%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV148^5 : 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:23 AM UTC 2026
% Result : Theorem 1.46s 1.33s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 13
% Syntax : Number of formulae : 218 ( 37 unt; 0 typ; 12 def)
% Number of atoms : 2088 ( 202 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 5985 ( 261 ~; 369 |; 448 &;3453 @)
% ( 12 <=>; 682 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 380 ( 380 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 33 con; 0-2 aty)
% ( 760 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 895 ( 789 ^; 106 !; 0 ?; 895 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK2: a > a > $o ).
thf(func_def_23,type,
sK3: a > a > $o ).
thf(func_def_24,type,
sK4: a ).
thf(func_def_25,type,
sK5: a ).
thf(func_def_26,type,
sK6: a > $o ).
thf(func_def_27,type,
sK7: a ).
thf(func_def_28,type,
sK8: a ).
thf(func_def_29,type,
sK9: a ).
thf(func_def_30,type,
sK10: a ).
thf(func_def_31,type,
sK11: a ).
thf(func_def_32,type,
sK12: a ).
thf(func_def_33,type,
sK13: a ).
thf(func_def_34,type,
sK14: a ).
thf(func_def_35,type,
sK15: a ).
thf(func_def_36,type,
sK16: a ).
thf(func_def_37,type,
sK17: a ).
thf(func_def_38,type,
sK18: a ).
thf(func_def_39,type,
sK19: a ).
thf(func_def_40,type,
sK20: a ).
thf(func_def_41,type,
sK21: a ).
thf(func_def_42,type,
sK22: a ).
thf(f1613,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f97,f184,f264,f423,f508,f622,f779,f902,f948,f1254,f1307,f1567,f1612]) ).
thf(f1612,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f1611]) ).
thf(f1611,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1610]) ).
thf(f1610,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1609]) ).
thf(f1609,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1608]) ).
thf(f1608,plain,
( ( ( ~ ( $true
| ( sK2 @ sK8 @ sK22 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f1606,f1587]) ).
thf(f1587,plain,
( ( ( sK3 @ sK8 @ sK22 )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f1583]) ).
thf(f1583,plain,
( ( $false
= ( ( sK3 @ sK8 @ sK22 )
=> ( sK6 @ sK22 ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f1581]) ).
thf(f1581,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK22 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f1566]) ).
thf(f1566,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f1565]) ).
thf(f1565,definition,
( spl0_14
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f1606,plain,
( ( $true
= ( ~ ( ( sK3 @ sK8 @ sK22 )
| ( sK2 @ sK8 @ sK22 ) ) ) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1595]) ).
thf(f1595,plain,
( ( $true
= ( ( ( sK3 @ sK8 @ sK22 )
| ( sK2 @ sK8 @ sK22 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f1330,f1586]) ).
thf(f1586,plain,
( ( $false
= ( sK6 @ sK22 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f1583]) ).
thf(f1330,plain,
( ! [X0: a] :
( ( ( ( sK3 @ sK8 @ X0 )
| ( sK2 @ sK8 @ X0 ) )
=> ( sK6 @ X0 ) )
= $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1325]) ).
thf(f1325,plain,
( ! [X0: a] :
( ( ( ( ( sK3 @ sK8 @ X0 )
| ( sK2 @ sK8 @ X0 ) )
& $true )
=> ( sK6 @ X0 ) )
= $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f50,f1312]) ).
thf(f1312,plain,
( ( ( sK6 @ sK8 )
= $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f1310]) ).
thf(f1310,plain,
( ( $false
= ( ( sK6 @ sK8 )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1309]) ).
thf(f1309,plain,
( ( ( ( $true
& ( sK6 @ sK8 ) )
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_1
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1308]) ).
thf(f1308,plain,
( ( $false
= ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
& ( sK6 @ sK8 ) )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f967,f422]) ).
thf(f422,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f421]) ).
thf(f421,definition,
( spl0_10
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f967,plain,
( ( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
& ( sK6 @ sK8 ) )
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f966]) ).
thf(f966,plain,
( ( ( ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK8 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK8 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK8 ) )
=> ( sK6 @ Y0 ) )
@ sK9 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f957]) ).
thf(f957,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK8 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK8 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK8 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f953]) ).
thf(f953,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl0_1
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f50,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( ( sK3 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f27,f31]) ).
thf(f31,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK2 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK2 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK2 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> ( sK6 @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK2 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK2 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK2 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK4 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK4 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y2 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y2 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( Y0 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y2 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y2 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( Y0 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a > a > $o,X3: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X7: a,X8: a] :
( ( ( X6 @ X7 )
& ( X2 @ X7 @ X8 ) )
=> ( X6 @ X8 ) )
& ! [X9: a] :
( ( X2 @ X0 @ X9 )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) )
| ! [X10: a > $o] :
( ( ! [X11: a] :
( ( X3 @ X0 @ X11 )
=> ( X10 @ X11 ) )
& ! [X12: a,X13: a] :
( ( ( X10 @ X12 )
& ( X3 @ X12 @ X13 ) )
=> ( X10 @ X13 ) ) )
=> ( X10 @ X5 ) ) )
=> ( X4 @ X5 ) )
& ! [X14: a,X15: a] :
( ( ( X4 @ X15 )
& ( ! [X16: a > $o] :
( ( ! [X17: a] :
( ( X3 @ X15 @ X17 )
=> ( X16 @ X17 ) )
& ! [X18: a,X19: a] :
( ( ( X16 @ X18 )
& ( X3 @ X18 @ X19 ) )
=> ( X16 @ X19 ) ) )
=> ( X16 @ X14 ) )
| ! [X20: a > $o] :
( ( ! [X21: a] :
( ( X2 @ X15 @ X21 )
=> ( X20 @ X21 ) )
& ! [X22: a,X23: a] :
( ( ( X20 @ X22 )
& ( X2 @ X22 @ X23 ) )
=> ( X20 @ X23 ) ) )
=> ( X20 @ X14 ) ) ) )
=> ( X4 @ X14 ) ) )
=> ( X4 @ X1 ) )
=> ! [X24: a > $o] :
( ( ! [X25: a,X26: a] :
( ( ( X24 @ X26 )
& ( ( X3 @ X26 @ X25 )
| ( X2 @ X26 @ X25 ) ) )
=> ( X24 @ X25 ) )
& ! [X27: a] :
( ( ( X3 @ X0 @ X27 )
| ( X2 @ X0 @ X27 ) )
=> ( X24 @ X27 ) ) )
=> ( X24 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X0 @ X8 @ X9 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X0 @ X2 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X1 @ X8 @ X9 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
& ! [X9: a,X8: a] :
( ( ( X4 @ X8 )
& ( ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X6 @ X5 ) )
& ! [X10: a,X11: a] :
( ( ( X6 @ X10 )
& ( X1 @ X10 @ X11 ) )
=> ( X6 @ X11 ) ) )
=> ( X6 @ X9 ) )
| ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X6 @ X5 ) )
& ! [X10: a,X11: a] :
( ( ( X6 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X6 @ X11 ) ) )
=> ( X6 @ X9 ) ) ) )
=> ( X4 @ X9 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X4 @ X8 )
& ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) ) )
=> ( X4 @ X9 ) )
& ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X0 @ X8 @ X9 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X0 @ X2 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X1 @ X8 @ X9 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
& ! [X9: a,X8: a] :
( ( ( X4 @ X8 )
& ( ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X6 @ X5 ) )
& ! [X10: a,X11: a] :
( ( ( X6 @ X10 )
& ( X1 @ X10 @ X11 ) )
=> ( X6 @ X11 ) ) )
=> ( X6 @ X9 ) )
| ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X6 @ X5 ) )
& ! [X10: a,X11: a] :
( ( ( X6 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X6 @ X11 ) ) )
=> ( X6 @ X9 ) ) ) )
=> ( X4 @ X9 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X4 @ X8 )
& ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) ) )
=> ( X4 @ X9 ) )
& ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.k0lBrjUgxb/DTF2THF_25182.p',cTHM251C_pme) ).
thf(f1567,plain,
( spl0_14
| spl0_12
| ~ spl0_1
| ~ spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f1561,f421,f92,f620,f1565]) ).
thf(f620,definition,
( spl0_12
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f1561,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f1547]) ).
thf(f1547,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_10 ),
inference(not_proxy_clausification,[status(thm)],[f1530]) ).
thf(f1530,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1521]) ).
thf(f1521,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f1504,f1314]) ).
thf(f1314,plain,
( ( ( sK6 @ sK9 )
= $false )
| ~ spl0_1
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1313]) ).
thf(f1313,plain,
( ( $false
= ( $true
=> ( sK6 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f1310,f1312]) ).
thf(f1504,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK8 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK9 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1503]) ).
thf(f1503,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ X1 )
= $true )
| ~ spl0_10 ),
inference(pi_clausification,[status(thm)],[f422]) ).
thf(f1307,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f1306]) ).
thf(f1306,plain,
( $false
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1305]) ).
thf(f1305,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1304]) ).
thf(f1304,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1303]) ).
thf(f1303,plain,
( ( $true
= ( ~ ( ( sK3 @ sK8 @ sK21 )
| $true ) ) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f1298,f1285]) ).
thf(f1285,plain,
( ( ( sK2 @ sK8 @ sK21 )
= $true )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f1270]) ).
thf(f1270,plain,
( ( ( ( sK2 @ sK8 @ sK21 )
=> ( sK6 @ sK21 ) )
= $false )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f1268]) ).
thf(f1268,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK21 )
= $false )
| ~ spl0_13 ),
inference(sigma_clausification,[status(thm)],[f1253]) ).
thf(f1253,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f1252]) ).
thf(f1252,definition,
( spl0_13
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f1298,plain,
( ( ( ~ ( ( sK3 @ sK8 @ sK21 )
| ( sK2 @ sK8 @ sK21 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1291]) ).
thf(f1291,plain,
( ( ( ( ( sK3 @ sK8 @ sK21 )
| ( sK2 @ sK8 @ sK21 ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f1003,f1284]) ).
thf(f1284,plain,
( ( $false
= ( sK6 @ sK21 ) )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f1270]) ).
thf(f1003,plain,
( ! [X0: a] :
( ( ( ( sK3 @ sK8 @ X0 )
| ( sK2 @ sK8 @ X0 ) )
=> ( sK6 @ X0 ) )
= $true )
| ~ spl0_1
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f998]) ).
thf(f998,plain,
( ! [X0: a] :
( ( ( ( ( sK3 @ sK8 @ X0 )
| ( sK2 @ sK8 @ X0 ) )
& $true )
=> ( sK6 @ X0 ) )
= $true )
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f50,f978]) ).
thf(f978,plain,
( ( ( sK6 @ sK8 )
= $true )
| ~ spl0_1
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f970]) ).
thf(f970,plain,
( ( $false
= ( ( sK6 @ sK8 )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f969]) ).
thf(f969,plain,
( ( ( ( $true
& ( sK6 @ sK8 ) )
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_1
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f968]) ).
thf(f968,plain,
( ( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| $true )
& ( sK6 @ sK8 ) )
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f967,f419]) ).
thf(f419,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f418]) ).
thf(f418,definition,
( spl0_9
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f1254,plain,
( spl0_8
| spl0_13
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f1248,f418,f92,f1252,f262]) ).
thf(f262,definition,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f1248,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f1236]) ).
thf(f1236,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_9 ),
inference(not_proxy_clausification,[status(thm)],[f1172]) ).
thf(f1172,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1167]) ).
thf(f1167,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f1153,f977]) ).
thf(f977,plain,
( ( ( sK6 @ sK9 )
= $false )
| ~ spl0_1
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f970]) ).
thf(f1153,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK8 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK9 ) )
= $true )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f1152]) ).
thf(f1152,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ X1 ) )
| ~ spl0_9 ),
inference(pi_clausification,[status(thm)],[f419]) ).
thf(f948,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[status(thm)],[f947]) ).
thf(f947,plain,
( $false
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f946]) ).
thf(f946,plain,
( ( $false = $true )
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f945,f913]) ).
thf(f913,plain,
( ( ( sK6 @ sK17 )
= $false )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f912]) ).
thf(f912,plain,
( ( $false
= ( ( ( sK3 @ sK18 @ sK17 )
& ( sK6 @ sK18 ) )
=> ( sK6 @ sK17 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f911]) ).
thf(f911,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK17 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK17 ) )
@ sK18 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f910]) ).
thf(f910,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK17 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK17 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f906]) ).
thf(f906,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) )
@ sK17 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f621]) ).
thf(f621,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f620]) ).
thf(f945,plain,
( ( ( sK6 @ sK17 )
= $true )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f944]) ).
thf(f944,plain,
( ( ( $true
=> ( sK6 @ sK17 ) )
= $true )
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f943,f937]) ).
thf(f937,plain,
( ( $true
= ( sK6 @ sK19 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f934]) ).
thf(f934,plain,
( ( ( ( sK3 @ sK19 @ sK17 )
& ( sK6 @ sK19 ) )
= $true )
| ~ spl0_12 ),
inference(not_proxy_clausification,[status(thm)],[f922]) ).
thf(f922,plain,
( ( ( ~ ( ( sK3 @ sK19 @ sK17 )
& ( sK6 @ sK19 ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f921]) ).
thf(f921,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK3 @ Y0 @ sK17 )
& ( sK6 @ Y0 ) )
@ sK19 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f918]) ).
thf(f918,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK3 @ Y0 @ sK17 )
& ( sK6 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f916]) ).
thf(f916,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK17 )
& ( sK6 @ Y0 ) )
=> $false ) ) )
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f910,f913]) ).
thf(f943,plain,
( ( $true
= ( ( sK6 @ sK19 )
=> ( sK6 @ sK17 ) ) )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f942]) ).
thf(f942,plain,
( ( ( ( $true
& ( sK6 @ sK19 ) )
=> ( sK6 @ sK17 ) )
= $true )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f941]) ).
thf(f941,plain,
( ( ( ( ( $true
| ( sK2 @ sK19 @ sK17 ) )
& ( sK6 @ sK19 ) )
=> ( sK6 @ sK17 ) )
= $true )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f50,f940]) ).
thf(f940,plain,
( ( ( sK3 @ sK19 @ sK17 )
= $true )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f939]) ).
thf(f939,plain,
( ( $true
= ( ( sK3 @ sK19 @ sK17 )
& $true ) )
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f934,f937]) ).
thf(f902,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[status(thm)],[f901]) ).
thf(f901,plain,
( $false
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f900]) ).
thf(f900,plain,
( ( $false = $true )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f899]) ).
thf(f899,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f898]) ).
thf(f898,plain,
( ( ( ~ ( $true
| ( sK2 @ sK5 @ sK16 ) ) )
= $true )
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f897,f884]) ).
thf(f884,plain,
( ( ( sK3 @ sK5 @ sK16 )
= $true )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f880]) ).
thf(f880,plain,
( ( $false
= ( ( sK3 @ sK5 @ sK16 )
=> ( sK6 @ sK16 ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f878]) ).
thf(f878,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK16 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f618]) ).
thf(f618,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f617]) ).
thf(f617,definition,
( spl0_11
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f897,plain,
( ( $true
= ( ~ ( ( sK3 @ sK5 @ sK16 )
| ( sK2 @ sK5 @ sK16 ) ) ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f891]) ).
thf(f891,plain,
( ( $true
= ( ( ( sK3 @ sK5 @ sK16 )
| ( sK2 @ sK5 @ sK16 ) )
=> $false ) )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f37,f886]) ).
thf(f886,plain,
( ( $false
= ( sK6 @ sK16 ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f885]) ).
thf(f885,plain,
( ( $false
= ( $true
=> ( sK6 @ sK16 ) ) )
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f880,f884]) ).
thf(f37,plain,
! [X1: a] :
( ( ( ( sK3 @ sK5 @ X1 )
| ( sK2 @ sK5 @ X1 ) )
=> ( sK6 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK2 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f779,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[status(thm)],[f778]) ).
thf(f778,plain,
( $false
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f777]) ).
thf(f777,plain,
( ( $false = $true )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f776,f725]) ).
thf(f725,plain,
( ( ( sK6 @ sK13 )
= $false )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f724]) ).
thf(f724,plain,
( ( $false
= ( $true
=> ( sK6 @ sK13 ) ) )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f721,f723]) ).
thf(f723,plain,
( ( $true
= ( ( sK2 @ sK14 @ sK13 )
& ( sK6 @ sK14 ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f721]) ).
thf(f721,plain,
( ( $false
= ( ( ( sK2 @ sK14 @ sK13 )
& ( sK6 @ sK14 ) )
=> ( sK6 @ sK13 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f720]) ).
thf(f720,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK13 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK13 ) )
@ sK14 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f717]) ).
thf(f717,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK13 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK13 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f715]) ).
thf(f715,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) )
@ sK13 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f263]) ).
thf(f263,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f262]) ).
thf(f776,plain,
( ( ( sK6 @ sK13 )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f775]) ).
thf(f775,plain,
( ( ( $true
=> ( sK6 @ sK13 ) )
= $true )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f774,f758]) ).
thf(f758,plain,
( ( ( sK6 @ sK15 )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f745]) ).
thf(f745,plain,
( ( ( ( sK2 @ sK15 @ sK13 )
& ( sK6 @ sK15 ) )
= $true )
| ~ spl0_8 ),
inference(not_proxy_clausification,[status(thm)],[f740]) ).
thf(f740,plain,
( ( $false
= ( ~ ( ( sK2 @ sK15 @ sK13 )
& ( sK6 @ sK15 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f739]) ).
thf(f739,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK2 @ Y0 @ sK13 )
& ( sK6 @ Y0 ) )
@ sK15 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f727]) ).
thf(f727,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK2 @ Y0 @ sK13 )
& ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f726]) ).
thf(f726,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK13 )
& ( sK6 @ Y0 ) )
=> $false ) ) )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f717,f725]) ).
thf(f774,plain,
( ( ( ( sK6 @ sK15 )
=> ( sK6 @ sK13 ) )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f773]) ).
thf(f773,plain,
( ( $true
= ( ( $true
& ( sK6 @ sK15 ) )
=> ( sK6 @ sK13 ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f772]) ).
thf(f772,plain,
( ( ( ( ( ( sK3 @ sK15 @ sK13 )
| $true )
& ( sK6 @ sK15 ) )
=> ( sK6 @ sK13 ) )
= $true )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f50,f761]) ).
thf(f761,plain,
( ( ( sK2 @ sK15 @ sK13 )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f760]) ).
thf(f760,plain,
( ( $true
= ( ( sK2 @ sK15 @ sK13 )
& $true ) )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f745,f758]) ).
thf(f622,plain,
( spl0_11
| spl0_12
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f613,f179,f95,f620,f617]) ).
thf(f95,definition,
( spl0_2
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f179,definition,
( spl0_3
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f613,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f605]) ).
thf(f605,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f583]) ).
thf(f583,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f580]) ).
thf(f580,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f563,f511]) ).
thf(f511,plain,
( ( ( sK6 @ sK7 )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f510]) ).
thf(f510,plain,
( ( ( $true
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f509]) ).
thf(f509,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) )
| $true )
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f435,f180]) ).
thf(f180,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f179]) ).
thf(f435,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f431]) ).
thf(f431,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f563,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK7 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f562]) ).
thf(f562,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f180]) ).
thf(f508,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f507]) ).
thf(f507,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f506]) ).
thf(f506,plain,
( ( $false = $true )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f505]) ).
thf(f505,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f504]) ).
thf(f504,plain,
( ( ( ~ ( ( sK3 @ sK5 @ sK10 )
| $true ) )
= $true )
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f498,f479]) ).
thf(f479,plain,
( ( ( sK2 @ sK5 @ sK10 )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f428]) ).
thf(f428,plain,
( ( $false
= ( ( sK2 @ sK5 @ sK10 )
=> ( sK6 @ sK10 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f426]) ).
thf(f426,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK10 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f260]) ).
thf(f260,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f259]) ).
thf(f259,definition,
( spl0_7
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f498,plain,
( ( ( ~ ( ( sK3 @ sK5 @ sK10 )
| ( sK2 @ sK5 @ sK10 ) ) )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f497]) ).
thf(f497,plain,
( ( ( ( ( sK3 @ sK5 @ sK10 )
| ( sK2 @ sK5 @ sK10 ) )
=> $false )
= $true )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f37,f478]) ).
thf(f478,plain,
( ( $false
= ( sK6 @ sK10 ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f428]) ).
thf(f423,plain,
( spl0_9
| spl0_10
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f416,f92,f421,f418]) ).
thf(f416,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f329]) ).
thf(f329,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f275]) ).
thf(f275,plain,
( ( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
& ( sK6 @ sK8 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f273]) ).
thf(f273,plain,
( ( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK8 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
& ( sK6 @ sK8 ) )
=> ( sK6 @ sK9 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f272]) ).
thf(f272,plain,
( ( ( ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK8 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK8 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK8 ) )
=> ( sK6 @ Y0 ) )
@ sK9 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f271]) ).
thf(f271,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK8 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK8 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK8 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f267]) ).
thf(f267,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f93]) ).
thf(f264,plain,
( spl0_7
| spl0_8
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f255,f182,f95,f262,f259]) ).
thf(f182,definition,
( spl0_4
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f255,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f249]) ).
thf(f249,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f242]) ).
thf(f242,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f240,f137]) ).
thf(f137,plain,
( ( ( sK6 @ sK7 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( ( $true
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f120,f135]) ).
thf(f135,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f96]) ).
thf(f240,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK7 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f239]) ).
thf(f239,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f182]) ).
thf(f184,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f177,f95,f182,f179]) ).
thf(f177,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f97,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f88,f95,f92]) ).
thf(f88,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
=> $false )
= $true ),
inference(superposition,[status(thm)],[f35,f29]) ).
thf(f29,plain,
( $false
= ( sK6 @ sK4 ) ),
inference(boolean_simplification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true
=> ( sK6 @ sK4 ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f25,f27]) ).
thf(f35,plain,
! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK4 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV148^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n021.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:40:53 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.43 ---- Original DTF file ---
% 0.15/0.43 thf(spec,logic,$$dhol).
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 % File : SEV148^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.43 % Domain : Set Theory (Relations)
% 0.15/0.43 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.15/0.43 % Version : Especial.
% 0.15/0.43 % English :
% 0.15/0.43
% 0.15/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.43 % Source : [Bro09]
% 0.15/0.43 % Names : tps_1186 [Bro09]
% 0.15/0.43
% 0.15/0.43 % Status : Theorem
% 0.15/0.43 % Rating : 0.25 v9.1.0, 0.38 v9.0.0, 0.25 v8.2.0, 0.27 v8.1.0, 0.33 v7.5.0, 0.50 v7.4.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.50 v5.2.0, 0.75 v4.1.0, 1.00 v4.0.0
% 0.15/0.43 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.15/0.43 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.15/0.43 % Maximal formula atoms : 0 ( 0 avg)
% 0.15/0.43 % Number of connectives : 83 ( 0 ~; 4 |; 12 &; 48 @)
% 0.15/0.43 % ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% 0.15/0.43 % Maximal formula depth : 23 ( 23 avg)
% 0.15/0.43 % Number of types : 2 ( 1 usr)
% 0.15/0.43 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.15/0.43 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.15/0.43 % Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% 0.15/0.43 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.43
% 0.15/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 thf(a_type,type,
% 0.15/0.43 a: $tType ).
% 0.15/0.43
% 0.15/0.43 thf(cTHM251C_pme,conjecture,
% 0.15/0.43 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.15/0.43 ( ! [Xq: a > $o] :
% 0.15/0.43 ( ( ! [Xw: a] :
% 0.15/0.43 ( ( ! [Xq0: a > $o] :
% 0.15/0.43 ( ( ! [Xw0: a] :
% 0.15/0.43 ( ( R @ Xx @ Xw0 )
% 0.15/0.43 => ( Xq0 @ Xw0 ) )
% 0.15/0.43 & ! [Xu: a,Xv: a] :
% 0.15/0.43 ( ( ( Xq0 @ Xu )
% 0.15/0.43 & ( R @ Xu @ Xv ) )
% 0.15/0.43 => ( Xq0 @ Xv ) ) )
% 0.15/0.43 => ( Xq0 @ Xw ) )
% 0.15/0.43 | ! [Xq0: a > $o] :
% 0.15/0.43 ( ( ! [Xw0: a] :
% 0.15/0.43 ( ( S @ Xx @ Xw0 )
% 0.15/0.43 => ( Xq0 @ Xw0 ) )
% 0.15/0.43 & ! [Xu: a,Xv: a] :
% 0.15/0.43 ( ( ( Xq0 @ Xu )
% 0.15/0.43 & ( S @ Xu @ Xv ) )
% 0.15/0.43 => ( Xq0 @ Xv ) ) )
% 0.15/0.43 => ( Xq0 @ Xw ) ) )
% 0.15/0.43 => ( Xq @ Xw ) )
% 0.15/0.43 & ! [Xu: a,Xv: a] :
% 0.15/0.43 ( ( ( Xq @ Xu )
% 0.15/0.43 & ( ! [Xq0: a > $o] :
% 0.15/0.43 ( ( ! [Xw: a] :
% 0.15/0.43 ( ( R @ Xu @ Xw )
% 0.15/0.43 => ( Xq0 @ Xw ) )
% 0.15/0.43 & ! [Xu0: a,Xv0: a] :
% 0.15/0.43 ( ( ( Xq0 @ Xu0 )
% 0.15/0.43 & ( R @ Xu0 @ Xv0 ) )
% 0.15/0.43 => ( Xq0 @ Xv0 ) ) )
% 0.15/0.43 => ( Xq0 @ Xv ) )
% 0.15/0.43 | ! [Xq0: a > $o] :
% 0.15/0.43 ( ( ! [Xw: a] :
% 0.15/0.43 ( ( S @ Xu @ Xw )
% 0.15/0.43 => ( Xq0 @ Xw ) )
% 0.15/0.43 & ! [Xu0: a,Xv0: a] :
% 0.15/0.43 ( ( ( Xq0 @ Xu0 )
% 0.15/0.43 & ( S @ Xu0 @ Xv0 ) )
% 0.15/0.43 => ( Xq0 @ Xv0 ) ) )
% 0.15/0.43 => ( Xq0 @ Xv ) ) ) )
% 0.15/0.43 => ( Xq @ Xv ) ) )
% 0.15/0.43 => ( Xq @ Xy ) )
% 0.15/0.43 => ! [Xq: a > $o] :
% 0.15/0.43 ( ( ! [Xw: a] :
% 0.15/0.43 ( ( ( R @ Xx @ Xw )
% 0.15/0.43 | ( S @ Xx @ Xw ) )
% 0.15/0.43 => ( Xq @ Xw ) )
% 0.15/0.43 & ! [Xu: a,Xv: a] :
% 0.15/0.43 ( ( ( Xq @ Xu )
% 0.15/0.43 & ( ( R @ Xu @ Xv )
% 0.15/0.43 | ( S @ Xu @ Xv ) ) )
% 0.15/0.43 => ( Xq @ Xv ) ) )
% 0.15/0.43 => ( Xq @ Xy ) ) ) ).
% 0.15/0.43
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 ------------------------
% 1.31/1.19 ---- Embedded in THF ---
% 1.31/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.31/1.19 %%% Generated on Tue Feb 24 12:40:54 EST 2026
% 1.31/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.31/1.19 %%% Logic specification used:
% 1.31/1.19 %%% thf(spec, logic, $$dhol).
% 1.31/1.19
% 1.31/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.k0lBrjUgxb/DTF2DTF25182.p
% See solution above
% 1.31/1.19 ------------------------
% 1.31/1.20 ---- Cleaned THF ---
% 1.46/1.20 thf(a_type,type,
% 1.46/1.20 a: $tType ).
% 1.46/1.20
% 1.46/1.20 thf(cTHM251C_pme,conjecture,
% 1.46/1.20 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.46/1.20 ( ! [Xq: a > $o] :
% 1.46/1.20 ( ( ! [Xw: a] :
% 1.46/1.20 ( ( ! [Xq0: a > $o] :
% 1.46/1.20 ( ( ! [Xw0: a] :
% 1.46/1.20 ( ( R @ Xx @ Xw0 )
% 1.46/1.20 => ( Xq0 @ Xw0 ) )
% 1.46/1.20 & ! [Xu: a,Xv: a] :
% 1.46/1.20 ( ( ( Xq0 @ Xu )
% 1.46/1.20 & ( R @ Xu @ Xv ) )
% 1.46/1.20 => ( Xq0 @ Xv ) ) )
% 1.46/1.20 => ( Xq0 @ Xw ) )
% 1.46/1.20 | ! [Xq0: a > $o] :
% 1.46/1.20 ( ( ! [Xw0: a] :
% 1.46/1.20 ( ( S @ Xx @ Xw0 )
% 1.46/1.20 => ( Xq0 @ Xw0 ) )
% 1.46/1.20 & ! [Xu: a,Xv: a] :
% 1.46/1.20 ( ( ( Xq0 @ Xu )
% 1.46/1.20 & ( S @ Xu @ Xv ) )
% 1.46/1.20 => ( Xq0 @ Xv ) ) )
% 1.46/1.20 => ( Xq0 @ Xw ) ) )
% 1.46/1.20 => ( Xq @ Xw ) )
% 1.46/1.20 & ! [Xu: a,Xv: a] :
% 1.46/1.20 ( ( ( Xq @ Xu )
% 1.46/1.20 & ( ! [Xq0: a > $o] :
% 1.46/1.20 ( ( ! [Xw: a] :
% 1.46/1.20 ( ( R @ Xu @ Xw )
% 1.46/1.20 => ( Xq0 @ Xw ) )
% 1.46/1.20 & ! [Xu0: a,Xv0: a] :
% 1.46/1.20 ( ( ( Xq0 @ Xu0 )
% 1.46/1.20 & ( R @ Xu0 @ Xv0 ) )
% 1.46/1.20 => ( Xq0 @ Xv0 ) ) )
% 1.46/1.20 => ( Xq0 @ Xv ) )
% 1.46/1.20 | ! [Xq0: a > $o] :
% 1.46/1.20 ( ( ! [Xw: a] :
% 1.46/1.20 ( ( S @ Xu @ Xw )
% 1.46/1.20 => ( Xq0 @ Xw ) )
% 1.46/1.20 & ! [Xu0: a,Xv0: a] :
% 1.46/1.20 ( ( ( Xq0 @ Xu0 )
% 1.46/1.20 & ( S @ Xu0 @ Xv0 ) )
% 1.46/1.20 => ( Xq0 @ Xv0 ) ) )
% 1.46/1.20 => ( Xq0 @ Xv ) ) ) )
% 1.46/1.20 => ( Xq @ Xv ) ) )
% 1.46/1.20 => ( Xq @ Xy ) )
% 1.46/1.20 => ! [Xq: a > $o] :
% 1.46/1.20 ( ( ! [Xw: a] :
% 1.46/1.20 ( ( ( R @ Xx @ Xw )
% 1.46/1.20 | ( S @ Xx @ Xw ) )
% 1.46/1.20 => ( Xq @ Xw ) )
% 1.46/1.20 & ! [Xu: a,Xv: a] :
% 1.46/1.20 ( ( ( Xq @ Xu )
% 1.46/1.20 & ( ( R @ Xu @ Xv )
% 1.46/1.20 | ( S @ Xu @ Xv ) ) )
% 1.46/1.20 => ( Xq @ Xv ) ) )
% 1.46/1.20 => ( Xq @ Xy ) ) ) ).
% 1.46/1.20 ------------------------
% 1.46/1.21 % (25327)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25182 for (3000ds/183Mi)
% 1.46/1.21 % (25331)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_25182 for (3000ds/2Mi)
% 1.46/1.21 % (25332)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_25182 for (3000ds/275Mi)
% 1.46/1.21 % (25333)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25182 for (3000ds/18Mi)
% 1.46/1.21 % (25328)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_25182 for (3000ds/4Mi)
% 1.46/1.21 % (25330)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25182 for (3000ds/2Mi)
% 1.46/1.21 % (25329)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_25182 for (3000ds/27Mi)
% 1.46/1.21 % (25330)Instruction limit reached!
% 1.46/1.21 % (25330)------------------------------
% 1.46/1.21 % (25330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.21 % (25330)Termination reason: Unknown
% 1.46/1.21 % (25330)Termination phase: Preprocessing 3
% 1.46/1.21
% 1.46/1.21 % (25330)Memory used [KB]: 1023
% 1.46/1.21 % (25330)Time elapsed: 0.003 s
% 1.46/1.21 % (25330)Instructions burned: 4 (million)
% 1.46/1.21 % (25330)------------------------------
% 1.46/1.21 % (25330)------------------------------
% 1.46/1.21 % (25331)Instruction limit reached!
% 1.46/1.21 % (25331)------------------------------
% 1.46/1.21 % (25331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.21 % (25331)Termination reason: Unknown
% 1.46/1.21 % (25331)Termination phase: Saturation
% 1.46/1.21
% 1.46/1.21 % (25331)Memory used [KB]: 1023
% 1.46/1.21 % (25331)Time elapsed: 0.003 s
% 1.46/1.21 % (25331)Instructions burned: 5 (million)
% 1.46/1.21 % (25331)------------------------------
% 1.46/1.21 % (25331)------------------------------
% 1.46/1.21 % (25328)Instruction limit reached!
% 1.46/1.21 % (25328)------------------------------
% 1.46/1.21 % (25328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.21 % (25328)Termination reason: Unknown
% 1.46/1.21 % (25328)Termination phase: Saturation
% 1.46/1.21
% 1.46/1.21 % (25328)Memory used [KB]: 5500
% 1.46/1.21 % (25328)Time elapsed: 0.004 s
% 1.46/1.21 % (25328)Instructions burned: 7 (million)
% 1.46/1.21 % (25328)------------------------------
% 1.46/1.21 % (25328)------------------------------
% 1.46/1.22 % (25333)Instruction limit reached!
% 1.46/1.22 % (25333)------------------------------
% 1.46/1.22 % (25333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.22 % (25333)Termination reason: Unknown
% 1.46/1.22 % (25333)Termination phase: Saturation
% 1.46/1.22
% 1.46/1.22 % (25333)Memory used [KB]: 5628
% 1.46/1.22 % (25333)Time elapsed: 0.008 s
% 1.46/1.22 % (25333)Instructions burned: 20 (million)
% 1.46/1.22 % (25333)------------------------------
% 1.46/1.22 % (25333)------------------------------
% 1.46/1.22 % (25329)Instruction limit reached!
% 1.46/1.22 % (25329)------------------------------
% 1.46/1.22 % (25329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.22 % (25329)Termination reason: Unknown
% 1.46/1.22 % (25329)Termination phase: Saturation
% 1.46/1.22
% 1.46/1.22 % (25329)Memory used [KB]: 5628
% 1.46/1.22 % (25329)Time elapsed: 0.010 s
% 1.46/1.22 % (25329)Instructions burned: 28 (million)
% 1.46/1.22 % (25329)------------------------------
% 1.46/1.22 % (25329)------------------------------
% 1.46/1.22 % (25339)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/3Mi)
% 1.46/1.22 % (25340)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_25182 for (2999ds/37Mi)
% 1.46/1.22 % (25341)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_25182 for (2999ds/15Mi)
% 1.46/1.22 % (25339)Instruction limit reached!
% 1.46/1.22 % (25339)------------------------------
% 1.46/1.22 % (25339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.22 % (25339)Termination reason: Unknown
% 1.46/1.22 % (25339)Termination phase: Preprocessing 3
% 1.46/1.22
% 1.46/1.22 % (25339)Memory used [KB]: 1023
% 1.46/1.22 % (25339)Time elapsed: 0.002 s
% 1.46/1.22 % (25339)Instructions burned: 3 (million)
% 1.46/1.22 % (25339)------------------------------
% 1.46/1.22 % (25339)------------------------------
% 1.46/1.23 % (25344)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_25182 for (2999ds/3Mi)
% 1.46/1.23 % (25341)Instruction limit reached!
% 1.46/1.23 % (25341)------------------------------
% 1.46/1.23 % (25341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.23 % (25341)Termination reason: Unknown
% 1.46/1.23 % (25341)Termination phase: Saturation
% 1.46/1.23
% 1.46/1.23 % (25341)Memory used [KB]: 5628
% 1.46/1.23 % (25341)Time elapsed: 0.006 s
% 1.46/1.23 % (25341)Instructions burned: 15 (million)
% 1.46/1.23 % (25341)------------------------------
% 1.46/1.23 % (25341)------------------------------
% 1.46/1.23 % (25344)Instruction limit reached!
% 1.46/1.23 % (25344)------------------------------
% 1.46/1.23 % (25344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.23 % (25344)Termination reason: Unknown
% 1.46/1.23 % (25344)Termination phase: Preprocessing 3
% 1.46/1.23
% 1.46/1.23 % (25344)Memory used [KB]: 1023
% 1.46/1.23 % (25344)Time elapsed: 0.002 s
% 1.46/1.23 % (25344)Instructions burned: 3 (million)
% 1.46/1.23 % (25344)------------------------------
% 1.46/1.23 % (25344)------------------------------
% 1.46/1.23 % (25347)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_25182 for (2999ds/1041Mi)
% 1.46/1.23 % (25349)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/7Mi)
% 1.46/1.23 % (25340)Instruction limit reached!
% 1.46/1.23 % (25340)------------------------------
% 1.46/1.23 % (25340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.23 % (25340)Termination reason: Unknown
% 1.46/1.23 % (25340)Termination phase: Saturation
% 1.46/1.23
% 1.46/1.23 % (25340)Memory used [KB]: 5628
% 1.46/1.23 % (25340)Time elapsed: 0.012 s
% 1.46/1.23 % (25340)Instructions burned: 38 (million)
% 1.46/1.23 % (25340)------------------------------
% 1.46/1.23 % (25340)------------------------------
% 1.46/1.23 % (25349)Instruction limit reached!
% 1.46/1.23 % (25349)------------------------------
% 1.46/1.23 % (25349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.23 % (25349)Termination reason: Unknown
% 1.46/1.23 % (25349)Termination phase: Saturation
% 1.46/1.23
% 1.46/1.23 % (25349)Memory used [KB]: 1023
% 1.46/1.23 % (25349)Time elapsed: 0.003 s
% 1.46/1.23 % (25349)Instructions burned: 7 (million)
% 1.46/1.23 % (25349)------------------------------
% 1.46/1.23 % (25349)------------------------------
% 1.46/1.24 % (25352)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/16Mi)
% 1.46/1.24 % (25353)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_25182 for (2999ds/3Mi)
% 1.46/1.24 % (25353)Instruction limit reached!
% 1.46/1.24 % (25353)------------------------------
% 1.46/1.24 % (25353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (25353)Termination reason: Unknown
% 1.46/1.24 % (25353)Termination phase: Preprocessing 3
% 1.46/1.24
% 1.46/1.24 % (25353)Memory used [KB]: 1023
% 1.46/1.24 % (25353)Time elapsed: 0.002 s
% 1.46/1.24 % (25353)Instructions burned: 4 (million)
% 1.46/1.24 % (25353)------------------------------
% 1.46/1.24 % (25353)------------------------------
% 1.46/1.24 % (25352)Instruction limit reached!
% 1.46/1.24 % (25352)------------------------------
% 1.46/1.24 % (25352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (25352)Termination reason: Unknown
% 1.46/1.24 % (25352)Termination phase: Saturation
% 1.46/1.24
% 1.46/1.24 % (25352)Memory used [KB]: 5628
% 1.46/1.24 % (25352)Time elapsed: 0.006 s
% 1.46/1.24 % (25352)Instructions burned: 18 (million)
% 1.46/1.24 % (25352)------------------------------
% 1.46/1.24 % (25352)------------------------------
% 1.46/1.24 % (25356)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_25182 for (2999ds/3Mi)
% 1.46/1.24 % (25356)Instruction limit reached!
% 1.46/1.24 % (25356)------------------------------
% 1.46/1.24 % (25356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (25356)Termination reason: Unknown
% 1.46/1.24 % (25356)Termination phase: Preprocessing 3
% 1.46/1.24
% 1.46/1.24 % (25356)Memory used [KB]: 1023
% 1.46/1.24 % (25356)Time elapsed: 0.002 s
% 1.46/1.24 % (25356)Instructions burned: 3 (million)
% 1.46/1.24 % (25356)------------------------------
% 1.46/1.24 % (25356)------------------------------
% 1.46/1.24 % (25358)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/7Mi)
% 1.46/1.24 % (25358)Instruction limit reached!
% 1.46/1.24 % (25358)------------------------------
% 1.46/1.24 % (25358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (25358)Termination reason: Unknown
% 1.46/1.24 % (25358)Termination phase: Saturation
% 1.46/1.24
% 1.46/1.24 % (25358)Memory used [KB]: 5628
% 1.46/1.24 % (25358)Time elapsed: 0.004 s
% 1.46/1.24 % (25358)Instructions burned: 9 (million)
% 1.46/1.24 % (25358)------------------------------
% 1.46/1.24 % (25358)------------------------------
% 1.46/1.25 % (25360)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/3Mi)
% 1.46/1.25 % (25360)Instruction limit reached!
% 1.46/1.25 % (25360)------------------------------
% 1.46/1.25 % (25360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (25360)Termination reason: Unknown
% 1.46/1.25 % (25360)Termination phase: Property scanning
% 1.46/1.25
% 1.46/1.25 % (25360)Memory used [KB]: 1023
% 1.46/1.25 % (25360)Time elapsed: 0.002 s
% 1.46/1.25 % (25360)Instructions burned: 3 (million)
% 1.46/1.25 % (25360)------------------------------
% 1.46/1.25 % (25360)------------------------------
% 1.46/1.25 % (25362)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/4Mi)
% 1.46/1.25 % (25363)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/18Mi)
% 1.46/1.25 % (25362)Instruction limit reached!
% 1.46/1.25 % (25362)------------------------------
% 1.46/1.25 % (25362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (25362)Termination reason: Unknown
% 1.46/1.25 % (25362)Termination phase: Saturation
% 1.46/1.25
% 1.46/1.25 % (25362)Memory used [KB]: 1023
% 1.46/1.25 % (25362)Time elapsed: 0.003 s
% 1.46/1.25 % (25362)Instructions burned: 6 (million)
% 1.46/1.25 % (25362)------------------------------
% 1.46/1.25 % (25362)------------------------------
% 1.46/1.25 % (25364)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/710Mi)
% 1.46/1.26 % (25365)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/6Mi)
% 1.46/1.26 % (25363)Instruction limit reached!
% 1.46/1.26 % (25363)------------------------------
% 1.46/1.26 % (25363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (25363)Termination reason: Unknown
% 1.46/1.26 % (25363)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (25363)Memory used [KB]: 5628
% 1.46/1.26 % (25363)Time elapsed: 0.007 s
% 1.46/1.26 % (25363)Instructions burned: 18 (million)
% 1.46/1.26 % (25363)------------------------------
% 1.46/1.26 % (25363)------------------------------
% 1.46/1.26 % (25365)Instruction limit reached!
% 1.46/1.26 % (25365)------------------------------
% 1.46/1.26 % (25365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (25365)Termination reason: Unknown
% 1.46/1.26 % (25365)Termination phase: shuffling
% 1.46/1.26
% 1.46/1.26 % (25365)Memory used [KB]: 1023
% 1.46/1.26 % (25365)Time elapsed: 0.003 s
% 1.46/1.26 % (25365)Instructions burned: 6 (million)
% 1.46/1.26 % (25365)------------------------------
% 1.46/1.26 % (25365)------------------------------
% 1.46/1.26 % (25367)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_25182 for (2999ds/902Mi)
% 1.46/1.26 % (25327)Instruction limit reached!
% 1.46/1.26 % (25327)------------------------------
% 1.46/1.26 % (25327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (25327)Termination reason: Unknown
% 1.46/1.26 % (25327)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (25327)Memory used [KB]: 6652
% 1.46/1.26 % (25327)Time elapsed: 0.057 s
% 1.46/1.26 % (25327)Instructions burned: 184 (million)
% 1.46/1.26 % (25327)------------------------------
% 1.46/1.26 % (25327)------------------------------
% 1.46/1.27 % (25371)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_25182 for (2999ds/21Mi)
% 1.46/1.27 % (25375)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/5Mi)
% 1.46/1.27 % (25375)Instruction limit reached!
% 1.46/1.27 % (25375)------------------------------
% 1.46/1.27 % (25375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (25375)Termination reason: Unknown
% 1.46/1.27 % (25375)Termination phase: Saturation
% 1.46/1.27
% 1.46/1.27 % (25375)Memory used [KB]: 5500
% 1.46/1.27 % (25375)Time elapsed: 0.003 s
% 1.46/1.27 % (25375)Instructions burned: 7 (million)
% 1.46/1.27 % (25375)------------------------------
% 1.46/1.27 % (25375)------------------------------
% 1.46/1.27 % (25371)Instruction limit reached!
% 1.46/1.27 % (25371)------------------------------
% 1.46/1.27 % (25371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (25371)Termination reason: Unknown
% 1.46/1.27 % (25371)Termination phase: Saturation
% 1.46/1.27
% 1.46/1.27 % (25371)Memory used [KB]: 5756
% 1.46/1.27 % (25371)Time elapsed: 0.008 s
% 1.46/1.27 % (25371)Instructions burned: 22 (million)
% 1.46/1.27 % (25371)------------------------------
% 1.46/1.27 % (25371)------------------------------
% 1.46/1.27 % (25378)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_25182 for (2999ds/6Mi)
% 1.46/1.28 % (25378)Instruction limit reached!
% 1.46/1.28 % (25378)------------------------------
% 1.46/1.28 % (25378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (25378)Termination reason: Unknown
% 1.46/1.28 % (25378)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (25378)Memory used [KB]: 5500
% 1.46/1.28 % (25378)Time elapsed: 0.003 s
% 1.46/1.28 % (25378)Instructions burned: 7 (million)
% 1.46/1.28 % (25378)------------------------------
% 1.46/1.28 % (25378)------------------------------
% 1.46/1.28 % (25379)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/377Mi)
% 1.46/1.28 % (25380)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_25182 for (2999ds/779Mi)
% 1.46/1.29 % (25381)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_25182 for (2999ds/19Mi)
% 1.46/1.29 % (25381)Instruction limit reached!
% 1.46/1.29 % (25381)------------------------------
% 1.46/1.29 % (25381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (25381)Termination reason: Unknown
% 1.46/1.29 % (25381)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (25381)Memory used [KB]: 5500
% 1.46/1.29 % (25381)Time elapsed: 0.006 s
% 1.46/1.29 % (25381)Instructions burned: 19 (million)
% 1.46/1.29 % (25381)------------------------------
% 1.46/1.29 % (25381)------------------------------
% 1.46/1.30 % (25332)Instruction limit reached!
% 1.46/1.30 % (25332)------------------------------
% 1.46/1.30 % (25332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (25332)Termination reason: Unknown
% 1.46/1.30 % (25332)Termination phase: Saturation
% 1.46/1.30
% 1.46/1.30 % (25332)Memory used [KB]: 6140
% 1.46/1.30 % (25332)Time elapsed: 0.088 s
% 1.46/1.30 % (25332)Instructions burned: 275 (million)
% 1.46/1.30 % (25332)------------------------------
% 1.46/1.30 % (25332)------------------------------
% 1.46/1.30 % (25393)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25182 for (2999ds/879Mi)
% 1.46/1.31 % (25396)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25182 for (2998ds/17Mi)
% 1.46/1.31 % (25396)Instruction limit reached!
% 1.46/1.31 % (25396)------------------------------
% 1.46/1.31 % (25396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.31 % (25396)Termination reason: Unknown
% 1.46/1.31 % (25396)Termination phase: Saturation
% 1.46/1.31
% 1.46/1.31 % (25396)Memory used [KB]: 5628
% 1.46/1.31 % (25396)Time elapsed: 0.007 s
% 1.46/1.31 % (25396)Instructions burned: 20 (million)
% 1.46/1.31 % (25396)------------------------------
% 1.46/1.31 % (25396)------------------------------
% 1.46/1.32 % (25347)First to succeed.
% 1.46/1.32 % (25404)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25182 for (2998ds/3Mi)
% 1.46/1.32 % (25404)Instruction limit reached!
% 1.46/1.32 % (25404)------------------------------
% 1.46/1.32 % (25404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.32 % (25404)Termination reason: Unknown
% 1.46/1.32 % (25404)Termination phase: Preprocessing 3
% 1.46/1.32
% 1.46/1.32 % (25404)Memory used [KB]: 1023
% 1.46/1.32 % (25404)Time elapsed: 0.002 s
% 1.46/1.32 % (25404)Instructions burned: 4 (million)
% 1.46/1.32 % (25404)------------------------------
% 1.46/1.32 % (25404)------------------------------
% 1.46/1.33 % (25347)Refutation found. Thanks to Tanya!
% 1.46/1.33 % SZS status Theorem for DTF2THF_25182
% 1.46/1.33 % SZS output start Proof for DTF2THF_25182
% 1.46/1.33 thf(type_def_5, type, a: $tType).
% 1.46/1.33 thf(func_def_0, type, a: $tType).
% 1.46/1.33 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)).
% 1.46/1.33 thf(func_def_22, type, sK2: a > a > $o).
% 1.46/1.33 thf(func_def_23, type, sK3: a > a > $o).
% 1.46/1.33 thf(func_def_24, type, sK4: a).
% 1.46/1.33 thf(func_def_25, type, sK5: a).
% 1.46/1.33 thf(func_def_26, type, sK6: a > $o).
% 1.46/1.33 thf(func_def_27, type, sK7: a).
% 1.46/1.33 thf(func_def_28, type, sK8: a).
% 1.46/1.33 thf(func_def_29, type, sK9: a).
% 1.46/1.33 thf(func_def_30, type, sK10: a).
% 1.46/1.33 thf(func_def_31, type, sK11: a).
% 1.46/1.33 thf(func_def_32, type, sK12: a).
% 1.46/1.33 thf(func_def_33, type, sK13: a).
% 1.46/1.33 thf(func_def_34, type, sK14: a).
% 1.46/1.33 thf(func_def_35, type, sK15: a).
% 1.46/1.33 thf(func_def_36, type, sK16: a).
% 1.46/1.33 thf(func_def_37, type, sK17: a).
% 1.46/1.33 thf(func_def_38, type, sK18: a).
% 1.46/1.33 thf(func_def_39, type, sK19: a).
% 1.46/1.33 thf(func_def_40, type, sK20: a).
% 1.46/1.33 thf(func_def_41, type, sK21: a).
% 1.46/1.33 thf(func_def_42, type, sK22: a).
% 1.46/1.33 thf(f1613,plain,(
% 1.46/1.33 $false),
% 1.46/1.33 inference(avatar_sat_refutation,[status(thm)],[f97,f184,f264,f423,f508,f622,f779,f902,f948,f1254,f1307,f1567,f1612])).
% 1.46/1.33 thf(f1612,plain,(
% 1.46/1.33 ~spl0_1 | ~spl0_10 | ~spl0_14),
% 1.46/1.33 inference(avatar_contradiction_clause,[status(thm)],[f1611])).
% 1.46/1.33 thf(f1611,plain,(
% 1.46/1.33 $false | (~spl0_1 | ~spl0_10 | ~spl0_14)),
% 1.46/1.33 inference(trivial_inequality_removal,[status(thm)],[f1610])).
% 1.46/1.33 thf(f1610,plain,(
% 1.46/1.33 ($false = $true) | (~spl0_1 | ~spl0_10 | ~spl0_14)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1609])).
% 1.46/1.33 thf(f1609,plain,(
% 1.46/1.33 ((~ $true) = $true) | (~spl0_1 | ~spl0_10 | ~spl0_14)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1608])).
% 1.46/1.33 thf(f1608,plain,(
% 1.46/1.33 ((~ ($true | (sK2 @ sK8 @ sK22))) = $true) | (~spl0_1 | ~spl0_10 | ~spl0_14)),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f1606,f1587])).
% 1.46/1.33 thf(f1587,plain,(
% 1.46/1.33 ((sK3 @ sK8 @ sK22) = $true) | ~spl0_14),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f1583])).
% 1.46/1.33 thf(f1583,plain,(
% 1.46/1.33 ($false = ((sK3 @ sK8 @ sK22) => (sK6 @ sK22))) | ~spl0_14),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f1581])).
% 1.46/1.33 thf(f1581,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK6 @ Y0))) @ sK22)) | ~spl0_14),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f1566])).
% 1.46/1.33 thf(f1566,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK6 @ Y0))))) | ~spl0_14),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f1565])).
% 1.46/1.33 thf(f1565,definition,(
% 1.46/1.33 spl0_14 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK6 @ Y0)))))),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.46/1.33 thf(f1606,plain,(
% 1.46/1.33 ($true = (~ ((sK3 @ sK8 @ sK22) | (sK2 @ sK8 @ sK22)))) | (~spl0_1 | ~spl0_10 | ~spl0_14)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1595])).
% 1.46/1.33 thf(f1595,plain,(
% 1.46/1.33 ($true = (((sK3 @ sK8 @ sK22) | (sK2 @ sK8 @ sK22)) => $false)) | (~spl0_1 | ~spl0_10 | ~spl0_14)),
% 1.46/1.33 inference(superposition,[status(thm)],[f1330,f1586])).
% 1.46/1.33 thf(f1586,plain,(
% 1.46/1.33 ($false = (sK6 @ sK22)) | ~spl0_14),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f1583])).
% 1.46/1.33 thf(f1330,plain,(
% 1.46/1.33 ( ! [X0 : a] : (((((sK3 @ sK8 @ X0) | (sK2 @ sK8 @ X0)) => (sK6 @ X0)) = $true)) ) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1325])).
% 1.46/1.33 thf(f1325,plain,(
% 1.46/1.33 ( ! [X0 : a] : ((((((sK3 @ sK8 @ X0) | (sK2 @ sK8 @ X0)) & $true) => (sK6 @ X0)) = $true)) ) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(superposition,[status(thm)],[f50,f1312])).
% 1.46/1.33 thf(f1312,plain,(
% 1.46/1.33 ((sK6 @ sK8) = $true) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f1310])).
% 1.46/1.33 thf(f1310,plain,(
% 1.46/1.33 ($false = ((sK6 @ sK8) => (sK6 @ sK9))) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1309])).
% 1.46/1.33 thf(f1309,plain,(
% 1.46/1.33 ((($true & (sK6 @ sK8)) => (sK6 @ sK9)) = $false) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1308])).
% 1.46/1.33 thf(f1308,plain,(
% 1.46/1.33 ($false = ((($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) & (sK6 @ sK8)) => (sK6 @ sK9))) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f967,f422])).
% 1.46/1.33 thf(f422,plain,(
% 1.46/1.33 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) = $true) | ~spl0_10),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f421])).
% 1.46/1.33 thf(f421,definition,(
% 1.46/1.33 spl0_10 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) = $true)),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.46/1.33 thf(f967,plain,(
% 1.46/1.33 (((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) & (sK6 @ sK8)) => (sK6 @ sK9)) = $false) | ~spl0_1),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f966])).
% 1.46/1.33 thf(f966,plain,(
% 1.46/1.33 (((^[Y0 : a]: ((((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK8 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK8 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) & (sK6 @ sK8)) => (sK6 @ Y0))) @ sK9) = $false) | ~spl0_1),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f957])).
% 1.46/1.33 thf(f957,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: ((((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK8 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK8 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) & (sK6 @ sK8)) => (sK6 @ Y0)))) = $false) | ~spl0_1),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f953])).
% 1.46/1.33 thf(f953,plain,(
% 1.46/1.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ sK8) = $false) | ~spl0_1),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f93])).
% 1.46/1.33 thf(f93,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1))))))) | ~spl0_1),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.46/1.33 thf(f92,definition,(
% 1.46/1.33 spl0_1 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))))),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.46/1.33 thf(f50,plain,(
% 1.46/1.33 ( ! [X2 : a,X1 : a] : (($true = ((((sK3 @ X1 @ X2) | (sK2 @ X1 @ X2)) & (sK6 @ X1)) => (sK6 @ X2)))) )),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.46/1.33 thf(f49,plain,(
% 1.46/1.33 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((((sK3 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) & (sK6 @ X1)) => (sK6 @ Y0))) @ X2) = $true)) )),
% 1.46/1.33 inference(pi_clausification,[status(thm)],[f45])).
% 1.46/1.33 thf(f45,plain,(
% 1.46/1.33 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((((sK3 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) & (sK6 @ X1)) => (sK6 @ Y0)))))) )),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.46/1.33 thf(f44,plain,(
% 1.46/1.33 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ X1) = $true)) )),
% 1.46/1.33 inference(pi_clausification,[status(thm)],[f33])).
% 1.46/1.33 thf(f33,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $true)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f32])).
% 1.46/1.33 thf(f32,plain,(
% 1.46/1.33 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1))))))) = $true)),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f27,f31])).
% 1.46/1.33 thf(f31,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK2 @ sK5 @ Y0)) => (sK6 @ Y0)))) = $true)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.46/1.33 thf(f27,plain,(
% 1.46/1.33 ($true = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK2 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1))))))))),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.46/1.33 thf(f25,plain,(
% 1.46/1.33 ($false = (((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK2 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1))))))) => (sK6 @ sK4)))),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.46/1.33 thf(f24,plain,(
% 1.46/1.33 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK2 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK4))) @ sK6) = $false)),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f18])).
% 1.46/1.33 thf(f18,plain,(
% 1.46/1.33 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK2 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK4)))))),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.46/1.33 thf(f17,plain,(
% 1.46/1.33 ($false = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ sK5 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ sK5 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1))))) => (Y0 @ sK4)))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK2 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK4))))))),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.46/1.33 thf(f16,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK3 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (Y1 @ Y2))))) => (Y1 @ sK4)))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ sK4)))))) @ sK5))),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f15])).
% 1.46/1.33 thf(f15,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK3 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (Y1 @ Y2))))) => (Y1 @ sK4)))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ sK4))))))) = $false)),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.46/1.33 thf(f14,plain,(
% 1.46/1.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK3 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4))))) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y1 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK3 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (Y2 @ Y3))))) => (Y2 @ Y0)))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))) @ sK4) = $false)),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f13])).
% 1.46/1.33 thf(f13,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK3 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4))))) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y1 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK3 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (Y2 @ Y3))))) => (Y2 @ Y0)))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))))))))),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.46/1.33 thf(f12,plain,(
% 1.46/1.33 (((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((sK2 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y2 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y0 @ Y2 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6))))))) => (Y5 @ Y4))))) => (Y3 @ Y4))))) => (Y3 @ Y1)))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((Y0 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))) @ sK3) = $false)),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f11])).
% 1.46/1.33 thf(f11,plain,(
% 1.46/1.33 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((sK2 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y2 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y0 @ Y2 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6))))))) => (Y5 @ Y4))))) => (Y3 @ Y4))))) => (Y3 @ Y1)))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((Y0 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y1))))))))))))),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.46/1.33 thf(f10,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y1 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6))))) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y3 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y3 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))) => (Y4 @ Y5))))) => (Y4 @ Y2)))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y0 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6))))))) => (Y4 @ Y2)))))))))))) @ sK2))),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f7])).
% 1.46/1.33 thf(f7,plain,(
% 1.46/1.33 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y1 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6))))) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y3 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y3 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))) => (Y4 @ Y5))))) => (Y4 @ Y2)))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y0 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6))))))) => (Y4 @ Y2))))))))))))) = $false)),
% 1.46/1.33 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.46/1.33 thf(f6,plain,(
% 1.46/1.33 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y1 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6))))) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y3 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y3 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))) => (Y4 @ Y5))))) => (Y4 @ Y2)))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y0 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6))))))) => (Y4 @ Y2)))))))))))))) = $true)),
% 1.46/1.33 inference(cnf_transformation,[status(thm)],[f5])).
% 1.46/1.33 thf(f5,plain,(
% 1.46/1.33 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y1 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6))))) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y3 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y3 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))) => (Y4 @ Y5))))) => (Y4 @ Y2)))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y0 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6))))))) => (Y4 @ Y2)))))))))))))) = $true)),
% 1.46/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.33 thf(f4,plain,(
% 1.46/1.33 ~! [X0 : a,X1 : a,X2 : a > a > $o,X3 : a > a > $o] : (! [X4 : a > $o] : ((! [X5 : a] : ((! [X6 : a > $o] : ((! [X7 : a,X8 : a] : (((X6 @ X7) & (X2 @ X7 @ X8)) => (X6 @ X8)) & ! [X9 : a] : ((X2 @ X0 @ X9) => (X6 @ X9))) => (X6 @ X5)) | ! [X10 : a > $o] : ((! [X11 : a] : ((X3 @ X0 @ X11) => (X10 @ X11)) & ! [X12 : a,X13 : a] : (((X10 @ X12) & (X3 @ X12 @ X13)) => (X10 @ X13))) => (X10 @ X5))) => (X4 @ X5)) & ! [X14 : a,X15 : a] : (((X4 @ X15) & (! [X16 : a > $o] : ((! [X17 : a] : ((X3 @ X15 @ X17) => (X16 @ X17)) & ! [X18 : a,X19 : a] : (((X16 @ X18) & (X3 @ X18 @ X19)) => (X16 @ X19))) => (X16 @ X14)) | ! [X20 : a > $o] : ((! [X21 : a] : ((X2 @ X15 @ X21) => (X20 @ X21)) & ! [X22 : a,X23 : a] : (((X20 @ X22) & (X2 @ X22 @ X23)) => (X20 @ X23))) => (X20 @ X14)))) => (X4 @ X14))) => (X4 @ X1)) => ! [X24 : a > $o] : ((! [X25 : a,X26 : a] : (((X24 @ X26) & ((X3 @ X26 @ X25) | (X2 @ X26 @ X25))) => (X24 @ X25)) & ! [X27 : a] : (((X3 @ X0 @ X27) | (X2 @ X0 @ X27)) => (X24 @ X27))) => (X24 @ X1)))),
% 1.46/1.33 inference(rectify,[status(thm)],[f2])).
% 1.46/1.33 thf(f2,negated_conjecture,(
% 1.46/1.33 ~! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (! [X4 : a > $o] : ((! [X5 : a] : ((! [X6 : a > $o] : ((! [X8 : a,X9 : a] : (((X6 @ X8) & (X0 @ X8 @ X9)) => (X6 @ X9)) & ! [X7 : a] : ((X0 @ X2 @ X7) => (X6 @ X7))) => (X6 @ X5)) | ! [X6 : a > $o] : ((! [X7 : a] : ((X1 @ X2 @ X7) => (X6 @ X7)) & ! [X8 : a,X9 : a] : (((X6 @ X8) & (X1 @ X8 @ X9)) => (X6 @ X9))) => (X6 @ X5))) => (X4 @ X5)) & ! [X9 : a,X8 : a] : (((X4 @ X8) & (! [X6 : a > $o] : ((! [X5 : a] : ((X1 @ X8 @ X5) => (X6 @ X5)) & ! [X10 : a,X11 : a] : (((X6 @ X10) & (X1 @ X10 @ X11)) => (X6 @ X11))) => (X6 @ X9)) | ! [X6 : a > $o] : ((! [X5 : a] : ((X0 @ X8 @ X5) => (X6 @ X5)) & ! [X10 : a,X11 : a] : (((X6 @ X10) & (X0 @ X10 @ X11)) => (X6 @ X11))) => (X6 @ X9)))) => (X4 @ X9))) => (X4 @ X3)) => ! [X4 : a > $o] : ((! [X9 : a,X8 : a] : (((X4 @ X8) & ((X1 @ X8 @ X9) | (X0 @ X8 @ X9))) => (X4 @ X9)) & ! [X5 : a] : (((X1 @ X2 @ X5) | (X0 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3)))),
% 1.46/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.33 thf(f1,conjecture,(
% 1.46/1.33 ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (! [X4 : a > $o] : ((! [X5 : a] : ((! [X6 : a > $o] : ((! [X8 : a,X9 : a] : (((X6 @ X8) & (X0 @ X8 @ X9)) => (X6 @ X9)) & ! [X7 : a] : ((X0 @ X2 @ X7) => (X6 @ X7))) => (X6 @ X5)) | ! [X6 : a > $o] : ((! [X7 : a] : ((X1 @ X2 @ X7) => (X6 @ X7)) & ! [X8 : a,X9 : a] : (((X6 @ X8) & (X1 @ X8 @ X9)) => (X6 @ X9))) => (X6 @ X5))) => (X4 @ X5)) & ! [X9 : a,X8 : a] : (((X4 @ X8) & (! [X6 : a > $o] : ((! [X5 : a] : ((X1 @ X8 @ X5) => (X6 @ X5)) & ! [X10 : a,X11 : a] : (((X6 @ X10) & (X1 @ X10 @ X11)) => (X6 @ X11))) => (X6 @ X9)) | ! [X6 : a > $o] : ((! [X5 : a] : ((X0 @ X8 @ X5) => (X6 @ X5)) & ! [X10 : a,X11 : a] : (((X6 @ X10) & (X0 @ X10 @ X11)) => (X6 @ X11))) => (X6 @ X9)))) => (X4 @ X9))) => (X4 @ X3)) => ! [X4 : a > $o] : ((! [X9 : a,X8 : a] : (((X4 @ X8) & ((X1 @ X8 @ X9) | (X0 @ X8 @ X9))) => (X4 @ X9)) & ! [X5 : a] : (((X1 @ X2 @ X5) | (X0 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3)))),
% 1.46/1.33 file('/export/starexec/sandbox2/tmp/tmp.k0lBrjUgxb/DTF2THF_25182.p',cTHM251C_pme)).
% 1.46/1.33 thf(f1567,plain,(
% 1.46/1.33 spl0_14 | spl0_12 | ~spl0_1 | ~spl0_10),
% 1.46/1.33 inference(avatar_split_clause,[status(thm)],[f1561,f421,f92,f620,f1565])).
% 1.46/1.33 thf(f620,definition,(
% 1.46/1.33 spl0_12 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) = $false)),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.46/1.33 thf(f1561,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK6 @ Y0))))) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f1547])).
% 1.46/1.33 thf(f1547,plain,(
% 1.46/1.33 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK6 @ Y0)))))) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(not_proxy_clausification,[status(thm)],[f1530])).
% 1.46/1.33 thf(f1530,plain,(
% 1.46/1.33 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK6 @ Y0)))))) = $true) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1521])).
% 1.46/1.33 thf(f1521,plain,(
% 1.46/1.33 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (sK6 @ Y0))))) => $false)) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(superposition,[status(thm)],[f1504,f1314])).
% 1.46/1.33 thf(f1314,plain,(
% 1.46/1.33 ((sK6 @ sK9) = $false) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1313])).
% 1.46/1.33 thf(f1313,plain,(
% 1.46/1.33 ($false = ($true => (sK6 @ sK9))) | (~spl0_1 | ~spl0_10)),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f1310,f1312])).
% 1.46/1.33 thf(f1504,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (X1 @ Y1)) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK8 @ Y0) => (X1 @ Y0))))) => (X1 @ sK9)))) ) | ~spl0_10),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f1503])).
% 1.46/1.33 thf(f1503,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))) @ X1) = $true)) ) | ~spl0_10),
% 1.46/1.33 inference(pi_clausification,[status(thm)],[f422])).
% 1.46/1.33 thf(f1307,plain,(
% 1.46/1.33 ~spl0_1 | ~spl0_9 | ~spl0_13),
% 1.46/1.33 inference(avatar_contradiction_clause,[status(thm)],[f1306])).
% 1.46/1.33 thf(f1306,plain,(
% 1.46/1.33 $false | (~spl0_1 | ~spl0_9 | ~spl0_13)),
% 1.46/1.33 inference(trivial_inequality_removal,[status(thm)],[f1305])).
% 1.46/1.33 thf(f1305,plain,(
% 1.46/1.33 ($false = $true) | (~spl0_1 | ~spl0_9 | ~spl0_13)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1304])).
% 1.46/1.33 thf(f1304,plain,(
% 1.46/1.33 ((~ $true) = $true) | (~spl0_1 | ~spl0_9 | ~spl0_13)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1303])).
% 1.46/1.33 thf(f1303,plain,(
% 1.46/1.33 ($true = (~ ((sK3 @ sK8 @ sK21) | $true))) | (~spl0_1 | ~spl0_9 | ~spl0_13)),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f1298,f1285])).
% 1.46/1.33 thf(f1285,plain,(
% 1.46/1.33 ((sK2 @ sK8 @ sK21) = $true) | ~spl0_13),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f1270])).
% 1.46/1.33 thf(f1270,plain,(
% 1.46/1.33 (((sK2 @ sK8 @ sK21) => (sK6 @ sK21)) = $false) | ~spl0_13),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f1268])).
% 1.46/1.33 thf(f1268,plain,(
% 1.46/1.33 (((^[Y0 : a]: ((sK2 @ sK8 @ Y0) => (sK6 @ Y0))) @ sK21) = $false) | ~spl0_13),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f1253])).
% 1.46/1.33 thf(f1253,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK8 @ Y0) => (sK6 @ Y0)))) = $false) | ~spl0_13),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f1252])).
% 1.46/1.33 thf(f1252,definition,(
% 1.46/1.33 spl0_13 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK8 @ Y0) => (sK6 @ Y0)))) = $false)),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.46/1.33 thf(f1298,plain,(
% 1.46/1.33 ((~ ((sK3 @ sK8 @ sK21) | (sK2 @ sK8 @ sK21))) = $true) | (~spl0_1 | ~spl0_9 | ~spl0_13)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1291])).
% 1.46/1.33 thf(f1291,plain,(
% 1.46/1.33 ((((sK3 @ sK8 @ sK21) | (sK2 @ sK8 @ sK21)) => $false) = $true) | (~spl0_1 | ~spl0_9 | ~spl0_13)),
% 1.46/1.33 inference(superposition,[status(thm)],[f1003,f1284])).
% 1.46/1.33 thf(f1284,plain,(
% 1.46/1.33 ($false = (sK6 @ sK21)) | ~spl0_13),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f1270])).
% 1.46/1.33 thf(f1003,plain,(
% 1.46/1.33 ( ! [X0 : a] : (((((sK3 @ sK8 @ X0) | (sK2 @ sK8 @ X0)) => (sK6 @ X0)) = $true)) ) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f998])).
% 1.46/1.33 thf(f998,plain,(
% 1.46/1.33 ( ! [X0 : a] : ((((((sK3 @ sK8 @ X0) | (sK2 @ sK8 @ X0)) & $true) => (sK6 @ X0)) = $true)) ) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(superposition,[status(thm)],[f50,f978])).
% 1.46/1.33 thf(f978,plain,(
% 1.46/1.33 ((sK6 @ sK8) = $true) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f970])).
% 1.46/1.33 thf(f970,plain,(
% 1.46/1.33 ($false = ((sK6 @ sK8) => (sK6 @ sK9))) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f969])).
% 1.46/1.33 thf(f969,plain,(
% 1.46/1.33 ((($true & (sK6 @ sK8)) => (sK6 @ sK9)) = $false) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f968])).
% 1.46/1.33 thf(f968,plain,(
% 1.46/1.33 (((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | $true) & (sK6 @ sK8)) => (sK6 @ sK9)) = $false) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f967,f419])).
% 1.46/1.33 thf(f419,plain,(
% 1.46/1.33 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) = $true) | ~spl0_9),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f418])).
% 1.46/1.33 thf(f418,definition,(
% 1.46/1.33 spl0_9 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) = $true)),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.46/1.33 thf(f1254,plain,(
% 1.46/1.33 spl0_8 | spl0_13 | ~spl0_1 | ~spl0_9),
% 1.46/1.33 inference(avatar_split_clause,[status(thm)],[f1248,f418,f92,f1252,f262])).
% 1.46/1.33 thf(f262,definition,(
% 1.46/1.33 spl0_8 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) = $false)),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.46/1.33 thf(f1248,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK8 @ Y0) => (sK6 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) = $false) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f1236])).
% 1.46/1.33 thf(f1236,plain,(
% 1.46/1.33 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK8 @ Y0) => (sK6 @ Y0))))) = $false) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(not_proxy_clausification,[status(thm)],[f1172])).
% 1.46/1.33 thf(f1172,plain,(
% 1.46/1.33 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK8 @ Y0) => (sK6 @ Y0)))))) = $true) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f1167])).
% 1.46/1.33 thf(f1167,plain,(
% 1.46/1.33 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK8 @ Y0) => (sK6 @ Y0))))) => $false) = $true) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(superposition,[status(thm)],[f1153,f977])).
% 1.46/1.33 thf(f977,plain,(
% 1.46/1.33 ((sK6 @ sK9) = $false) | (~spl0_1 | ~spl0_9)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f970])).
% 1.46/1.33 thf(f1153,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (X1 @ Y1)) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK8 @ Y0) => (X1 @ Y0))))) => (X1 @ sK9)) = $true)) ) | ~spl0_9),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f1152])).
% 1.46/1.33 thf(f1152,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))) @ X1))) ) | ~spl0_9),
% 1.46/1.33 inference(pi_clausification,[status(thm)],[f419])).
% 1.46/1.33 thf(f948,plain,(
% 1.46/1.33 ~spl0_12),
% 1.46/1.33 inference(avatar_contradiction_clause,[status(thm)],[f947])).
% 1.46/1.33 thf(f947,plain,(
% 1.46/1.33 $false | ~spl0_12),
% 1.46/1.33 inference(trivial_inequality_removal,[status(thm)],[f946])).
% 1.46/1.33 thf(f946,plain,(
% 1.46/1.33 ($false = $true) | ~spl0_12),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f945,f913])).
% 1.46/1.33 thf(f913,plain,(
% 1.46/1.33 ((sK6 @ sK17) = $false) | ~spl0_12),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f912])).
% 1.46/1.33 thf(f912,plain,(
% 1.46/1.33 ($false = (((sK3 @ sK18 @ sK17) & (sK6 @ sK18)) => (sK6 @ sK17))) | ~spl0_12),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f911])).
% 1.46/1.33 thf(f911,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: (((sK3 @ Y0 @ sK17) & (sK6 @ Y0)) => (sK6 @ sK17))) @ sK18)) | ~spl0_12),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f910])).
% 1.46/1.33 thf(f910,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (((sK3 @ Y0 @ sK17) & (sK6 @ Y0)) => (sK6 @ sK17))))) | ~spl0_12),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f906])).
% 1.46/1.33 thf(f906,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0))))) @ sK17)) | ~spl0_12),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f621])).
% 1.46/1.33 thf(f621,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) = $false) | ~spl0_12),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f620])).
% 1.46/1.33 thf(f945,plain,(
% 1.46/1.33 ((sK6 @ sK17) = $true) | ~spl0_12),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f944])).
% 1.46/1.33 thf(f944,plain,(
% 1.46/1.33 (($true => (sK6 @ sK17)) = $true) | ~spl0_12),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f943,f937])).
% 1.46/1.33 thf(f937,plain,(
% 1.46/1.33 ($true = (sK6 @ sK19)) | ~spl0_12),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f934])).
% 1.46/1.33 thf(f934,plain,(
% 1.46/1.33 (((sK3 @ sK19 @ sK17) & (sK6 @ sK19)) = $true) | ~spl0_12),
% 1.46/1.33 inference(not_proxy_clausification,[status(thm)],[f922])).
% 1.46/1.33 thf(f922,plain,(
% 1.46/1.33 ((~ ((sK3 @ sK19 @ sK17) & (sK6 @ sK19))) = $false) | ~spl0_12),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f921])).
% 1.46/1.33 thf(f921,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: (~ ((sK3 @ Y0 @ sK17) & (sK6 @ Y0)))) @ sK19)) | ~spl0_12),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f918])).
% 1.46/1.33 thf(f918,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK3 @ Y0 @ sK17) & (sK6 @ Y0)))))) | ~spl0_12),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f916])).
% 1.46/1.33 thf(f916,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (((sK3 @ Y0 @ sK17) & (sK6 @ Y0)) => $false)))) | ~spl0_12),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f910,f913])).
% 1.46/1.33 thf(f943,plain,(
% 1.46/1.33 ($true = ((sK6 @ sK19) => (sK6 @ sK17))) | ~spl0_12),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f942])).
% 1.46/1.33 thf(f942,plain,(
% 1.46/1.33 ((($true & (sK6 @ sK19)) => (sK6 @ sK17)) = $true) | ~spl0_12),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f941])).
% 1.46/1.33 thf(f941,plain,(
% 1.46/1.33 (((($true | (sK2 @ sK19 @ sK17)) & (sK6 @ sK19)) => (sK6 @ sK17)) = $true) | ~spl0_12),
% 1.46/1.33 inference(superposition,[status(thm)],[f50,f940])).
% 1.46/1.33 thf(f940,plain,(
% 1.46/1.33 ((sK3 @ sK19 @ sK17) = $true) | ~spl0_12),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f939])).
% 1.46/1.33 thf(f939,plain,(
% 1.46/1.33 ($true = ((sK3 @ sK19 @ sK17) & $true)) | ~spl0_12),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f934,f937])).
% 1.46/1.33 thf(f902,plain,(
% 1.46/1.33 ~spl0_11),
% 1.46/1.33 inference(avatar_contradiction_clause,[status(thm)],[f901])).
% 1.46/1.33 thf(f901,plain,(
% 1.46/1.33 $false | ~spl0_11),
% 1.46/1.33 inference(trivial_inequality_removal,[status(thm)],[f900])).
% 1.46/1.33 thf(f900,plain,(
% 1.46/1.33 ($false = $true) | ~spl0_11),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f899])).
% 1.46/1.33 thf(f899,plain,(
% 1.46/1.33 ((~ $true) = $true) | ~spl0_11),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f898])).
% 1.46/1.33 thf(f898,plain,(
% 1.46/1.33 ((~ ($true | (sK2 @ sK5 @ sK16))) = $true) | ~spl0_11),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f897,f884])).
% 1.46/1.33 thf(f884,plain,(
% 1.46/1.33 ((sK3 @ sK5 @ sK16) = $true) | ~spl0_11),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f880])).
% 1.46/1.33 thf(f880,plain,(
% 1.46/1.33 ($false = ((sK3 @ sK5 @ sK16) => (sK6 @ sK16))) | ~spl0_11),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f878])).
% 1.46/1.33 thf(f878,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: ((sK3 @ sK5 @ Y0) => (sK6 @ Y0))) @ sK16)) | ~spl0_11),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f618])).
% 1.46/1.33 thf(f618,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK5 @ Y0) => (sK6 @ Y0))))) | ~spl0_11),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f617])).
% 1.46/1.33 thf(f617,definition,(
% 1.46/1.33 spl0_11 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK5 @ Y0) => (sK6 @ Y0)))))),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.46/1.33 thf(f897,plain,(
% 1.46/1.33 ($true = (~ ((sK3 @ sK5 @ sK16) | (sK2 @ sK5 @ sK16)))) | ~spl0_11),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f891])).
% 1.46/1.33 thf(f891,plain,(
% 1.46/1.33 ($true = (((sK3 @ sK5 @ sK16) | (sK2 @ sK5 @ sK16)) => $false)) | ~spl0_11),
% 1.46/1.33 inference(superposition,[status(thm)],[f37,f886])).
% 1.46/1.33 thf(f886,plain,(
% 1.46/1.33 ($false = (sK6 @ sK16)) | ~spl0_11),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f885])).
% 1.46/1.33 thf(f885,plain,(
% 1.46/1.33 ($false = ($true => (sK6 @ sK16))) | ~spl0_11),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f880,f884])).
% 1.46/1.33 thf(f37,plain,(
% 1.46/1.33 ( ! [X1 : a] : (((((sK3 @ sK5 @ X1) | (sK2 @ sK5 @ X1)) => (sK6 @ X1)) = $true)) )),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.46/1.33 thf(f36,plain,(
% 1.46/1.33 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK2 @ sK5 @ Y0)) => (sK6 @ Y0))) @ X1) = $true)) )),
% 1.46/1.33 inference(pi_clausification,[status(thm)],[f31])).
% 1.46/1.33 thf(f779,plain,(
% 1.46/1.33 ~spl0_8),
% 1.46/1.33 inference(avatar_contradiction_clause,[status(thm)],[f778])).
% 1.46/1.33 thf(f778,plain,(
% 1.46/1.33 $false | ~spl0_8),
% 1.46/1.33 inference(trivial_inequality_removal,[status(thm)],[f777])).
% 1.46/1.33 thf(f777,plain,(
% 1.46/1.33 ($false = $true) | ~spl0_8),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f776,f725])).
% 1.46/1.33 thf(f725,plain,(
% 1.46/1.33 ((sK6 @ sK13) = $false) | ~spl0_8),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f724])).
% 1.46/1.33 thf(f724,plain,(
% 1.46/1.33 ($false = ($true => (sK6 @ sK13))) | ~spl0_8),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f721,f723])).
% 1.46/1.33 thf(f723,plain,(
% 1.46/1.33 ($true = ((sK2 @ sK14 @ sK13) & (sK6 @ sK14))) | ~spl0_8),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f721])).
% 1.46/1.33 thf(f721,plain,(
% 1.46/1.33 ($false = (((sK2 @ sK14 @ sK13) & (sK6 @ sK14)) => (sK6 @ sK13))) | ~spl0_8),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f720])).
% 1.46/1.33 thf(f720,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: (((sK2 @ Y0 @ sK13) & (sK6 @ Y0)) => (sK6 @ sK13))) @ sK14)) | ~spl0_8),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f717])).
% 1.46/1.33 thf(f717,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK13) & (sK6 @ Y0)) => (sK6 @ sK13))))) | ~spl0_8),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f715])).
% 1.46/1.33 thf(f715,plain,(
% 1.46/1.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0))))) @ sK13) = $false) | ~spl0_8),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f263])).
% 1.46/1.33 thf(f263,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) = $false) | ~spl0_8),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f262])).
% 1.46/1.33 thf(f776,plain,(
% 1.46/1.33 ((sK6 @ sK13) = $true) | ~spl0_8),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f775])).
% 1.46/1.33 thf(f775,plain,(
% 1.46/1.33 (($true => (sK6 @ sK13)) = $true) | ~spl0_8),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f774,f758])).
% 1.46/1.33 thf(f758,plain,(
% 1.46/1.33 ((sK6 @ sK15) = $true) | ~spl0_8),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f745])).
% 1.46/1.33 thf(f745,plain,(
% 1.46/1.33 (((sK2 @ sK15 @ sK13) & (sK6 @ sK15)) = $true) | ~spl0_8),
% 1.46/1.33 inference(not_proxy_clausification,[status(thm)],[f740])).
% 1.46/1.33 thf(f740,plain,(
% 1.46/1.33 ($false = (~ ((sK2 @ sK15 @ sK13) & (sK6 @ sK15)))) | ~spl0_8),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f739])).
% 1.46/1.33 thf(f739,plain,(
% 1.46/1.33 (((^[Y0 : a]: (~ ((sK2 @ Y0 @ sK13) & (sK6 @ Y0)))) @ sK15) = $false) | ~spl0_8),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f727])).
% 1.46/1.33 thf(f727,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: (~ ((sK2 @ Y0 @ sK13) & (sK6 @ Y0))))) = $false) | ~spl0_8),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f726])).
% 1.46/1.33 thf(f726,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK13) & (sK6 @ Y0)) => $false)))) | ~spl0_8),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f717,f725])).
% 1.46/1.33 thf(f774,plain,(
% 1.46/1.33 (((sK6 @ sK15) => (sK6 @ sK13)) = $true) | ~spl0_8),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f773])).
% 1.46/1.33 thf(f773,plain,(
% 1.46/1.33 ($true = (($true & (sK6 @ sK15)) => (sK6 @ sK13))) | ~spl0_8),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f772])).
% 1.46/1.33 thf(f772,plain,(
% 1.46/1.33 (((((sK3 @ sK15 @ sK13) | $true) & (sK6 @ sK15)) => (sK6 @ sK13)) = $true) | ~spl0_8),
% 1.46/1.33 inference(superposition,[status(thm)],[f50,f761])).
% 1.46/1.33 thf(f761,plain,(
% 1.46/1.33 ((sK2 @ sK15 @ sK13) = $true) | ~spl0_8),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f760])).
% 1.46/1.33 thf(f760,plain,(
% 1.46/1.33 ($true = ((sK2 @ sK15 @ sK13) & $true)) | ~spl0_8),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f745,f758])).
% 1.46/1.33 thf(f622,plain,(
% 1.46/1.33 spl0_11 | spl0_12 | ~spl0_2 | ~spl0_3),
% 1.46/1.33 inference(avatar_split_clause,[status(thm)],[f613,f179,f95,f620,f617])).
% 1.46/1.33 thf(f95,definition,(
% 1.46/1.33 spl0_2 <=> ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))))),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.46/1.33 thf(f179,definition,(
% 1.46/1.33 spl0_3 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK5 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK7)))))),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.46/1.33 thf(f613,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK5 @ Y0) => (sK6 @ Y0))))) | (~spl0_2 | ~spl0_3)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f605])).
% 1.46/1.33 thf(f605,plain,(
% 1.46/1.33 ($false = ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK5 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))))) | (~spl0_2 | ~spl0_3)),
% 1.46/1.33 inference(not_proxy_clausification,[status(thm)],[f583])).
% 1.46/1.33 thf(f583,plain,(
% 1.46/1.33 ($true = (~ ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK5 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0))))))))) | (~spl0_2 | ~spl0_3)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f580])).
% 1.46/1.33 thf(f580,plain,(
% 1.46/1.33 ((((!! @ a @ (^[Y0 : a]: ((sK3 @ sK5 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0))))))) => $false) = $true) | (~spl0_2 | ~spl0_3)),
% 1.46/1.33 inference(superposition,[status(thm)],[f563,f511])).
% 1.46/1.33 thf(f511,plain,(
% 1.46/1.33 ((sK6 @ sK7) = $false) | (~spl0_2 | ~spl0_3)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f510])).
% 1.46/1.33 thf(f510,plain,(
% 1.46/1.33 (($true => (sK6 @ sK7)) = $false) | (~spl0_2 | ~spl0_3)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f509])).
% 1.46/1.33 thf(f509,plain,(
% 1.46/1.33 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK5 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK7)))) | $true) => (sK6 @ sK7)) = $false) | (~spl0_2 | ~spl0_3)),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f435,f180])).
% 1.46/1.33 thf(f180,plain,(
% 1.46/1.33 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK5 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK7))))) | ~spl0_3),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f179])).
% 1.46/1.33 thf(f435,plain,(
% 1.46/1.33 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK5 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK7)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK5 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK7))))) => (sK6 @ sK7))) | ~spl0_2),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f431])).
% 1.46/1.33 thf(f431,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))) @ sK7)) | ~spl0_2),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f96])).
% 1.46/1.33 thf(f96,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))) | ~spl0_2),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.46/1.33 thf(f563,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((sK3 @ sK5 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) & (X1 @ Y1)) => (X1 @ Y0))))))) => (X1 @ sK7)))) ) | ~spl0_3),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f562])).
% 1.46/1.33 thf(f562,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK5 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK7))) @ X1))) ) | ~spl0_3),
% 1.46/1.33 inference(pi_clausification,[status(thm)],[f180])).
% 1.46/1.33 thf(f508,plain,(
% 1.46/1.33 ~spl0_7),
% 1.46/1.33 inference(avatar_contradiction_clause,[status(thm)],[f507])).
% 1.46/1.33 thf(f507,plain,(
% 1.46/1.33 $false | ~spl0_7),
% 1.46/1.33 inference(trivial_inequality_removal,[status(thm)],[f506])).
% 1.46/1.33 thf(f506,plain,(
% 1.46/1.33 ($false = $true) | ~spl0_7),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f505])).
% 1.46/1.33 thf(f505,plain,(
% 1.46/1.33 ((~ $true) = $true) | ~spl0_7),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f504])).
% 1.46/1.33 thf(f504,plain,(
% 1.46/1.33 ((~ ((sK3 @ sK5 @ sK10) | $true)) = $true) | ~spl0_7),
% 1.46/1.33 inference(forward_demodulation,[status(thm)],[f498,f479])).
% 1.46/1.33 thf(f479,plain,(
% 1.46/1.33 ((sK2 @ sK5 @ sK10) = $true) | ~spl0_7),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f428])).
% 1.46/1.33 thf(f428,plain,(
% 1.46/1.33 ($false = ((sK2 @ sK5 @ sK10) => (sK6 @ sK10))) | ~spl0_7),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f426])).
% 1.46/1.33 thf(f426,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: ((sK2 @ sK5 @ Y0) => (sK6 @ Y0))) @ sK10)) | ~spl0_7),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f260])).
% 1.46/1.33 thf(f260,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) => (sK6 @ Y0)))) = $false) | ~spl0_7),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f259])).
% 1.46/1.33 thf(f259,definition,(
% 1.46/1.33 spl0_7 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) => (sK6 @ Y0)))) = $false)),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.46/1.33 thf(f498,plain,(
% 1.46/1.33 ((~ ((sK3 @ sK5 @ sK10) | (sK2 @ sK5 @ sK10))) = $true) | ~spl0_7),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f497])).
% 1.46/1.33 thf(f497,plain,(
% 1.46/1.33 ((((sK3 @ sK5 @ sK10) | (sK2 @ sK5 @ sK10)) => $false) = $true) | ~spl0_7),
% 1.46/1.33 inference(superposition,[status(thm)],[f37,f478])).
% 1.46/1.33 thf(f478,plain,(
% 1.46/1.33 ($false = (sK6 @ sK10)) | ~spl0_7),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f428])).
% 1.46/1.33 thf(f423,plain,(
% 1.46/1.33 spl0_9 | spl0_10 | ~spl0_1),
% 1.46/1.33 inference(avatar_split_clause,[status(thm)],[f416,f92,f421,f418])).
% 1.46/1.33 thf(f416,plain,(
% 1.46/1.33 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) = $true) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) = $true) | ~spl0_1),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f329])).
% 1.46/1.33 thf(f329,plain,(
% 1.46/1.33 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) = $true) | ~spl0_1),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f275])).
% 1.46/1.33 thf(f275,plain,(
% 1.46/1.33 ($true = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) & (sK6 @ sK8))) | ~spl0_1),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f273])).
% 1.46/1.33 thf(f273,plain,(
% 1.46/1.33 (((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK8 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) & (sK6 @ sK8)) => (sK6 @ sK9)) = $false) | ~spl0_1),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f272])).
% 1.46/1.33 thf(f272,plain,(
% 1.46/1.33 (((^[Y0 : a]: ((((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK8 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK8 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) & (sK6 @ sK8)) => (sK6 @ Y0))) @ sK9) = $false) | ~spl0_1),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f271])).
% 1.46/1.33 thf(f271,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: ((((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ sK8 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK8 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) & (sK6 @ sK8)) => (sK6 @ Y0)))) = $false) | ~spl0_1),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f267])).
% 1.46/1.33 thf(f267,plain,(
% 1.46/1.33 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ sK8) = $false) | ~spl0_1),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f93])).
% 1.46/1.33 thf(f264,plain,(
% 1.46/1.33 spl0_7 | spl0_8 | ~spl0_2 | ~spl0_4),
% 1.46/1.33 inference(avatar_split_clause,[status(thm)],[f255,f182,f95,f262,f259])).
% 1.46/1.33 thf(f182,definition,(
% 1.46/1.33 spl0_4 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK5 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK7)))))),
% 1.46/1.33 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.46/1.33 thf(f255,plain,(
% 1.46/1.33 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) => (sK6 @ Y0)))) = $false) | (~spl0_2 | ~spl0_4)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f249])).
% 1.46/1.33 thf(f249,plain,(
% 1.46/1.33 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) => (sK6 @ Y0)))))) | (~spl0_2 | ~spl0_4)),
% 1.46/1.33 inference(not_proxy_clausification,[status(thm)],[f248])).
% 1.46/1.33 thf(f248,plain,(
% 1.46/1.33 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) => (sK6 @ Y0)))))) = $true) | (~spl0_2 | ~spl0_4)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f242])).
% 1.46/1.33 thf(f242,plain,(
% 1.46/1.33 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) => (sK6 @ Y0))))) => $false)) | (~spl0_2 | ~spl0_4)),
% 1.46/1.33 inference(superposition,[status(thm)],[f240,f137])).
% 1.46/1.33 thf(f137,plain,(
% 1.46/1.33 ((sK6 @ sK7) = $false) | ~spl0_2),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f136])).
% 1.46/1.33 thf(f136,plain,(
% 1.46/1.33 (($true => (sK6 @ sK7)) = $false) | ~spl0_2),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f120,f135])).
% 1.46/1.33 thf(f135,plain,(
% 1.46/1.33 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK5 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK7)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK5 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK7)))))) | ~spl0_2),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f120])).
% 1.46/1.33 thf(f120,plain,(
% 1.46/1.33 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK5 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK7)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK5 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK7))))) => (sK6 @ sK7))) | ~spl0_2),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.46/1.33 thf(f116,plain,(
% 1.46/1.33 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))) @ sK7)) | ~spl0_2),
% 1.46/1.33 inference(sigma_clausification,[status(thm)],[f96])).
% 1.46/1.33 thf(f240,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (X1 @ Y1)) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK5 @ Y0) => (X1 @ Y0))))) => (X1 @ sK7)) = $true)) ) | ~spl0_4),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f239])).
% 1.46/1.33 thf(f239,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK5 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK7))) @ X1) = $true)) ) | ~spl0_4),
% 1.46/1.33 inference(pi_clausification,[status(thm)],[f183])).
% 1.46/1.33 thf(f183,plain,(
% 1.46/1.33 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK5 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK7))))) | ~spl0_4),
% 1.46/1.33 inference(avatar_component_clause,[status(thm)],[f182])).
% 1.46/1.33 thf(f184,plain,(
% 1.46/1.33 spl0_3 | spl0_4 | ~spl0_2),
% 1.46/1.33 inference(avatar_split_clause,[status(thm)],[f177,f95,f182,f179])).
% 1.46/1.33 thf(f177,plain,(
% 1.46/1.33 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK5 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK7))))) | ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK5 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK7))))) | ~spl0_2),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.46/1.33 thf(f97,plain,(
% 1.46/1.33 spl0_1 | spl0_2),
% 1.46/1.33 inference(avatar_split_clause,[status(thm)],[f88,f95,f92])).
% 1.46/1.33 thf(f88,plain,(
% 1.46/1.33 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))))),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.46/1.33 thf(f74,plain,(
% 1.46/1.33 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))))),
% 1.46/1.33 inference(not_proxy_clausification,[status(thm)],[f40])).
% 1.46/1.33 thf(f40,plain,(
% 1.46/1.33 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))))) = $true)),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f39])).
% 1.46/1.33 thf(f39,plain,(
% 1.46/1.33 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))) => $false) = $true)),
% 1.46/1.33 inference(superposition,[status(thm)],[f35,f29])).
% 1.46/1.33 thf(f29,plain,(
% 1.46/1.33 ($false = (sK6 @ sK4))),
% 1.46/1.33 inference(boolean_simplification,[status(thm)],[f28])).
% 1.46/1.33 thf(f28,plain,(
% 1.46/1.33 (($true => (sK6 @ sK4)) = $false)),
% 1.46/1.33 inference(backward_demodulation,[status(thm)],[f25,f27])).
% 1.46/1.33 thf(f35,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (X1 @ Y0)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK5 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK5 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (X1 @ Y0))))) => (X1 @ sK4)) = $true)) )),
% 1.46/1.33 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.46/1.33 thf(f34,plain,(
% 1.46/1.33 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ sK5 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ sK5 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1))))) => (Y0 @ sK4))) @ X1) = $true)) )),
% 1.46/1.33 inference(pi_clausification,[status(thm)],[f19])).
% 1.46/1.33 thf(f19,plain,(
% 1.46/1.33 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ sK5 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ sK5 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (Y0 @ Y1))))) => (Y0 @ sK4)))) = $true)),
% 1.46/1.33 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.46/1.33 % SZS output end Proof for DTF2THF_25182
% 1.46/1.33 % (25347)------------------------------
% 1.46/1.33 % (25347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.33 % (25347)Termination reason: Refutation
% 1.46/1.33
% 1.46/1.33 % (25347)Memory used [KB]: 6396
% 1.46/1.33 % (25347)Time elapsed: 0.100 s
% 1.46/1.33 % (25347)Instructions burned: 268 (million)
% 1.46/1.33 % (25347)------------------------------
% 1.46/1.33 % (25347)------------------------------
% 1.46/1.33 % (25326)Success in time 0.135 s
%------------------------------------------------------------------------------