%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV157^5 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:26 AM UTC 2026
% Result : Theorem 8.06s 2.33s
% Output : Refutation 8.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 13
% Syntax : Number of formulae : 259 ( 30 unt; 0 typ; 12 def)
% Number of atoms : 3224 ( 242 equ; 0 cnn)
% Maximal formula atoms : 4 ( 12 avg)
% Number of connectives : 11755 ( 356 ~; 595 |; 635 &;7525 @)
% ( 12 <=>; 971 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1002 (1002 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 37 usr; 34 con; 0-2 aty)
% (1661 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1950 (1708 ^; 242 !; 0 ?;1950 :)
% 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 ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a ).
thf(func_def_24,type,
sK5: a > a > $o ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a > a > $o ).
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 > a > $o ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(f800,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f181,f191,f234,f288,f375,f492,f526,f577,f583,f591,f664,f799]) ).
thf(f799,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f798]) ).
thf(f798,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f797]) ).
thf(f797,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f796]) ).
thf(f796,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f791,f739]) ).
thf(f739,plain,
( ( ( sK12 @ sK23 @ sK24 )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f730]) ).
thf(f730,plain,
( ( ( ( sK12 @ sK25 @ sK23 )
& ( sK12 @ sK23 @ sK24 ) )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f728]) ).
thf(f728,plain,
( ( $false
= ( ( ( sK12 @ sK25 @ sK23 )
& ( sK12 @ sK23 @ sK24 ) )
=> ( sK12 @ sK25 @ sK24 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f727]) ).
thf(f727,plain,
( ( ( ^ [Y0: a] :
( ( ( sK12 @ Y0 @ sK23 )
& ( sK12 @ sK23 @ sK24 ) )
=> ( sK12 @ Y0 @ sK24 ) )
@ sK25 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f726]) ).
thf(f726,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK12 @ Y0 @ sK23 )
& ( sK12 @ sK23 @ sK24 ) )
=> ( sK12 @ Y0 @ sK24 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f725]) ).
thf(f725,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 @ sK23 )
& ( sK12 @ sK23 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ sK24 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f709]) ).
thf(f709,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 @ sK23 )
& ( sK12 @ sK23 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f707]) ).
thf(f707,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y0 )
& ( sK12 @ Y0 @ Y1 ) )
=> ( sK12 @ Y2 @ Y1 ) ) ) )
@ sK23 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f287]) ).
thf(f287,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y0 )
& ( sK12 @ Y0 @ Y1 ) )
=> ( sK12 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f286]) ).
thf(f286,definition,
( spl0_8
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y0 )
& ( sK12 @ Y0 @ Y1 ) )
=> ( sK12 @ Y2 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f791,plain,
( ( ( ~ ( sK12 @ sK23 @ sK24 ) )
= $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f788]) ).
thf(f788,plain,
( ( ( ( sK12 @ sK23 @ sK24 )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f772,f729]) ).
thf(f729,plain,
( ( ( sK12 @ sK25 @ sK24 )
= $false )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f728]) ).
thf(f772,plain,
( ! [X0: a] :
( ( ( sK12 @ sK23 @ X0 )
=> ( sK12 @ sK25 @ X0 ) )
= $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f764]) ).
thf(f764,plain,
( ! [X0: a] :
( ( ( $true
& ( sK12 @ sK23 @ X0 ) )
=> ( sK12 @ sK25 @ X0 ) )
= $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f748,f742]) ).
thf(f742,plain,
( ( ( sK12 @ sK25 @ sK23 )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f741]) ).
thf(f741,plain,
( ( ( ( sK12 @ sK25 @ sK23 )
& $true )
= $true )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f730,f739]) ).
thf(f748,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK12 @ X1 @ X3 )
& ( sK12 @ X3 @ X2 ) )
=> ( sK12 @ X1 @ X2 ) )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f747]) ).
thf(f747,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK12 @ X1 @ Y0 )
& ( sK12 @ Y0 @ X2 ) )
=> ( sK12 @ X1 @ X2 ) )
@ X3 )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f744]) ).
thf(f744,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK12 @ X1 @ Y0 )
& ( sK12 @ Y0 @ X2 ) )
=> ( sK12 @ X1 @ X2 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f743]) ).
thf(f743,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ X1 @ Y1 )
& ( sK12 @ Y1 @ Y0 ) )
=> ( sK12 @ X1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f738]) ).
thf(f738,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ X1 @ Y1 )
& ( sK12 @ Y1 @ Y0 ) )
=> ( sK12 @ X1 @ Y0 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f737]) ).
thf(f737,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f626]) ).
thf(f626,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f623]) ).
thf(f623,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f618]) ).
thf(f618,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK12 @ sK10 @ sK11 ) )
= $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f617]) ).
thf(f617,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ sK12 ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f613]) ).
thf(f613,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f612]) ).
thf(f612,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f611]) ).
thf(f611,plain,
( ( ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f610,f230]) ).
thf(f230,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f229]) ).
thf(f229,definition,
( spl0_5
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f610,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f609]) ).
thf(f609,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f600]) ).
thf(f600,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f599]) ).
thf(f599,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f190]) ).
thf(f190,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f189]) ).
thf(f189,definition,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f664,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f663]) ).
thf(f663,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f662]) ).
thf(f662,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f661]) ).
thf(f661,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f660]) ).
thf(f660,plain,
( ( ( ~ ( $true
| ( sK3 @ sK22 @ sK21 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f659,f639]) ).
thf(f639,plain,
( ( ( sK5 @ sK22 @ sK21 )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f635]) ).
thf(f635,plain,
( ( $false
= ( ( sK5 @ sK22 @ sK21 )
=> ( sK12 @ sK22 @ sK21 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f634]) ).
thf(f634,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK5 @ Y0 @ sK21 )
=> ( sK12 @ Y0 @ sK21 ) )
@ sK22 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f631]) ).
thf(f631,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 @ sK21 )
=> ( sK12 @ Y0 @ sK21 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f630]) ).
thf(f630,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ sK21 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f284]) ).
thf(f284,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f283]) ).
thf(f283,definition,
( spl0_7
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f659,plain,
( ( ( ~ ( ( sK5 @ sK22 @ sK21 )
| ( sK3 @ sK22 @ sK21 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f658]) ).
thf(f658,plain,
( ( ( ( ( sK5 @ sK22 @ sK21 )
| ( sK3 @ sK22 @ sK21 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f637,f638]) ).
thf(f638,plain,
( ( $false
= ( sK12 @ sK22 @ sK21 ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f635]) ).
thf(f637,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK5 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
=> ( sK12 @ X2 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f636]) ).
thf(f636,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK12 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f633]) ).
thf(f633,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK12 @ Y0 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f632]) ).
thf(f632,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f629]) ).
thf(f629,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f628]) ).
thf(f628,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& $true )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f623,f626]) ).
thf(f591,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f590]) ).
thf(f590,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f589]) ).
thf(f589,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f588]) ).
thf(f588,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f586]) ).
thf(f586,plain,
( ( ( ~ ( $true
| ( sK3 @ sK20 @ sK19 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f565,f573]) ).
thf(f573,plain,
( ( ( sK5 @ sK20 @ sK19 )
= $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f572]) ).
thf(f572,definition,
( spl0_11
<=> ( ( sK5 @ sK20 @ sK19 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f565,plain,
( ( ( ~ ( ( sK5 @ sK20 @ sK19 )
| ( sK3 @ sK20 @ sK19 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f561]) ).
thf(f561,plain,
( ( ( ( ( sK5 @ sK20 @ sK19 )
| ( sK3 @ sK20 @ sK19 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f410,f557]) ).
thf(f557,plain,
( ( ( sK18 @ sK20 @ sK19 )
= $false )
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f556]) ).
thf(f556,plain,
( ( ( $true
=> ( sK18 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f550,f555]) ).
thf(f555,plain,
( ( ( ( sK3 @ sK20 @ sK19 )
| ( sK5 @ sK20 @ sK19 ) )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f550]) ).
thf(f550,plain,
( ( ( ( ( sK3 @ sK20 @ sK19 )
| ( sK5 @ sK20 @ sK19 ) )
=> ( sK18 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f549]) ).
thf(f549,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK19 )
| ( sK5 @ Y0 @ sK19 ) )
=> ( sK18 @ Y0 @ sK19 ) )
@ sK20 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f535]) ).
thf(f535,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK19 )
| ( sK5 @ Y0 @ sK19 ) )
=> ( sK18 @ Y0 @ sK19 ) ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f532]) ).
thf(f532,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) )
@ sK19 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f488]) ).
thf(f488,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f487]) ).
thf(f487,definition,
( spl0_9
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f410,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK5 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
=> ( sK18 @ X1 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f409]) ).
thf(f409,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK18 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f407]) ).
thf(f407,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK18 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f406]) ).
thf(f406,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f403]) ).
thf(f403,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f402]) ).
thf(f402,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f393,f401]) ).
thf(f401,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y1 @ Y0 )
& ( sK18 @ Y2 @ Y1 ) )
=> ( sK18 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f393]) ).
thf(f393,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y1 @ Y0 )
& ( sK18 @ Y2 @ Y1 ) )
=> ( sK18 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f391]) ).
thf(f391,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y1 @ Y0 )
& ( sK18 @ Y2 @ Y1 ) )
=> ( sK18 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) ) )
=> ( sK18 @ sK17 @ sK15 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f390]) ).
thf(f390,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK15 ) )
@ sK18 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f384]) ).
thf(f384,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK15 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f383]) ).
thf(f383,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK17 @ sK16 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK15 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f382]) ).
thf(f382,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK16 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK16 @ sK15 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK15 ) ) ) )
@ sK17 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f381]) ).
thf(f381,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK16 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK16 @ sK15 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK15 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f380]) ).
thf(f380,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK15 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ sK15 ) ) ) ) )
@ sK16 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f379]) ).
thf(f379,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK15 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ sK15 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f378]) ).
thf(f378,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) )
@ sK15 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f186]) ).
thf(f186,definition,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f583,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f582]) ).
thf(f582,plain,
( $false
| ~ spl0_3
| ~ spl0_9
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f581]) ).
thf(f581,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f580]) ).
thf(f580,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f578]) ).
thf(f578,plain,
( ( ( ~ ( ( sK5 @ sK20 @ sK19 )
| $true ) )
= $true )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f565,f576]) ).
thf(f576,plain,
( ( ( sK3 @ sK20 @ sK19 )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f575]) ).
thf(f575,definition,
( spl0_12
<=> ( ( sK3 @ sK20 @ sK19 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f577,plain,
( spl0_11
| spl0_12
| ~ spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f568,f487,f575,f572]) ).
thf(f568,plain,
( ( ( sK3 @ sK20 @ sK19 )
= $true )
| ( ( sK5 @ sK20 @ sK19 )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f555]) ).
thf(f526,plain,
( spl0_9
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f525,f490,f186,f487]) ).
thf(f490,definition,
( spl0_10
<=> ( ( sK18 @ sK16 @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f525,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_10 ),
inference(not_proxy_clausification,[status(thm)],[f508]) ).
thf(f508,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f507]) ).
thf(f507,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f447,f505]) ).
thf(f505,plain,
( ( $false
= ( sK18 @ sK17 @ sK16 ) )
| ~ spl0_3
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f495]) ).
thf(f495,plain,
( ( ( $true
& ( sK18 @ sK17 @ sK16 ) )
= $false )
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f469,f491]) ).
thf(f491,plain,
( ( ( sK18 @ sK16 @ sK15 )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f490]) ).
thf(f469,plain,
( ! [X0: a] :
( ( ( sK18 @ X0 @ sK15 )
& ( sK18 @ sK17 @ X0 ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f464]) ).
thf(f464,plain,
( ! [X0: a] :
( ( ~ ( ( sK18 @ X0 @ sK15 )
& ( sK18 @ sK17 @ X0 ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f461]) ).
thf(f461,plain,
( ! [X0: a] :
( ( ( ( sK18 @ X0 @ sK15 )
& ( sK18 @ sK17 @ X0 ) )
=> $false )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f459,f395]) ).
thf(f395,plain,
( ( ( sK18 @ sK17 @ sK15 )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f394]) ).
thf(f394,plain,
( ( ( $true
=> ( sK18 @ sK17 @ sK15 ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f391,f393]) ).
thf(f459,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK18 @ X2 @ X1 )
& ( sK18 @ X3 @ X2 ) )
=> ( sK18 @ X3 @ X1 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f458]) ).
thf(f458,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK18 @ X2 @ X1 )
& ( sK18 @ Y0 @ X2 ) )
=> ( sK18 @ Y0 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f457]) ).
thf(f457,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK18 @ X2 @ X1 )
& ( sK18 @ Y0 @ X2 ) )
=> ( sK18 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f456]) ).
thf(f456,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK18 @ Y0 @ X1 )
& ( sK18 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f446]) ).
thf(f446,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK18 @ Y0 @ X1 )
& ( sK18 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ X1 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f442]) ).
thf(f442,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y1 @ Y0 )
& ( sK18 @ Y2 @ Y1 ) )
=> ( sK18 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f401]) ).
thf(f447,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) )
=> ( sK18 @ sK17 @ sK16 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f443]) ).
thf(f443,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) )
=> ( sK18 @ sK17 @ sK16 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f405,f401]) ).
thf(f405,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y0 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK17 @ sK16 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f404]) ).
thf(f404,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK17 @ sK16 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f399]) ).
thf(f399,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK17 @ sK16 ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f398]) ).
thf(f398,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK17 @ sK16 ) ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f385,f396]) ).
thf(f396,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f385]) ).
thf(f385,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK17 @ sK16 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f383]) ).
thf(f492,plain,
( spl0_9
| spl0_10
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f485,f186,f490,f487]) ).
thf(f485,plain,
( ( ( sK18 @ sK16 @ sK15 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f445]) ).
thf(f445,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) )
=> ( sK18 @ sK16 @ sK15 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f444]) ).
thf(f444,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) )
& $true )
=> ( sK18 @ sK16 @ sK15 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f426,f401]) ).
thf(f426,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y0 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK16 @ sK15 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f425]) ).
thf(f425,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f396]) ).
thf(f375,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f374]) ).
thf(f374,plain,
( $false
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f373]) ).
thf(f373,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f372]) ).
thf(f372,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f371]) ).
thf(f371,plain,
( ( ( ~ ( ( sK5 @ sK14 @ sK13 )
| $true ) )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f365,f358]) ).
thf(f358,plain,
( ( ( sK3 @ sK14 @ sK13 )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f356]) ).
thf(f356,plain,
( ( ( ( sK3 @ sK14 @ sK13 )
=> ( sK12 @ sK14 @ sK13 ) )
= $false )
| ~ spl0_4
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f355]) ).
thf(f355,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 @ sK13 )
=> ( sK12 @ Y0 @ sK13 ) )
@ sK14 )
= $false )
| ~ spl0_4
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f354]) ).
thf(f354,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ sK13 )
=> ( sK12 @ Y0 @ sK13 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f350]) ).
thf(f350,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f347]) ).
thf(f347,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_6 ),
inference(not_proxy_clausification,[status(thm)],[f315]) ).
thf(f315,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f314]) ).
thf(f314,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f312,f207]) ).
thf(f207,plain,
( ( ( sK12 @ sK10 @ sK11 )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f206]) ).
thf(f206,plain,
( ( $false
= ( $true
=> ( sK12 @ sK10 @ sK11 ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f203,f205]) ).
thf(f205,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f203]) ).
thf(f203,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK12 @ sK10 @ sK11 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f202]) ).
thf(f202,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f201]) ).
thf(f201,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f200]) ).
thf(f200,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f197,f199]) ).
thf(f199,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f196]) ).
thf(f196,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f195]) ).
thf(f195,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f194]) ).
thf(f194,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f190]) ).
thf(f312,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
=> ( sK12 @ sK10 @ sK11 ) )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f310]) ).
thf(f310,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
=> ( sK12 @ sK10 @ sK11 ) )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f298,f211]) ).
thf(f211,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f210]) ).
thf(f210,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f205,f209]) ).
thf(f209,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f205]) ).
thf(f298,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK10 @ sK11 ) )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f297]) ).
thf(f297,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ X1 ) )
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f232]) ).
thf(f232,definition,
( spl0_6
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f365,plain,
( ( ( ~ ( ( sK5 @ sK14 @ sK13 )
| ( sK3 @ sK14 @ sK13 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f361]) ).
thf(f361,plain,
( ( ( ( ( sK5 @ sK14 @ sK13 )
| ( sK3 @ sK14 @ sK13 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f261,f360]) ).
thf(f360,plain,
( ( $false
= ( sK12 @ sK14 @ sK13 ) )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f359]) ).
thf(f359,plain,
( ( $false
= ( $true
=> ( sK12 @ sK14 @ sK13 ) ) )
| ~ spl0_4
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f356,f358]) ).
thf(f261,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK5 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
=> ( sK12 @ X2 @ X1 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f260]) ).
thf(f260,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK12 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f259]) ).
thf(f259,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK12 @ Y0 @ X1 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f258]) ).
thf(f258,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f209]) ).
thf(f288,plain,
( spl0_7
| spl0_8
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f279,f229,f189,f286,f283]) ).
thf(f279,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y0 )
& ( sK12 @ Y0 @ Y1 ) )
=> ( sK12 @ Y2 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f273]) ).
thf(f273,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y0 )
& ( sK12 @ Y0 @ Y1 ) )
=> ( sK12 @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(not_proxy_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y0 )
& ( sK12 @ Y0 @ Y1 ) )
=> ( sK12 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f256]) ).
thf(f256,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y0 )
& ( sK12 @ Y0 @ Y1 ) )
=> ( sK12 @ Y2 @ Y1 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f247,f207]) ).
thf(f247,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK10 @ sK11 ) )
= $true )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f246]) ).
thf(f246,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ X1 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f230]) ).
thf(f234,plain,
( spl0_5
| spl0_6
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f227,f189,f232,f229]) ).
thf(f227,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f199]) ).
thf(f191,plain,
( spl0_3
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f184,f29,f189,f186]) ).
thf(f29,definition,
( spl0_1
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f184,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f181,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f180]) ).
thf(f180,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f179]) ).
thf(f179,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f178]) ).
thf(f178,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f172,f145]) ).
thf(f145,plain,
( ( ( sK6 @ sK8 @ sK7 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
( ( ( ( sK6 @ sK7 @ sK9 )
& ( sK6 @ sK8 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ( ( ( sK6 @ sK7 @ sK9 )
& ( sK6 @ sK8 @ sK7 ) )
=> ( sK6 @ sK8 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK7 @ Y0 )
& ( sK6 @ sK8 @ sK7 ) )
=> ( sK6 @ sK8 @ Y0 ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK7 @ Y0 )
& ( sK6 @ sK8 @ sK7 ) )
=> ( sK6 @ sK8 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f119]) ).
thf(f119,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK7 @ Y1 )
& ( sK6 @ Y0 @ sK7 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK7 @ Y1 )
& ( sK6 @ Y0 @ sK7 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f47,f48]) ).
thf(f48,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK2 @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) )
@ sK6 ) ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ sK4 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK2 @ sK4 ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ sK4 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK2 @ sK4 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ sK2 @ Y1 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ sK2 @ Y1 ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ sK2 @ Y1 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ sK2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a > a > $o,X3: a] :
( ~ ( ( ! [X4: a,X5: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X2 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X9: a,X10: a,X11: a] :
( ( ( X6 @ X9 @ X10 )
& ( X6 @ X11 @ X9 ) )
=> ( X6 @ X11 @ X10 ) ) )
=> ( X6 @ X5 @ X4 ) )
| ! [X12: a > a > $o] :
( ( ! [X13: a,X14: a,X15: a] :
( ( ( X12 @ X15 @ X14 )
& ( X12 @ X13 @ X15 ) )
=> ( X12 @ X13 @ X14 ) )
& ! [X16: a,X17: a] :
( ( X0 @ X16 @ X17 )
=> ( X12 @ X16 @ X17 ) ) )
=> ( X12 @ X5 @ X4 ) ) )
=> ! [X18: a > a > $o] :
( ( ! [X19: a,X20: a,X21: a] :
( ( ( X18 @ X19 @ X20 )
& ( X18 @ X21 @ X19 ) )
=> ( X18 @ X21 @ X20 ) )
& ! [X22: a,X23: a] :
( ( ( X2 @ X22 @ X23 )
| ( X0 @ X22 @ X23 ) )
=> ( X18 @ X22 @ X23 ) ) )
=> ( X18 @ X5 @ X4 ) ) )
& ! [X24: a,X25: a,X26: a] :
( ( ! [X27: a > a > $o] :
( ( ! [X28: a,X29: a,X30: a] :
( ( ( X27 @ X28 @ X29 )
& ( X27 @ X29 @ X30 ) )
=> ( X27 @ X28 @ X30 ) )
& ! [X31: a,X32: a] :
( ( ( X0 @ X31 @ X32 )
| ( X2 @ X31 @ X32 ) )
=> ( X27 @ X31 @ X32 ) ) )
=> ( X27 @ X25 @ X26 ) )
& ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( X0 @ X34 @ X35 )
| ( X2 @ X34 @ X35 ) )
=> ( X33 @ X34 @ X35 ) )
& ! [X36: a,X37: a,X38: a] :
( ( ( X33 @ X36 @ X37 )
& ( X33 @ X37 @ X38 ) )
=> ( X33 @ X36 @ X38 ) ) )
=> ( X33 @ X24 @ X25 ) ) )
=> ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a] :
( ( ( X2 @ X41 @ X40 )
| ( X0 @ X41 @ X40 ) )
=> ( X39 @ X41 @ X40 ) )
& ! [X42: a,X43: a,X44: a] :
( ( ( X39 @ X42 @ X43 )
& ( X39 @ X43 @ X44 ) )
=> ( X39 @ X42 @ X44 ) ) )
=> ( X39 @ X24 @ X26 ) ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a,X48: a] :
( ( ( X45 @ X47 @ X48 )
& ( X45 @ X48 @ X46 ) )
=> ( X45 @ X47 @ X46 ) )
& ! [X49: a,X50: a] :
( ( ( X0 @ X50 @ X49 )
| ( X2 @ X50 @ X49 ) )
=> ( X45 @ X50 @ X49 ) ) )
=> ( X45 @ X3 @ X1 ) ) )
| ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a] :
( ( ( X0 @ X53 @ X52 )
| ( X2 @ X53 @ X52 ) )
=> ( X51 @ X53 @ X52 ) )
& ! [X54: a,X55: a,X56: a] :
( ( ( X51 @ X56 @ X54 )
& ( X51 @ X55 @ X56 ) )
=> ( X51 @ X55 @ X54 ) ) )
=> ( X51 @ X3 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X3: a,X1: a > a > $o,X2: a] :
( ~ ( ( ! [X6: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X8: a,X7: a,X9: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ! [X5: a,X6: a,X7: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X6 @ X7 ) )
& ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X7 ) ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
| ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X3: a,X1: a > a > $o,X2: a] :
( ~ ( ( ! [X6: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X8: a,X7: a,X9: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ! [X5: a,X6: a,X7: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X6 @ X7 ) )
& ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X7 ) ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
| ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oKqq4mYP0P/DTF2THF_20901.p',cTHM250G_pme) ).
thf(f47,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f44,f37]) ).
thf(f37,plain,
( ( sK6 @ sK2 @ sK4 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f44,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK2 @ sK4 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl0_2
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f172,plain,
( ( ( ~ ( sK6 @ sK8 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f169]) ).
thf(f169,plain,
( ( ( ( sK6 @ sK8 @ sK7 )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f155,f129]) ).
thf(f129,plain,
( ( ( sK6 @ sK8 @ sK9 )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f155,plain,
( ! [X0: a] :
( ( ( sK6 @ X0 @ sK7 )
=> ( sK6 @ X0 @ sK9 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f151]) ).
thf(f151,plain,
( ! [X0: a] :
( ( ( ( sK6 @ X0 @ sK7 )
& $true )
=> ( sK6 @ X0 @ sK9 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f59,f148]) ).
thf(f148,plain,
( ( ( sK6 @ sK7 @ sK9 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( ( ( sK6 @ sK7 @ sK9 )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f130,f145]) ).
thf(f59,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ X1 @ X3 ) )
=> ( sK6 @ X2 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ X1 @ Y0 ) )
=> ( sK6 @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ X1 @ Y0 ) )
=> ( sK6 @ X2 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ X1 )
& ( sK6 @ X1 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ X1 )
& ( sK6 @ X1 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f38,f48]) ).
thf(f34,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f32,f29]) ).
thf(f27,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
= $true )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
= ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( $false
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f17,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV157^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:41:25 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEV157^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory (Relations)
% 0.31/0.46 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_1234 [Bro09]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.42 v9.1.0, 0.50 v9.0.0, 0.42 v8.2.0, 0.27 v8.1.0, 0.42 v7.5.0, 0.58 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.46 % Number of connectives : 162 ( 1 ~; 8 |; 18 &; 108 @)
% 0.31/0.46 % ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 24 ( 24 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.46 % Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(cTHM250G_pme,conjecture,
% 0.31/0.46 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.31/0.46 ( ! [Xp1: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx0: a,Xy0: a] :
% 0.31/0.46 ( ( ( R @ Xx0 @ Xy0 )
% 0.31/0.46 | ( S @ Xx0 @ Xy0 ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.31/0.46 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.31/0.46 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.31/0.46 & ( Xp1 @ Xy0 @ Xz ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.31/0.46 => ( Xp1 @ Xx @ Xy ) )
% 0.31/0.46 | ~ ( ( ! [Xx0: a,Xy0: a] :
% 0.31/0.46 ( ( ! [Xp1: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.31/0.46 ( ( R @ Xx1 @ Xy1 )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.31/0.46 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.31/0.46 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.31/0.46 & ( Xp1 @ Xy1 @ Xz ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.31/0.46 | ! [Xp1: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.31/0.46 ( ( S @ Xx1 @ Xy1 )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.31/0.46 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.31/0.46 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.31/0.46 & ( Xp1 @ Xy1 @ Xz ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 0.31/0.46 => ! [Xp1: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.31/0.46 ( ( ( R @ Xx1 @ Xy1 )
% 0.31/0.46 | ( S @ Xx1 @ Xy1 ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.31/0.46 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.31/0.46 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.31/0.46 & ( Xp1 @ Xy1 @ Xz ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 0.31/0.46 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.31/0.46 ( ( ! [Xp1: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.31/0.46 ( ( ( R @ Xx1 @ Xy1 )
% 0.31/0.46 | ( S @ Xx1 @ Xy1 ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.31/0.46 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.31/0.46 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.31/0.46 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.31/0.46 & ! [Xp1: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.31/0.46 ( ( ( R @ Xx1 @ Xy1 )
% 0.31/0.46 | ( S @ Xx1 @ Xy1 ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.31/0.46 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.31/0.46 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.31/0.46 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.31/0.46 => ( Xp1 @ Xy0 @ Xz ) ) )
% 0.31/0.46 => ! [Xp1: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.31/0.46 ( ( ( R @ Xx1 @ Xy1 )
% 0.31/0.46 | ( S @ Xx1 @ Xy1 ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.31/0.46 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.31/0.46 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.31/0.46 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.31/0.46 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xz ) ) ) )
% 0.31/0.46 => ! [Xp1: a > a > $o] :
% 0.31/0.46 ( ( ! [Xx0: a,Xy0: a] :
% 0.31/0.46 ( ( ( R @ Xx0 @ Xy0 )
% 0.31/0.46 | ( S @ Xx0 @ Xy0 ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.31/0.46 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.31/0.46 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.31/0.46 & ( Xp1 @ Xy0 @ Xz ) )
% 0.31/0.46 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.31/0.46 => ( Xp1 @ Xx @ Xy ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.54/1.26 ---- Embedded in THF ---
% 1.54/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.27 %%% Generated on Tue Feb 24 12:41:26 EST 2026
% 1.54/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.27 %%% Logic specification used:
% 1.54/1.27 %%% thf(spec, logic, $$dhol).
% 1.54/1.27
% 1.54/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oKqq4mYP0P/DTF2DTF20901.p
% See solution above
% 1.54/1.27 ------------------------
% 1.54/1.28 ---- Cleaned THF ---
% 1.54/1.28 thf(a_type,type,
% 1.54/1.28 a: $tType ).
% 1.54/1.28
% 1.54/1.28 thf(cTHM250G_pme,conjecture,
% 1.54/1.28 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.54/1.28 ( ! [Xp1: a > a > $o] :
% 1.54/1.28 ( ( ! [Xx0: a,Xy0: a] :
% 1.54/1.28 ( ( ( R @ Xx0 @ Xy0 )
% 1.54/1.28 | ( S @ Xx0 @ Xy0 ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.54/1.28 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.54/1.28 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.54/1.28 & ( Xp1 @ Xy0 @ Xz ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.54/1.28 => ( Xp1 @ Xx @ Xy ) )
% 1.54/1.28 | ~ ( ( ! [Xx0: a,Xy0: a] :
% 1.54/1.28 ( ( ! [Xp1: a > a > $o] :
% 1.54/1.28 ( ( ! [Xx1: a,Xy1: a] :
% 1.54/1.28 ( ( R @ Xx1 @ Xy1 )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.54/1.28 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.54/1.28 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.54/1.28 & ( Xp1 @ Xy1 @ Xz ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.54/1.28 | ! [Xp1: a > a > $o] :
% 1.54/1.28 ( ( ! [Xx1: a,Xy1: a] :
% 1.54/1.28 ( ( S @ Xx1 @ Xy1 )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.54/1.28 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.54/1.28 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.54/1.28 & ( Xp1 @ Xy1 @ Xz ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 1.54/1.28 => ! [Xp1: a > a > $o] :
% 1.54/1.28 ( ( ! [Xx1: a,Xy1: a] :
% 1.54/1.28 ( ( ( R @ Xx1 @ Xy1 )
% 1.54/1.28 | ( S @ Xx1 @ Xy1 ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.54/1.28 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.54/1.28 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.54/1.28 & ( Xp1 @ Xy1 @ Xz ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 1.54/1.28 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.54/1.28 ( ( ! [Xp1: a > a > $o] :
% 1.54/1.28 ( ( ! [Xx1: a,Xy1: a] :
% 1.54/1.28 ( ( ( R @ Xx1 @ Xy1 )
% 1.54/1.28 | ( S @ Xx1 @ Xy1 ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.54/1.28 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.54/1.28 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.54/1.28 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.54/1.28 & ! [Xp1: a > a > $o] :
% 1.54/1.28 ( ( ! [Xx1: a,Xy1: a] :
% 1.54/1.28 ( ( ( R @ Xx1 @ Xy1 )
% 1.54/1.28 | ( S @ Xx1 @ Xy1 ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.54/1.28 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.54/1.28 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.54/1.28 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.54/1.28 => ( Xp1 @ Xy0 @ Xz ) ) )
% 1.54/1.28 => ! [Xp1: a > a > $o] :
% 1.54/1.28 ( ( ! [Xx1: a,Xy1: a] :
% 1.54/1.28 ( ( ( R @ Xx1 @ Xy1 )
% 1.54/1.28 | ( S @ Xx1 @ Xy1 ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.54/1.28 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.54/1.28 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.54/1.28 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.54/1.28 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xz ) ) ) )
% 1.54/1.28 => ! [Xp1: a > a > $o] :
% 1.54/1.28 ( ( ! [Xx0: a,Xy0: a] :
% 1.54/1.28 ( ( ( R @ Xx0 @ Xy0 )
% 1.54/1.28 | ( S @ Xx0 @ Xy0 ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.54/1.28 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.54/1.28 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.54/1.28 & ( Xp1 @ Xy0 @ Xz ) )
% 1.54/1.28 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.54/1.28 => ( Xp1 @ Xx @ Xy ) ) ) ) ).
% 1.54/1.28 ------------------------
% 1.54/1.29 % (21168)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/18Mi)
% 1.54/1.29 % (21165)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/2Mi)
% 1.54/1.29 % (21165)Instruction limit reached!
% 1.54/1.29 % (21165)------------------------------
% 1.54/1.29 % (21165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.29 % (21165)Termination reason: Unknown
% 1.54/1.29 % (21165)Termination phase: Property scanning
% 1.54/1.29
% 1.54/1.29 % (21165)Memory used [KB]: 1023
% 1.54/1.29 % (21165)Time elapsed: 0.002 s
% 1.54/1.29 % (21165)Instructions burned: 3 (million)
% 1.54/1.29 % (21165)------------------------------
% 1.54/1.29 % (21165)------------------------------
% 1.68/1.30 % (21168)Instruction limit reached!
% 1.68/1.30 % (21168)------------------------------
% 1.68/1.30 % (21168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.30 % (21168)Termination reason: Unknown
% 1.68/1.30 % (21168)Termination phase: Saturation
% 1.68/1.30
% 1.68/1.30 % (21168)Memory used [KB]: 5628
% 1.68/1.30 % (21168)Time elapsed: 0.007 s
% 1.68/1.30 % (21168)Instructions burned: 19 (million)
% 1.68/1.30 % (21168)------------------------------
% 1.68/1.30 % (21168)------------------------------
% 1.68/1.30 % (21162)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/183Mi)
% 1.68/1.30 % (21166)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_20901 for (2999ds/2Mi)
% 1.68/1.30 % (21164)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_20901 for (2999ds/27Mi)
% 1.68/1.30 % (21167)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_20901 for (2999ds/275Mi)
% 1.68/1.30 % (21163)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_20901 for (2999ds/4Mi)
% 1.68/1.30 % (21166)Instruction limit reached!
% 1.68/1.30 % (21166)------------------------------
% 1.68/1.30 % (21166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.30 % (21166)Termination reason: Unknown
% 1.68/1.30 % (21166)Termination phase: shuffling
% 1.68/1.30
% 1.68/1.30 % (21166)Memory used [KB]: 1023
% 1.68/1.30 % (21166)Time elapsed: 0.003 s
% 1.68/1.30 % (21166)Instructions burned: 2 (million)
% 1.68/1.30 % (21166)------------------------------
% 1.68/1.30 % (21166)------------------------------
% 1.68/1.30 % (21163)Instruction limit reached!
% 1.68/1.30 % (21163)------------------------------
% 1.68/1.30 % (21163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.30 % (21163)Termination reason: Unknown
% 1.68/1.30 % (21163)Termination phase: Preprocessing 3
% 1.68/1.30
% 1.68/1.30 % (21163)Memory used [KB]: 1023
% 1.68/1.30 % (21163)Time elapsed: 0.004 s
% 1.68/1.30 % (21163)Instructions burned: 4 (million)
% 1.68/1.30 % (21163)------------------------------
% 1.68/1.30 % (21163)------------------------------
% 1.68/1.30 % (21169)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/3Mi)
% 1.68/1.31 % (21169)Instruction limit reached!
% 1.68/1.31 % (21169)------------------------------
% 1.68/1.31 % (21169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.31 % (21169)Termination reason: Unknown
% 1.68/1.31 % (21169)Termination phase: Preprocessing 3
% 1.68/1.31
% 1.68/1.31 % (21169)Memory used [KB]: 1023
% 1.68/1.31 % (21169)Time elapsed: 0.003 s
% 1.68/1.31 % (21169)Instructions burned: 4 (million)
% 1.68/1.31 % (21169)------------------------------
% 1.68/1.31 % (21169)------------------------------
% 1.68/1.31 % (21170)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_20901 for (2999ds/37Mi)
% 1.68/1.31 % (21164)Instruction limit reached!
% 1.68/1.31 % (21164)------------------------------
% 1.68/1.31 % (21164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.31 % (21164)Termination reason: Unknown
% 1.68/1.31 % (21164)Termination phase: Saturation
% 1.68/1.31
% 1.68/1.31 % (21164)Memory used [KB]: 5756
% 1.68/1.31 % (21164)Time elapsed: 0.016 s
% 1.68/1.31 % (21164)Instructions burned: 27 (million)
% 1.68/1.31 % (21164)------------------------------
% 1.68/1.31 % (21164)------------------------------
% 1.68/1.32 % (21173)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_20901 for (2999ds/1041Mi)
% 1.68/1.32 % (21170)Instruction limit reached!
% 1.68/1.32 % (21170)------------------------------
% 1.68/1.32 % (21170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (21170)Termination reason: Unknown
% 1.68/1.32 % (21170)Termination phase: Saturation
% 1.68/1.32
% 1.68/1.32 % (21170)Memory used [KB]: 5628
% 1.68/1.32 % (21170)Time elapsed: 0.011 s
% 1.68/1.32 % (21170)Instructions burned: 37 (million)
% 1.68/1.32 % (21170)------------------------------
% 1.68/1.32 % (21170)------------------------------
% 1.68/1.32 % (21171)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_20901 for (2999ds/15Mi)
% 1.68/1.32 % (21172)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_20901 for (2999ds/3Mi)
% 1.68/1.32 % (21172)Instruction limit reached!
% 1.68/1.32 % (21172)------------------------------
% 1.68/1.32 % (21172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (21172)Termination reason: Unknown
% 1.68/1.32 % (21172)Termination phase: Naming
% 1.68/1.32
% 1.68/1.32 % (21172)Memory used [KB]: 1023
% 1.68/1.32 % (21172)Time elapsed: 0.004 s
% 1.68/1.32 % (21172)Instructions burned: 4 (million)
% 1.68/1.32 % (21172)------------------------------
% 1.68/1.32 % (21172)------------------------------
% 1.68/1.33 % (21174)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/7Mi)
% 1.68/1.33 % (21175)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/16Mi)
% 1.68/1.33 % (21171)Instruction limit reached!
% 1.68/1.33 % (21171)------------------------------
% 1.68/1.33 % (21171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (21171)Termination reason: Unknown
% 1.68/1.33 % (21171)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (21171)Memory used [KB]: 5756
% 1.68/1.33 % (21171)Time elapsed: 0.011 s
% 1.68/1.33 % (21171)Instructions burned: 16 (million)
% 1.68/1.33 % (21171)------------------------------
% 1.68/1.33 % (21171)------------------------------
% 1.68/1.33 % (21174)Instruction limit reached!
% 1.68/1.33 % (21174)------------------------------
% 1.68/1.33 % (21174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (21174)Termination reason: Unknown
% 1.68/1.33 % (21174)Termination phase: Preprocessing 3
% 1.68/1.33
% 1.68/1.33 % (21174)Memory used [KB]: 1151
% 1.68/1.33 % (21174)Time elapsed: 0.004 s
% 1.68/1.33 % (21174)Instructions burned: 7 (million)
% 1.68/1.33 % (21174)------------------------------
% 1.68/1.33 % (21174)------------------------------
% 1.68/1.33 % (21175)Instruction limit reached!
% 1.68/1.33 % (21175)------------------------------
% 1.68/1.33 % (21175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (21175)Termination reason: Unknown
% 1.68/1.33 % (21175)Termination phase: Property scanning
% 1.68/1.33
% 1.68/1.33 % (21175)Memory used [KB]: 1151
% 1.68/1.33 % (21175)Time elapsed: 0.006 s
% 1.68/1.33 % (21175)Instructions burned: 18 (million)
% 1.68/1.33 % (21175)------------------------------
% 1.68/1.33 % (21175)------------------------------
% 1.68/1.34 % (21178)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/7Mi)
% 1.68/1.34 % (21176)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_20901 for (2999ds/3Mi)
% 1.68/1.34 % (21179)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/3Mi)
% 1.68/1.34 % (21176)Instruction limit reached!
% 1.68/1.34 % (21176)------------------------------
% 1.68/1.34 % (21176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (21176)Termination reason: Unknown
% 1.68/1.34 % (21176)Termination phase: Naming
% 1.68/1.34
% 1.68/1.34 % (21176)Memory used [KB]: 1023
% 1.68/1.34 % (21176)Time elapsed: 0.004 s
% 1.68/1.34 % (21176)Instructions burned: 4 (million)
% 1.68/1.34 % (21178)Instruction limit reached!
% 1.68/1.34 % (21178)------------------------------
% 1.68/1.34 % (21178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (21176)------------------------------
% 1.68/1.34 % (21176)------------------------------
% 1.68/1.34 % (21178)Termination reason: Unknown
% 1.68/1.34 % (21178)Termination phase: Property scanning
% 1.68/1.34
% 1.68/1.34 % (21178)Memory used [KB]: 1151
% 1.68/1.34 % (21178)Time elapsed: 0.004 s
% 1.68/1.34 % (21178)Instructions burned: 7 (million)
% 1.68/1.34 % (21178)------------------------------
% 1.68/1.34 % (21178)------------------------------
% 1.68/1.34 % (21179)Instruction limit reached!
% 1.68/1.34 % (21179)------------------------------
% 1.68/1.34 % (21179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (21179)Termination reason: Unknown
% 1.68/1.34 % (21179)Termination phase: shuffling
% 1.68/1.34
% 1.68/1.34 % (21179)Memory used [KB]: 1023
% 1.68/1.34 % (21179)Time elapsed: 0.002 s
% 1.68/1.34 % (21179)Instructions burned: 4 (million)
% 1.68/1.34 % (21179)------------------------------
% 1.68/1.34 % (21179)------------------------------
% 1.68/1.35 % (21177)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_20901 for (2999ds/3Mi)
% 1.68/1.35 % (21177)Instruction limit reached!
% 1.68/1.35 % (21177)------------------------------
% 1.68/1.35 % (21177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.35 % (21177)Termination reason: Unknown
% 1.68/1.35 % (21177)Termination phase: Naming
% 1.68/1.35
% 1.68/1.35 % (21177)Memory used [KB]: 1023
% 1.68/1.35 % (21177)Time elapsed: 0.004 s
% 1.68/1.35 % (21177)Instructions burned: 4 (million)
% 1.68/1.35 % (21177)------------------------------
% 1.68/1.35 % (21177)------------------------------
% 1.68/1.35 % (21182)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/710Mi)
% 1.68/1.36 % (21180)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/4Mi)
% 1.68/1.36 % (21181)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/18Mi)
% 1.68/1.36 % (21180)Instruction limit reached!
% 1.68/1.36 % (21180)------------------------------
% 1.68/1.36 % (21180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (21180)Termination reason: Unknown
% 1.68/1.36 % (21180)Termination phase: Naming
% 1.68/1.36
% 1.68/1.36 % (21180)Memory used [KB]: 1023
% 1.68/1.36 % (21180)Time elapsed: 0.004 s
% 1.68/1.36 % (21180)Instructions burned: 4 (million)
% 1.68/1.36 % (21180)------------------------------
% 1.68/1.36 % (21180)------------------------------
% 1.68/1.36 % (21183)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/6Mi)
% 1.68/1.37 % (21183)Instruction limit reached!
% 1.68/1.37 % (21183)------------------------------
% 1.68/1.37 % (21183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (21183)Termination reason: Unknown
% 1.68/1.37 % (21183)Termination phase: Preprocessing 3
% 1.68/1.37
% 1.68/1.37 % (21183)Memory used [KB]: 1023
% 1.68/1.37 % (21183)Time elapsed: 0.005 s
% 1.68/1.37 % (21183)Instructions burned: 6 (million)
% 1.68/1.37 % (21183)------------------------------
% 1.68/1.37 % (21183)------------------------------
% 1.68/1.37 % (21162)Instruction limit reached!
% 1.68/1.37 % (21162)------------------------------
% 1.68/1.37 % (21162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (21162)Termination reason: Unknown
% 1.68/1.37 % (21162)Termination phase: Saturation
% 1.68/1.37
% 1.68/1.37 % (21162)Memory used [KB]: 6140
% 1.68/1.37 % (21162)Time elapsed: 0.071 s
% 1.68/1.37 % (21162)Instructions burned: 185 (million)
% 1.68/1.37 % (21162)------------------------------
% 1.68/1.37 % (21162)------------------------------
% 1.68/1.37 % (21181)Instruction limit reached!
% 1.68/1.37 % (21181)------------------------------
% 1.68/1.37 % (21181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (21181)Termination reason: Unknown
% 1.68/1.37 % (21181)Termination phase: Saturation
% 1.68/1.37
% 1.68/1.37 % (21181)Memory used [KB]: 5628
% 1.68/1.37 % (21181)Time elapsed: 0.012 s
% 1.68/1.37 % (21181)Instructions burned: 18 (million)
% 1.68/1.37 % (21181)------------------------------
% 1.68/1.37 % (21181)------------------------------
% 1.68/1.38 % (21184)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_20901 for (2999ds/902Mi)
% 1.68/1.38 % (21186)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/5Mi)
% 1.68/1.38 % (21186)Instruction limit reached!
% 1.68/1.38 % (21186)------------------------------
% 1.68/1.38 % (21186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (21186)Termination reason: Unknown
% 1.68/1.38 % (21186)Termination phase: Property scanning
% 1.68/1.38
% 1.68/1.38 % (21186)Memory used [KB]: 1023
% 1.68/1.38 % (21186)Time elapsed: 0.003 s
% 1.68/1.38 % (21186)Instructions burned: 5 (million)
% 1.68/1.38 % (21186)------------------------------
% 1.68/1.38 % (21186)------------------------------
% 1.68/1.38 % (21185)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_20901 for (2999ds/21Mi)
% 1.68/1.39 % (21187)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_20901 for (2999ds/6Mi)
% 1.68/1.39 % (21187)Instruction limit reached!
% 1.68/1.39 % (21187)------------------------------
% 1.68/1.39 % (21187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (21187)Termination reason: Unknown
% 1.68/1.39 % (21187)Termination phase: Preprocessing 1
% 1.68/1.39
% 1.68/1.39 % (21187)Memory used [KB]: 1023
% 1.68/1.39 % (21187)Time elapsed: 0.005 s
% 1.68/1.39 % (21187)Instructions burned: 6 (million)
% 1.68/1.39 % (21187)------------------------------
% 1.68/1.39 % (21187)------------------------------
% 1.68/1.39 % (21188)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20901 for (2999ds/377Mi)
% 1.68/1.39 % (21185)Instruction limit reached!
% 1.68/1.39 % (21185)------------------------------
% 1.68/1.39 % (21185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (21185)Termination reason: Unknown
% 1.68/1.39 % (21185)Termination phase: Saturation
% 1.68/1.39
% 1.68/1.39 % (21185)Memory used [KB]: 5756
% 1.68/1.39 % (21185)Time elapsed: 0.012 s
% 1.68/1.39 % (21185)Instructions burned: 21 (million)
% 1.68/1.39 % (21185)------------------------------
% 1.68/1.39 % (21185)------------------------------
% 1.68/1.40 % (21189)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_20901 for (2999ds/779Mi)
% 1.68/1.41 % (21190)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_20901 for (2998ds/19Mi)
% 1.68/1.41 % (21190)Instruction limit reached!
% 1.68/1.41 % (21190)------------------------------
% 1.68/1.41 % (21190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.41 % (21190)Termination reason: Unknown
% 1.68/1.41 % (21190)Termination phase: Saturation
% 1.68/1.41
% 1.68/1.41 % (21190)Memory used [KB]: 5500
% 1.68/1.41 % (21190)Time elapsed: 0.007 s
% 1.68/1.41 % (21190)Instructions burned: 20 (million)
% 1.68/1.41 % (21190)------------------------------
% 1.68/1.41 % (21190)------------------------------
% 1.68/1.42 % (21191)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20901 for (2998ds/879Mi)
% 1.68/1.43 % (21167)Instruction limit reached!
% 1.68/1.43 % (21167)------------------------------
% 1.68/1.43 % (21167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.43 % (21167)Termination reason: Unknown
% 1.68/1.43 % (21167)Termination phase: Saturation
% 1.68/1.43
% 1.68/1.43 % (21167)Memory used [KB]: 6396
% 1.68/1.43 % (21167)Time elapsed: 0.134 s
% 1.68/1.43 % (21167)Instructions burned: 275 (million)
% 1.68/1.43 % (21167)------------------------------
% 1.68/1.43 % (21167)------------------------------
% 1.68/1.44 % (21192)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20901 for (2998ds/17Mi)
% 1.68/1.45 % (21192)Instruction limit reached!
% 1.68/1.45 % (21192)------------------------------
% 1.68/1.45 % (21192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.45 % (21192)Termination reason: Unknown
% 1.68/1.45 % (21192)Termination phase: Saturation
% 1.68/1.45
% 1.68/1.45 % (21192)Memory used [KB]: 5756
% 1.68/1.45 % (21192)Time elapsed: 0.008 s
% 1.68/1.45 % (21192)Instructions burned: 18 (million)
% 1.68/1.45 % (21192)------------------------------
% 1.68/1.45 % (21192)------------------------------
% 1.68/1.46 % (21193)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20901 for (2998ds/3Mi)
% 1.68/1.46 % (21193)Instruction limit reached!
% 1.68/1.46 % (21193)------------------------------
% 1.68/1.46 % (21193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.46 % (21193)Termination reason: Unknown
% 1.68/1.46 % (21193)Termination phase: Preprocessing 3
% 1.68/1.46
% 1.68/1.46 % (21193)Memory used [KB]: 1023
% 1.68/1.46 % (21193)Time elapsed: 0.003 s
% 1.68/1.46 % (21193)Instructions burned: 4 (million)
% 1.68/1.46 % (21193)------------------------------
% 1.68/1.46 % (21193)------------------------------
% 1.68/1.47 % (21194)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20901 for (2998ds/30Mi)
% 1.68/1.48 % (21194)Instruction limit reached!
% 1.68/1.48 % (21194)------------------------------
% 1.68/1.48 % (21194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (21194)Termination reason: Unknown
% 1.68/1.48 % (21194)Termination phase: Saturation
% 1.68/1.48
% 1.68/1.48 % (21194)Memory used [KB]: 5756
% 1.68/1.48 % (21194)Time elapsed: 0.011 s
% 1.68/1.48 % (21194)Instructions burned: 30 (million)
% 1.68/1.48 % (21194)------------------------------
% 1.68/1.48 % (21194)------------------------------
% 1.68/1.49 % (21195)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20901 for (2998ds/127Mi)
% 1.68/1.51 % (21188)Instruction limit reached!
% 1.68/1.51 % (21188)------------------------------
% 1.68/1.51 % (21188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.51 % (21188)Termination reason: Unknown
% 1.68/1.51 % (21188)Termination phase: Saturation
% 1.68/1.51
% 1.68/1.51 % (21188)Memory used [KB]: 6012
% 1.68/1.51 % (21188)Time elapsed: 0.120 s
% 1.68/1.51 % (21188)Instructions burned: 377 (million)
% 1.68/1.51 % (21188)------------------------------
% 1.68/1.51 % (21188)------------------------------
% 1.68/1.52 % (21196)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20901 for (2997ds/100Mi)
% 1.68/1.53 % (21195)Instruction limit reached!
% 1.68/1.53 % (21195)------------------------------
% 1.68/1.53 % (21195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.53 % (21195)Termination reason: Unknown
% 1.68/1.53 % (21195)Termination phase: Saturation
% 1.68/1.53
% 1.68/1.53 % (21195)Memory used [KB]: 6268
% 1.68/1.53 % (21195)Time elapsed: 0.064 s
% 1.68/1.53 % (21195)Instructions burned: 129 (million)
% 1.68/1.53 % (21195)------------------------------
% 1.68/1.53 % (21195)------------------------------
% 1.68/1.54 % (21197)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_20901 for (2997ds/3Mi)
% 1.68/1.54 % (21197)Instruction limit reached!
% 1.68/1.54 % (21197)------------------------------
% 1.68/1.54 % (21197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.54 % (21197)Termination reason: Unknown
% 1.68/1.54 % (21197)Termination phase: Property scanning
% 1.68/1.54
% 1.68/1.54 % (21197)Memory used [KB]: 1023
% 1.68/1.54 % (21197)Time elapsed: 0.003 s
% 1.68/1.54 % (21197)Instructions burned: 5 (million)
% 1.68/1.54 % (21197)------------------------------
% 1.68/1.54 % (21197)------------------------------
% 1.68/1.55 % (21198)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_20901 for (2997ds/20Mi)
% 1.68/1.55 % (21182)Instruction limit reached!
% 1.68/1.55 % (21182)------------------------------
% 1.68/1.55 % (21182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.55 % (21182)Termination reason: Unknown
% 1.68/1.55 % (21182)Termination phase: Saturation
% 1.68/1.55
% 1.68/1.55 % (21182)Memory used [KB]: 7547
% 1.68/1.55 % (21182)Time elapsed: 0.201 s
% 1.68/1.55 % (21182)Instructions burned: 710 (million)
% 1.68/1.55 % (21182)------------------------------
% 1.68/1.55 % (21182)------------------------------
% 1.68/1.55 % (21196)Instruction limit reached!
% 1.68/1.55 % (21196)------------------------------
% 1.68/1.55 % (21196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.55 % (21196)Termination reason: Unknown
% 1.68/1.55 % (21196)Termination phase: Saturation
% 1.68/1.55
% 1.68/1.55 % (21196)Memory used [KB]: 6012
% 1.68/1.55 % (21196)Time elapsed: 0.058 s
% 1.68/1.55 % (21196)Instructions burned: 102 (million)
% 1.68/1.55 % (21196)------------------------------
% 1.68/1.55 % (21196)------------------------------
% 1.68/1.56 % (21198)Instruction limit reached!
% 1.68/1.56 % (21198)------------------------------
% 1.68/1.56 % (21198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.56 % (21198)Termination reason: Unknown
% 1.68/1.56 % (21198)Termination phase: Saturation
% 1.68/1.56
% 1.68/1.56 % (21198)Memory used [KB]: 5628
% 1.68/1.56 % (21198)Time elapsed: 0.008 s
% 1.68/1.56 % (21198)Instructions burned: 21 (million)
% 1.68/1.56 % (21198)------------------------------
% 1.68/1.56 % (21198)------------------------------
% 1.68/1.56 % (21199)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_20901 for (2997ds/86Mi)
% 1.68/1.56 % (21200)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_20901 for (2997ds/107Mi)
% 1.68/1.57 % (21201)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_20901 for (2997ds/39Mi)
% 1.68/1.58 % (21201)Instruction limit reached!
% 1.68/1.58 % (21201)------------------------------
% 1.68/1.58 % (21201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.58 % (21201)Termination reason: Unknown
% 1.68/1.58 % (21201)Termination phase: Saturation
% 1.68/1.58
% 1.68/1.58 % (21201)Memory used [KB]: 5628
% 1.68/1.58 % (21201)Time elapsed: 0.038 s
% 1.68/1.58 % (21201)Instructions burned: 40 (million)
% 1.68/1.58 % (21201)------------------------------
% 1.68/1.58 % (21201)------------------------------
% 1.68/1.59 % (21199)Instruction limit reached!
% 1.68/1.59 % (21199)------------------------------
% 1.68/1.59 % (21199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.59 % (21199)Termination reason: Unknown
% 1.68/1.59 % (21199)Termination phase: Saturation
% 1.68/1.59
% 1.68/1.59 % (21199)Memory used [KB]: 6140
% 1.68/1.59 % (21199)Time elapsed: 0.050 s
% 1.68/1.59 % (21199)Instructions burned: 88 (million)
% 1.68/1.59 % (21199)------------------------------
% 1.68/1.59 % (21199)------------------------------
% 1.68/1.59 % (21202)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_20901 for (2997ds/448Mi)
% 1.68/1.60 % (21203)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/46Mi)
% 1.68/1.60 % (21200)Instruction limit reached!
% 1.68/1.60 % (21200)------------------------------
% 1.68/1.60 % (21200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.60 % (21200)Termination reason: Unknown
% 1.68/1.60 % (21200)Termination phase: Saturation
% 1.68/1.60
% 1.68/1.60 % (21200)Memory used [KB]: 6012
% 1.68/1.60 % (21200)Time elapsed: 0.062 s
% 1.68/1.60 % (21200)Instructions burned: 107 (million)
% 1.68/1.60 % (21200)------------------------------
% 1.68/1.60 % (21200)------------------------------
% 1.68/1.61 % (21204)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/98Mi)
% 1.68/1.61 % (21203)Instruction limit reached!
% 1.68/1.61 % (21203)------------------------------
% 1.68/1.61 % (21203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.61 % (21203)Termination reason: Unknown
% 1.68/1.61 % (21203)Termination phase: Saturation
% 1.68/1.61
% 1.68/1.61 % (21203)Memory used [KB]: 5884
% 1.68/1.61 % (21203)Time elapsed: 0.014 s
% 1.68/1.61 % (21203)Instructions burned: 46 (million)
% 1.68/1.61 % (21203)------------------------------
% 1.68/1.61 % (21203)------------------------------
% 1.68/1.62 % (21205)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/507Mi)
% 1.68/1.64 % (21204)Instruction limit reached!
% 1.68/1.64 % (21204)------------------------------
% 1.68/1.64 % (21204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.64 % (21204)Termination reason: Unknown
% 1.68/1.64 % (21204)Termination phase: Saturation
% 1.68/1.64
% 1.68/1.64 % (21204)Memory used [KB]: 1279
% 1.68/1.64 % (21204)Time elapsed: 0.032 s
% 1.68/1.64 % (21204)Instructions burned: 100 (million)
% 1.68/1.64 % (21204)------------------------------
% 1.68/1.64 % (21204)------------------------------
% 1.68/1.64 % (21189)Instruction limit reached!
% 1.68/1.64 % (21189)------------------------------
% 1.68/1.64 % (21189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.64 % (21189)Termination reason: Unknown
% 1.68/1.64 % (21189)Termination phase: Saturation
% 1.68/1.64
% 1.68/1.64 % (21189)Memory used [KB]: 6652
% 1.68/1.64 % (21189)Time elapsed: 0.246 s
% 1.68/1.64 % (21189)Instructions burned: 779 (million)
% 1.68/1.64 % (21189)------------------------------
% 1.68/1.64 % (21189)------------------------------
% 1.68/1.65 % (21206)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/149Mi)
% 1.68/1.65 % (21207)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/39Mi)
% 1.68/1.66 % (21173)Instruction limit reached!
% 1.68/1.66 % (21173)------------------------------
% 1.68/1.66 % (21173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.66 % (21173)Termination reason: Unknown
% 1.68/1.66 % (21173)Termination phase: Saturation
% 1.68/1.66
% 1.68/1.66 % (21173)Memory used [KB]: 8827
% 1.68/1.66 % (21173)Time elapsed: 0.346 s
% 1.68/1.66 % (21173)Instructions burned: 1041 (million)
% 1.68/1.66 % (21173)------------------------------
% 1.68/1.66 % (21173)------------------------------
% 1.68/1.66 % (21184)Instruction limit reached!
% 1.68/1.66 % (21184)------------------------------
% 1.68/1.66 % (21184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.66 % (21184)Termination reason: Unknown
% 1.68/1.66 % (21184)Termination phase: Saturation
% 1.68/1.66
% 1.68/1.66 % (21184)Memory used [KB]: 9722
% 1.68/1.66 % (21184)Time elapsed: 0.286 s
% 1.68/1.66 % (21184)Instructions burned: 902 (million)
% 1.68/1.66 % (21184)------------------------------
% 1.68/1.66 % (21184)------------------------------
% 1.68/1.67 % (21207)Instruction limit reached!
% 1.68/1.67 % (21207)------------------------------
% 1.68/1.67 % (21207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.67 % (21207)Termination reason: Unknown
% 1.68/1.67 % (21207)Termination phase: Saturation
% 1.68/1.67
% 1.68/1.67 % (21207)Memory used [KB]: 5756
% 1.68/1.67 % (21207)Time elapsed: 0.015 s
% 1.68/1.67 % (21207)Instructions burned: 40 (million)
% 1.68/1.67 % (21207)------------------------------
% 1.68/1.67 % (21207)------------------------------
% 1.68/1.67 % (21208)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/6Mi)
% 1.68/1.67 % (21208)Instruction limit reached!
% 1.68/1.67 % (21208)------------------------------
% 1.68/1.67 % (21208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.67 % (21208)Termination reason: Unknown
% 1.68/1.67 % (21208)Termination phase: Saturation
% 1.68/1.67
% 1.68/1.67 % (21208)Memory used [KB]: 9978
% 1.68/1.67 % (21208)Time elapsed: 0.003 s
% 1.68/1.67 % (21208)Instructions burned: 8 (million)
% 1.68/1.67 % (21208)------------------------------
% 1.68/1.67 % (21208)------------------------------
% 1.68/1.67 % (21209)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/1087Mi)
% 1.68/1.68 % (21211)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/47Mi)
% 1.68/1.68 % (21212)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_20901 for (2996ds/44Mi)
% 1.68/1.68 % (21206)Instruction limit reached!
% 1.68/1.68 % (21206)------------------------------
% 1.68/1.68 % (21206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.68 % (21206)Termination reason: Unknown
% 1.68/1.68 % (21206)Termination phase: Property scanning
% 1.68/1.68
% 1.68/1.68 % (21206)Memory used [KB]: 2046
% 1.68/1.68 % (21206)Time elapsed: 0.036 s
% 1.68/1.68 % (21206)Instructions burned: 150 (million)
% 1.68/1.68 % (21206)------------------------------
% 1.68/1.68 % (21206)------------------------------
% 1.68/1.69 % (21212)Instruction limit reached!
% 1.68/1.69 % (21212)------------------------------
% 1.68/1.69 % (21212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.69 % (21212)Termination reason: Unknown
% 1.68/1.69 % (21212)Termination phase: Saturation
% 1.68/1.69
% 1.68/1.69 % (21212)Memory used [KB]: 1151
% 1.68/1.69 % (21212)Time elapsed: 0.012 s
% 1.68/1.69 % (21212)Instructions burned: 45 (million)
% 1.68/1.69 % (21212)------------------------------
% 1.68/1.69 % (21212)------------------------------
% 1.68/1.69 % (21213)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/432Mi)
% 1.68/1.69 % (21211)Instruction limit reached!
% 1.68/1.69 % (21211)------------------------------
% 1.68/1.69 % (21211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.69 % (21211)Termination reason: Unknown
% 1.68/1.69 % (21211)Termination phase: Saturation
% 1.68/1.69
% 1.68/1.69 % (21211)Memory used [KB]: 5756
% 1.68/1.69 % (21211)Time elapsed: 0.017 s
% 1.68/1.69 % (21211)Instructions burned: 48 (million)
% 1.68/1.69 % (21211)------------------------------
% 1.68/1.69 % (21211)------------------------------
% 1.68/1.70 % (21214)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/62Mi)
% 1.68/1.70 % (21215)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/31Mi)
% 1.68/1.70 % (21191)Instruction limit reached!
% 1.68/1.70 % (21191)------------------------------
% 1.68/1.70 % (21191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.70 % (21191)Termination reason: Unknown
% 1.68/1.70 % (21191)Termination phase: Saturation
% 1.68/1.70
% 1.68/1.70 % (21191)Memory used [KB]: 7419
% 1.68/1.70 % (21191)Time elapsed: 0.305 s
% 1.68/1.70 % (21191)Instructions burned: 880 (million)
% 1.68/1.70 % (21191)------------------------------
% 1.68/1.70 % (21191)------------------------------
% 1.68/1.71 % (21215)Instruction limit reached!
% 1.68/1.71 % (21215)------------------------------
% 1.68/1.71 % (21215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.71 % (21215)Termination reason: Unknown
% 1.68/1.71 % (21215)Termination phase: Saturation
% 1.68/1.71
% 1.68/1.71 % (21215)Memory used [KB]: 5756
% 1.68/1.71 % (21215)Time elapsed: 0.010 s
% 1.68/1.71 % (21215)Instructions burned: 32 (million)
% 1.68/1.71 % (21215)------------------------------
% 1.68/1.71 % (21215)------------------------------
% 1.68/1.71 % (21216)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/96Mi)
% 1.68/1.72 % (21214)Instruction limit reached!
% 1.68/1.72 % (21214)------------------------------
% 1.68/1.72 % (21214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.72 % (21214)Termination reason: Unknown
% 1.68/1.72 % (21214)Termination phase: Saturation
% 1.68/1.72
% 1.68/1.72 % (21214)Memory used [KB]: 5628
% 1.68/1.72 % (21214)Time elapsed: 0.018 s
% 1.68/1.72 % (21214)Instructions burned: 64 (million)
% 1.68/1.72 % (21214)------------------------------
% 1.68/1.72 % (21214)------------------------------
% 1.68/1.72 % (21217)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/453Mi)
% 1.68/1.73 % (21202)Instruction limit reached!
% 1.68/1.73 % (21202)------------------------------
% 1.68/1.73 % (21202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.73 % (21202)Termination reason: Unknown
% 1.68/1.73 % (21202)Termination phase: Saturation
% 1.68/1.73
% 1.68/1.73 % (21202)Memory used [KB]: 6524
% 1.68/1.73 % (21202)Time elapsed: 0.140 s
% 1.68/1.73 % (21202)Instructions burned: 449 (million)
% 1.68/1.73 % (21202)------------------------------
% 1.68/1.73 % (21202)------------------------------
% 1.68/1.73 % (21218)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/71Mi)
% 1.68/1.74 % (21219)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/83Mi)
% 1.68/1.75 % (21216)Instruction limit reached!
% 1.68/1.75 % (21216)------------------------------
% 1.68/1.75 % (21216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.75 % (21216)Termination reason: Unknown
% 1.68/1.75 % (21216)Termination phase: Saturation
% 1.68/1.75
% 1.68/1.75 % (21216)Memory used [KB]: 6012
% 1.68/1.75 % (21216)Time elapsed: 0.032 s
% 1.68/1.75 % (21216)Instructions burned: 97 (million)
% 1.68/1.75 % (21216)------------------------------
% 1.68/1.75 % (21216)------------------------------
% 1.68/1.75 % (21218)Instruction limit reached!
% 1.68/1.75 % (21218)------------------------------
% 1.68/1.75 % (21218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.75 % (21218)Termination reason: Unknown
% 1.68/1.75 % (21218)Termination phase: Saturation
% 1.68/1.75
% 1.68/1.75 % (21218)Memory used [KB]: 6012
% 1.68/1.75 % (21218)Time elapsed: 0.024 s
% 1.68/1.75 % (21218)Instructions burned: 73 (million)
% 1.68/1.75 % (21218)------------------------------
% 1.68/1.75 % (21218)------------------------------
% 1.68/1.75 % (21220)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/11Mi)
% 1.68/1.76 % (21220)Instruction limit reached!
% 1.68/1.76 % (21220)------------------------------
% 1.68/1.76 % (21220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.76 % (21220)Termination reason: Unknown
% 1.68/1.76 % (21220)Termination phase: Saturation
% 1.68/1.76
% 1.68/1.76 % (21220)Memory used [KB]: 5500
% 1.68/1.76 % (21220)Time elapsed: 0.004 s
% 1.68/1.76 % (21220)Instructions burned: 12 (million)
% 1.68/1.76 % (21220)------------------------------
% 1.68/1.76 % (21220)------------------------------
% 1.68/1.76 % (21221)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/41Mi)
% 1.68/1.76 % (21219)Instruction limit reached!
% 1.68/1.76 % (21219)------------------------------
% 1.68/1.76 % (21219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.76 % (21219)Termination reason: Unknown
% 1.68/1.76 % (21219)Termination phase: Saturation
% 1.68/1.76
% 1.68/1.76 % (21219)Memory used [KB]: 5756
% 1.68/1.76 % (21219)Time elapsed: 0.026 s
% 1.68/1.76 % (21219)Instructions burned: 86 (million)
% 1.68/1.76 % (21219)------------------------------
% 1.68/1.76 % (21219)------------------------------
% 1.68/1.77 % (21222)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/6Mi)
% 1.68/1.77 % (21222)Instruction limit reached!
% 1.68/1.77 % (21222)------------------------------
% 1.68/1.77 % (21222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.77 % (21222)Termination reason: Unknown
% 1.68/1.77 % (21222)Termination phase: Preprocessing 3
% 1.68/1.77
% 1.68/1.77 % (21222)Memory used [KB]: 1151
% 1.68/1.77 % (21222)Time elapsed: 0.003 s
% 1.68/1.77 % (21222)Instructions burned: 6 (million)
% 1.68/1.77 % (21222)------------------------------
% 1.68/1.77 % (21222)------------------------------
% 1.68/1.77 % (21221)Instruction limit reached!
% 1.68/1.77 % (21221)------------------------------
% 1.68/1.77 % (21221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.77 % (21221)Termination reason: Unknown
% 1.68/1.77 % (21221)Termination phase: Saturation
% 1.68/1.77
% 1.68/1.77 % (21221)Memory used [KB]: 5628
% 1.68/1.77 % (21221)Time elapsed: 0.012 s
% 1.68/1.77 % (21221)Instructions burned: 42 (million)
% 1.68/1.77 % (21221)------------------------------
% 1.68/1.77 % (21221)------------------------------
% 1.68/1.77 % (21223)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/150Mi)
% 1.68/1.77 % (21205)Instruction limit reached!
% 1.68/1.77 % (21205)------------------------------
% 1.68/1.77 % (21205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.77 % (21205)Termination reason: Unknown
% 1.68/1.77 % (21205)Termination phase: Saturation
% 1.68/1.77
% 1.68/1.77 % (21205)Memory used [KB]: 6908
% 1.68/1.77 % (21205)Time elapsed: 0.156 s
% 1.68/1.77 % (21205)Instructions burned: 508 (million)
% 1.68/1.77 % (21205)------------------------------
% 1.68/1.77 % (21205)------------------------------
% 1.68/1.78 % (21224)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/343Mi)
% 1.68/1.78 % (21225)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/109Mi)
% 1.68/1.78 % (21226)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_20901 for (2995ds/253Mi)
% 1.68/1.81 % (21225)Instruction limit reached!
% 1.68/1.81 % (21225)------------------------------
% 1.68/1.81 % (21225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.81 % (21225)Termination reason: Unknown
% 1.68/1.81 % (21225)Termination phase: Saturation
% 1.68/1.81
% 1.68/1.81 % (21225)Memory used [KB]: 6140
% 1.68/1.81 % (21225)Time elapsed: 0.032 s
% 1.68/1.81 % (21225)Instructions burned: 110 (million)
% 1.68/1.81 % (21225)------------------------------
% 1.68/1.81 % (21225)------------------------------
% 1.68/1.81 % (21213)Instruction limit reached!
% 1.68/1.81 % (21213)------------------------------
% 1.68/1.81 % (21213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.81 % (21213)Termination reason: Unknown
% 1.68/1.81 % (21213)Termination phase: Saturation
% 1.68/1.81
% 1.68/1.81 % (21213)Memory used [KB]: 3454
% 1.68/1.81 % (21213)Time elapsed: 0.121 s
% 1.68/1.81 % (21213)Instructions burned: 434 (million)
% 1.68/1.81 % (21213)------------------------------
% 1.68/1.81 % (21213)------------------------------
% 1.68/1.82 % (21223)Instruction limit reached!
% 1.68/1.82 % (21223)------------------------------
% 1.68/1.82 % (21223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.82 % (21223)Termination reason: Unknown
% 1.68/1.82 % (21223)Termination phase: Saturation
% 1.68/1.82
% 1.68/1.82 % (21223)Memory used [KB]: 6268
% 1.68/1.82 % (21223)Time elapsed: 0.045 s
% 1.68/1.82 % (21223)Instructions burned: 150 (million)
% 1.68/1.82 % (21223)------------------------------
% 1.68/1.82 % (21223)------------------------------
% 1.68/1.82 % (21227)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_20901 for (2994ds/140Mi)
% 1.68/1.82 % (21228)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_20901 for (2994ds/614Mi)
% 1.68/1.83 % (21229)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_20901 for (2994ds/202Mi)
% 1.68/1.85 % (21217)Instruction limit reached!
% 1.68/1.85 % (21217)------------------------------
% 1.68/1.85 % (21217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.85 % (21217)Termination reason: Unknown
% 1.68/1.85 % (21217)Termination phase: Saturation
% 1.68/1.85
% 1.68/1.85 % (21217)Memory used [KB]: 6012
% 1.68/1.85 % (21217)Time elapsed: 0.131 s
% 1.68/1.85 % (21217)Instructions burned: 454 (million)
% 1.68/1.85 % (21217)------------------------------
% 1.68/1.85 % (21217)------------------------------
% 1.68/1.86 % (21226)Instruction limit reached!
% 1.68/1.86 % (21226)------------------------------
% 1.68/1.86 % (21226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.86 % (21226)Termination reason: Unknown
% 1.68/1.86 % (21226)Termination phase: Saturation
% 1.68/1.86
% 1.68/1.86 % (21226)Memory used [KB]: 6780
% 1.68/1.86 % (21226)Time elapsed: 0.076 s
% 1.68/1.86 % (21226)Instructions burned: 255 (million)
% 1.68/1.86 % (21226)------------------------------
% 1.68/1.86 % (21226)------------------------------
% 1.68/1.86 % (21230)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_20901 for (2994ds/339Mi)
% 1.68/1.86 % (21227)Instruction limit reached!
% 1.68/1.86 % (21227)------------------------------
% 1.68/1.86 % (21227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.86 % (21227)Termination reason: Unknown
% 1.68/1.86 % (21227)Termination phase: Saturation
% 1.68/1.86
% 1.68/1.86 % (21227)Memory used [KB]: 6268
% 1.68/1.86 % (21227)Time elapsed: 0.044 s
% 1.68/1.86 % (21227)Instructions burned: 140 (million)
% 1.68/1.86 % (21227)------------------------------
% 1.68/1.86 % (21227)------------------------------
% 1.68/1.87 % (21231)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_20901 for (2994ds/283Mi)
% 1.68/1.87 % (21232)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_20901 for (2994ds/134Mi)
% 1.68/1.88 % (21224)Instruction limit reached!
% 1.68/1.88 % (21224)------------------------------
% 1.68/1.88 % (21224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.88 % (21224)Termination reason: Unknown
% 1.68/1.88 % (21224)Termination phase: Saturation
% 1.68/1.88
% 1.68/1.88 % (21224)Memory used [KB]: 6652
% 1.68/1.88 % (21224)Time elapsed: 0.104 s
% 1.68/1.88 % (21224)Instructions burned: 344 (million)
% 1.68/1.88 % (21224)------------------------------
% 1.68/1.88 % (21224)------------------------------
% 1.68/1.88 % (21229)Instruction limit reached!
% 1.68/1.88 % (21229)------------------------------
% 1.68/1.88 % (21229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.88 % (21229)Termination reason: Unknown
% 1.68/1.88 % (21229)Termination phase: Saturation
% 1.68/1.88
% 1.68/1.88 % (21229)Memory used [KB]: 6140
% 1.68/1.88 % (21229)Time elapsed: 0.058 s
% 1.68/1.88 % (21229)Instructions burned: 203 (million)
% 1.68/1.88 % (21229)------------------------------
% 1.68/1.88 % (21229)------------------------------
% 1.68/1.89 % (21233)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_20901 for (2994ds/298Mi)
% 1.68/1.89 % (21234)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_20901 for (2994ds/192Mi)
% 1.68/1.91 % (21232)Instruction limit reached!
% 1.68/1.91 % (21232)------------------------------
% 1.68/1.91 % (21232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.91 % (21232)Termination reason: Unknown
% 1.68/1.91 % (21232)Termination phase: Saturation
% 1.68/1.91
% 1.68/1.91 % (21232)Memory used [KB]: 6268
% 1.68/1.91 % (21232)Time elapsed: 0.040 s
% 1.68/1.91 % (21232)Instructions burned: 134 (million)
% 1.68/1.91 % (21232)------------------------------
% 1.68/1.91 % (21232)------------------------------
% 1.68/1.92 % (21235)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_20901 for (2993ds/258Mi)
% 1.68/1.94 % (21231)Instruction limit reached!
% 1.68/1.94 % (21231)------------------------------
% 1.68/1.94 % (21231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.94 % (21231)Termination reason: Unknown
% 1.68/1.94 % (21231)Termination phase: Saturation
% 1.68/1.94
% 1.68/1.94 % (21231)Memory used [KB]: 7931
% 1.68/1.94 % (21231)Time elapsed: 0.074 s
% 1.68/1.94 % (21231)Instructions burned: 283 (million)
% 1.68/1.94 % (21231)------------------------------
% 1.68/1.94 % (21231)------------------------------
% 1.68/1.94 % (21234)Instruction limit reached!
% 1.68/1.94 % (21234)------------------------------
% 1.68/1.94 % (21234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.94 % (21234)Termination reason: Unknown
% 1.68/1.94 % (21234)Termination phase: Saturation
% 1.68/1.94
% 1.68/1.94 % (21234)Memory used [KB]: 6140
% 1.68/1.94 % (21234)Time elapsed: 0.054 s
% 1.68/1.94 % (21234)Instructions burned: 193 (million)
% 1.68/1.94 % (21234)------------------------------
% 1.68/1.94 % (21234)------------------------------
% 1.68/1.95 % (21236)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_20901 for (2993ds/90Mi)
% 1.68/1.95 % (21237)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_20901 for (2993ds/231Mi)
% 1.68/1.96 % (21230)Instruction limit reached!
% 1.68/1.96 % (21230)------------------------------
% 1.68/1.96 % (21230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.96 % (21230)Termination reason: Unknown
% 1.68/1.96 % (21230)Termination phase: Saturation
% 1.68/1.96
% 1.68/1.96 % (21230)Memory used [KB]: 6396
% 1.68/1.96 % (21230)Time elapsed: 0.103 s
% 1.68/1.96 % (21230)Instructions burned: 340 (million)
% 1.68/1.96 % (21230)------------------------------
% 1.68/1.96 % (21230)------------------------------
% 1.68/1.97 % (21238)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_20901 for (2993ds/458Mi)
% 1.68/1.98 % (21233)Instruction limit reached!
% 1.68/1.98 % (21233)------------------------------
% 1.68/1.98 % (21233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.98 % (21233)Termination reason: Unknown
% 1.68/1.98 % (21233)Termination phase: Saturation
% 1.68/1.98
% 1.68/1.98 % (21233)Memory used [KB]: 6268
% 1.68/1.98 % (21233)Time elapsed: 0.087 s
% 1.68/1.98 % (21233)Instructions burned: 298 (million)
% 1.68/1.98 % (21233)------------------------------
% 1.68/1.98 % (21233)------------------------------
% 1.68/1.98 % (21236)Instruction limit reached!
% 1.68/1.98 % (21236)------------------------------
% 1.68/1.98 % (21236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.98 % (21236)Termination reason: Unknown
% 1.68/1.98 % (21236)Termination phase: Saturation
% 1.68/1.98
% 1.68/1.98 % (21236)Memory used [KB]: 6012
% 1.68/1.98 % (21236)Time elapsed: 0.051 s
% 1.68/1.98 % (21236)Instructions burned: 92 (million)
% 1.68/1.98 % (21236)------------------------------
% 1.68/1.98 % (21236)------------------------------
% 1.68/1.98 % (21235)Instruction limit reached!
% 1.68/1.98 % (21235)------------------------------
% 1.68/1.98 % (21235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.98 % (21235)Termination reason: Unknown
% 1.68/1.98 % (21235)Termination phase: Property scanning
% 1.68/1.98
% 1.68/1.98 % (21235)Memory used [KB]: 2046
% 1.68/1.98 % (21235)Time elapsed: 0.061 s
% 1.68/1.98 % (21235)Instructions burned: 260 (million)
% 1.68/1.98 % (21235)------------------------------
% 1.68/1.98 % (21235)------------------------------
% 1.68/1.99 % (21239)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/31Mi)
% 1.68/1.99 % (21240)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/297Mi)
% 1.68/1.99 % (21241)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/987Mi)
% 1.68/2.00 % (21239)Instruction limit reached!
% 1.68/2.00 % (21239)------------------------------
% 1.68/2.00 % (21239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/2.00 % (21239)Termination reason: Unknown
% 1.68/2.00 % (21239)Termination phase: Saturation
% 1.68/2.00
% 1.68/2.00 % (21239)Memory used [KB]: 5756
% 1.68/2.00 % (21239)Time elapsed: 0.011 s
% 1.68/2.00 % (21239)Instructions burned: 33 (million)
% 1.68/2.00 % (21239)------------------------------
% 1.68/2.00 % (21239)------------------------------
% 1.68/2.00 % (21209)Instruction limit reached!
% 1.68/2.00 % (21209)------------------------------
% 1.68/2.00 % (21209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/2.00 % (21209)Termination reason: Unknown
% 1.68/2.00 % (21209)Termination phase: Saturation
% 1.68/2.00
% 1.68/2.00 % (21209)Memory used [KB]: 8059
% 1.68/2.00 % (21209)Time elapsed: 0.332 s
% 1.68/2.00 % (21209)Instructions burned: 1087 (million)
% 1.68/2.00 % (21209)------------------------------
% 1.68/2.00 % (21209)------------------------------
% 1.68/2.01 % (21242)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/182Mi)
% 1.68/2.01 % (21228)Instruction limit reached!
% 1.68/2.01 % (21228)------------------------------
% 1.68/2.01 % (21228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/2.01 % (21228)Termination reason: Unknown
% 1.68/2.01 % (21228)Termination phase: Saturation
% 1.68/2.01
% 1.68/2.01 % (21228)Memory used [KB]: 7291
% 1.68/2.01 % (21228)Time elapsed: 0.185 s
% 1.68/2.01 % (21228)Instructions burned: 614 (million)
% 1.68/2.01 % (21228)------------------------------
% 1.68/2.01 % (21228)------------------------------
% 6.72/2.02 % (21244)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/154Mi)
% 6.72/2.02 % (21237)Instruction limit reached!
% 6.72/2.02 % (21237)------------------------------
% 6.72/2.02 % (21237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.02 % (21237)Termination reason: Unknown
% 6.72/2.02 % (21237)Termination phase: Saturation
% 6.72/2.02
% 6.72/2.02 % (21237)Memory used [KB]: 6140
% 6.72/2.02 % (21237)Time elapsed: 0.064 s
% 6.72/2.02 % (21237)Instructions burned: 233 (million)
% 6.72/2.02 % (21237)------------------------------
% 6.72/2.02 % (21237)------------------------------
% 6.72/2.02 % (21243)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/182Mi)
% 6.72/2.03 % (21245)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/79Mi)
% 6.72/2.05 % (21242)Instruction limit reached!
% 6.72/2.05 % (21242)------------------------------
% 6.72/2.05 % (21242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.05 % (21242)Termination reason: Unknown
% 6.72/2.05 % (21242)Termination phase: Property scanning
% 6.72/2.05
% 6.72/2.05 % (21242)Memory used [KB]: 2046
% 6.72/2.05 % (21242)Time elapsed: 0.043 s
% 6.72/2.05 % (21242)Instructions burned: 184 (million)
% 6.72/2.05 % (21242)------------------------------
% 6.72/2.05 % (21242)------------------------------
% 6.72/2.05 % (21245)Instruction limit reached!
% 6.72/2.05 % (21245)------------------------------
% 6.72/2.05 % (21245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.05 % (21245)Termination reason: Unknown
% 6.72/2.05 % (21245)Termination phase: Saturation
% 6.72/2.05
% 6.72/2.05 % (21245)Memory used [KB]: 6140
% 6.72/2.05 % (21245)Time elapsed: 0.026 s
% 6.72/2.05 % (21245)Instructions burned: 80 (million)
% 6.72/2.05 % (21245)------------------------------
% 6.72/2.05 % (21245)------------------------------
% 6.72/2.06 % (21246)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/216Mi)
% 6.72/2.06 % (21244)Instruction limit reached!
% 6.72/2.06 % (21244)------------------------------
% 6.72/2.06 % (21244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.06 % (21244)Termination reason: Unknown
% 6.72/2.06 % (21244)Termination phase: Saturation
% 6.72/2.06
% 6.72/2.06 % (21244)Memory used [KB]: 6140
% 6.72/2.06 % (21244)Time elapsed: 0.046 s
% 6.72/2.06 % (21244)Instructions burned: 157 (million)
% 6.72/2.06 % (21244)------------------------------
% 6.72/2.06 % (21244)------------------------------
% 6.72/2.06 % (21247)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/114Mi)
% 6.72/2.06 % (21240)Instruction limit reached!
% 6.72/2.06 % (21240)------------------------------
% 6.72/2.06 % (21240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.06 % (21240)Termination reason: Unknown
% 6.72/2.06 % (21240)Termination phase: Saturation
% 6.72/2.06
% 6.72/2.06 % (21240)Memory used [KB]: 5628
% 6.72/2.06 % (21240)Time elapsed: 0.075 s
% 6.72/2.06 % (21240)Instructions burned: 297 (million)
% 6.72/2.06 % (21240)------------------------------
% 6.72/2.06 % (21240)------------------------------
% 6.72/2.07 % (21248)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/922Mi)
% 6.72/2.07 % (21249)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_20901 for (2992ds/182Mi)
% 6.72/2.10 % (21247)Instruction limit reached!
% 6.72/2.10 % (21247)------------------------------
% 6.72/2.10 % (21247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.10 % (21247)Termination reason: Unknown
% 6.72/2.10 % (21247)Termination phase: Saturation
% 6.72/2.10
% 6.72/2.10 % (21247)Memory used [KB]: 6140
% 6.72/2.10 % (21247)Time elapsed: 0.036 s
% 6.72/2.10 % (21247)Instructions burned: 115 (million)
% 6.72/2.10 % (21247)------------------------------
% 6.72/2.10 % (21247)------------------------------
% 6.72/2.11 % (21250)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_20901 for (2991ds/164Mi)
% 7.18/2.11 % (21238)Instruction limit reached!
% 7.18/2.11 % (21238)------------------------------
% 7.18/2.11 % (21238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.11 % (21238)Termination reason: Unknown
% 7.18/2.11 % (21238)Termination phase: Saturation
% 7.18/2.11
% 7.18/2.11 % (21238)Memory used [KB]: 7036
% 7.18/2.11 % (21238)Time elapsed: 0.143 s
% 7.18/2.11 % (21238)Instructions burned: 458 (million)
% 7.18/2.11 % (21238)------------------------------
% 7.18/2.11 % (21238)------------------------------
% 7.18/2.12 % (21246)Instruction limit reached!
% 7.18/2.12 % (21246)------------------------------
% 7.18/2.12 % (21246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.12 % (21246)Termination reason: Unknown
% 7.18/2.12 % (21246)Termination phase: Saturation
% 7.18/2.12
% 7.18/2.12 % (21246)Memory used [KB]: 5756
% 7.18/2.12 % (21246)Time elapsed: 0.064 s
% 7.18/2.12 % (21246)Instructions burned: 216 (million)
% 7.18/2.12 % (21246)------------------------------
% 7.18/2.12 % (21246)------------------------------
% 7.18/2.12 % (21251)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_20901 for (2991ds/50Mi)
% 7.18/2.12 % (21249)Instruction limit reached!
% 7.18/2.12 % (21249)------------------------------
% 7.18/2.12 % (21249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.12 % (21249)Termination reason: Unknown
% 7.18/2.12 % (21249)Termination phase: Saturation
% 7.18/2.12
% 7.18/2.12 % (21249)Memory used [KB]: 5756
% 7.18/2.12 % (21249)Time elapsed: 0.054 s
% 7.18/2.12 % (21249)Instructions burned: 183 (million)
% 7.18/2.12 % (21249)------------------------------
% 7.18/2.12 % (21249)------------------------------
% 7.18/2.13 % (21243)Instruction limit reached!
% 7.18/2.13 % (21243)------------------------------
% 7.18/2.13 % (21243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.13 % (21243)Termination reason: Unknown
% 7.18/2.13 % (21243)Termination phase: Saturation
% 7.18/2.13
% 7.18/2.13 % (21243)Memory used [KB]: 6268
% 7.18/2.13 % (21243)Time elapsed: 0.108 s
% 7.18/2.13 % (21243)Instructions burned: 182 (million)
% 7.18/2.13 % (21243)------------------------------
% 7.18/2.13 % (21243)------------------------------
% 7.18/2.13 % (21252)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_20901 for (2991ds/368Mi)
% 7.18/2.13 % (21253)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_20901 for (2991ds/1021Mi)
% 7.18/2.14 % (21251)Instruction limit reached!
% 7.18/2.14 % (21251)------------------------------
% 7.18/2.14 % (21251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.14 % (21251)Termination reason: Unknown
% 7.18/2.14 % (21251)Termination phase: Saturation
% 7.18/2.14
% 7.18/2.14 % (21251)Memory used [KB]: 10106
% 7.18/2.14 % (21251)Time elapsed: 0.016 s
% 7.18/2.14 % (21251)Instructions burned: 51 (million)
% 7.18/2.14 % (21251)------------------------------
% 7.18/2.14 % (21251)------------------------------
% 7.18/2.14 % (21254)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_20901 for (2991ds/267Mi)
% 7.18/2.15 % (21255)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_20901 for (2991ds/204Mi)
% 7.18/2.15 % (21250)Instruction limit reached!
% 7.18/2.15 % (21250)------------------------------
% 7.18/2.15 % (21250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.15 % (21250)Termination reason: Unknown
% 7.18/2.15 % (21250)Termination phase: Saturation
% 7.18/2.15
% 7.18/2.15 % (21250)Memory used [KB]: 1407
% 7.18/2.15 % (21250)Time elapsed: 0.050 s
% 7.18/2.15 % (21250)Instructions burned: 166 (million)
% 7.18/2.15 % (21250)------------------------------
% 7.18/2.15 % (21250)------------------------------
% 7.18/2.16 % (21256)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_20901 for (2991ds/26Mi)
% 7.18/2.17 % (21256)Instruction limit reached!
% 7.18/2.17 % (21256)------------------------------
% 7.18/2.17 % (21256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.17 % (21256)Termination reason: Unknown
% 7.18/2.17 % (21256)Termination phase: Saturation
% 7.18/2.17
% 7.18/2.17 % (21256)Memory used [KB]: 5628
% 7.18/2.17 % (21256)Time elapsed: 0.008 s
% 7.18/2.17 % (21256)Instructions burned: 28 (million)
% 7.18/2.17 % (21256)------------------------------
% 7.18/2.17 % (21256)------------------------------
% 7.18/2.18 % (21257)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_20901 for (2991ds/53Mi)
% 7.18/2.19 % (21257)Instruction limit reached!
% 7.18/2.19 % (21257)------------------------------
% 7.18/2.19 % (21257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.19 % (21257)Termination reason: Unknown
% 7.18/2.19 % (21257)Termination phase: Saturation
% 7.18/2.19
% 7.18/2.19 % (21257)Memory used [KB]: 5628
% 7.18/2.19 % (21257)Time elapsed: 0.015 s
% 7.18/2.19 % (21257)Instructions burned: 56 (million)
% 7.18/2.19 % (21257)------------------------------
% 7.18/2.19 % (21257)------------------------------
% 7.65/2.20 % (21258)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_20901 for (2990ds/4436Mi)
% 7.65/2.21 % (21255)Instruction limit reached!
% 7.65/2.21 % (21255)------------------------------
% 7.65/2.21 % (21255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.21 % (21255)Termination reason: Unknown
% 7.65/2.21 % (21255)Termination phase: Saturation
% 7.65/2.21
% 7.65/2.21 % (21255)Memory used [KB]: 6268
% 7.65/2.21 % (21255)Time elapsed: 0.066 s
% 7.65/2.21 % (21255)Instructions burned: 206 (million)
% 7.65/2.21 % (21255)------------------------------
% 7.65/2.21 % (21255)------------------------------
% 7.65/2.22 % (21259)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_20901 for (2990ds/1539Mi)
% 7.65/2.23 % (21254)Instruction limit reached!
% 7.65/2.23 % (21254)------------------------------
% 7.65/2.23 % (21254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.23 % (21254)Termination reason: Unknown
% 7.65/2.23 % (21254)Termination phase: Saturation
% 7.65/2.23
% 7.65/2.23 % (21254)Memory used [KB]: 6396
% 7.65/2.23 % (21254)Time elapsed: 0.086 s
% 7.65/2.23 % (21254)Instructions burned: 267 (million)
% 7.65/2.23 % (21254)------------------------------
% 7.65/2.23 % (21254)------------------------------
% 7.65/2.24 % (21252)Instruction limit reached!
% 7.65/2.24 % (21252)------------------------------
% 7.65/2.24 % (21252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.24 % (21252)Termination reason: Unknown
% 7.65/2.24 % (21252)Termination phase: Saturation
% 7.65/2.24
% 7.65/2.24 % (21252)Memory used [KB]: 7036
% 7.65/2.24 % (21252)Time elapsed: 0.107 s
% 7.65/2.24 % (21252)Instructions burned: 368 (million)
% 7.65/2.24 % (21252)------------------------------
% 7.65/2.24 % (21252)------------------------------
% 7.65/2.24 % (21260)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_20901 for (2990ds/408Mi)
% 7.65/2.24 % (21261)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_20901 for (2990ds/5205Mi)
% 7.65/2.29 % (21241)Instruction limit reached!
% 7.65/2.29 % (21241)------------------------------
% 7.65/2.29 % (21241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.29 % (21241)Termination reason: Unknown
% 7.65/2.29 % (21241)Termination phase: Saturation
% 7.65/2.29
% 7.65/2.29 % (21241)Memory used [KB]: 7675
% 7.65/2.29 % (21241)Time elapsed: 0.303 s
% 7.65/2.29 % (21241)Instructions burned: 987 (million)
% 7.65/2.29 % (21241)------------------------------
% 7.65/2.29 % (21241)------------------------------
% 8.06/2.30 % (21262)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_20901 for (2989ds/1913Mi)
% 8.06/2.32 % (21261)First to succeed.
% 8.06/2.33 % (21261)Refutation found. Thanks to Tanya!
% 8.06/2.33 % SZS status Theorem for DTF2THF_20901
% 8.06/2.33 % SZS output start Proof for DTF2THF_20901
% 8.06/2.33 thf(type_def_5, type, a: $tType).
% 8.06/2.33 thf(func_def_0, type, a: $tType).
% 8.06/2.33 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 8.06/2.33 thf(func_def_21, type, sK2: a).
% 8.06/2.33 thf(func_def_22, type, sK3: a > a > $o).
% 8.06/2.33 thf(func_def_23, type, sK4: a).
% 8.06/2.33 thf(func_def_24, type, sK5: a > a > $o).
% 8.06/2.33 thf(func_def_25, type, sK6: a > a > $o).
% 8.06/2.33 thf(func_def_26, type, sK7: a).
% 8.06/2.33 thf(func_def_27, type, sK8: a).
% 8.06/2.33 thf(func_def_28, type, sK9: a).
% 8.06/2.33 thf(func_def_29, type, sK10: a).
% 8.06/2.33 thf(func_def_30, type, sK11: a).
% 8.06/2.33 thf(func_def_31, type, sK12: a > a > $o).
% 8.06/2.33 thf(func_def_32, type, sK13: a).
% 8.06/2.33 thf(func_def_33, type, sK14: a).
% 8.06/2.33 thf(func_def_34, type, sK15: a).
% 8.06/2.33 thf(func_def_35, type, sK16: a).
% 8.06/2.33 thf(func_def_36, type, sK17: a).
% 8.06/2.33 thf(func_def_37, type, sK18: a > a > $o).
% 8.06/2.33 thf(func_def_38, type, sK19: a).
% 8.06/2.33 thf(func_def_39, type, sK20: a).
% 8.06/2.33 thf(func_def_40, type, sK21: a).
% 8.06/2.33 thf(func_def_41, type, sK22: a).
% 8.06/2.33 thf(func_def_42, type, sK23: a).
% 8.06/2.33 thf(func_def_43, type, sK24: a).
% 8.06/2.33 thf(func_def_44, type, sK25: a).
% 8.06/2.33 thf(f800,plain,(
% 8.06/2.33 $false),
% 8.06/2.33 inference(avatar_sat_refutation,[status(thm)],[f34,f181,f191,f234,f288,f375,f492,f526,f577,f583,f591,f664,f799])).
% 8.06/2.33 thf(f799,plain,(
% 8.06/2.33 ~spl0_4 | ~spl0_5 | ~spl0_8),
% 8.06/2.33 inference(avatar_contradiction_clause,[status(thm)],[f798])).
% 8.06/2.33 thf(f798,plain,(
% 8.06/2.33 $false | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 8.06/2.33 inference(trivial_inequality_removal,[status(thm)],[f797])).
% 8.06/2.33 thf(f797,plain,(
% 8.06/2.33 ($false = $true) | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f796])).
% 8.06/2.33 thf(f796,plain,(
% 8.06/2.33 ((~ $true) = $true) | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 8.06/2.33 inference(forward_demodulation,[status(thm)],[f791,f739])).
% 8.06/2.33 thf(f739,plain,(
% 8.06/2.33 ((sK12 @ sK23 @ sK24) = $true) | ~spl0_8),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f730])).
% 8.06/2.33 thf(f730,plain,(
% 8.06/2.33 (((sK12 @ sK25 @ sK23) & (sK12 @ sK23 @ sK24)) = $true) | ~spl0_8),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f728])).
% 8.06/2.33 thf(f728,plain,(
% 8.06/2.33 ($false = (((sK12 @ sK25 @ sK23) & (sK12 @ sK23 @ sK24)) => (sK12 @ sK25 @ sK24))) | ~spl0_8),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f727])).
% 8.06/2.33 thf(f727,plain,(
% 8.06/2.33 (((^[Y0 : a]: (((sK12 @ Y0 @ sK23) & (sK12 @ sK23 @ sK24)) => (sK12 @ Y0 @ sK24))) @ sK25) = $false) | ~spl0_8),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f726])).
% 8.06/2.33 thf(f726,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (((sK12 @ Y0 @ sK23) & (sK12 @ sK23 @ sK24)) => (sK12 @ Y0 @ sK24))))) | ~spl0_8),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f725])).
% 8.06/2.33 thf(f725,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK12 @ Y1 @ sK23) & (sK12 @ sK23 @ Y0)) => (sK12 @ Y1 @ Y0))))) @ sK24)) | ~spl0_8),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f709])).
% 8.06/2.33 thf(f709,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK12 @ Y1 @ sK23) & (sK12 @ sK23 @ Y0)) => (sK12 @ Y1 @ Y0)))))) = $false) | ~spl0_8),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f707])).
% 8.06/2.33 thf(f707,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y2 @ Y0) & (sK12 @ Y0 @ Y1)) => (sK12 @ Y2 @ Y1))))))) @ sK23) = $false) | ~spl0_8),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f287])).
% 8.06/2.33 thf(f287,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y2 @ Y0) & (sK12 @ Y0 @ Y1)) => (sK12 @ Y2 @ Y1))))))))) | ~spl0_8),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f286])).
% 8.06/2.33 thf(f286,definition,(
% 8.06/2.33 spl0_8 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y2 @ Y0) & (sK12 @ Y0 @ Y1)) => (sK12 @ Y2 @ Y1)))))))))),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 8.06/2.33 thf(f791,plain,(
% 8.06/2.33 ((~ (sK12 @ sK23 @ sK24)) = $true) | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f788])).
% 8.06/2.33 thf(f788,plain,(
% 8.06/2.33 (((sK12 @ sK23 @ sK24) => $false) = $true) | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 8.06/2.33 inference(superposition,[status(thm)],[f772,f729])).
% 8.06/2.33 thf(f729,plain,(
% 8.06/2.33 ((sK12 @ sK25 @ sK24) = $false) | ~spl0_8),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f728])).
% 8.06/2.33 thf(f772,plain,(
% 8.06/2.33 ( ! [X0 : a] : ((((sK12 @ sK23 @ X0) => (sK12 @ sK25 @ X0)) = $true)) ) | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f764])).
% 8.06/2.33 thf(f764,plain,(
% 8.06/2.33 ( ! [X0 : a] : (((($true & (sK12 @ sK23 @ X0)) => (sK12 @ sK25 @ X0)) = $true)) ) | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 8.06/2.33 inference(superposition,[status(thm)],[f748,f742])).
% 8.06/2.33 thf(f742,plain,(
% 8.06/2.33 ((sK12 @ sK25 @ sK23) = $true) | ~spl0_8),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f741])).
% 8.06/2.33 thf(f741,plain,(
% 8.06/2.33 (((sK12 @ sK25 @ sK23) & $true) = $true) | ~spl0_8),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f730,f739])).
% 8.06/2.33 thf(f748,plain,(
% 8.06/2.33 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK12 @ X1 @ X3) & (sK12 @ X3 @ X2)) => (sK12 @ X1 @ X2)) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f747])).
% 8.06/2.33 thf(f747,plain,(
% 8.06/2.33 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK12 @ X1 @ Y0) & (sK12 @ Y0 @ X2)) => (sK12 @ X1 @ X2))) @ X3) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f744])).
% 8.06/2.33 thf(f744,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK12 @ X1 @ Y0) & (sK12 @ Y0 @ X2)) => (sK12 @ X1 @ X2)))) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f743])).
% 8.06/2.33 thf(f743,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK12 @ X1 @ Y1) & (sK12 @ Y1 @ Y0)) => (sK12 @ X1 @ Y0))))) @ X2) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f738])).
% 8.06/2.33 thf(f738,plain,(
% 8.06/2.33 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK12 @ X1 @ Y1) & (sK12 @ Y1 @ Y0)) => (sK12 @ X1 @ Y0)))))) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f737])).
% 8.06/2.33 thf(f737,plain,(
% 8.06/2.33 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y0 @ Y2) & (sK12 @ Y2 @ Y1)) => (sK12 @ Y0 @ Y1))))))) @ X1) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f626])).
% 8.06/2.33 thf(f626,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y0 @ Y2) & (sK12 @ Y2 @ Y1)) => (sK12 @ Y0 @ Y1)))))))) = $true) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f623])).
% 8.06/2.33 thf(f623,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y0 @ Y2) & (sK12 @ Y2 @ Y1)) => (sK12 @ Y0 @ Y1))))))))) = $true) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f618])).
% 8.06/2.33 thf(f618,plain,(
% 8.06/2.33 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y0 @ Y2) & (sK12 @ Y2 @ Y1)) => (sK12 @ Y0 @ Y1))))))))) => (sK12 @ sK10 @ sK11)) = $false) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f617])).
% 8.06/2.33 thf(f617,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11))) @ sK12)) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f613])).
% 8.06/2.33 thf(f613,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))) = $false) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f612])).
% 8.06/2.33 thf(f612,plain,(
% 8.06/2.33 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11))))) = $false) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f611])).
% 8.06/2.33 thf(f611,plain,(
% 8.06/2.33 ((($true | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK11))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11))))) = $false) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(forward_demodulation,[status(thm)],[f610,f230])).
% 8.06/2.33 thf(f230,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))) = $true) | ~spl0_5),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f229])).
% 8.06/2.33 thf(f229,definition,(
% 8.06/2.33 spl0_5 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))) = $true)),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 8.06/2.33 thf(f610,plain,(
% 8.06/2.33 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK11))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))))) | ~spl0_4),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f609])).
% 8.06/2.33 thf(f609,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK5 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK10 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK5 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))))) @ sK11)) | ~spl0_4),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f600])).
% 8.06/2.33 thf(f600,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK5 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK10 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK5 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))))))) | ~spl0_4),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f599])).
% 8.06/2.33 thf(f599,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))))) @ sK10) = $false) | ~spl0_4),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f190])).
% 8.06/2.33 thf(f190,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))))))) = $false) | ~spl0_4),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f189])).
% 8.06/2.33 thf(f189,definition,(
% 8.06/2.33 spl0_4 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))))))) = $false)),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 8.06/2.33 thf(f664,plain,(
% 8.06/2.33 ~spl0_4 | ~spl0_5 | ~spl0_7),
% 8.06/2.33 inference(avatar_contradiction_clause,[status(thm)],[f663])).
% 8.06/2.33 thf(f663,plain,(
% 8.06/2.33 $false | (~spl0_4 | ~spl0_5 | ~spl0_7)),
% 8.06/2.33 inference(trivial_inequality_removal,[status(thm)],[f662])).
% 8.06/2.33 thf(f662,plain,(
% 8.06/2.33 ($false = $true) | (~spl0_4 | ~spl0_5 | ~spl0_7)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f661])).
% 8.06/2.33 thf(f661,plain,(
% 8.06/2.33 ((~ $true) = $true) | (~spl0_4 | ~spl0_5 | ~spl0_7)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f660])).
% 8.06/2.33 thf(f660,plain,(
% 8.06/2.33 ((~ ($true | (sK3 @ sK22 @ sK21))) = $true) | (~spl0_4 | ~spl0_5 | ~spl0_7)),
% 8.06/2.33 inference(forward_demodulation,[status(thm)],[f659,f639])).
% 8.06/2.33 thf(f639,plain,(
% 8.06/2.33 ((sK5 @ sK22 @ sK21) = $true) | ~spl0_7),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f635])).
% 8.06/2.33 thf(f635,plain,(
% 8.06/2.33 ($false = ((sK5 @ sK22 @ sK21) => (sK12 @ sK22 @ sK21))) | ~spl0_7),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f634])).
% 8.06/2.33 thf(f634,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a]: ((sK5 @ Y0 @ sK21) => (sK12 @ Y0 @ sK21))) @ sK22)) | ~spl0_7),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f631])).
% 8.06/2.33 thf(f631,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: ((sK5 @ Y0 @ sK21) => (sK12 @ Y0 @ sK21)))) = $false) | ~spl0_7),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f630])).
% 8.06/2.33 thf(f630,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0))))) @ sK21)) | ~spl0_7),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f284])).
% 8.06/2.33 thf(f284,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0))))))) | ~spl0_7),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f283])).
% 8.06/2.33 thf(f283,definition,(
% 8.06/2.33 spl0_7 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0)))))))),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 8.06/2.33 thf(f659,plain,(
% 8.06/2.33 ((~ ((sK5 @ sK22 @ sK21) | (sK3 @ sK22 @ sK21))) = $true) | (~spl0_4 | ~spl0_5 | ~spl0_7)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f658])).
% 8.06/2.33 thf(f658,plain,(
% 8.06/2.33 ((((sK5 @ sK22 @ sK21) | (sK3 @ sK22 @ sK21)) => $false) = $true) | (~spl0_4 | ~spl0_5 | ~spl0_7)),
% 8.06/2.33 inference(superposition,[status(thm)],[f637,f638])).
% 8.06/2.33 thf(f638,plain,(
% 8.06/2.33 ($false = (sK12 @ sK22 @ sK21)) | ~spl0_7),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f635])).
% 8.06/2.33 thf(f637,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : (((((sK5 @ X2 @ X1) | (sK3 @ X2 @ X1)) => (sK12 @ X2 @ X1)) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f636])).
% 8.06/2.33 thf(f636,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK5 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK12 @ Y0 @ X1))) @ X2) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f633])).
% 8.06/2.33 thf(f633,plain,(
% 8.06/2.33 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK5 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK12 @ Y0 @ X1)))))) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f632])).
% 8.06/2.33 thf(f632,plain,(
% 8.06/2.33 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0))))) @ X1) = $true)) ) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f629])).
% 8.06/2.33 thf(f629,plain,(
% 8.06/2.33 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0))))))) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f628])).
% 8.06/2.33 thf(f628,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0)))))) & $true) = $true) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f623,f626])).
% 8.06/2.33 thf(f591,plain,(
% 8.06/2.33 ~spl0_3 | ~spl0_9 | ~spl0_11),
% 8.06/2.33 inference(avatar_contradiction_clause,[status(thm)],[f590])).
% 8.06/2.33 thf(f590,plain,(
% 8.06/2.33 $false | (~spl0_3 | ~spl0_9 | ~spl0_11)),
% 8.06/2.33 inference(trivial_inequality_removal,[status(thm)],[f589])).
% 8.06/2.33 thf(f589,plain,(
% 8.06/2.33 ($false = $true) | (~spl0_3 | ~spl0_9 | ~spl0_11)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f588])).
% 8.06/2.33 thf(f588,plain,(
% 8.06/2.33 ((~ $true) = $true) | (~spl0_3 | ~spl0_9 | ~spl0_11)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f586])).
% 8.06/2.33 thf(f586,plain,(
% 8.06/2.33 ((~ ($true | (sK3 @ sK20 @ sK19))) = $true) | (~spl0_3 | ~spl0_9 | ~spl0_11)),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f565,f573])).
% 8.06/2.33 thf(f573,plain,(
% 8.06/2.33 ((sK5 @ sK20 @ sK19) = $true) | ~spl0_11),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f572])).
% 8.06/2.33 thf(f572,definition,(
% 8.06/2.33 spl0_11 <=> ((sK5 @ sK20 @ sK19) = $true)),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 8.06/2.33 thf(f565,plain,(
% 8.06/2.33 ((~ ((sK5 @ sK20 @ sK19) | (sK3 @ sK20 @ sK19))) = $true) | (~spl0_3 | ~spl0_9)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f561])).
% 8.06/2.33 thf(f561,plain,(
% 8.06/2.33 ((((sK5 @ sK20 @ sK19) | (sK3 @ sK20 @ sK19)) => $false) = $true) | (~spl0_3 | ~spl0_9)),
% 8.06/2.33 inference(superposition,[status(thm)],[f410,f557])).
% 8.06/2.33 thf(f557,plain,(
% 8.06/2.33 ((sK18 @ sK20 @ sK19) = $false) | ~spl0_9),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f556])).
% 8.06/2.33 thf(f556,plain,(
% 8.06/2.33 (($true => (sK18 @ sK20 @ sK19)) = $false) | ~spl0_9),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f550,f555])).
% 8.06/2.33 thf(f555,plain,(
% 8.06/2.33 (((sK3 @ sK20 @ sK19) | (sK5 @ sK20 @ sK19)) = $true) | ~spl0_9),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f550])).
% 8.06/2.33 thf(f550,plain,(
% 8.06/2.33 ((((sK3 @ sK20 @ sK19) | (sK5 @ sK20 @ sK19)) => (sK18 @ sK20 @ sK19)) = $false) | ~spl0_9),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f549])).
% 8.06/2.33 thf(f549,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a]: (((sK3 @ Y0 @ sK19) | (sK5 @ Y0 @ sK19)) => (sK18 @ Y0 @ sK19))) @ sK20)) | ~spl0_9),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f535])).
% 8.06/2.33 thf(f535,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (((sK3 @ Y0 @ sK19) | (sK5 @ Y0 @ sK19)) => (sK18 @ Y0 @ sK19)))) = $false) | ~spl0_9),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f532])).
% 8.06/2.33 thf(f532,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0))))) @ sK19) = $false) | ~spl0_9),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f488])).
% 8.06/2.33 thf(f488,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0)))))) = $false) | ~spl0_9),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f487])).
% 8.06/2.33 thf(f487,definition,(
% 8.06/2.33 spl0_9 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0)))))) = $false)),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 8.06/2.33 thf(f410,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : (((((sK5 @ X1 @ X2) | (sK3 @ X1 @ X2)) => (sK18 @ X1 @ X2)) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f409])).
% 8.06/2.33 thf(f409,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK5 @ X1 @ Y0) | (sK3 @ X1 @ Y0)) => (sK18 @ X1 @ Y0))) @ X2) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f407])).
% 8.06/2.33 thf(f407,plain,(
% 8.06/2.33 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK5 @ X1 @ Y0) | (sK3 @ X1 @ Y0)) => (sK18 @ X1 @ Y0)))) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f406])).
% 8.06/2.33 thf(f406,plain,(
% 8.06/2.33 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_3),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f403])).
% 8.06/2.33 thf(f403,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) = $true) | ~spl0_3),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f402])).
% 8.06/2.33 thf(f402,plain,(
% 8.06/2.33 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1))))))) = $true) | ~spl0_3),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f393,f401])).
% 8.06/2.33 thf(f401,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y0) & (sK18 @ Y2 @ Y1)) => (sK18 @ Y2 @ Y0)))))))) = $true) | ~spl0_3),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f393])).
% 8.06/2.33 thf(f393,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y0) & (sK18 @ Y2 @ Y1)) => (sK18 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1))))))) = $true) | ~spl0_3),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f391])).
% 8.06/2.33 thf(f391,plain,(
% 8.06/2.33 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y0) & (sK18 @ Y2 @ Y1)) => (sK18 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1))))))) => (sK18 @ sK17 @ sK15))) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f390])).
% 8.06/2.33 thf(f390,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK17 @ sK15))) @ sK18)) | ~spl0_3),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f384])).
% 8.06/2.33 thf(f384,plain,(
% 8.06/2.33 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK17 @ sK15))))) | ~spl0_3),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f383])).
% 8.06/2.33 thf(f383,plain,(
% 8.06/2.33 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK17 @ sK16)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK16 @ sK15))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK17 @ sK15))))) = $false) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f382])).
% 8.06/2.33 thf(f382,plain,(
% 8.06/2.33 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK5 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK16)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK5 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ sK16 @ sK15))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK5 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK15)))))) @ sK17) = $false) | ~spl0_3),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f381])).
% 8.06/2.33 thf(f381,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK5 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK16)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK5 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ sK16 @ sK15))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK5 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK15))))))) = $false) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f380])).
% 8.06/2.33 thf(f380,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK5 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK5 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ sK15))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ sK15)))))))) @ sK16)) | ~spl0_3),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f379])).
% 8.06/2.33 thf(f379,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK5 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK5 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ sK15))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ sK15))))))))) = $false) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f378])).
% 8.06/2.33 thf(f378,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0)))))))))) @ sK15) = $false) | ~spl0_3),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f187])).
% 8.06/2.33 thf(f187,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0)))))))))))) | ~spl0_3),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f186])).
% 8.06/2.33 thf(f186,definition,(
% 8.06/2.33 spl0_3 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))))),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 8.06/2.33 thf(f583,plain,(
% 8.06/2.33 ~spl0_3 | ~spl0_9 | ~spl0_12),
% 8.06/2.33 inference(avatar_contradiction_clause,[status(thm)],[f582])).
% 8.06/2.33 thf(f582,plain,(
% 8.06/2.33 $false | (~spl0_3 | ~spl0_9 | ~spl0_12)),
% 8.06/2.33 inference(trivial_inequality_removal,[status(thm)],[f581])).
% 8.06/2.33 thf(f581,plain,(
% 8.06/2.33 ($false = $true) | (~spl0_3 | ~spl0_9 | ~spl0_12)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f580])).
% 8.06/2.33 thf(f580,plain,(
% 8.06/2.33 ((~ $true) = $true) | (~spl0_3 | ~spl0_9 | ~spl0_12)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f578])).
% 8.06/2.33 thf(f578,plain,(
% 8.06/2.33 ((~ ((sK5 @ sK20 @ sK19) | $true)) = $true) | (~spl0_3 | ~spl0_9 | ~spl0_12)),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f565,f576])).
% 8.06/2.33 thf(f576,plain,(
% 8.06/2.33 ((sK3 @ sK20 @ sK19) = $true) | ~spl0_12),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f575])).
% 8.06/2.33 thf(f575,definition,(
% 8.06/2.33 spl0_12 <=> ((sK3 @ sK20 @ sK19) = $true)),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 8.06/2.33 thf(f577,plain,(
% 8.06/2.33 spl0_11 | spl0_12 | ~spl0_9),
% 8.06/2.33 inference(avatar_split_clause,[status(thm)],[f568,f487,f575,f572])).
% 8.06/2.33 thf(f568,plain,(
% 8.06/2.33 ((sK3 @ sK20 @ sK19) = $true) | ((sK5 @ sK20 @ sK19) = $true) | ~spl0_9),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f555])).
% 8.06/2.33 thf(f526,plain,(
% 8.06/2.33 spl0_9 | ~spl0_3 | ~spl0_10),
% 8.06/2.33 inference(avatar_split_clause,[status(thm)],[f525,f490,f186,f487])).
% 8.06/2.33 thf(f490,definition,(
% 8.06/2.33 spl0_10 <=> ((sK18 @ sK16 @ sK15) = $true)),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 8.06/2.33 thf(f525,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0)))))) = $false) | (~spl0_3 | ~spl0_10)),
% 8.06/2.33 inference(not_proxy_clausification,[status(thm)],[f508])).
% 8.06/2.33 thf(f508,plain,(
% 8.06/2.33 ((~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0))))))) = $true) | (~spl0_3 | ~spl0_10)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f507])).
% 8.06/2.33 thf(f507,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0)))))) => $false) = $true) | (~spl0_3 | ~spl0_10)),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f447,f505])).
% 8.06/2.33 thf(f505,plain,(
% 8.06/2.33 ($false = (sK18 @ sK17 @ sK16)) | (~spl0_3 | ~spl0_10)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f495])).
% 8.06/2.33 thf(f495,plain,(
% 8.06/2.33 (($true & (sK18 @ sK17 @ sK16)) = $false) | (~spl0_3 | ~spl0_10)),
% 8.06/2.33 inference(superposition,[status(thm)],[f469,f491])).
% 8.06/2.33 thf(f491,plain,(
% 8.06/2.33 ((sK18 @ sK16 @ sK15) = $true) | ~spl0_10),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f490])).
% 8.06/2.33 thf(f469,plain,(
% 8.06/2.33 ( ! [X0 : a] : ((((sK18 @ X0 @ sK15) & (sK18 @ sK17 @ X0)) = $false)) ) | ~spl0_3),
% 8.06/2.33 inference(not_proxy_clausification,[status(thm)],[f464])).
% 8.06/2.33 thf(f464,plain,(
% 8.06/2.33 ( ! [X0 : a] : (((~ ((sK18 @ X0 @ sK15) & (sK18 @ sK17 @ X0))) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f461])).
% 8.06/2.33 thf(f461,plain,(
% 8.06/2.33 ( ! [X0 : a] : (((((sK18 @ X0 @ sK15) & (sK18 @ sK17 @ X0)) => $false) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(superposition,[status(thm)],[f459,f395])).
% 8.06/2.33 thf(f395,plain,(
% 8.06/2.33 ((sK18 @ sK17 @ sK15) = $false) | ~spl0_3),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f394])).
% 8.06/2.33 thf(f394,plain,(
% 8.06/2.33 (($true => (sK18 @ sK17 @ sK15)) = $false) | ~spl0_3),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f391,f393])).
% 8.06/2.33 thf(f459,plain,(
% 8.06/2.33 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK18 @ X2 @ X1) & (sK18 @ X3 @ X2)) => (sK18 @ X3 @ X1)) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f458])).
% 8.06/2.33 thf(f458,plain,(
% 8.06/2.33 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK18 @ X2 @ X1) & (sK18 @ Y0 @ X2)) => (sK18 @ Y0 @ X1))) @ X3) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f457])).
% 8.06/2.33 thf(f457,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK18 @ X2 @ X1) & (sK18 @ Y0 @ X2)) => (sK18 @ Y0 @ X1)))) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f456])).
% 8.06/2.33 thf(f456,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0 @ X1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y1 @ X1))))) @ X2) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f446])).
% 8.06/2.33 thf(f446,plain,(
% 8.06/2.33 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0 @ X1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y1 @ X1)))))))) ) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f442])).
% 8.06/2.33 thf(f442,plain,(
% 8.06/2.33 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y0) & (sK18 @ Y2 @ Y1)) => (sK18 @ Y2 @ Y0))))))) @ X1) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f401])).
% 8.06/2.33 thf(f447,plain,(
% 8.06/2.33 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0)))))) => (sK18 @ sK17 @ sK16))) | ~spl0_3),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f443])).
% 8.06/2.33 thf(f443,plain,(
% 8.06/2.33 ((($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0))))))) => (sK18 @ sK17 @ sK16)) = $true) | ~spl0_3),
% 8.06/2.33 inference(superposition,[status(thm)],[f405,f401])).
% 8.06/2.33 thf(f405,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y0) & (X1 @ Y2 @ Y1)) => (X1 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK17 @ sK16)) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f404])).
% 8.06/2.33 thf(f404,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK17 @ sK16))) @ X1) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f399])).
% 8.06/2.33 thf(f399,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK17 @ sK16)))) = $true) | ~spl0_3),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f398])).
% 8.06/2.33 thf(f398,plain,(
% 8.06/2.33 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK17 @ sK16)))) & $true) = $true) | ~spl0_3),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f385,f396])).
% 8.06/2.33 thf(f396,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK16 @ sK15)))) = $true) | ~spl0_3),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f385])).
% 8.06/2.33 thf(f385,plain,(
% 8.06/2.33 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK17 @ sK16)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK16 @ sK15))))) = $true) | ~spl0_3),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f383])).
% 8.06/2.33 thf(f492,plain,(
% 8.06/2.33 spl0_9 | spl0_10 | ~spl0_3),
% 8.06/2.33 inference(avatar_split_clause,[status(thm)],[f485,f186,f490,f487])).
% 8.06/2.33 thf(f485,plain,(
% 8.06/2.33 ((sK18 @ sK16 @ sK15) = $true) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0)))))) = $false) | ~spl0_3),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f445])).
% 8.06/2.33 thf(f445,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0)))))) => (sK18 @ sK16 @ sK15)) = $true) | ~spl0_3),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f444])).
% 8.06/2.33 thf(f444,plain,(
% 8.06/2.33 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (sK18 @ Y1 @ Y0)))))) & $true) => (sK18 @ sK16 @ sK15)) = $true) | ~spl0_3),
% 8.06/2.33 inference(superposition,[status(thm)],[f426,f401])).
% 8.06/2.33 thf(f426,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y0) & (X1 @ Y2 @ Y1)) => (X1 @ Y2 @ Y0))))))))) => (X1 @ sK16 @ sK15)) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f425])).
% 8.06/2.33 thf(f425,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK16 @ sK15))) @ X1) = $true)) ) | ~spl0_3),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f396])).
% 8.06/2.33 thf(f375,plain,(
% 8.06/2.33 ~spl0_4 | ~spl0_6),
% 8.06/2.33 inference(avatar_contradiction_clause,[status(thm)],[f374])).
% 8.06/2.33 thf(f374,plain,(
% 8.06/2.33 $false | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(trivial_inequality_removal,[status(thm)],[f373])).
% 8.06/2.33 thf(f373,plain,(
% 8.06/2.33 ($false = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f372])).
% 8.06/2.33 thf(f372,plain,(
% 8.06/2.33 ((~ $true) = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f371])).
% 8.06/2.33 thf(f371,plain,(
% 8.06/2.33 ((~ ((sK5 @ sK14 @ sK13) | $true)) = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(forward_demodulation,[status(thm)],[f365,f358])).
% 8.06/2.33 thf(f358,plain,(
% 8.06/2.33 ((sK3 @ sK14 @ sK13) = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f356])).
% 8.06/2.33 thf(f356,plain,(
% 8.06/2.33 (((sK3 @ sK14 @ sK13) => (sK12 @ sK14 @ sK13)) = $false) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f355])).
% 8.06/2.33 thf(f355,plain,(
% 8.06/2.33 (((^[Y0 : a]: ((sK3 @ Y0 @ sK13) => (sK12 @ Y0 @ sK13))) @ sK14) = $false) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f354])).
% 8.06/2.33 thf(f354,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ sK13) => (sK12 @ Y0 @ sK13)))) = $false) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f350])).
% 8.06/2.33 thf(f350,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0))))) @ sK13) = $false) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f347])).
% 8.06/2.33 thf(f347,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0))))))) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(not_proxy_clausification,[status(thm)],[f315])).
% 8.06/2.33 thf(f315,plain,(
% 8.06/2.33 ((~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0))))))) = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f314])).
% 8.06/2.33 thf(f314,plain,(
% 8.06/2.33 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0)))))) => $false)) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(forward_demodulation,[status(thm)],[f312,f207])).
% 8.06/2.33 thf(f207,plain,(
% 8.06/2.33 ((sK12 @ sK10 @ sK11) = $false) | ~spl0_4),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f206])).
% 8.06/2.33 thf(f206,plain,(
% 8.06/2.33 ($false = ($true => (sK12 @ sK10 @ sK11))) | ~spl0_4),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f203,f205])).
% 8.06/2.33 thf(f205,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y0 @ Y2) & (sK12 @ Y2 @ Y1)) => (sK12 @ Y0 @ Y1))))))))) = $true) | ~spl0_4),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f203])).
% 8.06/2.33 thf(f203,plain,(
% 8.06/2.33 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y0 @ Y2) & (sK12 @ Y2 @ Y1)) => (sK12 @ Y0 @ Y1))))))))) => (sK12 @ sK10 @ sK11)) = $false) | ~spl0_4),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f202])).
% 8.06/2.33 thf(f202,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11))) @ sK12)) | ~spl0_4),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f201])).
% 8.06/2.33 thf(f201,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))) = $false) | ~spl0_4),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f200])).
% 8.06/2.33 thf(f200,plain,(
% 8.06/2.33 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11))))) = $false) | ~spl0_4),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f197,f199])).
% 8.06/2.33 thf(f199,plain,(
% 8.06/2.33 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK11))))) = $true) | ~spl0_4),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f197])).
% 8.06/2.33 thf(f197,plain,(
% 8.06/2.33 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK11))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))))) | ~spl0_4),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f196])).
% 8.06/2.33 thf(f196,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK5 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK10 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK5 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))))) @ sK11)) | ~spl0_4),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f195])).
% 8.06/2.33 thf(f195,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK5 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK10 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK5 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))))))) | ~spl0_4),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f194])).
% 8.06/2.33 thf(f194,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))))) @ sK10) = $false) | ~spl0_4),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f190])).
% 8.06/2.33 thf(f312,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0)))))) => (sK12 @ sK10 @ sK11)) = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f310])).
% 8.06/2.33 thf(f310,plain,(
% 8.06/2.33 ((($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0))))))) => (sK12 @ sK10 @ sK11)) = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(superposition,[status(thm)],[f298,f211])).
% 8.06/2.33 thf(f211,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y0 @ Y2) & (sK12 @ Y2 @ Y1)) => (sK12 @ Y0 @ Y1)))))))) = $true) | ~spl0_4),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f210])).
% 8.06/2.33 thf(f210,plain,(
% 8.06/2.33 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y0 @ Y2) & (sK12 @ Y2 @ Y1)) => (sK12 @ Y0 @ Y1))))))))) = $true) | ~spl0_4),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f205,f209])).
% 8.06/2.33 thf(f209,plain,(
% 8.06/2.33 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0))))))) | ~spl0_4),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f205])).
% 8.06/2.33 thf(f298,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y2) & (X1 @ Y2 @ Y1)) => (X1 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK10 @ sK11)) = $true)) ) | ~spl0_6),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f297])).
% 8.06/2.33 thf(f297,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK11))) @ X1))) ) | ~spl0_6),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f233])).
% 8.06/2.33 thf(f233,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK11)))) = $true) | ~spl0_6),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f232])).
% 8.06/2.33 thf(f232,definition,(
% 8.06/2.33 spl0_6 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK11)))) = $true)),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 8.06/2.33 thf(f365,plain,(
% 8.06/2.33 ((~ ((sK5 @ sK14 @ sK13) | (sK3 @ sK14 @ sK13))) = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f361])).
% 8.06/2.33 thf(f361,plain,(
% 8.06/2.33 ((((sK5 @ sK14 @ sK13) | (sK3 @ sK14 @ sK13)) => $false) = $true) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(superposition,[status(thm)],[f261,f360])).
% 8.06/2.33 thf(f360,plain,(
% 8.06/2.33 ($false = (sK12 @ sK14 @ sK13)) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f359])).
% 8.06/2.33 thf(f359,plain,(
% 8.06/2.33 ($false = ($true => (sK12 @ sK14 @ sK13))) | (~spl0_4 | ~spl0_6)),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f356,f358])).
% 8.06/2.33 thf(f261,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : (((((sK5 @ X2 @ X1) | (sK3 @ X2 @ X1)) => (sK12 @ X2 @ X1)) = $true)) ) | ~spl0_4),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f260])).
% 8.06/2.33 thf(f260,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK5 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK12 @ Y0 @ X1))) @ X2) = $true)) ) | ~spl0_4),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f259])).
% 8.06/2.33 thf(f259,plain,(
% 8.06/2.33 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK5 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK12 @ Y0 @ X1)))))) ) | ~spl0_4),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f258])).
% 8.06/2.33 thf(f258,plain,(
% 8.06/2.33 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK12 @ Y1 @ Y0))))) @ X1) = $true)) ) | ~spl0_4),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f209])).
% 8.06/2.33 thf(f288,plain,(
% 8.06/2.33 spl0_7 | spl0_8 | ~spl0_4 | ~spl0_5),
% 8.06/2.33 inference(avatar_split_clause,[status(thm)],[f279,f229,f189,f286,f283])).
% 8.06/2.33 thf(f279,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y2 @ Y0) & (sK12 @ Y0 @ Y1)) => (sK12 @ Y2 @ Y1))))))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0))))))) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f273])).
% 8.06/2.33 thf(f273,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y2 @ Y0) & (sK12 @ Y0 @ Y1)) => (sK12 @ Y2 @ Y1))))))))) = $false) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(not_proxy_clausification,[status(thm)],[f257])).
% 8.06/2.33 thf(f257,plain,(
% 8.06/2.33 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y2 @ Y0) & (sK12 @ Y0 @ Y1)) => (sK12 @ Y2 @ Y1)))))))))) = $true) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f256])).
% 8.06/2.33 thf(f256,plain,(
% 8.06/2.33 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK12 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK12 @ Y2 @ Y0) & (sK12 @ Y0 @ Y1)) => (sK12 @ Y2 @ Y1))))))))) => $false) = $true) | (~spl0_4 | ~spl0_5)),
% 8.06/2.33 inference(superposition,[status(thm)],[f247,f207])).
% 8.06/2.33 thf(f247,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y0) & (X1 @ Y0 @ Y1)) => (X1 @ Y2 @ Y1))))))))) => (X1 @ sK10 @ sK11)) = $true)) ) | ~spl0_5),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f246])).
% 8.06/2.33 thf(f246,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK11))) @ X1) = $true)) ) | ~spl0_5),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f230])).
% 8.06/2.33 thf(f234,plain,(
% 8.06/2.33 spl0_5 | spl0_6 | ~spl0_4),
% 8.06/2.33 inference(avatar_split_clause,[status(thm)],[f227,f189,f232,f229])).
% 8.06/2.33 thf(f227,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK10 @ sK11)))) = $true) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK11)))) = $true) | ~spl0_4),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f199])).
% 8.06/2.33 thf(f191,plain,(
% 8.06/2.33 spl0_3 | spl0_4 | ~spl0_1),
% 8.06/2.33 inference(avatar_split_clause,[status(thm)],[f184,f29,f189,f186])).
% 8.06/2.33 thf(f29,definition,(
% 8.06/2.33 spl0_1 <=> ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))))))))),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 8.06/2.33 thf(f184,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0)))))))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))))))) = $false) | ~spl0_1),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 8.06/2.33 thf(f30,plain,(
% 8.06/2.33 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))))))))) | ~spl0_1),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f29])).
% 8.06/2.33 thf(f181,plain,(
% 8.06/2.33 ~spl0_2),
% 8.06/2.33 inference(avatar_contradiction_clause,[status(thm)],[f180])).
% 8.06/2.33 thf(f180,plain,(
% 8.06/2.33 $false | ~spl0_2),
% 8.06/2.33 inference(trivial_inequality_removal,[status(thm)],[f179])).
% 8.06/2.33 thf(f179,plain,(
% 8.06/2.33 ($false = $true) | ~spl0_2),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f178])).
% 8.06/2.33 thf(f178,plain,(
% 8.06/2.33 ((~ $true) = $true) | ~spl0_2),
% 8.06/2.33 inference(forward_demodulation,[status(thm)],[f172,f145])).
% 8.06/2.33 thf(f145,plain,(
% 8.06/2.33 ((sK6 @ sK8 @ sK7) = $true) | ~spl0_2),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 8.06/2.33 thf(f130,plain,(
% 8.06/2.33 (((sK6 @ sK7 @ sK9) & (sK6 @ sK8 @ sK7)) = $true) | ~spl0_2),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 8.06/2.33 thf(f128,plain,(
% 8.06/2.33 ((((sK6 @ sK7 @ sK9) & (sK6 @ sK8 @ sK7)) => (sK6 @ sK8 @ sK9)) = $false) | ~spl0_2),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f127])).
% 8.06/2.33 thf(f127,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a]: (((sK6 @ sK7 @ Y0) & (sK6 @ sK8 @ sK7)) => (sK6 @ sK8 @ Y0))) @ sK9)) | ~spl0_2),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f120])).
% 8.06/2.33 thf(f120,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK7 @ Y0) & (sK6 @ sK8 @ sK7)) => (sK6 @ sK8 @ Y0))))) | ~spl0_2),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f119])).
% 8.06/2.33 thf(f119,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ sK7 @ Y1) & (sK6 @ Y0 @ sK7)) => (sK6 @ Y0 @ Y1))))) @ sK8) = $false) | ~spl0_2),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f110])).
% 8.06/2.33 thf(f110,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ sK7 @ Y1) & (sK6 @ Y0 @ sK7)) => (sK6 @ Y0 @ Y1))))))) | ~spl0_2),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f108])).
% 8.06/2.33 thf(f108,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2))))))) @ sK7) = $false) | ~spl0_2),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f99])).
% 8.06/2.33 thf(f99,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2)))))))) = $false) | ~spl0_2),
% 8.06/2.33 inference(not_proxy_clausification,[status(thm)],[f52])).
% 8.06/2.33 thf(f52,plain,(
% 8.06/2.33 ((~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2))))))))) = $true) | ~spl0_2),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f50])).
% 8.06/2.33 thf(f50,plain,(
% 8.06/2.33 ($true = (~ ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2))))))))))) | ~spl0_2),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f47,f48])).
% 8.06/2.33 thf(f48,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) = $true)),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 8.06/2.33 thf(f38,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))) = $true)),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 8.06/2.33 thf(f26,plain,(
% 8.06/2.33 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))) => (sK6 @ sK2 @ sK4)))),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f25])).
% 8.06/2.33 thf(f25,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK2 @ sK4))) @ sK6))),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f19])).
% 8.06/2.33 thf(f19,plain,(
% 8.06/2.33 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK2 @ sK4)))))),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 8.06/2.33 thf(f17,plain,(
% 8.06/2.33 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK2 @ sK4)))) | (~ (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK4))))))) = $false)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f16])).
% 8.06/2.33 thf(f16,plain,(
% 8.06/2.33 (((^[Y0 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) | (Y0 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK2 @ sK4)))) | (~ (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y1))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y1 @ Y2)))))))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) | (Y0 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK2 @ sK4)))))))) @ sK5) = $false)),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f15])).
% 8.06/2.33 thf(f15,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) | (Y0 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK2 @ sK4)))) | (~ (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y1))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y1 @ Y2)))))))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) | (Y0 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK2 @ sK4))))))))) = $false)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f14])).
% 8.06/2.33 thf(f14,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (Y1 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK2 @ Y0)))) | (~ (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y8 @ Y6)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) & (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y8 @ Y6))))))))) => (Y5 @ Y3 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y8 @ Y6)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y1 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y4 @ Y2))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y6 @ Y5) | (sK3 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y2 @ Y3)))))))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (Y1 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ sK2 @ Y0)))))))))) @ sK4) = $false)),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f13])).
% 8.06/2.33 thf(f13,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (Y1 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK2 @ Y0)))) | (~ (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y8 @ Y6)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) & (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y8 @ Y6))))))))) => (Y5 @ Y3 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y8 @ Y6)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y1 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y4 @ Y2))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y6 @ Y5) | (sK3 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y2 @ Y3)))))))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (Y1 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ sK2 @ Y0))))))))))) = $false)),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f12])).
% 8.06/2.33 thf(f12,plain,(
% 8.06/2.33 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y4 @ Y5) | (Y2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ sK2 @ Y1)))) | (~ (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y9 @ Y7)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y9 @ Y7))))))))) => (Y6 @ Y4 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y9 @ Y7)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y5 @ Y3))))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y0 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y3 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y2 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7))))))))) => (Y5 @ Y3 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y4 @ Y5) | (Y2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ sK2 @ Y1)))))))))))) @ sK3))),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f11])).
% 8.06/2.33 thf(f11,plain,(
% 8.06/2.33 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y4 @ Y5) | (Y2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ sK2 @ Y1)))) | (~ (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y9 @ Y7)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y9 @ Y7))))))))) => (Y6 @ Y4 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y9 @ Y7)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y5 @ Y3))))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y0 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y3 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y2 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7))))))))) => (Y5 @ Y3 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y4 @ Y5) | (Y2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ sK2 @ Y1))))))))))))))),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f10])).
% 8.06/2.33 thf(f10,plain,(
% 8.06/2.33 (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y0 @ Y2)))) | (~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8))))))))) => (Y7 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y3 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y6 @ Y4))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y4 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y1 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y3 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y4 @ Y5)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y0 @ Y2)))))))))))))) @ sK2) = $false)),
% 8.06/2.33 inference(sigma_clausification,[status(thm)],[f7])).
% 8.06/2.33 thf(f7,plain,(
% 8.06/2.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y0 @ Y2)))) | (~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8))))))))) => (Y7 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y3 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y6 @ Y4))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y4 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y1 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y3 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y4 @ Y5)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y0 @ Y2))))))))))))))))),
% 8.06/2.33 inference(not_proxy_clausification,[status(thm)],[f6])).
% 8.06/2.33 thf(f6,plain,(
% 8.06/2.33 ((~ (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y0 @ Y2)))) | (~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8))))))))) => (Y7 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y3 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y6 @ Y4))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y4 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y1 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y3 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y4 @ Y5)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y0 @ Y2)))))))))))))))) = $true)),
% 8.06/2.33 inference(cnf_transformation,[status(thm)],[f5])).
% 8.06/2.33 thf(f5,plain,(
% 8.06/2.33 ((~ (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y0 @ Y2)))) | (~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8))))))))) => (Y7 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y10 @ Y8)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y3 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y6 @ Y4))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y4 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y1 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y3 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y4 @ Y5)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y0 @ Y2)))))))))))))))) = $true)),
% 8.06/2.33 inference(fool_elimination,[status(thm)],[f4])).
% 8.06/2.33 thf(f4,plain,(
% 8.06/2.33 ~! [X0 : a > a > $o,X1 : a,X2 : a > a > $o,X3 : a] : (~((! [X4 : a,X5 : a] : ((! [X6 : a > a > $o] : ((! [X7 : a,X8 : a] : ((X2 @ X7 @ X8) => (X6 @ X7 @ X8)) & ! [X9 : a,X10 : a,X11 : a] : (((X6 @ X9 @ X10) & (X6 @ X11 @ X9)) => (X6 @ X11 @ X10))) => (X6 @ X5 @ X4)) | ! [X12 : a > a > $o] : ((! [X13 : a,X14 : a,X15 : a] : (((X12 @ X15 @ X14) & (X12 @ X13 @ X15)) => (X12 @ X13 @ X14)) & ! [X16 : a,X17 : a] : ((X0 @ X16 @ X17) => (X12 @ X16 @ X17))) => (X12 @ X5 @ X4))) => ! [X18 : a > a > $o] : ((! [X19 : a,X20 : a,X21 : a] : (((X18 @ X19 @ X20) & (X18 @ X21 @ X19)) => (X18 @ X21 @ X20)) & ! [X22 : a,X23 : a] : (((X2 @ X22 @ X23) | (X0 @ X22 @ X23)) => (X18 @ X22 @ X23))) => (X18 @ X5 @ X4))) & ! [X24 : a,X25 : a,X26 : a] : ((! [X27 : a > a > $o] : ((! [X28 : a,X29 : a,X30 : a] : (((X27 @ X28 @ X29) & (X27 @ X29 @ X30)) => (X27 @ X28 @ X30)) & ! [X31 : a,X32 : a] : (((X0 @ X31 @ X32) | (X2 @ X31 @ X32)) => (X27 @ X31 @ X32))) => (X27 @ X25 @ X26)) & ! [X33 : a > a > $o] : ((! [X34 : a,X35 : a] : (((X0 @ X34 @ X35) | (X2 @ X34 @ X35)) => (X33 @ X34 @ X35)) & ! [X36 : a,X37 : a,X38 : a] : (((X33 @ X36 @ X37) & (X33 @ X37 @ X38)) => (X33 @ X36 @ X38))) => (X33 @ X24 @ X25))) => ! [X39 : a > a > $o] : ((! [X40 : a,X41 : a] : (((X2 @ X41 @ X40) | (X0 @ X41 @ X40)) => (X39 @ X41 @ X40)) & ! [X42 : a,X43 : a,X44 : a] : (((X39 @ X42 @ X43) & (X39 @ X43 @ X44)) => (X39 @ X42 @ X44))) => (X39 @ X24 @ X26)))) => ! [X45 : a > a > $o] : ((! [X46 : a,X47 : a,X48 : a] : (((X45 @ X47 @ X48) & (X45 @ X48 @ X46)) => (X45 @ X47 @ X46)) & ! [X49 : a,X50 : a] : (((X0 @ X50 @ X49) | (X2 @ X50 @ X49)) => (X45 @ X50 @ X49))) => (X45 @ X3 @ X1))) | ! [X51 : a > a > $o] : ((! [X52 : a,X53 : a] : (((X0 @ X53 @ X52) | (X2 @ X53 @ X52)) => (X51 @ X53 @ X52)) & ! [X54 : a,X55 : a,X56 : a] : (((X51 @ X56 @ X54) & (X51 @ X55 @ X56)) => (X51 @ X55 @ X54))) => (X51 @ X3 @ X1)))),
% 8.06/2.33 inference(rectify,[status(thm)],[f2])).
% 8.06/2.33 thf(f2,negated_conjecture,(
% 8.06/2.33 ~! [X0 : a > a > $o,X3 : a,X1 : a > a > $o,X2 : a] : (~((! [X6 : a,X5 : a] : ((! [X4 : a > a > $o] : ((! [X8 : a,X9 : a] : ((X1 @ X8 @ X9) => (X4 @ X8 @ X9)) & ! [X9 : a,X7 : a,X8 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7))) => (X4 @ X5 @ X6)) | ! [X4 : a > a > $o] : ((! [X8 : a,X7 : a,X9 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X8 : a,X9 : a] : ((X0 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) => ! [X4 : a > a > $o] : ((! [X9 : a,X7 : a,X8 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X8 : a,X9 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) & ! [X5 : a,X6 : a,X7 : a] : ((! [X4 : a > a > $o] : ((! [X8 : a,X9 : a,X10 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X6 @ X7)) & ! [X4 : a > a > $o] : ((! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9)) & ! [X8 : a,X9 : a,X10 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10))) => (X4 @ X5 @ X6))) => ! [X4 : a > a > $o] : ((! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9)) & ! [X8 : a,X9 : a,X10 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10))) => (X4 @ X5 @ X7)))) => ! [X4 : a > a > $o] : ((! [X7 : a,X5 : a,X6 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7)) & ! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3))) | ! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6)) & ! [X7 : a,X5 : a,X6 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)))),
% 8.06/2.33 inference(negated_conjecture,[status(cth)],[f1])).
% 8.06/2.33 thf(f1,conjecture,(
% 8.06/2.33 ! [X0 : a > a > $o,X3 : a,X1 : a > a > $o,X2 : a] : (~((! [X6 : a,X5 : a] : ((! [X4 : a > a > $o] : ((! [X8 : a,X9 : a] : ((X1 @ X8 @ X9) => (X4 @ X8 @ X9)) & ! [X9 : a,X7 : a,X8 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7))) => (X4 @ X5 @ X6)) | ! [X4 : a > a > $o] : ((! [X8 : a,X7 : a,X9 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X8 : a,X9 : a] : ((X0 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) => ! [X4 : a > a > $o] : ((! [X9 : a,X7 : a,X8 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X8 : a,X9 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) & ! [X5 : a,X6 : a,X7 : a] : ((! [X4 : a > a > $o] : ((! [X8 : a,X9 : a,X10 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X6 @ X7)) & ! [X4 : a > a > $o] : ((! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9)) & ! [X8 : a,X9 : a,X10 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10))) => (X4 @ X5 @ X6))) => ! [X4 : a > a > $o] : ((! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9)) & ! [X8 : a,X9 : a,X10 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10))) => (X4 @ X5 @ X7)))) => ! [X4 : a > a > $o] : ((! [X7 : a,X5 : a,X6 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7)) & ! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3))) | ! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6)) & ! [X7 : a,X5 : a,X6 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)))),
% 8.06/2.33 file('/export/starexec/sandbox2/tmp/tmp.oKqq4mYP0P/DTF2THF_20901.p',cTHM250G_pme)).
% 8.06/2.33 thf(f47,plain,(
% 8.06/2.33 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2)))))))))) = $true) | ~spl0_2),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f46])).
% 8.06/2.33 thf(f46,plain,(
% 8.06/2.33 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2))))))))) => $false) = $true) | ~spl0_2),
% 8.06/2.33 inference(superposition,[status(thm)],[f44,f37])).
% 8.06/2.33 thf(f37,plain,(
% 8.06/2.33 ((sK6 @ sK2 @ sK4) = $false)),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 8.06/2.33 thf(f44,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y2) & (X1 @ Y1 @ Y0)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK2 @ sK4)) = $true)) ) | ~spl0_2),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f43])).
% 8.06/2.33 thf(f43,plain,(
% 8.06/2.33 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK4))) @ X1) = $true)) ) | ~spl0_2),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f33])).
% 8.06/2.33 thf(f33,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK4)))) = $true) | ~spl0_2),
% 8.06/2.33 inference(avatar_component_clause,[status(thm)],[f32])).
% 8.06/2.33 thf(f32,definition,(
% 8.06/2.33 spl0_2 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK4)))) = $true)),
% 8.06/2.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 8.06/2.33 thf(f172,plain,(
% 8.06/2.33 ((~ (sK6 @ sK8 @ sK7)) = $true) | ~spl0_2),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f169])).
% 8.06/2.33 thf(f169,plain,(
% 8.06/2.33 (((sK6 @ sK8 @ sK7) => $false) = $true) | ~spl0_2),
% 8.06/2.33 inference(superposition,[status(thm)],[f155,f129])).
% 8.06/2.33 thf(f129,plain,(
% 8.06/2.33 ((sK6 @ sK8 @ sK9) = $false) | ~spl0_2),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 8.06/2.33 thf(f155,plain,(
% 8.06/2.33 ( ! [X0 : a] : ((((sK6 @ X0 @ sK7) => (sK6 @ X0 @ sK9)) = $true)) ) | ~spl0_2),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f151])).
% 8.06/2.33 thf(f151,plain,(
% 8.06/2.33 ( ! [X0 : a] : (((((sK6 @ X0 @ sK7) & $true) => (sK6 @ X0 @ sK9)) = $true)) ) | ~spl0_2),
% 8.06/2.33 inference(superposition,[status(thm)],[f59,f148])).
% 8.06/2.33 thf(f148,plain,(
% 8.06/2.33 ((sK6 @ sK7 @ sK9) = $true) | ~spl0_2),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f147])).
% 8.06/2.33 thf(f147,plain,(
% 8.06/2.33 (((sK6 @ sK7 @ sK9) & $true) = $true) | ~spl0_2),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f130,f145])).
% 8.06/2.33 thf(f59,plain,(
% 8.06/2.33 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK6 @ X2 @ X1) & (sK6 @ X1 @ X3)) => (sK6 @ X2 @ X3)) = $true)) )),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f58])).
% 8.06/2.33 thf(f58,plain,(
% 8.06/2.33 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK6 @ X2 @ X1) & (sK6 @ X1 @ Y0)) => (sK6 @ X2 @ Y0))) @ X3) = $true)) )),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f57])).
% 8.06/2.33 thf(f57,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X2 @ X1) & (sK6 @ X1 @ Y0)) => (sK6 @ X2 @ Y0)))) = $true)) )),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f56])).
% 8.06/2.33 thf(f56,plain,(
% 8.06/2.33 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ X1) & (sK6 @ X1 @ Y1)) => (sK6 @ Y0 @ Y1))))) @ X2) = $true)) )),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f55])).
% 8.06/2.33 thf(f55,plain,(
% 8.06/2.33 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ X1) & (sK6 @ X1 @ Y1)) => (sK6 @ Y0 @ Y1)))))) = $true)) )),
% 8.06/2.33 inference(beta_eta_normalization,[status(thm)],[f54])).
% 8.06/2.33 thf(f54,plain,(
% 8.06/2.33 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2))))))) @ X1))) )),
% 8.06/2.33 inference(pi_clausification,[status(thm)],[f53])).
% 8.06/2.33 thf(f53,plain,(
% 8.06/2.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2)))))))) = $true)),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f51])).
% 8.06/2.33 thf(f51,plain,(
% 8.06/2.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2)))))))) & $true) = $true)),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f38,f48])).
% 8.06/2.33 thf(f34,plain,(
% 8.06/2.33 spl0_1 | spl0_2),
% 8.06/2.33 inference(avatar_split_clause,[status(thm)],[f27,f32,f29])).
% 8.06/2.33 thf(f27,plain,(
% 8.06/2.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK4)))) = $true) | ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))))))))),
% 8.06/2.33 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 8.06/2.33 thf(f22,plain,(
% 8.06/2.33 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK4))))) = $true)),
% 8.06/2.33 inference(not_proxy_clausification,[status(thm)],[f21])).
% 8.06/2.33 thf(f21,plain,(
% 8.06/2.33 ($false = (~ (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK4)))))))),
% 8.06/2.33 inference(boolean_simplification,[status(thm)],[f20])).
% 8.06/2.33 thf(f20,plain,(
% 8.06/2.33 ($false = ($false | (~ (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK5 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK5 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK4))))))))),
% 8.06/2.33 inference(backward_demodulation,[status(thm)],[f17,f19])).
% 8.06/2.33 % SZS output end Proof for DTF2THF_20901
% 8.06/2.33 % (21261)------------------------------
% 8.06/2.33 % (21261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.33 % (21261)Termination reason: Refutation
% 8.06/2.33
% 8.06/2.33 % (21261)Memory used [KB]: 6908
% 8.06/2.33 % (21261)Time elapsed: 0.106 s
% 8.06/2.33 % (21261)Instructions burned: 237 (million)
% 8.06/2.33 % (21261)------------------------------
% 8.06/2.33 % (21261)------------------------------
% 8.06/2.33 % (21161)Success in time 1.057 s
%------------------------------------------------------------------------------