f73,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) )
=> ( sK7 @ sK5 @ sK6 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f65,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f32,f25]) ).
thf(f32,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl0_3
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f62,plain,
( spl0_5
| spl0_6
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f53,f31,f27,f60,f57]) ).
thf(f53,plain,
( ( $false
= ( sK4 @ sK7 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f40,f47]) ).
thf(f47,plain,
( ( ( sK7 @ sK5 @ sK6 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( $true
=> ( sK7 @ sK5 @ sK6 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f43,f45]) ).
thf(f45,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) )
=> ( sK7 @ sK5 @ sK6 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f40,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ X1 ) )
=> ( X1 @ sK5 @ sK6 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f36,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f21,f34,f31]) ).
thf(f21,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ sK5 @ Y0 ) ) )
@ sK6 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK4 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK4 @ Y4 ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ sK5 @ Y0 ) ) )
@ sK6 ) ),
inference(negative_extensionality,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ sK5 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK4 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK4 @ Y4 ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ sK5 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK5 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK4 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK4 @ Y5 ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK4 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK4 @ Y5 ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK4 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK4 @ Y5 ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: ( a > a > $o ) > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( Y0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( Y0 @ Y6 ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y0: ( a > a > $o ) > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( Y0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( Y0 @ Y6 ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( Y1 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( sK2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( Y1 @ Y7 ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( Y1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( Y1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( Y1 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( sK2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( Y1 @ Y7 ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( Y1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( Y1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y2: ( a > a > $o ) > $o] :
( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y7 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y1 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) )
& ( Y2 @ Y8 ) )
=> ( Y8 @ Y7 @ Y6 ) ) ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y2: ( a > a > $o ) > $o] :
( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y7 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y1 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) )
& ( Y2 @ Y8 ) )
=> ( Y8 @ Y7 @ Y6 ) ) ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y2: ( a > a > $o ) > $o] :
( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y7 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y1 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) )
& ( Y2 @ Y8 ) )
=> ( Y8 @ Y7 @ Y6 ) ) ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y2: ( a > a > $o ) > $o] :
( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y7 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y1 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) )
& ( Y2 @ Y8 ) )
=> ( Y8 @ Y7 @ Y6 ) ) ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a > a > $o,X2: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ( X0 @ X8 )
& ! [X9: a,X10: a] :
( ( X1 @ X10 @ X9 )
=> ( X8 @ X10 @ X9 ) ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X2 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X14: a,X15: a] :
! [X16: a > a > $o] :
( ( ( X0 @ X16 )
& ! [X17: a,X18: a] :
( ( ( X1 @ X17 @ X18 )
| ( X2 @ X17 @ X18 ) )
=> ( X16 @ X17 @ X18 ) ) )
=> ( X16 @ X14 @ X15 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > $o ) > $o,X2: a > a > $o,X1: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ( X0 @ X8 )
& ! [X10: a,X9: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ( X2 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > $o ) > $o,X2: a > a > $o,X1: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ( X0 @ X8 )
& ! [X10: a,X9: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ( X2 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vXxvqWtk5q/DTF2THF_10759.p',cTHM252_pme) ).
thf(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f22,f27,f24]) ).
thf(f22,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV119^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:40:45 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : SEV119^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.44 % Domain : Set Theory (Relations)
% 0.16/0.44 % Problem : TPS problem THM252
% 0.16/0.44 % Version : Especial.
% 0.16/0.44 % English :
% 0.16/0.44
% 0.16/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.44 % Source : [Bro09]
% 0.16/0.44 % Names : tps_0371 [Bro09]
% 0.16/0.44 % : THM252 [TPS]
% 0.16/0.44 % : THM252C [TPS]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.56 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.16/0.44 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.44 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 1 ( 1 avg)
% 0.16/0.44 % Number of connectives : 42 ( 0 ~; 2 |; 4 &; 28 @)
% 0.16/0.44 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 4 ( 4 avg)
% 0.16/0.44 % Number of types : 2 ( 1 usr)
% 0.16/0.44 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.44 % Number of variables : 19 ( 4 ^; 15 !; 0 ?; 19 :)
% 0.16/0.44 % SPC : TH0_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.44 % : Polymorphic definitions expanded.
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 thf(a_type,type,
% 0.16/0.44 a: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(cTHM252_pme,conjecture,
% 0.16/0.44 ! [PROP: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o] :
% 0.16/0.44 ( ( ^ [Xx: a,Xy: a] :
% 0.16/0.44 ! [Xp: a > a > $o] :
% 0.16/0.44 ( ( ! [Xx0: a,Xy0: a] :
% 0.16/0.44 ( ( ( R @ Xx0 @ Xy0 )
% 0.16/0.44 | ( S @ Xx0 @ Xy0 ) )
% 0.16/0.44 => ( Xp @ Xx0 @ Xy0 ) )
% 0.16/0.44 & ( PROP @ Xp ) )
% 0.16/0.44 => ( Xp @ Xx @ Xy ) ) )
% 0.16/0.44 = ( ^ [Xx: a,Xy: a] :
% 0.16/0.44 ! [Xp: a > a > $o] :
% 0.16/0.44 ( ( ! [Xx0: a,Xy0: a] :
% 0.16/0.44 ( ( ! [Xp0: a > a > $o] :
% 0.16/0.44 ( ( ! [Xx1: a,Xy1: a] :
% 0.16/0.44 ( ( R @ Xx1 @ Xy1 )
% 0.16/0.44 => ( Xp0 @ Xx1 @ Xy1 ) )
% 0.16/0.44 & ( PROP @ Xp0 ) )
% 0.16/0.44 => ( Xp0 @ Xx0 @ Xy0 ) )
% 0.16/0.44 | ! [Xp0: a > a > $o] :
% 0.16/0.44 ( ( ! [Xx1: a,Xy1: a] :
% 0.16/0.44 ( ( S @ Xx1 @ Xy1 )
% 0.16/0.44 => ( Xp0 @ Xx1 @ Xy1 ) )
% 0.16/0.44 & ( PROP @ Xp0 ) )
% 0.16/0.44 => ( Xp0 @ Xx0 @ Xy0 ) ) )
% 0.16/0.44 => ( Xp @ Xx0 @ Xy0 ) )
% 0.16/0.44 & ( PROP @ Xp ) )
% 0.16/0.44 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 1.13/1.11 ---- Embedded in THF ---
% 1.13/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.13/1.11 %%% Generated on Tue Feb 24 12:40:46 EST 2026
% 1.13/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.13/1.11 %%% Logic specification used:
% 1.13/1.11 %%% thf(spec, logic, $$dhol).
% 1.13/1.11
% 1.13/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vXxvqWtk5q/DTF2DTF10759.p
% See solution above
% 1.13/1.11 ------------------------
% 1.33/1.12 ---- Cleaned THF ---
% 1.33/1.12 thf(a_type,type,
% 1.33/1.12 a: $tType ).
% 1.33/1.12
% 1.33/1.12 thf(cTHM252_pme,conjecture,
% 1.33/1.12 ! [PROP: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o] :
% 1.33/1.12 ( ( ^ [Xx: a,Xy: a] :
% 1.33/1.12 ! [Xp: a > a > $o] :
% 1.33/1.12 ( ( ! [Xx0: a,Xy0: a] :
% 1.33/1.12 ( ( ( R @ Xx0 @ Xy0 )
% 1.33/1.12 | ( S @ Xx0 @ Xy0 ) )
% 1.33/1.12 => ( Xp @ Xx0 @ Xy0 ) )
% 1.33/1.12 & ( PROP @ Xp ) )
% 1.33/1.12 => ( Xp @ Xx @ Xy ) ) )
% 1.33/1.12 = ( ^ [Xx: a,Xy: a] :
% 1.33/1.12 ! [Xp: a > a > $o] :
% 1.33/1.12 ( ( ! [Xx0: a,Xy0: a] :
% 1.33/1.12 ( ( ! [Xp0: a > a > $o] :
% 1.33/1.12 ( ( ! [Xx1: a,Xy1: a] :
% 1.33/1.12 ( ( R @ Xx1 @ Xy1 )
% 1.33/1.12 => ( Xp0 @ Xx1 @ Xy1 ) )
% 1.33/1.12 & ( PROP @ Xp0 ) )
% 1.33/1.12 => ( Xp0 @ Xx0 @ Xy0 ) )
% 1.33/1.12 | ! [Xp0: a > a > $o] :
% 1.33/1.12 ( ( ! [Xx1: a,Xy1: a] :
% 1.33/1.12 ( ( S @ Xx1 @ Xy1 )
% 1.33/1.12 => ( Xp0 @ Xx1 @ Xy1 ) )
% 1.33/1.12 & ( PROP @ Xp0 ) )
% 1.33/1.12 => ( Xp0 @ Xx0 @ Xy0 ) ) )
% 1.33/1.12 => ( Xp @ Xx0 @ Xy0 ) )
% 1.33/1.12 & ( PROP @ Xp ) )
% 1.33/1.12 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 1.33/1.12 ------------------------
% 1.33/1.13 % (10856)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/183Mi)
% 1.33/1.14 % (10859)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/2Mi)
% 1.33/1.14 % (10860)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_10759 for (2999ds/2Mi)
% 1.33/1.14 % (10858)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_10759 for (2999ds/27Mi)
% 1.33/1.14 % (10861)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_10759 for (2999ds/275Mi)
% 1.33/1.14 % (10862)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/18Mi)
% 1.33/1.14 % (10859)Instruction limit reached!
% 1.33/1.14 % (10859)------------------------------
% 1.33/1.14 % (10859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.14 % (10859)Termination reason: Unknown
% 1.33/1.14 % (10859)Termination phase: Property scanning
% 1.33/1.14 % (10860)Instruction limit reached!
% 1.33/1.14 % (10860)------------------------------
% 1.33/1.14 % (10860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.14
% 1.33/1.14 % (10859)Memory used [KB]: 1023
% 1.33/1.14 % (10859)Time elapsed: 0.003 s
% 1.33/1.14 % (10859)Instructions burned: 3 (million)
% 1.33/1.14 % (10859)------------------------------
% 1.33/1.14 % (10859)------------------------------
% 1.33/1.14 % (10860)Termination reason: Unknown
% 1.33/1.14 % (10860)Termination phase: Saturation
% 1.33/1.14
% 1.33/1.14 % (10860)Memory used [KB]: 5500
% 1.33/1.14 % (10860)Time elapsed: 0.003 s
% 1.33/1.14 % (10860)Instructions burned: 3 (million)
% 1.33/1.14 % (10860)------------------------------
% 1.33/1.14 % (10860)------------------------------
% 1.33/1.14 % (10857)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_10759 for (2999ds/4Mi)
% 1.33/1.14 % (10857)Instruction limit reached!
% 1.33/1.14 % (10857)------------------------------
% 1.33/1.14 % (10857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.14 % (10857)Termination reason: Unknown
% 1.33/1.14 % (10857)Termination phase: Saturation
% 1.33/1.14
% 1.33/1.14 % (10857)Memory used [KB]: 5500
% 1.33/1.14 % (10857)Time elapsed: 0.004 s
% 1.33/1.14 % (10857)Instructions burned: 5 (million)
% 1.33/1.14 % (10857)------------------------------
% 1.33/1.14 % (10857)------------------------------
% 1.33/1.14 % (10862)Instruction limit reached!
% 1.33/1.14 % (10862)------------------------------
% 1.33/1.14 % (10862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.14 % (10862)Termination reason: Unknown
% 1.33/1.14 % (10862)Termination phase: Saturation
% 1.33/1.14
% 1.33/1.14 % (10862)Memory used [KB]: 5500
% 1.33/1.14 % (10862)Time elapsed: 0.010 s
% 1.33/1.14 % (10862)Instructions burned: 18 (million)
% 1.33/1.14 % (10862)------------------------------
% 1.33/1.14 % (10862)------------------------------
% 1.33/1.15 % (10858)Instruction limit reached!
% 1.33/1.15 % (10858)------------------------------
% 1.33/1.15 % (10858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.15 % (10858)Termination reason: Unknown
% 1.33/1.15 % (10858)Termination phase: Saturation
% 1.33/1.15
% 1.33/1.15 % (10858)Memory used [KB]: 5628
% 1.33/1.15 % (10858)Time elapsed: 0.014 s
% 1.33/1.15 % (10858)Instructions burned: 27 (million)
% 1.33/1.15 % (10858)------------------------------
% 1.33/1.15 % (10858)------------------------------
% 1.33/1.16 % (10864)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_10759 for (2999ds/37Mi)
% 1.33/1.16 % (10863)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/3Mi)
% 1.33/1.16 % (10863)Instruction limit reached!
% 1.33/1.16 % (10863)------------------------------
% 1.33/1.16 % (10863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.16 % (10863)Termination reason: Unknown
% 1.33/1.16 % (10863)Termination phase: Preprocessing 3
% 1.33/1.16
% 1.33/1.16 % (10863)Memory used [KB]: 1023
% 1.33/1.16 % (10863)Time elapsed: 0.003 s
% 1.33/1.16 % (10863)Instructions burned: 3 (million)
% 1.33/1.16 % (10863)------------------------------
% 1.33/1.16 % (10863)------------------------------
% 1.33/1.16 % (10865)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_10759 for (2999ds/15Mi)
% 1.33/1.16 % (10866)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_10759 for (2999ds/3Mi)
% 1.33/1.16 % (10866)Instruction limit reached!
% 1.33/1.16 % (10866)------------------------------
% 1.33/1.16 % (10866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.16 % (10866)Termination reason: Unknown
% 1.33/1.16 % (10866)Termination phase: Saturation
% 1.33/1.16
% 1.33/1.16 % (10866)Memory used [KB]: 1023
% 1.33/1.16 % (10866)Time elapsed: 0.003 s
% 1.33/1.16 % (10866)Instructions burned: 3 (million)
% 1.33/1.16 % (10866)------------------------------
% 1.33/1.16 % (10866)------------------------------
% 1.33/1.16 % (10867)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_10759 for (2999ds/1041Mi)
% 1.33/1.16 % (10865)Instruction limit reached!
% 1.33/1.16 % (10865)------------------------------
% 1.33/1.16 % (10865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.16 % (10865)Termination reason: Unknown
% 1.33/1.16 % (10865)Termination phase: Saturation
% 1.33/1.16
% 1.33/1.16 % (10865)Memory used [KB]: 5628
% 1.33/1.16 % (10865)Time elapsed: 0.009 s
% 1.33/1.16 % (10865)Instructions burned: 15 (million)
% 1.33/1.16 % (10865)------------------------------
% 1.33/1.16 % (10865)------------------------------
% 1.33/1.17 % (10868)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/7Mi)
% 1.33/1.17 % (10864)Instruction limit reached!
% 1.33/1.17 % (10864)------------------------------
% 1.33/1.17 % (10864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.17 % (10864)Termination reason: Unknown
% 1.33/1.17 % (10864)Termination phase: Saturation
% 1.33/1.17
% 1.33/1.17 % (10864)Memory used [KB]: 5628
% 1.33/1.17 % (10864)Time elapsed: 0.020 s
% 1.33/1.17 % (10864)Instructions burned: 38 (million)
% 1.33/1.17 % (10864)------------------------------
% 1.33/1.17 % (10864)------------------------------
% 1.33/1.18 % (10868)Instruction limit reached!
% 1.33/1.18 % (10868)------------------------------
% 1.33/1.18 % (10868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.18 % (10868)Termination reason: Unknown
% 1.33/1.18 % (10868)Termination phase: Saturation
% 1.33/1.18
% 1.33/1.18 % (10868)Memory used [KB]: 1023
% 1.33/1.18 % (10868)Time elapsed: 0.026 s
% 1.33/1.18 % (10868)Instructions burned: 7 (million)
% 1.33/1.18 % (10868)------------------------------
% 1.33/1.18 % (10868)------------------------------
% 1.33/1.18 % (10869)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/16Mi)
% 1.33/1.18 % (10856)Instruction limit reached!
% 1.33/1.18 % (10856)------------------------------
% 1.33/1.18 % (10856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.18 % (10856)Termination reason: Unknown
% 1.33/1.18 % (10856)Termination phase: Saturation
% 1.33/1.18
% 1.33/1.18 % (10856)Memory used [KB]: 7675
% 1.33/1.18 % (10856)Time elapsed: 0.052 s
% 1.33/1.18 % (10856)Instructions burned: 186 (million)
% 1.33/1.18 % (10856)------------------------------
% 1.33/1.18 % (10856)------------------------------
% 1.33/1.18 % (10870)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_10759 for (2999ds/3Mi)
% 1.33/1.18 % (10870)Instruction limit reached!
% 1.33/1.18 % (10870)------------------------------
% 1.33/1.18 % (10870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.18 % (10870)Termination reason: Unknown
% 1.33/1.18 % (10870)Termination phase: Preprocessing 3
% 1.33/1.18
% 1.33/1.18 % (10870)Memory used [KB]: 1023
% 1.33/1.18 % (10870)Time elapsed: 0.003 s
% 1.33/1.18 % (10870)Instructions burned: 3 (million)
% 1.33/1.18 % (10870)------------------------------
% 1.33/1.18 % (10870)------------------------------
% 1.33/1.19 % (10869)Instruction limit reached!
% 1.33/1.19 % (10869)------------------------------
% 1.33/1.19 % (10869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.19 % (10869)Termination reason: Unknown
% 1.33/1.19 % (10869)Termination phase: Saturation
% 1.33/1.19
% 1.33/1.19 % (10869)Memory used [KB]: 5756
% 1.33/1.19 % (10869)Time elapsed: 0.034 s
% 1.33/1.19 % (10869)Instructions burned: 16 (million)
% 1.33/1.19 % (10869)------------------------------
% 1.33/1.19 % (10869)------------------------------
% 1.33/1.19 % (10873)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/3Mi)
% 1.33/1.19 % (10873)Instruction limit reached!
% 1.33/1.19 % (10873)------------------------------
% 1.33/1.19 % (10873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.19 % (10873)Termination reason: Unknown
% 1.33/1.19 % (10873)Termination phase: Saturation
% 1.33/1.19
% 1.33/1.19 % (10873)Memory used [KB]: 5500
% 1.33/1.19 % (10873)Time elapsed: 0.002 s
% 1.33/1.19 % (10873)Instructions burned: 4 (million)
% 1.33/1.19 % (10873)------------------------------
% 1.33/1.19 % (10873)------------------------------
% 1.33/1.19 % (10871)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_10759 for (2999ds/3Mi)
% 1.33/1.19 % (10871)Instruction limit reached!
% 1.33/1.19 % (10871)------------------------------
% 1.33/1.19 % (10871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.19 % (10871)Termination reason: Unknown
% 1.33/1.19 % (10871)Termination phase: Property scanning
% 1.33/1.19
% 1.33/1.19 % (10871)Memory used [KB]: 1023
% 1.33/1.19 % (10871)Time elapsed: 0.003 s
% 1.33/1.19 % (10871)Instructions burned: 4 (million)
% 1.33/1.19 % (10871)------------------------------
% 1.33/1.19 % (10871)------------------------------
% 1.33/1.19 % (10872)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/7Mi)
% 1.35/1.20 % (10872)Instruction limit reached!
% 1.35/1.20 % (10872)------------------------------
% 1.35/1.20 % (10872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.20 % (10872)Termination reason: Unknown
% 1.35/1.20 % (10872)Termination phase: Saturation
% 1.35/1.20
% 1.35/1.20 % (10872)Memory used [KB]: 5500
% 1.35/1.20 % (10872)Time elapsed: 0.005 s
% 1.35/1.20 % (10872)Instructions burned: 7 (million)
% 1.35/1.20 % (10872)------------------------------
% 1.35/1.20 % (10872)------------------------------
% 1.35/1.20 % (10874)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/4Mi)
% 1.35/1.20 % (10874)Instruction limit reached!
% 1.35/1.20 % (10874)------------------------------
% 1.35/1.20 % (10874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.20 % (10874)Termination reason: Unknown
% 1.35/1.20 % (10874)Termination phase: Saturation
% 1.35/1.20
% 1.35/1.20 % (10874)Memory used [KB]: 5500
% 1.35/1.20 % (10874)Time elapsed: 0.004 s
% 1.35/1.20 % (10874)Instructions burned: 4 (million)
% 1.35/1.20 % (10874)------------------------------
% 1.35/1.20 % (10874)------------------------------
% 1.35/1.20 % (10875)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/18Mi)
% 1.35/1.20 % (10876)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/710Mi)
% 1.35/1.21 % (10877)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/6Mi)
% 1.35/1.21 % (10875)Instruction limit reached!
% 1.35/1.21 % (10875)------------------------------
% 1.35/1.21 % (10875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.21 % (10875)Termination reason: Unknown
% 1.35/1.21 % (10875)Termination phase: Saturation
% 1.35/1.21
% 1.35/1.21 % (10875)Memory used [KB]: 5500
% 1.35/1.21 % (10875)Time elapsed: 0.010 s
% 1.35/1.21 % (10875)Instructions burned: 18 (million)
% 1.35/1.21 % (10875)------------------------------
% 1.35/1.21 % (10875)------------------------------
% 1.35/1.21 % (10877)Instruction limit reached!
% 1.35/1.21 % (10877)------------------------------
% 1.35/1.21 % (10877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.21 % (10877)Termination reason: Unknown
% 1.35/1.21 % (10877)Termination phase: Saturation
% 1.35/1.21
% 1.35/1.21 % (10877)Memory used [KB]: 5500
% 1.35/1.21 % (10877)Time elapsed: 0.005 s
% 1.35/1.21 % (10877)Instructions burned: 8 (million)
% 1.35/1.21 % (10877)------------------------------
% 1.35/1.21 % (10877)------------------------------
% 1.35/1.21 % (10878)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_10759 for (2999ds/902Mi)
% 1.35/1.22 % (10879)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_10759 for (2999ds/21Mi)
% 1.35/1.23 % (10880)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10759 for (2999ds/5Mi)
% 1.35/1.23 % (10881)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_10759 for (2999ds/6Mi)
% 1.35/1.23 % (10880)Instruction limit reached!
% 1.35/1.23 % (10880)------------------------------
% 1.35/1.23 % (10880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.23 % (10880)Termination reason: Unknown
% 1.35/1.23 % (10880)Termination phase: Saturation
% 1.35/1.23
% 1.35/1.23 % (10880)Memory used [KB]: 5500
% 1.35/1.23 % (10880)Time elapsed: 0.004 s
% 1.35/1.23 % (10880)Instructions burned: 5 (million)
% 1.35/1.23 % (10880)------------------------------
% 1.35/1.23 % (10880)------------------------------
% 1.35/1.23 % (10879)Instruction limit reached!
% 1.35/1.23 % (10879)------------------------------
% 1.35/1.23 % (10879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.23 % (10879)Termination reason: Unknown
% 1.35/1.23 % (10879)Termination phase: Saturation
% 1.35/1.23
% 1.35/1.23 % (10879)Memory used [KB]: 5628
% 1.35/1.23 % (10879)Time elapsed: 0.014 s
% 1.35/1.23 % (10879)Instructions burned: 22 (million)
% 1.35/1.23 % (10879)------------------------------
% 1.35/1.23 % (10879)------------------------------
% 1.35/1.23 % (10881)Instruction limit reached!
% 1.35/1.23 % (10881)------------------------------
% 1.35/1.23 % (10881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.23 % (10881)Termination reason: Unknown
% 1.35/1.23 % (10881)Termination phase: Saturation
% 1.35/1.23
% 1.35/1.23 % (10881)Memory used [KB]: 5500
% 1.35/1.23 % (10881)Time elapsed: 0.004 s
% 1.35/1.23 % (10881)Instructions burned: 6 (million)
% 1.35/1.23 % (10881)------------------------------
% 1.35/1.23 % (10881)------------------------------
% 1.35/1.24 % (10882)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10759 for (2998ds/377Mi)
% 1.35/1.25 % (10883)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_10759 for (2998ds/779Mi)
% 1.35/1.25 % (10884)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_10759 for (2998ds/19Mi)
% 1.35/1.25 % (10867)First to succeed.
% 1.35/1.25 % (10884)Instruction limit reached!
% 1.35/1.25 % (10884)------------------------------
% 1.35/1.25 % (10884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.25 % (10884)Termination reason: Unknown
% 1.35/1.25 % (10884)Termination phase: Saturation
% 1.35/1.25
% 1.35/1.25 % (10884)Memory used [KB]: 5500
% 1.35/1.25 % (10884)Time elapsed: 0.010 s
% 1.35/1.25 % (10884)Instructions burned: 19 (million)
% 1.35/1.25 % (10884)------------------------------
% 1.35/1.25 % (10884)------------------------------
% 1.35/1.26 % (10867)Refutation found. Thanks to Tanya!
% 1.35/1.26 % SZS status Theorem for DTF2THF_10759
% 1.35/1.26 % SZS output start Proof for DTF2THF_10759
% 1.35/1.26 thf(type_def_5, type, a: $tType).
% 1.35/1.26 thf(func_def_0, type, a: $tType).
% 1.35/1.26 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.35/1.26 thf(func_def_21, type, sK2: a > a > $o).
% 1.35/1.26 thf(func_def_22, type, sK3: a > a > $o).
% 1.35/1.26 thf(func_def_23, type, sK4: (a > a > $o) > $o).
% 1.35/1.26 thf(func_def_24, type, sK5: a).
% 1.35/1.26 thf(func_def_25, type, sK6: a).
% 1.35/1.26 thf(func_def_26, type, sK7: a > a > $o).
% 1.35/1.26 thf(func_def_27, type, sK8: a > a > $o).
% 1.35/1.26 thf(func_def_28, type, sK9: a).
% 1.35/1.26 thf(func_def_29, type, sK10: a).
% 1.35/1.26 thf(func_def_30, type, sK11: a).
% 1.35/1.26 thf(func_def_31, type, sK12: a).
% 1.35/1.26 thf(func_def_32, type, sK13: a).
% 1.35/1.26 thf(func_def_33, type, sK14: a).
% 1.35/1.26 thf(func_def_34, type, sK15: a).
% 1.35/1.26 thf(func_def_35, type, sK16: a).
% 1.35/1.26 thf(func_def_36, type, sK17: a).
% 1.35/1.26 thf(func_def_37, type, sK18: a).
% 1.35/1.26 thf(func_def_38, type, sK19: a).
% 1.35/1.26 thf(func_def_39, type, sK20: a).
% 1.35/1.26 thf(func_def_40, type, sK21: a > a > $o).
% 1.35/1.26 thf(func_def_41, type, sK22: a > a > $o).
% 1.35/1.26 thf(func_def_42, type, sK23: a > a > $o).
% 1.35/1.26 thf(func_def_43, type, sK24: a > a > $o).
% 1.35/1.26 thf(f781,plain,(
% 1.35/1.26 $false),
% 1.35/1.26 inference(avatar_sat_refutation,[status(thm)],[f29,f36,f62,f65,f78,f171,f174,f241,f333,f336,f440,f774,f777])).
% 1.35/1.26 thf(f777,plain,(
% 1.35/1.26 spl0_14 | ~spl0_2 | ~spl0_6),
% 1.35/1.26 inference(avatar_split_clause,[status(thm)],[f776,f60,f27,f468])).
% 1.35/1.26 thf(f468,definition,(
% 1.35/1.26 spl0_14 <=> ((sK2 @ sK20 @ sK19) = $true)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.35/1.26 thf(f27,definition,(
% 1.35/1.26 spl0_2 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $false)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.35/1.26 thf(f60,definition,(
% 1.35/1.26 spl0_6 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK7 @ Y1 @ Y0)))))) = $false)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.35/1.26 thf(f776,plain,(
% 1.35/1.26 ((sK2 @ sK20 @ sK19) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f775])).
% 1.35/1.26 thf(f775,plain,(
% 1.35/1.26 (((sK2 @ sK20 @ sK19) | $false) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f456,f703])).
% 1.35/1.26 thf(f703,plain,(
% 1.35/1.26 ((sK3 @ sK20 @ sK19) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(not_proxy_clausification,[status(thm)],[f696])).
% 1.35/1.26 thf(f696,plain,(
% 1.35/1.26 ((~ (sK3 @ sK20 @ sK19)) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f692])).
% 1.35/1.26 thf(f692,plain,(
% 1.35/1.26 (((sK3 @ sK20 @ sK19) => $false) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(superposition,[status(thm)],[f689,f664])).
% 1.35/1.26 thf(f664,plain,(
% 1.35/1.26 ((sK23 @ sK20 @ sK19) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f663])).
% 1.35/1.26 thf(f663,plain,(
% 1.35/1.26 ($false = ($true => (sK23 @ sK20 @ sK19))) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f645,f662])).
% 1.35/1.26 thf(f662,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1)))))) & (sK4 @ sK23)) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f645])).
% 1.35/1.26 thf(f645,plain,(
% 1.35/1.26 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1)))))) & (sK4 @ sK23)) => (sK23 @ sK20 @ sK19))) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f643])).
% 1.35/1.26 thf(f643,plain,(
% 1.35/1.26 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK20 @ sK19))) @ sK23) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f636])).
% 1.35/1.26 thf(f636,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK20 @ sK19)))) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f635])).
% 1.35/1.26 thf(f635,plain,(
% 1.35/1.26 (($false | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK20 @ sK19))))) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f624,f632])).
% 1.35/1.26 thf(f632,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f624])).
% 1.35/1.26 thf(f624,plain,(
% 1.35/1.26 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK20 @ sK19))))) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(not_proxy_clausification,[status(thm)],[f512])).
% 1.35/1.26 thf(f512,plain,(
% 1.35/1.26 ((~ ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK20 @ sK19)))))) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f511])).
% 1.35/1.26 thf(f511,plain,(
% 1.35/1.26 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK20 @ sK19))))) => $false) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(superposition,[status(thm)],[f498,f455])).
% 1.35/1.26 thf(f455,plain,(
% 1.35/1.26 ((sK7 @ sK20 @ sK19) = $false) | ~spl0_6),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f447])).
% 1.35/1.26 thf(f447,plain,(
% 1.35/1.26 ((((sK2 @ sK20 @ sK19) | (sK3 @ sK20 @ sK19)) => (sK7 @ sK20 @ sK19)) = $false) | ~spl0_6),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f446])).
% 1.35/1.26 thf(f446,plain,(
% 1.35/1.26 (((^[Y0 : a]: (((sK2 @ Y0 @ sK19) | (sK3 @ Y0 @ sK19)) => (sK7 @ Y0 @ sK19))) @ sK20) = $false) | ~spl0_6),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f443])).
% 1.35/1.26 thf(f443,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK19) | (sK3 @ Y0 @ sK19)) => (sK7 @ Y0 @ sK19)))) = $false) | ~spl0_6),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f442])).
% 1.35/1.26 thf(f442,plain,(
% 1.35/1.26 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK7 @ Y1 @ Y0))))) @ sK19) = $false) | ~spl0_6),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f61])).
% 1.35/1.26 thf(f61,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK7 @ Y1 @ Y0)))))) = $false) | ~spl0_6),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.35/1.26 thf(f498,plain,(
% 1.35/1.26 ( ! [X2 : a,X1 : a] : (((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ X2 @ X1)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ X2 @ X1))))) => (sK7 @ X2 @ X1)) = $true)) ) | ~spl0_2),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f497])).
% 1.35/1.26 thf(f497,plain,(
% 1.35/1.26 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK4 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ X1)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK4 @ Y1)) => (Y1 @ Y0 @ X1))))) => (sK7 @ Y0 @ X1))) @ X2) = $true)) ) | ~spl0_2),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f496])).
% 1.35/1.26 thf(f496,plain,(
% 1.35/1.26 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK4 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ X1)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK4 @ Y1)) => (Y1 @ Y0 @ X1))))) => (sK7 @ Y0 @ X1)))) = $true)) ) | ~spl0_2),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f495])).
% 1.35/1.26 thf(f495,plain,(
% 1.35/1.26 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0))))) @ X1) = $true)) ) | ~spl0_2),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f490])).
% 1.35/1.26 thf(f490,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0)))))) = $true) | ~spl0_2),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f489])).
% 1.35/1.26 thf(f489,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0)))))) & $true) = $true) | ~spl0_2),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f477,f487])).
% 1.35/1.26 thf(f487,plain,(
% 1.35/1.26 ((sK4 @ sK7) = $true) | ~spl0_2),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f477])).
% 1.35/1.26 thf(f477,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0)))))) & (sK4 @ sK7)) = $true) | ~spl0_2),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f465])).
% 1.35/1.26 thf(f465,plain,(
% 1.35/1.26 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0)))))) & (sK4 @ sK7)) => (sK7 @ sK5 @ sK6)) = $false) | ~spl0_2),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f464])).
% 1.35/1.26 thf(f464,plain,(
% 1.35/1.26 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6))) @ sK7) = $false) | ~spl0_2),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f28])).
% 1.35/1.26 thf(f28,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $false) | ~spl0_2),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.35/1.26 thf(f689,plain,(
% 1.35/1.26 ( ! [X2 : a,X1 : a] : ((((sK3 @ X1 @ X2) => (sK23 @ X1 @ X2)) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f688])).
% 1.35/1.26 thf(f688,plain,(
% 1.35/1.26 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK23 @ X1 @ Y0))) @ X2) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f685])).
% 1.35/1.26 thf(f685,plain,(
% 1.35/1.26 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK23 @ X1 @ Y0)))) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f684])).
% 1.35/1.26 thf(f684,plain,(
% 1.35/1.26 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1))))) @ X1) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f668])).
% 1.35/1.26 thf(f668,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1)))))) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f667])).
% 1.35/1.26 thf(f667,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK23 @ Y0 @ Y1)))))) & $true) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f662,f665])).
% 1.35/1.26 thf(f665,plain,(
% 1.35/1.26 ((sK4 @ sK23) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f662])).
% 1.35/1.26 thf(f456,plain,(
% 1.35/1.26 (((sK2 @ sK20 @ sK19) | (sK3 @ sK20 @ sK19)) = $true) | ~spl0_6),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f447])).
% 1.35/1.26 thf(f774,plain,(
% 1.35/1.26 ~spl0_2 | ~spl0_6 | ~spl0_14),
% 1.35/1.26 inference(avatar_contradiction_clause,[status(thm)],[f773])).
% 1.35/1.26 thf(f773,plain,(
% 1.35/1.26 $false | (~spl0_2 | ~spl0_6 | ~spl0_14)),
% 1.35/1.26 inference(trivial_inequality_removal,[status(thm)],[f772])).
% 1.35/1.26 thf(f772,plain,(
% 1.35/1.26 ($false = $true) | (~spl0_2 | ~spl0_6 | ~spl0_14)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f771])).
% 1.35/1.26 thf(f771,plain,(
% 1.35/1.26 ((~ $true) = $true) | (~spl0_2 | ~spl0_6 | ~spl0_14)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f764,f469])).
% 1.35/1.26 thf(f469,plain,(
% 1.35/1.26 ((sK2 @ sK20 @ sK19) = $true) | ~spl0_14),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f468])).
% 1.35/1.26 thf(f764,plain,(
% 1.35/1.26 ((~ (sK2 @ sK20 @ sK19)) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f761])).
% 1.35/1.26 thf(f761,plain,(
% 1.35/1.26 (((sK2 @ sK20 @ sK19) => $false) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(superposition,[status(thm)],[f755,f709])).
% 1.35/1.26 thf(f709,plain,(
% 1.35/1.26 ($false = (sK24 @ sK20 @ sK19)) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f708])).
% 1.35/1.26 thf(f708,plain,(
% 1.35/1.26 (($true => (sK24 @ sK20 @ sK19)) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f699,f707])).
% 1.35/1.26 thf(f707,plain,(
% 1.35/1.26 (((sK4 @ sK24) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK24 @ Y1 @ Y0))))))) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f699])).
% 1.35/1.26 thf(f699,plain,(
% 1.35/1.26 ((((sK4 @ sK24) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK24 @ Y1 @ Y0))))))) => (sK24 @ sK20 @ sK19)) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f697])).
% 1.35/1.26 thf(f697,plain,(
% 1.35/1.26 (((^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19))) @ sK24) = $false) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f632])).
% 1.35/1.26 thf(f755,plain,(
% 1.35/1.26 ( ! [X2 : a,X1 : a] : ((((sK2 @ X2 @ X1) => (sK24 @ X2 @ X1)) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f754])).
% 1.35/1.26 thf(f754,plain,(
% 1.35/1.26 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK2 @ Y0 @ X1) => (sK24 @ Y0 @ X1))) @ X2) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f749])).
% 1.35/1.26 thf(f749,plain,(
% 1.35/1.26 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ X1) => (sK24 @ Y0 @ X1)))) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f746])).
% 1.35/1.26 thf(f746,plain,(
% 1.35/1.26 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK24 @ Y1 @ Y0))))) @ X1) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f728])).
% 1.35/1.26 thf(f728,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK24 @ Y1 @ Y0)))))) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f727])).
% 1.35/1.26 thf(f727,plain,(
% 1.35/1.26 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK24 @ Y1 @ Y0))))))) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f707,f724])).
% 1.35/1.26 thf(f724,plain,(
% 1.35/1.26 ((sK4 @ sK24) = $true) | (~spl0_2 | ~spl0_6)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f707])).
% 1.35/1.26 thf(f440,plain,(
% 1.35/1.26 ~spl0_1 | ~spl0_4 | ~spl0_8),
% 1.35/1.26 inference(avatar_contradiction_clause,[status(thm)],[f439])).
% 1.35/1.26 thf(f439,plain,(
% 1.35/1.26 $false | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(trivial_inequality_removal,[status(thm)],[f438])).
% 1.35/1.26 thf(f438,plain,(
% 1.35/1.26 ($false = $true) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f437])).
% 1.35/1.26 thf(f437,plain,(
% 1.35/1.26 ((~ $true) = $true) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f436])).
% 1.35/1.26 thf(f436,plain,(
% 1.35/1.26 ((~ ((sK2 @ sK17 @ sK18) | $true)) = $true) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f435,f431])).
% 1.35/1.26 thf(f431,plain,(
% 1.35/1.26 ((sK3 @ sK17 @ sK18) = $true) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f429])).
% 1.35/1.26 thf(f429,plain,(
% 1.35/1.26 (((sK3 @ sK17 @ sK18) => (sK8 @ sK17 @ sK18)) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f428])).
% 1.35/1.26 thf(f428,plain,(
% 1.35/1.26 (((^[Y0 : a]: ((sK3 @ sK17 @ Y0) => (sK8 @ sK17 @ Y0))) @ sK18) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f425])).
% 1.35/1.26 thf(f425,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK17 @ Y0) => (sK8 @ sK17 @ Y0)))) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f423])).
% 1.35/1.26 thf(f423,plain,(
% 1.35/1.26 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK8 @ Y0 @ Y1))))) @ sK17) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f420])).
% 1.35/1.26 thf(f420,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK8 @ Y0 @ Y1)))))) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(not_proxy_clausification,[status(thm)],[f380])).
% 1.35/1.26 thf(f380,plain,(
% 1.35/1.26 ((~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK8 @ Y0 @ Y1))))))) = $true) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f379])).
% 1.35/1.26 thf(f379,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK8 @ Y0 @ Y1)))))) => $false) = $true) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f376,f341])).
% 1.35/1.26 thf(f341,plain,(
% 1.35/1.26 ($false = (sK8 @ sK10 @ sK9)) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f340])).
% 1.35/1.26 thf(f340,plain,(
% 1.35/1.26 (($true => (sK8 @ sK10 @ sK9)) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f339])).
% 1.35/1.26 thf(f339,plain,(
% 1.35/1.26 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK9)))) | $true) => (sK8 @ sK10 @ sK9)) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f255,f170])).
% 1.35/1.26 thf(f170,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK10 @ sK9)))) = $true) | ~spl0_8),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f169])).
% 1.35/1.26 thf(f169,definition,(
% 1.35/1.26 spl0_8 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK10 @ sK9)))) = $true)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.35/1.26 thf(f255,plain,(
% 1.35/1.26 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK9)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK10 @ sK9))))) => (sK8 @ sK10 @ sK9)) = $false) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f254])).
% 1.35/1.26 thf(f254,plain,(
% 1.35/1.26 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK4 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK9)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK4 @ Y1)) => (Y1 @ Y0 @ sK9))))) => (sK8 @ Y0 @ sK9))) @ sK10) = $false) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f246])).
% 1.35/1.26 thf(f246,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK4 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK9)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK4 @ Y1)) => (Y1 @ Y0 @ sK9))))) => (sK8 @ Y0 @ sK9)))) = $false) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f244])).
% 1.35/1.26 thf(f244,plain,(
% 1.35/1.26 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0))))) @ sK9)) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f231])).
% 1.35/1.26 thf(f231,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0)))))) = $false) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(not_proxy_clausification,[status(thm)],[f195])).
% 1.35/1.26 thf(f195,plain,(
% 1.35/1.26 ((~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0))))))) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f193])).
% 1.35/1.26 thf(f193,plain,(
% 1.35/1.26 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0)))))) & $true)) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f188,f191])).
% 1.35/1.26 thf(f191,plain,(
% 1.35/1.26 ($true = (sK4 @ sK8)) | ~spl0_1),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f182])).
% 1.35/1.26 thf(f182,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y0)))))) & (sK4 @ sK8)) = $true) | ~spl0_1),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f179])).
% 1.35/1.26 thf(f179,plain,(
% 1.35/1.26 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y0)))))) & (sK4 @ sK8)) => (sK8 @ sK5 @ sK6))) | ~spl0_1),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f178])).
% 1.35/1.26 thf(f178,plain,(
% 1.35/1.26 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6))) @ sK8)) | ~spl0_1),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f25])).
% 1.35/1.26 thf(f25,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $false) | ~spl0_1),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.35/1.26 thf(f24,definition,(
% 1.35/1.26 spl0_1 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $false)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.35/1.26 thf(f188,plain,(
% 1.35/1.26 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0)))))) & (sK4 @ sK8))) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f187])).
% 1.35/1.26 thf(f187,plain,(
% 1.35/1.26 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0)))))) & (sK4 @ sK8)) => $false) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(superposition,[status(thm)],[f90,f181])).
% 1.35/1.26 thf(f181,plain,(
% 1.35/1.26 ((sK8 @ sK5 @ sK6) = $false) | ~spl0_1),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f179])).
% 1.35/1.26 thf(f90,plain,(
% 1.35/1.26 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (X1 @ Y1 @ Y0)))))) & (sK4 @ X1)) => (X1 @ sK5 @ sK6)) = $true)) ) | ~spl0_4),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.35/1.26 thf(f89,plain,(
% 1.35/1.26 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6))) @ X1) = $true)) ) | ~spl0_4),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f35])).
% 1.35/1.26 thf(f35,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $true) | ~spl0_4),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.35/1.26 thf(f34,definition,(
% 1.35/1.26 spl0_4 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $true)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.35/1.26 thf(f376,plain,(
% 1.35/1.26 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK8 @ Y0 @ Y1)))))) => (sK8 @ sK10 @ sK9))) | (~spl0_1 | ~spl0_8)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f373])).
% 1.35/1.26 thf(f373,plain,(
% 1.35/1.26 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK8 @ Y0 @ Y1)))))) & $true) => (sK8 @ sK10 @ sK9)) = $true) | (~spl0_1 | ~spl0_8)),
% 1.35/1.26 inference(superposition,[status(thm)],[f362,f191])).
% 1.35/1.26 thf(f362,plain,(
% 1.35/1.26 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))) & (sK4 @ X1)) => (X1 @ sK10 @ sK9)) = $true)) ) | ~spl0_8),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f361])).
% 1.35/1.26 thf(f361,plain,(
% 1.35/1.26 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK10 @ sK9))) @ X1) = $true)) ) | ~spl0_8),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f170])).
% 1.35/1.26 thf(f435,plain,(
% 1.35/1.26 ((~ ((sK2 @ sK17 @ sK18) | (sK3 @ sK17 @ sK18))) = $true) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f434])).
% 1.35/1.26 thf(f434,plain,(
% 1.35/1.26 ($true = (((sK2 @ sK17 @ sK18) | (sK3 @ sK17 @ sK18)) => $false)) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(superposition,[status(thm)],[f206,f433])).
% 1.35/1.26 thf(f433,plain,(
% 1.35/1.26 ((sK8 @ sK17 @ sK18) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f432])).
% 1.35/1.26 thf(f432,plain,(
% 1.35/1.26 ($false = ($true => (sK8 @ sK17 @ sK18))) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f429,f431])).
% 1.35/1.26 thf(f206,plain,(
% 1.35/1.26 ( ! [X2 : a,X1 : a] : (((((sK2 @ X2 @ X1) | (sK3 @ X2 @ X1)) => (sK8 @ X2 @ X1)) = $true)) ) | ~spl0_1),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f205])).
% 1.35/1.26 thf(f205,plain,(
% 1.35/1.26 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK8 @ Y0 @ X1))) @ X2) = $true)) ) | ~spl0_1),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f198])).
% 1.35/1.26 thf(f198,plain,(
% 1.35/1.26 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK8 @ Y0 @ X1)))) = $true)) ) | ~spl0_1),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f197])).
% 1.35/1.26 thf(f197,plain,(
% 1.35/1.26 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y0))))) @ X1) = $true)) ) | ~spl0_1),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f196])).
% 1.35/1.26 thf(f196,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y0)))))) = $true) | ~spl0_1),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f194])).
% 1.35/1.26 thf(f194,plain,(
% 1.35/1.26 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y0)))))) & $true)) | ~spl0_1),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f182,f191])).
% 1.35/1.26 thf(f336,plain,(
% 1.35/1.26 ~spl0_1 | ~spl0_4 | ~spl0_7 | ~spl0_9),
% 1.35/1.26 inference(avatar_contradiction_clause,[status(thm)],[f335])).
% 1.35/1.26 thf(f335,plain,(
% 1.35/1.26 $false | (~spl0_1 | ~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.35/1.26 inference(trivial_inequality_removal,[status(thm)],[f334])).
% 1.35/1.26 thf(f334,plain,(
% 1.35/1.26 ($false = $true) | (~spl0_1 | ~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f237,f258])).
% 1.35/1.26 thf(f258,plain,(
% 1.35/1.26 ($false = (sK8 @ sK10 @ sK9)) | (~spl0_1 | ~spl0_4 | ~spl0_7)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f257])).
% 1.35/1.26 thf(f257,plain,(
% 1.35/1.26 (($true => (sK8 @ sK10 @ sK9)) = $false) | (~spl0_1 | ~spl0_4 | ~spl0_7)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f256])).
% 1.35/1.26 thf(f256,plain,(
% 1.35/1.26 ($false = (($true | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK10 @ sK9))))) => (sK8 @ sK10 @ sK9))) | (~spl0_1 | ~spl0_4 | ~spl0_7)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f255,f167])).
% 1.35/1.26 thf(f167,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK9)))) = $true) | ~spl0_7),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f166])).
% 1.35/1.26 thf(f166,definition,(
% 1.35/1.26 spl0_7 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK9)))) = $true)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.35/1.26 thf(f237,plain,(
% 1.35/1.26 ($true = (sK8 @ sK10 @ sK9)) | ~spl0_9),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f236])).
% 1.35/1.26 thf(f236,definition,(
% 1.35/1.26 spl0_9 <=> ($true = (sK8 @ sK10 @ sK9))),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.35/1.26 thf(f333,plain,(
% 1.35/1.26 ~spl0_1 | ~spl0_10),
% 1.35/1.26 inference(avatar_contradiction_clause,[status(thm)],[f332])).
% 1.35/1.26 thf(f332,plain,(
% 1.35/1.26 $false | (~spl0_1 | ~spl0_10)),
% 1.35/1.26 inference(trivial_inequality_removal,[status(thm)],[f331])).
% 1.35/1.26 thf(f331,plain,(
% 1.35/1.26 ($false = $true) | (~spl0_1 | ~spl0_10)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f330])).
% 1.35/1.26 thf(f330,plain,(
% 1.35/1.26 ((~ $true) = $true) | (~spl0_1 | ~spl0_10)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f329])).
% 1.35/1.26 thf(f329,plain,(
% 1.35/1.26 ((~ ($true | (sK3 @ sK12 @ sK11))) = $true) | (~spl0_1 | ~spl0_10)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f328,f319])).
% 1.35/1.26 thf(f319,plain,(
% 1.35/1.26 ((sK2 @ sK12 @ sK11) = $true) | ~spl0_10),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f305])).
% 1.35/1.26 thf(f305,plain,(
% 1.35/1.26 (((sK2 @ sK12 @ sK11) => (sK8 @ sK12 @ sK11)) = $false) | ~spl0_10),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f304])).
% 1.35/1.26 thf(f304,plain,(
% 1.35/1.26 (((^[Y0 : a]: ((sK2 @ Y0 @ sK11) => (sK8 @ Y0 @ sK11))) @ sK12) = $false) | ~spl0_10),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f251])).
% 1.35/1.26 thf(f251,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ sK11) => (sK8 @ Y0 @ sK11)))) = $false) | ~spl0_10),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f249])).
% 1.35/1.26 thf(f249,plain,(
% 1.35/1.26 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0))))) @ sK11) = $false) | ~spl0_10),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f240])).
% 1.35/1.26 thf(f240,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0)))))) = $false) | ~spl0_10),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f239])).
% 1.35/1.26 thf(f239,definition,(
% 1.35/1.26 spl0_10 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0)))))) = $false)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.35/1.26 thf(f328,plain,(
% 1.35/1.26 ((~ ((sK2 @ sK12 @ sK11) | (sK3 @ sK12 @ sK11))) = $true) | (~spl0_1 | ~spl0_10)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f327])).
% 1.35/1.26 thf(f327,plain,(
% 1.35/1.26 ((((sK2 @ sK12 @ sK11) | (sK3 @ sK12 @ sK11)) => $false) = $true) | (~spl0_1 | ~spl0_10)),
% 1.35/1.26 inference(superposition,[status(thm)],[f206,f321])).
% 1.35/1.26 thf(f321,plain,(
% 1.35/1.26 ((sK8 @ sK12 @ sK11) = $false) | ~spl0_10),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f320])).
% 1.35/1.26 thf(f320,plain,(
% 1.35/1.26 (($true => (sK8 @ sK12 @ sK11)) = $false) | ~spl0_10),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f305,f319])).
% 1.35/1.26 thf(f241,plain,(
% 1.35/1.26 spl0_9 | spl0_10 | ~spl0_1 | ~spl0_7),
% 1.35/1.26 inference(avatar_split_clause,[status(thm)],[f234,f166,f24,f239,f236])).
% 1.35/1.26 thf(f234,plain,(
% 1.35/1.26 ($true = (sK8 @ sK10 @ sK9)) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0)))))) = $false) | (~spl0_1 | ~spl0_7)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f201])).
% 1.35/1.26 thf(f201,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0)))))) => (sK8 @ sK10 @ sK9)) = $true) | (~spl0_1 | ~spl0_7)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f199])).
% 1.35/1.26 thf(f199,plain,(
% 1.35/1.26 ((($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0))))))) => (sK8 @ sK10 @ sK9)) = $true) | (~spl0_1 | ~spl0_7)),
% 1.35/1.26 inference(superposition,[status(thm)],[f177,f191])).
% 1.35/1.26 thf(f177,plain,(
% 1.35/1.26 ( ! [X1 : a > a > $o] : (($true = (((sK4 @ X1) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK10 @ sK9)))) ) | ~spl0_7),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f176])).
% 1.35/1.26 thf(f176,plain,(
% 1.35/1.26 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK9))) @ X1) = $true)) ) | ~spl0_7),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f167])).
% 1.35/1.26 thf(f174,plain,(
% 1.35/1.26 ~spl0_2 | ~spl0_4),
% 1.35/1.26 inference(avatar_contradiction_clause,[status(thm)],[f173])).
% 1.35/1.26 thf(f173,plain,(
% 1.35/1.26 $false | (~spl0_2 | ~spl0_4)),
% 1.35/1.26 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.35/1.26 thf(f172,plain,(
% 1.35/1.26 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f35,f28])).
% 1.35/1.26 thf(f171,plain,(
% 1.35/1.26 spl0_7 | spl0_8 | ~spl0_1 | ~spl0_4),
% 1.35/1.26 inference(avatar_split_clause,[status(thm)],[f164,f34,f24,f169,f166])).
% 1.35/1.26 thf(f164,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK10 @ sK9)))) = $true) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK9)))) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.35/1.26 thf(f140,plain,(
% 1.35/1.26 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK9)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK10 @ sK9))))) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.35/1.26 thf(f132,plain,(
% 1.35/1.26 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK4 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK9)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (sK4 @ Y0)) => (Y0 @ sK10 @ sK9))))) => (sK8 @ sK10 @ sK9)) = $false) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.35/1.26 thf(f131,plain,(
% 1.35/1.26 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK4 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK9)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK4 @ Y1)) => (Y1 @ Y0 @ sK9))))) => (sK8 @ Y0 @ sK9))) @ sK10) = $false) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f122])).
% 1.35/1.26 thf(f122,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK4 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK9)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (sK4 @ Y1)) => (Y1 @ Y0 @ sK9))))) => (sK8 @ Y0 @ sK9)))) = $false) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.35/1.26 thf(f120,plain,(
% 1.35/1.26 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0))))) @ sK9)) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f114])).
% 1.35/1.26 thf(f114,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0)))))) = $false) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(not_proxy_clausification,[status(thm)],[f102])).
% 1.35/1.26 thf(f102,plain,(
% 1.35/1.26 ((~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0))))))) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f101])).
% 1.35/1.26 thf(f101,plain,(
% 1.35/1.26 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0)))))) & $true)) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f94,f100])).
% 1.35/1.26 thf(f100,plain,(
% 1.35/1.26 ($true = (sK4 @ sK8)) | ~spl0_1),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f99])).
% 1.35/1.26 thf(f99,plain,(
% 1.35/1.26 (($true & (sK4 @ sK8)) = $true) | ~spl0_1),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f84,f98])).
% 1.35/1.26 thf(f98,plain,(
% 1.35/1.26 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y0)))))) = $true) | ~spl0_1),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 1.35/1.26 thf(f84,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y0)))))) & (sK4 @ sK8)) = $true) | ~spl0_1),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.35/1.26 thf(f82,plain,(
% 1.35/1.26 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y0)))))) & (sK4 @ sK8)) => (sK8 @ sK5 @ sK6))) | ~spl0_1),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.35/1.26 thf(f81,plain,(
% 1.35/1.26 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6))) @ sK8)) | ~spl0_1),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f25])).
% 1.35/1.26 thf(f94,plain,(
% 1.35/1.26 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0)))))) & (sK4 @ sK8))) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f92])).
% 1.35/1.26 thf(f92,plain,(
% 1.35/1.26 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK8 @ Y1 @ Y0)))))) & (sK4 @ sK8)) => $false) = $true) | (~spl0_1 | ~spl0_4)),
% 1.35/1.26 inference(superposition,[status(thm)],[f90,f83])).
% 1.35/1.26 thf(f83,plain,(
% 1.35/1.26 ((sK8 @ sK5 @ sK6) = $false) | ~spl0_1),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.35/1.26 thf(f78,plain,(
% 1.35/1.26 ~spl0_2 | ~spl0_5),
% 1.35/1.26 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.35/1.26 thf(f77,plain,(
% 1.35/1.26 $false | (~spl0_2 | ~spl0_5)),
% 1.35/1.26 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.35/1.26 thf(f76,plain,(
% 1.35/1.26 ($false = $true) | (~spl0_2 | ~spl0_5)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f75])).
% 1.35/1.26 thf(f75,plain,(
% 1.35/1.26 (($false => (sK7 @ sK5 @ sK6)) = $false) | (~spl0_2 | ~spl0_5)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f74])).
% 1.35/1.26 thf(f74,plain,(
% 1.35/1.26 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0)))))) & $false) => (sK7 @ sK5 @ sK6)) = $false) | (~spl0_2 | ~spl0_5)),
% 1.35/1.26 inference(forward_demodulation,[status(thm)],[f73,f58])).
% 1.35/1.26 thf(f58,plain,(
% 1.35/1.26 ($false = (sK4 @ sK7)) | ~spl0_5),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.35/1.26 thf(f57,definition,(
% 1.35/1.26 spl0_5 <=> ($false = (sK4 @ sK7))),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.35/1.26 thf(f73,plain,(
% 1.35/1.26 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0)))))) & (sK4 @ sK7)) => (sK7 @ sK5 @ sK6)) = $false) | ~spl0_2),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.35/1.26 thf(f72,plain,(
% 1.35/1.26 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6))) @ sK7) = $false) | ~spl0_2),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f28])).
% 1.35/1.26 thf(f65,plain,(
% 1.35/1.26 ~spl0_1 | ~spl0_3),
% 1.35/1.26 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.35/1.26 thf(f64,plain,(
% 1.35/1.26 $false | (~spl0_1 | ~spl0_3)),
% 1.35/1.26 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.35/1.26 thf(f63,plain,(
% 1.35/1.26 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f32,f25])).
% 1.35/1.26 thf(f32,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $true) | ~spl0_3),
% 1.35/1.26 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.35/1.26 thf(f31,definition,(
% 1.35/1.26 spl0_3 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $true)),
% 1.35/1.26 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.35/1.26 thf(f62,plain,(
% 1.35/1.26 spl0_5 | spl0_6 | ~spl0_2 | ~spl0_3),
% 1.35/1.26 inference(avatar_split_clause,[status(thm)],[f53,f31,f27,f60,f57])).
% 1.35/1.26 thf(f53,plain,(
% 1.35/1.26 ($false = (sK4 @ sK7)) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK7 @ Y1 @ Y0)))))) = $false) | (~spl0_2 | ~spl0_3)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.35/1.26 thf(f50,plain,(
% 1.35/1.26 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK7 @ Y1 @ Y0)))))) & (sK4 @ sK7))) | (~spl0_2 | ~spl0_3)),
% 1.35/1.26 inference(not_proxy_clausification,[status(thm)],[f49])).
% 1.35/1.26 thf(f49,plain,(
% 1.35/1.26 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK7 @ Y1 @ Y0)))))) & (sK4 @ sK7))) = $true) | (~spl0_2 | ~spl0_3)),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f48])).
% 1.35/1.26 thf(f48,plain,(
% 1.35/1.26 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK7 @ Y1 @ Y0)))))) & (sK4 @ sK7)) => $false)) | (~spl0_2 | ~spl0_3)),
% 1.35/1.26 inference(superposition,[status(thm)],[f40,f47])).
% 1.35/1.26 thf(f47,plain,(
% 1.35/1.26 ((sK7 @ sK5 @ sK6) = $false) | ~spl0_2),
% 1.35/1.26 inference(boolean_simplification,[status(thm)],[f46])).
% 1.35/1.26 thf(f46,plain,(
% 1.35/1.26 (($true => (sK7 @ sK5 @ sK6)) = $false) | ~spl0_2),
% 1.35/1.26 inference(backward_demodulation,[status(thm)],[f43,f45])).
% 1.35/1.26 thf(f45,plain,(
% 1.35/1.26 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0)))))) & (sK4 @ sK7)) = $true) | ~spl0_2),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.35/1.26 thf(f43,plain,(
% 1.35/1.26 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK4 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (sK4 @ Y2)) => (Y2 @ Y1 @ Y0))))) => (sK7 @ Y1 @ Y0)))))) & (sK4 @ sK7)) => (sK7 @ sK5 @ sK6)) = $false) | ~spl0_2),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.35/1.26 thf(f42,plain,(
% 1.35/1.26 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6))) @ sK7) = $false) | ~spl0_2),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f28])).
% 1.35/1.26 thf(f40,plain,(
% 1.35/1.26 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (X1 @ Y1 @ Y0)))))) & (sK4 @ X1)) => (X1 @ sK5 @ sK6)) = $true)) ) | ~spl0_3),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.35/1.26 thf(f39,plain,(
% 1.35/1.26 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6))) @ X1) = $true)) ) | ~spl0_3),
% 1.35/1.26 inference(pi_clausification,[status(thm)],[f32])).
% 1.35/1.26 thf(f36,plain,(
% 1.35/1.26 spl0_3 | spl0_4),
% 1.35/1.26 inference(avatar_split_clause,[status(thm)],[f21,f34,f31])).
% 1.35/1.26 thf(f21,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $true) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $true)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.35/1.26 thf(f20,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) != (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))))),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.35/1.26 thf(f19,plain,(
% 1.35/1.26 (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (sK4 @ Y1)) => (Y1 @ sK5 @ Y0))))) @ sK6) != ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((sK4 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (sK4 @ Y4)) => (Y4 @ Y3 @ Y2))))) => (Y1 @ Y3 @ Y2)))))) & (sK4 @ Y1)) => (Y1 @ sK5 @ Y0))))) @ sK6))),
% 1.35/1.26 inference(negative_extensionality,[status(thm)],[f18])).
% 1.35/1.26 thf(f18,plain,(
% 1.35/1.26 ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (sK4 @ Y1)) => (Y1 @ sK5 @ Y0))))) != (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((sK4 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (sK4 @ Y4)) => (Y4 @ Y3 @ Y2))))) => (Y1 @ Y3 @ Y2)))))) & (sK4 @ Y1)) => (Y1 @ sK5 @ Y0))))))),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.35/1.26 thf(f17,plain,(
% 1.35/1.26 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (sK4 @ Y2)) => (Y2 @ Y0 @ Y1))))))) @ sK5) != ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((sK4 @ Y5) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (sK4 @ Y5)) => (Y5 @ Y4 @ Y3))))) => (Y2 @ Y4 @ Y3)))))) & (sK4 @ Y2)) => (Y2 @ Y0 @ Y1))))))) @ sK5))),
% 1.35/1.26 inference(negative_extensionality,[status(thm)],[f16])).
% 1.35/1.26 thf(f16,plain,(
% 1.35/1.26 ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (sK4 @ Y2)) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((sK4 @ Y5) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (sK4 @ Y5)) => (Y5 @ Y4 @ Y3))))) => (Y2 @ Y4 @ Y3)))))) & (sK4 @ Y2)) => (Y2 @ Y0 @ Y1))))))))),
% 1.35/1.26 inference(equality_proxy_clausification,[status(thm)],[f15])).
% 1.35/1.26 thf(f15,plain,(
% 1.35/1.26 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((sK4 @ Y5) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (sK4 @ Y5)) => (Y5 @ Y4 @ Y3))))) => (Y2 @ Y4 @ Y3)))))) & (sK4 @ Y2)) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (sK4 @ Y2)) => (Y2 @ Y0 @ Y1)))))))) = $false)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.35/1.26 thf(f14,plain,(
% 1.35/1.26 (((^[Y0 : (a > a > $o) > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((Y0 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (Y0 @ Y6)) => (Y6 @ Y5 @ Y4))))) => (Y3 @ Y5 @ Y4)))))) & (Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))) @ sK4) = $false)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f13])).
% 1.35/1.26 thf(f13,plain,(
% 1.35/1.26 ((!! @ ((a > a > $o) > $o) @ (^[Y0 : (a > a > $o) > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((Y0 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (Y0 @ Y6)) => (Y6 @ Y5 @ Y4))))) => (Y3 @ Y5 @ Y4)))))) & (Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (Y0 @ Y3)) => (Y3 @ Y1 @ Y2)))))))))) = $false)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.35/1.26 thf(f12,plain,(
% 1.35/1.26 ($false = ((^[Y0 : a > a > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y1 : (a > a > $o) > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((Y1 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((sK2 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (Y1 @ Y7)) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5)))))) & (Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))))))))) @ sK3))),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f11])).
% 1.35/1.26 thf(f11,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y1 : (a > a > $o) > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((Y1 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((sK2 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (Y1 @ Y7)) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5)))))) & (Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (Y1 @ Y4)) => (Y4 @ Y2 @ Y3)))))))))))) = $false)),
% 1.35/1.26 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.35/1.26 thf(f10,plain,(
% 1.35/1.26 (((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y2 : (a > a > $o) > $o]: ((^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((Y2 @ Y8) & (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y0 @ Y10 @ Y9) => (Y8 @ Y10 @ Y9))))))) => (Y8 @ Y7 @ Y6)))) | (!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y1 @ Y9 @ Y10) => (Y8 @ Y9 @ Y10)))))) & (Y2 @ Y8)) => (Y8 @ Y7 @ Y6))))) => (Y5 @ Y7 @ Y6)))))) & (Y2 @ Y5)) => (Y5 @ Y3 @ Y4))))))) = (^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (Y2 @ Y5)) => (Y5 @ Y3 @ Y4))))))))))))) @ sK2) = $false)),
% 1.35/1.26 inference(sigma_clausification,[status(thm)],[f7])).
% 1.35/1.26 thf(f7,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y2 : (a > a > $o) > $o]: ((^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((Y2 @ Y8) & (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y0 @ Y10 @ Y9) => (Y8 @ Y10 @ Y9))))))) => (Y8 @ Y7 @ Y6)))) | (!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y1 @ Y9 @ Y10) => (Y8 @ Y9 @ Y10)))))) & (Y2 @ Y8)) => (Y8 @ Y7 @ Y6))))) => (Y5 @ Y7 @ Y6)))))) & (Y2 @ Y5)) => (Y5 @ Y3 @ Y4))))))) = (^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (Y2 @ Y5)) => (Y5 @ Y3 @ Y4)))))))))))))) = $false)),
% 1.35/1.26 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.35/1.26 thf(f6,plain,(
% 1.35/1.26 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y2 : (a > a > $o) > $o]: ((^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((Y2 @ Y8) & (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y0 @ Y10 @ Y9) => (Y8 @ Y10 @ Y9))))))) => (Y8 @ Y7 @ Y6)))) | (!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y1 @ Y9 @ Y10) => (Y8 @ Y9 @ Y10)))))) & (Y2 @ Y8)) => (Y8 @ Y7 @ Y6))))) => (Y5 @ Y7 @ Y6)))))) & (Y2 @ Y5)) => (Y5 @ Y3 @ Y4))))))) = (^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (Y2 @ Y5)) => (Y5 @ Y3 @ Y4))))))))))))))) = $true)),
% 1.35/1.26 inference(cnf_transformation,[status(thm)],[f5])).
% 1.35/1.26 thf(f5,plain,(
% 1.35/1.26 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y2 : (a > a > $o) > $o]: ((^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((Y2 @ Y8) & (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y0 @ Y10 @ Y9) => (Y8 @ Y10 @ Y9))))))) => (Y8 @ Y7 @ Y6)))) | (!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y1 @ Y9 @ Y10) => (Y8 @ Y9 @ Y10)))))) & (Y2 @ Y8)) => (Y8 @ Y7 @ Y6))))) => (Y5 @ Y7 @ Y6)))))) & (Y2 @ Y5)) => (Y5 @ Y3 @ Y4))))))) = (^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (Y2 @ Y5)) => (Y5 @ Y3 @ Y4))))))))))))))) = $true)),
% 1.35/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.35/1.26 thf(f4,plain,(
% 1.35/1.26 ~! [X0 : (a > a > $o) > $o,X1 : a > a > $o,X2 : a > a > $o] : ((^[X3 : a, X4 : a] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : (((X0 @ X8) & ! [X9 : a,X10 : a] : ((X1 @ X10 @ X9) => (X8 @ X10 @ X9))) => (X8 @ X6 @ X7)) | ! [X11 : a > a > $o] : ((! [X12 : a,X13 : a] : ((X2 @ X12 @ X13) => (X11 @ X12 @ X13)) & (X0 @ X11)) => (X11 @ X6 @ X7))) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)))) = (^[X14 : a, X15 : a] : (! [X16 : a > a > $o] : (((X0 @ X16) & ! [X17 : a,X18 : a] : (((X1 @ X17 @ X18) | (X2 @ X17 @ X18)) => (X16 @ X17 @ X18))) => (X16 @ X14 @ X15)))))),
% 1.35/1.26 inference(rectify,[status(thm)],[f2])).
% 1.35/1.26 thf(f2,negated_conjecture,(
% 1.35/1.26 ~! [X0 : (a > a > $o) > $o,X2 : a > a > $o,X1 : a > a > $o] : ((^[X3 : a, X4 : a] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : (((X0 @ X8) & ! [X10 : a,X9 : a] : ((X2 @ X9 @ X10) => (X8 @ X9 @ X10))) => (X8 @ X6 @ X7)) | ! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X6 @ X7))) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)))) = (^[X3 : a, X4 : a] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : (((X2 @ X6 @ X7) | (X1 @ X6 @ X7)) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)))))),
% 1.35/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.35/1.26 thf(f1,conjecture,(
% 1.35/1.26 ! [X0 : (a > a > $o) > $o,X2 : a > a > $o,X1 : a > a > $o] : ((^[X3 : a, X4 : a] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : ((! [X8 : a > a > $o] : (((X0 @ X8) & ! [X10 : a,X9 : a] : ((X2 @ X9 @ X10) => (X8 @ X9 @ X10))) => (X8 @ X6 @ X7)) | ! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & (X0 @ X8)) => (X8 @ X6 @ X7))) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)))) = (^[X3 : a, X4 : a] : (! [X5 : a > a > $o] : (((X0 @ X5) & ! [X6 : a,X7 : a] : (((X2 @ X6 @ X7) | (X1 @ X6 @ X7)) => (X5 @ X6 @ X7))) => (X5 @ X3 @ X4)))))),
% 1.35/1.26 file('/export/starexec/sandbox2/tmp/tmp.vXxvqWtk5q/DTF2THF_10759.p',cTHM252_pme)).
% 1.35/1.26 thf(f29,plain,(
% 1.35/1.26 spl0_1 | spl0_2),
% 1.35/1.26 inference(avatar_split_clause,[status(thm)],[f22,f27,f24])).
% 1.35/1.26 thf(f22,plain,(
% 1.35/1.26 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $false) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK4 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (sK4 @ Y3)) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1)))))) & (sK4 @ Y0)) => (Y0 @ sK5 @ sK6)))) = $false)),
% 1.35/1.26 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.35/1.26 % SZS output end Proof for DTF2THF_10759
% 1.35/1.26 % (10867)------------------------------
% 1.35/1.26 % (10867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.26 % (10867)Termination reason: Refutation
% 1.35/1.26
% 1.35/1.26 % (10867)Memory used [KB]: 6140
% 1.35/1.26 % (10867)Time elapsed: 0.115 s
% 1.35/1.26 % (10867)Instructions burned: 173 (million)
% 1.35/1.26 % (10867)------------------------------
% 1.35/1.26 % (10867)------------------------------
% 1.35/1.26 % (10855)Success in time 0.133 s
%------------------------------------------------------------------------------