%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV125^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:20 AM UTC 2026
% Result : Theorem 1.63s 1.78s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 3
% Syntax : Number of formulae : 169 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 2224 ( 527 equ; 0 cnn)
% Maximal formula atoms : 13 ( 13 avg)
% Number of connectives : 4369 ( 146 ~; 482 |; 253 &;2767 @)
% ( 2 <=>; 262 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1176 (1176 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 8 con; 0-5 aty)
% ( 344 !!; 113 ??; 0 @@+; 0 @@-)
% Number of variables : 937 ( 647 ^; 281 !; 9 ?; 937 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: ( a > a > $o ) > $o ).
thf(func_def_22,type,
sK3: ( a > a > $o ) > $o ).
thf(func_def_23,type,
sK4: a ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_26,type,
sK7: ( a > a > $o ) > a ).
thf(func_def_27,type,
sK8: ( a > a > $o ) > a > a > $o ).
thf(func_def_28,type,
sK9: a > a > $o ).
thf(func_def_29,type,
sK10: a > a > ( a > a > $o ) > a > a > $o ).
thf(func_def_30,type,
sK11: a > a > $o ).
thf(func_def_31,type,
sK12: ( a > a > $o ) > a ).
thf(func_def_32,type,
sK13: ( a > a > $o ) > a ).
thf(func_def_33,type,
sK14: ( a > a > $o ) > a > a > $o ).
thf(func_def_34,type,
sK15: ( a > a > $o ) > a > a > $o ).
thf(func_def_35,type,
sK16: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_36,type,
sK17: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(f363,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f130,f362]) ).
thf(f362,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f361]) ).
thf(f361,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f360]) ).
thf(f360,plain,
( ( $true = $false )
| ~ spl0_1
| spl0_2 ),
inference(backward_demodulation,[status(thm)],[f136,f359]) ).
thf(f359,plain,
( ( ( sK2 @ sK11 )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f358]) ).
thf(f358,plain,
( ( $true = $false )
| ( ( sK2 @ sK11 )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f351,f133]) ).
thf(f133,plain,
( ( ( sK11 @ sK4 @ sK5 )
= $false )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $false
= ( ( ( sK2 @ sK11 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
=> ( sK11 @ sK4 @ sK5 ) ) )
| spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK11 ) )
| spl0_2 ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl0_2
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f351,plain,
( ( $true
= ( sK11 @ sK4 @ sK5 ) )
| ( ( sK2 @ sK11 )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f350]) ).
thf(f350,plain,
( ( ( sK2 @ sK11 )
= $false )
| ( $true = $false )
| ( $true
= ( sK11 @ sK4 @ sK5 ) )
| ~ spl0_1
| spl0_2 ),
inference(superposition,[status(thm)],[f207,f321]) ).
thf(f321,plain,
( ( ( sK3 @ ( sK15 @ sK11 ) )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f320]) ).
thf(f320,plain,
( ( ( sK3 @ ( sK15 @ sK11 ) )
= $false )
| ( $true = $false )
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f319,f136]) ).
thf(f319,plain,
( ( ( sK2 @ sK11 )
= $false )
| ( ( sK3 @ ( sK15 @ sK11 ) )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f318]) ).
thf(f318,plain,
( ( $true = $false )
| ( ( sK3 @ ( sK15 @ sK11 ) )
= $false )
| ( ( sK2 @ sK11 )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f317,f133]) ).
thf(f317,plain,
( ( $true
= ( sK11 @ sK4 @ sK5 ) )
| ( ( sK3 @ ( sK15 @ sK11 ) )
= $false )
| ( ( sK2 @ sK11 )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f316]) ).
thf(f316,plain,
( ( $true
= ( sK11 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK3 @ ( sK15 @ sK11 ) )
= $false )
| ( ( sK2 @ sK11 )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(duplicate_literal_removal,[status(thm)],[f311]) ).
thf(f311,plain,
( ( $true
= ( sK11 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK3 @ ( sK15 @ sK11 ) )
= $false )
| ( ( sK2 @ sK11 )
= $false )
| ( $true
= ( sK11 @ sK4 @ sK5 ) )
| ( ( sK2 @ sK11 )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(superposition,[status(thm)],[f162,f307]) ).
thf(f307,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK11 @ ( sK12 @ X0 ) @ ( sK13 @ X0 ) ) )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true ) )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f306]) ).
thf(f306,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( $true
= ( sK11 @ ( sK12 @ X0 ) @ ( sK13 @ X0 ) ) )
| ( ( sK2 @ X0 )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false ) )
| ~ spl0_1
| spl0_2 ),
inference(duplicate_literal_removal,[status(thm)],[f300]) ).
thf(f300,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ sK4 @ sK5 )
= $true )
| ( $true = $false )
| ( $true
= ( sK11 @ ( sK12 @ X0 ) @ ( sK13 @ X0 ) ) )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( sK2 @ X0 )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false ) )
| ~ spl0_1
| spl0_2 ),
inference(superposition,[status(thm)],[f178,f291]) ).
thf(f291,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( $true
= ( sK11 @ X1 @ X2 ) ) )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f290]) ).
thf(f290,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false != $false )
| ( $true
= ( sK11 @ X1 @ X2 ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true ) )
| ~ spl0_1
| spl0_2 ),
inference(duplicate_literal_removal,[status(thm)],[f289]) ).
thf(f289,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( $true
= ( sK11 @ X1 @ X2 ) )
| ( $true
= ( sK11 @ X1 @ X2 ) )
| ( $false != $false )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false ) )
| ~ spl0_1
| spl0_2 ),
inference(equality_factoring,[status(thm)],[f284]) ).
thf(f284,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK14 @ X0 @ X3 @ X4 ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false )
| ( $true
= ( sK11 @ X1 @ X2 ) )
| ( ( sK2 @ X0 )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( $true
= ( sK11 @ X3 @ X4 ) ) )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f283]) ).
thf(f283,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( sK11 @ X1 @ X2 ) )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $true = $false )
| ( $false
= ( sK14 @ X0 @ X3 @ X4 ) )
| ( $true
= ( sK11 @ X3 @ X4 ) )
| ( ( sK2 @ X0 )
= $false ) )
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f281,f136]) ).
thf(f281,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK3 @ ( sK15 @ X0 ) )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( sK2 @ sK11 )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( $true
= ( sK11 @ X1 @ X2 ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $false
= ( sK14 @ X0 @ X3 @ X4 ) )
| ( $true
= ( sK11 @ X3 @ X4 ) ) )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f280]) ).
thf(f280,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK2 @ sK11 )
= $false )
| ( $false
= ( sK14 @ X0 @ X3 @ X4 ) )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( $true
= ( sK11 @ X3 @ X4 ) )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( sK11 @ X1 @ X2 ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK2 @ X0 )
= $false ) )
| ~ spl0_1
| spl0_2 ),
inference(duplicate_literal_removal,[status(thm)],[f272]) ).
thf(f272,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK2 @ X0 )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( ( sK3 @ ( sK15 @ X0 ) )
= $false )
| ( $true = $false )
| ( $false
= ( sK14 @ X0 @ X3 @ X4 ) )
| ( $true
= ( sK11 @ X1 @ X2 ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK11 @ X3 @ X4 ) )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( sK2 @ sK11 )
= $false ) )
| ~ spl0_1
| spl0_2 ),
inference(superposition,[status(thm)],[f224,f258]) ).
thf(f258,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( X1 @ ( sK16 @ X0 @ sK11 ) @ ( sK17 @ X0 @ sK11 ) )
= $false )
| ( ( sK14 @ X0 @ X2 @ X3 )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( sK2 @ X0 )
= $false )
| ( $true
= ( sK11 @ X2 @ X3 ) )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f257]) ).
thf(f257,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK3 @ X1 ) )
| ( $true
= ( sK11 @ X2 @ X3 ) )
| ( $true = $false )
| ( ( sK14 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( X1 @ ( sK16 @ X0 @ sK11 ) @ ( sK17 @ X0 @ sK11 ) )
= $false ) )
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f256,f136]) ).
thf(f256,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK2 @ sK11 )
= $false )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( $true
= ( sK11 @ X2 @ X3 ) )
| ( ( sK2 @ X0 )
= $false )
| ( ( X1 @ ( sK16 @ X0 @ sK11 ) @ ( sK17 @ X0 @ sK11 ) )
= $false )
| ( ( sK14 @ X0 @ X2 @ X3 )
= $false )
| ( $false
= ( sK3 @ X1 ) ) )
| ~ spl0_1
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f249]) ).
thf(f249,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK14 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK2 @ X0 )
= $false )
| ( $false
= ( sK3 @ X1 ) )
| ( ( X0 @ sK4 @ sK5 )
= $true )
| ( ( sK2 @ sK11 )
= $false )
| ( $true = $false )
| ( ( X1 @ ( sK16 @ X0 @ sK11 ) @ ( sK17 @ X0 @ sK11 ) )
= $false )
| ( $true
= ( sK11 @ X2 @ X3 ) ) )
| ~ spl0_1
| spl0_2 ),
inference(superposition,[status(thm)],[f148,f223]) ).
thf(f223,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( X4 @ ( sK16 @ X1 @ X4 ) @ ( sK17 @ X1 @ X4 ) )
= $false )
| ( ( sK2 @ X4 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( ( sK2 @ X1 )
= $false )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f222]) ).
thf(f222,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( sK2 @ X4 )
= $false )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( ( ( sK15 @ X1 @ ( sK16 @ X1 @ X4 ) @ ( sK17 @ X1 @ X4 ) )
=> ( X4 @ ( sK16 @ X1 @ X4 ) @ ( sK17 @ X1 @ X4 ) ) )
= $false )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f221]) ).
thf(f221,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( ( sK2 @ X4 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK15 @ X1 @ ( sK16 @ X1 @ X4 ) @ Y0 )
=> ( X4 @ ( sK16 @ X1 @ X4 ) @ Y0 ) )
@ ( sK17 @ X1 @ X4 ) )
= $false ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f220]) ).
thf(f220,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ X1 @ ( sK16 @ X1 @ X4 ) @ Y0 )
=> ( X4 @ ( sK16 @ X1 @ X4 ) @ Y0 ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( ( sK2 @ X1 )
= $false )
| ( ( sK2 @ X4 )
= $false )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f219]) ).
thf(f219,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( sK2 @ X1 )
= $false )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( ( sK2 @ X4 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ X1 @ Y0 @ Y1 )
=> ( X4 @ Y0 @ Y1 ) ) )
@ ( sK16 @ X1 @ X4 ) )
= $false ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f218]) ).
thf(f218,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ X1 @ Y0 @ Y1 )
=> ( X4 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( ( sK2 @ X1 )
= $false )
| ( ( sK2 @ X4 )
= $false ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ( sK2 @ X4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ X1 @ Y0 @ Y1 )
=> ( X4 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f216]) ).
thf(f216,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( $true
= ( ( ( sK2 @ X4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ X1 @ Y0 @ Y1 )
=> ( X4 @ Y0 @ Y1 ) ) ) ) )
=> ( X4 @ X2 @ X3 ) ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f215]) ).
thf(f215,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK15 @ X1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X2 @ X3 ) )
@ X4 )
= $true )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f213]) ).
thf(f213,plain,
( ! [X2: a,X3: a,X1: a > a > $o] :
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK15 @ X1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X2 @ X3 ) ) ) )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
( ! [X2: a,X3: a,X1: a > a > $o] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK15 @ X1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X2 @ X3 ) ) )
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f211]) ).
thf(f211,plain,
( ! [X2: a,X3: a,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false )
| ( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK15 @ X1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ X2 @ Y0 ) ) )
@ X3 )
= ( sK14 @ X1 @ X2 @ X3 ) ) )
| ~ spl0_1 ),
inference(argument_congruence,[status(thm)],[f210]) ).
thf(f210,plain,
( ! [X2: a,X1: a > a > $o] :
( ( ( sK14 @ X1 @ X2 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK15 @ X1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ X2 @ Y0 ) ) ) ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f209]) ).
thf(f209,plain,
( ! [X2: a,X1: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2 )
= ( sK14 @ X1 @ X2 ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(argument_congruence,[status(thm)],[f208]) ).
thf(f208,plain,
( ! [X1: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK14 @ X1 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f206]) ).
thf(f206,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK14 @ X1 ) ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f205]) ).
thf(f205,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( ( sK3 @ ( sK15 @ X1 ) )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK14 @ X1 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f204]) ).
thf(f204,plain,
( ! [X1: a > a > $o] :
( ( ( sK2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( sK14 @ X1 ) ) )
@ ( sK15 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( sK14 @ X1 ) ) ) ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( sK14 @ X1 ) ) ) )
& ( sK14 @ X1 @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f176]) ).
thf(f176,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK2 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= Y0 ) ) )
& ( Y0 @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) ) )
@ ( sK14 @ X1 ) ) ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK2 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= Y0 ) ) )
& ( Y0 @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) ) ) ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f161,plain,
( ! [X1: a > a > $o] :
( ( ( sK2 @ X1 )
= $false )
| ( $false
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK2 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= Y0 ) ) )
& ( Y0 @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) ) ) )
=> ( X1 @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f160]) ).
thf(f160,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK2 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= Y1 ) ) )
& ( Y1 @ ( sK12 @ X1 ) @ Y0 ) ) )
=> ( X1 @ ( sK12 @ X1 ) @ Y0 ) )
@ ( sK13 @ X1 ) )
= $false )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
( ! [X1: a > a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK2 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= Y1 ) ) )
& ( Y1 @ ( sK12 @ X1 ) @ Y0 ) ) )
=> ( X1 @ ( sK12 @ X1 ) @ Y0 ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f158]) ).
thf(f158,plain,
( ! [X1: a > a > $o] :
( ( ( sK2 @ X1 )
= $false )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK2 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
= Y2 ) ) )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) )
@ ( sK12 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
( ! [X1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK2 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
= Y2 ) ) )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
= $false )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ( sK2 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK2 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
= Y2 ) ) )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
= $false ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( sK2 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK2 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
= Y2 ) ) )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl0_1
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f148,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK11 @ X1 @ X2 ) )
| ( ( sK3 @ X3 )
= $false )
| ( ( X3 @ X1 @ X2 )
= $false ) )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ( sK3 @ X3 )
& ( X3 @ X1 @ X2 ) ) )
| ( $true
= ( sK11 @ X1 @ X2 ) ) )
| spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f146]) ).
thf(f146,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( ( ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( Y0 @ X1 @ X2 ) )
@ X3 )
= $false )
| ( $true
= ( sK11 @ X1 @ X2 ) ) )
| spl0_2 ),
inference(pi_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( Y0 @ X1 @ X2 ) ) )
= $false )
| ( $true
= ( sK11 @ X1 @ X2 ) ) )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( Y0 @ X1 @ X2 ) ) )
=> ( sK11 @ X1 @ X2 ) )
= $true )
| spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f139]) ).
thf(f139,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( Y1 @ X1 @ Y0 ) ) )
=> ( sK11 @ X1 @ Y0 ) )
@ X2 )
= $true )
| spl0_2 ),
inference(pi_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( Y1 @ X1 @ Y0 ) ) )
=> ( sK11 @ X1 @ Y0 ) ) )
= $true )
| spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f137]) ).
thf(f137,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| spl0_2 ),
inference(pi_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( ( sK2 @ sK11 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $true )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f224,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $true
= ( sK15 @ X1 @ ( sK16 @ X1 @ X4 ) @ ( sK17 @ X1 @ X4 ) ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( $false
= ( sK14 @ X1 @ X2 @ X3 ) )
| ( ( sK2 @ X4 )
= $false ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f222]) ).
thf(f178,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( sK14 @ X1 @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f177]) ).
thf(f162,plain,
( ! [X1: a > a > $o] :
( ( $false
= ( X1 @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f207,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( sK3 @ ( sK15 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f205]) ).
thf(f136,plain,
( ( ( sK2 @ sK11 )
= $true )
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f130,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f129]) ).
thf(f129,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f49,f127]) ).
thf(f127,plain,
( ( $false
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f125,f46]) ).
thf(f46,plain,
( ( $false
= ( sK9 @ sK4 @ sK5 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $false
= ( ( ( sK2 @ sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK2 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
= Y2 ) ) )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> ( sK9 @ sK4 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK9 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true = $false )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f18,f26]) ).
thf(f26,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f18,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( Y4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK3 @ Y5 )
& ( ( ^ [Y6: a,Y7: a] :
( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( sK2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y5 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) )
= Y4 ) ) )
& ( Y4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK3 @ Y5 )
& ( ( ^ [Y6: a,Y7: a] :
( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( sK2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y5 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) )
= Y4 ) ) )
& ( Y4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK2 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( Y4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( sK3 @ Y6 )
& ( ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( sK2 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) )
= Y5 ) ) )
& ( Y5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK3 @ Y5 )
& ( Y5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK3 @ Y5 )
& ( Y5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( sK3 @ Y6 )
& ( ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( sK2 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) )
= Y5 ) ) )
& ( Y5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK3 @ Y5 )
& ( Y5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( sK3 @ Y6 )
& ( ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( sK2 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) )
= Y5 ) ) )
& ( Y5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: ( a > a > $o ) > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y0 @ Y6 )
& ( Y6 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( Y0 @ Y7 )
& ( ( ^ [Y8: a,Y9: a] :
( !! @ ( a > a > $o )
@ ^ [Y10: a > a > $o] :
( ( ( sK2 @ Y10 )
& ( !! @ a
@ ^ [Y11: a] :
( !! @ a
@ ^ [Y12: a] :
( ( Y7 @ Y11 @ Y12 )
=> ( Y10 @ Y11 @ Y12 ) ) ) ) )
=> ( Y10 @ Y8 @ Y9 ) ) ) )
= Y6 ) ) )
& ( Y6 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( $false
= ( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y0: ( a > a > $o ) > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y0 @ Y6 )
& ( Y6 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( Y0 @ Y7 )
& ( ( ^ [Y8: a,Y9: a] :
( !! @ ( a > a > $o )
@ ^ [Y10: a > a > $o] :
( ( ( sK2 @ Y10 )
& ( !! @ a
@ ^ [Y11: a] :
( !! @ a
@ ^ [Y12: a] :
( ( Y7 @ Y11 @ Y12 )
=> ( Y10 @ Y11 @ Y12 ) ) ) ) )
=> ( Y10 @ Y8 @ Y9 ) ) ) )
= Y6 ) ) )
& ( Y6 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: ( a > a > $o ) > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( Y1 @ Y7 )
& ( Y7 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( Y1 @ Y8 )
& ( ( ^ [Y9: a,Y10: a] :
( !! @ ( a > a > $o )
@ ^ [Y11: a > a > $o] :
( ( ( Y0 @ Y11 )
& ( !! @ a
@ ^ [Y12: a] :
( !! @ a
@ ^ [Y13: a] :
( ( Y8 @ Y12 @ Y13 )
=> ( Y11 @ Y12 @ Y13 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) ) )
= Y7 ) ) )
& ( Y7 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y0: ( a > a > $o ) > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( Y1 @ Y7 )
& ( Y7 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( Y1 @ Y8 )
& ( ( ^ [Y9: a,Y10: a] :
( !! @ ( a > a > $o )
@ ^ [Y11: a > a > $o] :
( ( ( Y0 @ Y11 )
& ( !! @ a
@ ^ [Y12: a] :
( !! @ a
@ ^ [Y13: a] :
( ( Y8 @ Y12 @ Y13 )
=> ( Y11 @ Y12 @ Y13 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) ) )
= Y7 ) ) )
& ( Y7 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y0: ( a > a > $o ) > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( Y1 @ Y7 )
& ( Y7 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( Y1 @ Y8 )
& ( ( ^ [Y9: a,Y10: a] :
( !! @ ( a > a > $o )
@ ^ [Y11: a > a > $o] :
( ( ( Y0 @ Y11 )
& ( !! @ a
@ ^ [Y12: a] :
( !! @ a
@ ^ [Y13: a] :
( ( Y8 @ Y12 @ Y13 )
=> ( Y11 @ Y12 @ Y13 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) ) )
= Y7 ) ) )
& ( Y7 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y0: ( a > a > $o ) > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( Y1 @ Y7 )
& ( Y7 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( Y1 @ Y8 )
& ( ( ^ [Y9: a,Y10: a] :
( !! @ ( a > a > $o )
@ ^ [Y11: a > a > $o] :
( ( ( Y0 @ Y11 )
& ( !! @ a
@ ^ [Y12: a] :
( !! @ a
@ ^ [Y13: a] :
( ( Y8 @ Y12 @ Y13 )
=> ( Y11 @ Y12 @ Y13 ) ) ) ) )
=> ( Y11 @ Y9 @ Y10 ) ) ) )
= Y7 ) ) )
& ( Y7 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X6 @ X5 )
& ( X0 @ X7 ) )
=> ( X4 @ X6 @ X5 ) )
& ( X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ( ! [X11: a,X12: a] :
( ? [X13: a > a > $o] :
( ( X13 @ X12 @ X11 )
& ? [X14: a > a > $o] :
( ( ( ^ [X15: a,X16: a] :
! [X17: a > a > $o] :
( ( ! [X18: a,X19: a] :
( ( X14 @ X19 @ X18 )
=> ( X17 @ X19 @ X18 ) )
& ( X1 @ X17 ) )
=> ( X17 @ X15 @ X16 ) ) )
= X13 )
& ( X0 @ X14 ) ) )
=> ( X10 @ X12 @ X11 ) )
& ( X1 @ X10 ) )
=> ( X10 @ X8 @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X5 @ X6 )
& ( X1 @ X7 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X5 @ X6 )
& ? [X8: a > a > $o] :
( ( ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X13: a,X12: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) )
= X7 )
& ( X1 @ X8 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X5 @ X6 )
& ( X1 @ X7 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ( X7 @ X5 @ X6 )
& ? [X8: a > a > $o] :
( ( ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X13: a,X12: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) )
= X7 )
& ( X1 @ X8 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iE0IFtsIlX/DTF2THF_19563.p',cTHM254_pme) ).
thf(f125,plain,
( ( $true
= ( sK9 @ sK4 @ sK5 ) )
| ( $false
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $true
= ( sK9 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( $false
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f121,f43]) ).
thf(f43,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( sK3 @ ( sK8 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X1: a > a > $o] :
( ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( ( sK3 @ ( sK8 @ X1 ) )
& ( sK8 @ X1 @ ( sK6 @ X1 ) @ ( sK7 @ X1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( Y0 @ ( sK6 @ X1 ) @ ( sK7 @ X1 ) ) )
@ ( sK8 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ! [X1: a > a > $o] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( Y0 @ ( sK6 @ X1 ) @ ( sK7 @ X1 ) ) ) )
= $true )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ! [X1: a > a > $o] :
( ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( Y0 @ ( sK6 @ X1 ) @ ( sK7 @ X1 ) ) ) )
=> ( X1 @ ( sK6 @ X1 ) @ ( sK7 @ X1 ) ) )
= $false ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
( ! [X1: a > a > $o] :
( ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( Y1 @ ( sK6 @ X1 ) @ Y0 ) ) )
=> ( X1 @ ( sK6 @ X1 ) @ Y0 ) )
@ ( sK7 @ X1 ) )
= $false ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ! [X1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( Y1 @ ( sK6 @ X1 ) @ Y0 ) ) )
=> ( X1 @ ( sK6 @ X1 ) @ Y0 ) ) )
= $false )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( ! [X1: a > a > $o] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) )
@ ( sK6 @ X1 ) )
= $false )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ! [X1: a > a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $false
= ( ( sK2 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( sK2 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f121,plain,
( ( ( sK3 @ ( sK8 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( ( sK3 @ ( sK8 @ sK9 ) )
= $false )
| ( $true = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f119,f49]) ).
thf(f119,plain,
( ( ( sK3 @ ( sK8 @ sK9 ) )
= $false )
| ( $false
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $true = $false )
| ( ( sK3 @ ( sK8 @ sK9 ) )
= $false )
| ( $false
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f117,f46]) ).
thf(f117,plain,
( ( $true
= ( sK9 @ sK4 @ sK5 ) )
| ( $false
= ( sK2 @ sK9 ) )
| ( ( sK3 @ ( sK8 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
( ( ( sK3 @ ( sK8 @ sK9 ) )
= $false )
| ( $true
= ( sK9 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( $false
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f42,f97]) ).
thf(f97,plain,
( ! [X0: a > a > $o] :
( ( $false
= ( X0 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) ) )
| ( ( sK3 @ X0 )
= $false ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( ( sK3 @ X0 )
= $false )
| ( $false
= ( X0 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f95,f49]) ).
thf(f95,plain,
( ! [X0: a > a > $o] :
( ( ( sK3 @ X0 )
= $false )
| ( $false
= ( sK2 @ sK9 ) )
| ( $false
= ( X0 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ! [X0: a > a > $o] :
( ( ( sK3 @ X0 )
= $false )
| ( $false
= ( X0 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) ) )
| ( $true = $false )
| ( $false
= ( sK2 @ sK9 ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f93,f46]) ).
thf(f93,plain,
( ! [X0: a > a > $o] :
( ( ( sK3 @ X0 )
= $false )
| ( $true
= ( sK9 @ sK4 @ sK5 ) )
| ( $false
= ( X0 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) ) )
| ( $false
= ( sK2 @ sK9 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ! [X0: a > a > $o] :
( ( ( sK3 @ X0 )
= $false )
| ( $true = $false )
| ( $false
= ( sK2 @ sK9 ) )
| ( $true
= ( sK9 @ sK4 @ sK5 ) )
| ( $false
= ( X0 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f38,f84]) ).
thf(f84,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( ( sK9 @ X1 @ X0 )
= $true )
| ( ( X2 @ X1 @ X0 )
= $false )
| ( $false
= ( sK3 @ X2 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( ( sK9 @ X1 @ X0 )
= $true )
| ( $false
= ( sK3 @ X2 ) )
| ( ( X2 @ X1 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( $false
= ( sK3 @ X2 ) )
| ( ( X2 @ X1 @ X0 )
= $false )
| ( $false
= ( sK3 @ X2 ) )
| ( ( sK9 @ X1 @ X0 )
= $true )
| ( $true = $false )
| ( ( sK9 @ X1 @ X0 )
= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f74,f66]) ).
thf(f66,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( $false
= ( sK10 @ X1 @ X0 @ X2 @ X0 @ X1 ) )
| ( $true
= ( sK9 @ X0 @ X1 ) )
| ( $false
= ( sK3 @ X2 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( $true
= ( sK9 @ X0 @ X1 ) )
| ( $false
= ( ( ( sK2 @ ( sK10 @ X1 @ X0 @ X2 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X2 @ Y0 @ Y1 )
=> ( sK10 @ X1 @ X0 @ X2 @ Y0 @ Y1 ) ) ) ) )
=> ( sK10 @ X1 @ X0 @ X2 @ X0 @ X1 ) ) )
| ( $false
= ( sK3 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( $true
= ( sK9 @ X0 @ X1 ) )
| ( $false
= ( sK3 @ X2 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( X2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X0 @ X1 ) )
@ ( sK10 @ X1 @ X0 @ X2 ) )
= $false ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( X2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X0 @ X1 ) ) )
= $false )
| ( $true
= ( sK9 @ X0 @ X1 ) )
| ( $false
= ( sK3 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( $true
= ( sK9 @ X0 @ X1 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0
@ X1 )
= $false )
| ( $false
= ( sK3 @ X2 ) ) )
| ~ spl0_2 ),
inference(equality_resolution,[status(thm)],[f61]) ).
thf(f61,plain,
( ! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( $true
= ( sK9 @ X1 @ X2 ) )
| ( ( sK3 @ X4 )
= $false )
| ( ( X3 @ X1 @ X2 )
= $false ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( $false
= ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X3 ) )
| ( $true
= ( sK9 @ X1 @ X2 ) )
| ( ( sK3 @ X4 )
= $false )
| ( ( X3 @ X1 @ X2 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( X3 @ X1 @ X2 )
= $false )
| ( ( ( sK3 @ X4 )
& ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK2 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= X3 ) )
= $false )
| ( $true
= ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
( ! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= X3 ) )
@ X4 ) )
| ( $true
= ( sK9 @ X1 @ X2 ) )
| ( ( X3 @ X1 @ X2 )
= $false ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= X3 ) ) )
= $false )
| ( $true
= ( sK9 @ X1 @ X2 ) )
| ( ( X3 @ X1 @ X2 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK3 @ Y0 )
& ( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK2 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= X3 ) ) )
& ( X3 @ X1 @ X2 ) ) )
| ( $true
= ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK2 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= Y0 ) ) )
& ( Y0 @ X1 @ X2 ) )
@ X3 ) )
| ( $true
= ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X2: a,X1: a] :
( ( $false
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK2 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= Y0 ) ) )
& ( Y0 @ X1 @ X2 ) ) ) )
| ( $true
= ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK3 @ Y1 )
& ( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK2 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= Y0 ) ) )
& ( Y0 @ X1 @ X2 ) ) )
=> ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK2 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= Y1 ) ) )
& ( Y1 @ X1 @ Y0 ) ) )
=> ( sK9 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK3 @ Y2 )
& ( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK2 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= Y1 ) ) )
& ( Y1 @ X1 @ Y0 ) ) )
=> ( sK9 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK2 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
= Y2 ) ) )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK2 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
= Y2 ) ) )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( ( sK2 @ sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK2 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
= Y2 ) ) )
& ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f74,plain,
( ! [X2: a > a > $o,X3: a,X0: a,X1: a,X4: a] :
( ( $true
= ( sK10 @ X1 @ X0 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK3 @ X2 ) )
| ( $true
= ( sK9 @ X0 @ X1 ) )
| ( ( X2 @ X3 @ X4 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ! [X2: a > a > $o,X3: a,X0: a,X1: a,X4: a] :
( ( $true
= ( ( X2 @ X3 @ X4 )
=> ( sK10 @ X1 @ X0 @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( sK3 @ X2 ) )
| ( $true
= ( sK9 @ X0 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
( ! [X2: a > a > $o,X3: a,X0: a,X1: a,X4: a] :
( ( $true
= ( ^ [Y0: a] :
( ( X2 @ X3 @ Y0 )
=> ( sK10 @ X1 @ X0 @ X2 @ X3 @ Y0 ) )
@ X4 ) )
| ( $false
= ( sK3 @ X2 ) )
| ( $true
= ( sK9 @ X0 @ X1 ) ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ! [X2: a > a > $o,X3: a,X0: a,X1: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ X3 @ Y0 )
=> ( sK10 @ X1 @ X0 @ X2 @ X3 @ Y0 ) ) ) )
| ( $false
= ( sK3 @ X2 ) )
| ( $true
= ( sK9 @ X0 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X2: a > a > $o,X3: a,X0: a,X1: a] :
( ( $false
= ( sK3 @ X2 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X2 @ Y0 @ Y1 )
=> ( sK10 @ X1 @ X0 @ X2 @ Y0 @ Y1 ) ) )
@ X3 ) )
| ( $true
= ( sK9 @ X0 @ X1 ) ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X2 @ Y0 @ Y1 )
=> ( sK10 @ X1 @ X0 @ X2 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( sK9 @ X0 @ X1 ) )
| ( $false
= ( sK3 @ X2 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ! [X2: a > a > $o,X0: a,X1: a] :
( ( $true
= ( sK9 @ X0 @ X1 ) )
| ( ( ( sK2 @ ( sK10 @ X1 @ X0 @ X2 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X2 @ Y0 @ Y1 )
=> ( sK10 @ X1 @ X0 @ X2 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( sK3 @ X2 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f38,plain,
( ! [X1: a > a > $o] :
( ( $false
= ( X1 @ ( sK6 @ X1 ) @ ( sK7 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f42,plain,
( ! [X1: a > a > $o] :
( ( ( sK8 @ X1 @ ( sK6 @ X1 ) @ ( sK7 @ X1 ) )
= $true )
| ( ( sK2 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f49,plain,
( ( $true
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f27,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f24,f20]) ).
thf(f17,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK3 @ Y4 )
& ( ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK2 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
= Y3 ) ) )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK2 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK3 @ Y3 )
& ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEV125^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:41:10 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.25/0.44 ---- Original DTF file ---
% 0.25/0.44 thf(spec,logic,$$dhol).
% 0.25/0.44 %------------------------------------------------------------------------------
% 0.25/0.44 % File : SEV125^5 : TPTP v9.2.1. Released v4.0.0.
% 0.25/0.44 % Domain : Set Theory (Relations)
% 0.25/0.44 % Problem : TPS problem from SETS-OF-RELNS-THMS
% 0.25/0.44 % Version : Especial.
% 0.25/0.44 % English :
% 0.25/0.44
% 0.25/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.25/0.44 % Source : [Bro09]
% 0.25/0.44 % Names : tps_1087 [Bro09]
% 0.25/0.44
% 0.25/0.44 % Status : Theorem
% 0.25/0.44 % Rating : 0.67 v9.1.0, 0.75 v9.0.0, 0.90 v8.2.0, 0.92 v8.1.0, 0.91 v7.5.0, 1.00 v4.0.0
% 0.25/0.44 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.25/0.44 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.25/0.44 % Maximal formula atoms : 1 ( 2 avg)
% 0.25/0.44 % Number of connectives : 35 ( 0 ~; 0 |; 6 &; 23 @)
% 0.25/0.44 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.25/0.44 % Maximal formula depth : 3 ( 3 avg)
% 0.25/0.44 % Number of types : 2 ( 1 usr)
% 0.25/0.44 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.25/0.44 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.25/0.44 % Number of variables : 20 ( 6 ^; 11 !; 3 ?; 20 :)
% 0.25/0.44 % SPC : TH0_THM_EQU_NAR
% 0.25/0.44
% 0.25/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.25/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.25/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.25/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.25/0.44 %------------------------------------------------------------------------------
% 0.25/0.44 thf(a_type,type,
% 0.25/0.44 a: $tType ).
% 0.25/0.44
% 0.25/0.44 thf(cTHM254_pme,conjecture,
% 0.25/0.44 ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o] :
% 0.25/0.44 ( ( ^ [Xx: a,Xy: a] :
% 0.25/0.44 ! [Xp: a > a > $o] :
% 0.25/0.44 ( ( ! [Xx0: a,Xy0: a] :
% 0.25/0.44 ( ? [R: a > a > $o] :
% 0.25/0.44 ( ( S @ R )
% 0.25/0.44 & ( R @ Xx0 @ Xy0 ) )
% 0.25/0.44 => ( Xp @ Xx0 @ Xy0 ) )
% 0.25/0.44 & ( PROP @ Xp ) )
% 0.25/0.44 => ( Xp @ Xx @ Xy ) ) )
% 0.25/0.44 = ( ^ [Xx: a,Xy: a] :
% 0.25/0.44 ! [Xp: a > a > $o] :
% 0.25/0.44 ( ( ! [Xx0: a,Xy0: a] :
% 0.25/0.44 ( ? [R: a > a > $o] :
% 0.25/0.44 ( ? [Q: a > a > $o] :
% 0.25/0.44 ( ( S @ Q )
% 0.25/0.44 & ( R
% 0.25/0.44 = ( ^ [Xx1: a,Xy1: a] :
% 0.25/0.44 ! [Xp0: a > a > $o] :
% 0.25/0.44 ( ( ! [Xx2: a,Xy2: a] :
% 0.25/0.44 ( ( Q @ Xx2 @ Xy2 )
% 0.25/0.44 => ( Xp0 @ Xx2 @ Xy2 ) )
% 0.25/0.44 & ( PROP @ Xp0 ) )
% 0.25/0.44 => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
% 0.25/0.44 & ( R @ Xx0 @ Xy0 ) )
% 0.25/0.44 => ( Xp @ Xx0 @ Xy0 ) )
% 0.25/0.44 & ( PROP @ Xp ) )
% 0.25/0.44 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 0.25/0.44
% 0.25/0.44 %------------------------------------------------------------------------------
% 0.25/0.44 ------------------------
% 1.50/1.26 ---- Embedded in THF ---
% 1.50/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.26 %%% Generated on Tue Feb 24 12:41:11 EST 2026
% 1.50/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.26 %%% Logic specification used:
% 1.50/1.26 %%% thf(spec, logic, $$dhol).
% 1.50/1.26
% 1.50/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.iE0IFtsIlX/DTF2DTF19563.p
% See solution above
% 1.50/1.26 ------------------------
% 1.50/1.27 ---- Cleaned THF ---
% 1.50/1.27 thf(a_type,type,
% 1.50/1.27 a: $tType ).
% 1.50/1.27
% 1.50/1.27 thf(cTHM254_pme,conjecture,
% 1.50/1.27 ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o] :
% 1.50/1.27 ( ( ^ [Xx: a,Xy: a] :
% 1.50/1.27 ! [Xp: a > a > $o] :
% 1.50/1.27 ( ( ! [Xx0: a,Xy0: a] :
% 1.50/1.27 ( ? [R: a > a > $o] :
% 1.50/1.27 ( ( S @ R )
% 1.50/1.27 & ( R @ Xx0 @ Xy0 ) )
% 1.50/1.27 => ( Xp @ Xx0 @ Xy0 ) )
% 1.50/1.27 & ( PROP @ Xp ) )
% 1.50/1.27 => ( Xp @ Xx @ Xy ) ) )
% 1.50/1.27 = ( ^ [Xx: a,Xy: a] :
% 1.50/1.27 ! [Xp: a > a > $o] :
% 1.50/1.27 ( ( ! [Xx0: a,Xy0: a] :
% 1.50/1.27 ( ? [R: a > a > $o] :
% 1.50/1.27 ( ? [Q: a > a > $o] :
% 1.50/1.27 ( ( S @ Q )
% 1.50/1.27 & ( R
% 1.50/1.27 = ( ^ [Xx1: a,Xy1: a] :
% 1.50/1.27 ! [Xp0: a > a > $o] :
% 1.50/1.27 ( ( ! [Xx2: a,Xy2: a] :
% 1.50/1.27 ( ( Q @ Xx2 @ Xy2 )
% 1.50/1.27 => ( Xp0 @ Xx2 @ Xy2 ) )
% 1.50/1.27 & ( PROP @ Xp0 ) )
% 1.50/1.27 => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
% 1.50/1.27 & ( R @ Xx0 @ Xy0 ) )
% 1.50/1.27 => ( Xp @ Xx0 @ Xy0 ) )
% 1.50/1.27 & ( PROP @ Xp ) )
% 1.50/1.27 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 1.50/1.27 ------------------------
% 1.50/1.28 % (19819)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_19563 for (2999ds/2Mi)
% 1.50/1.29 % (19819)Instruction limit reached!
% 1.50/1.29 % (19819)------------------------------
% 1.50/1.29 % (19819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (19819)Termination reason: Unknown
% 1.50/1.29 % (19819)Termination phase: shuffling
% 1.50/1.29
% 1.50/1.29 % (19819)Memory used [KB]: 1023
% 1.50/1.29 % (19819)Time elapsed: 0.002 s
% 1.50/1.29 % (19819)Instructions burned: 2 (million)
% 1.50/1.29 % (19819)------------------------------
% 1.50/1.29 % (19819)------------------------------
% 1.50/1.29 % (19817)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_19563 for (2999ds/27Mi)
% 1.50/1.29 % (19815)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/183Mi)
% 1.50/1.29 % (19816)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_19563 for (2999ds/4Mi)
% 1.50/1.29 % (19818)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/2Mi)
% 1.50/1.29 % (19820)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_19563 for (2999ds/275Mi)
% 1.50/1.29 % (19821)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/18Mi)
% 1.50/1.29 % (19817)Instruction limit reached!
% 1.50/1.29 % (19817)------------------------------
% 1.50/1.29 % (19817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (19817)Termination reason: Unknown
% 1.50/1.29 % (19817)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (19817)Memory used [KB]: 5628
% 1.50/1.29 % (19817)Time elapsed: 0.010 s
% 1.50/1.29 % (19817)Instructions burned: 28 (million)
% 1.50/1.29 % (19817)------------------------------
% 1.50/1.29 % (19817)------------------------------
% 1.50/1.29 % (19818)Instruction limit reached!
% 1.50/1.29 % (19818)------------------------------
% 1.50/1.29 % (19818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (19818)Termination reason: Unknown
% 1.50/1.29 % (19818)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (19818)Memory used [KB]: 1023
% 1.50/1.29 % (19818)Time elapsed: 0.004 s
% 1.50/1.29 % (19818)Instructions burned: 3 (million)
% 1.50/1.29 % (19818)------------------------------
% 1.50/1.29 % (19818)------------------------------
% 1.50/1.30 % (19822)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/3Mi)
% 1.50/1.30 % (19816)Instruction limit reached!
% 1.50/1.30 % (19816)------------------------------
% 1.50/1.30 % (19816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.30 % (19816)Termination reason: Unknown
% 1.50/1.30 % (19816)Termination phase: Saturation
% 1.50/1.30
% 1.50/1.30 % (19816)Memory used [KB]: 5500
% 1.50/1.30 % (19816)Time elapsed: 0.005 s
% 1.50/1.30 % (19816)Instructions burned: 5 (million)
% 1.50/1.30 % (19816)------------------------------
% 1.50/1.30 % (19816)------------------------------
% 1.50/1.30 % (19822)Instruction limit reached!
% 1.50/1.30 % (19822)------------------------------
% 1.50/1.30 % (19822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.30 % (19822)Termination reason: Unknown
% 1.50/1.30 % (19822)Termination phase: Saturation
% 1.50/1.30
% 1.50/1.30 % (19822)Memory used [KB]: 1023
% 1.50/1.30 % (19822)Time elapsed: 0.002 s
% 1.50/1.30 % (19822)Instructions burned: 3 (million)
% 1.50/1.30 % (19822)------------------------------
% 1.50/1.30 % (19822)------------------------------
% 1.63/1.30 % (19821)Instruction limit reached!
% 1.63/1.30 % (19821)------------------------------
% 1.63/1.30 % (19821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (19821)Termination reason: Unknown
% 1.63/1.30 % (19821)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (19821)Memory used [KB]: 5500
% 1.63/1.30 % (19821)Time elapsed: 0.012 s
% 1.63/1.30 % (19821)Instructions burned: 18 (million)
% 1.63/1.30 % (19821)------------------------------
% 1.63/1.30 % (19821)------------------------------
% 1.63/1.30 % (19823)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_19563 for (2999ds/37Mi)
% 1.63/1.31 % (19827)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_19563 for (2999ds/1041Mi)
% 1.63/1.31 % (19826)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_19563 for (2999ds/3Mi)
% 1.63/1.31 % (19826)Instruction limit reached!
% 1.63/1.31 % (19826)------------------------------
% 1.63/1.31 % (19826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (19826)Termination reason: Unknown
% 1.63/1.31 % (19826)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (19826)Memory used [KB]: 1023
% 1.63/1.31 % (19826)Time elapsed: 0.003 s
% 1.63/1.31 % (19826)Instructions burned: 3 (million)
% 1.63/1.31 % (19826)------------------------------
% 1.63/1.31 % (19826)------------------------------
% 1.63/1.31 % (19825)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_19563 for (2999ds/15Mi)
% 1.63/1.32 % (19823)Instruction limit reached!
% 1.63/1.32 % (19823)------------------------------
% 1.63/1.32 % (19823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (19823)Termination reason: Unknown
% 1.63/1.32 % (19823)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (19823)Memory used [KB]: 5628
% 1.63/1.32 % (19823)Time elapsed: 0.014 s
% 1.63/1.32 % (19823)Instructions burned: 38 (million)
% 1.63/1.32 % (19823)------------------------------
% 1.63/1.32 % (19823)------------------------------
% 1.63/1.32 % (19825)Instruction limit reached!
% 1.63/1.32 % (19825)------------------------------
% 1.63/1.32 % (19825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (19825)Termination reason: Unknown
% 1.63/1.32 % (19825)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (19825)Memory used [KB]: 5628
% 1.63/1.32 % (19825)Time elapsed: 0.010 s
% 1.63/1.32 % (19825)Instructions burned: 15 (million)
% 1.63/1.32 % (19825)------------------------------
% 1.63/1.32 % (19825)------------------------------
% 1.63/1.32 % (19828)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/7Mi)
% 1.63/1.32 % (19829)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/16Mi)
% 1.63/1.32 % (19828)Instruction limit reached!
% 1.63/1.32 % (19828)------------------------------
% 1.63/1.32 % (19828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (19828)Termination reason: Unknown
% 1.63/1.32 % (19828)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (19828)Memory used [KB]: 1023
% 1.63/1.32 % (19828)Time elapsed: 0.006 s
% 1.63/1.32 % (19828)Instructions burned: 7 (million)
% 1.63/1.32 % (19828)------------------------------
% 1.63/1.32 % (19828)------------------------------
% 1.63/1.33 % (19830)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_19563 for (2999ds/3Mi)
% 1.63/1.33 % (19830)Instruction limit reached!
% 1.63/1.33 % (19830)------------------------------
% 1.63/1.33 % (19830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (19830)Termination reason: Unknown
% 1.63/1.33 % (19830)Termination phase: Twee Goal Transformation
% 1.63/1.33
% 1.63/1.33 % (19830)Memory used [KB]: 1023
% 1.63/1.33 % (19830)Time elapsed: 0.003 s
% 1.63/1.33 % (19830)Instructions burned: 4 (million)
% 1.63/1.33 % (19830)------------------------------
% 1.63/1.33 % (19830)------------------------------
% 1.63/1.33 % (19829)Instruction limit reached!
% 1.63/1.33 % (19829)------------------------------
% 1.63/1.33 % (19829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (19829)Termination reason: Unknown
% 1.63/1.33 % (19829)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (19829)Memory used [KB]: 5756
% 1.63/1.33 % (19829)Time elapsed: 0.008 s
% 1.63/1.33 % (19829)Instructions burned: 17 (million)
% 1.63/1.33 % (19829)------------------------------
% 1.63/1.33 % (19829)------------------------------
% 1.63/1.34 % (19831)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_19563 for (2999ds/3Mi)
% 1.63/1.34 % (19833)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/3Mi)
% 1.63/1.34 % (19834)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/4Mi)
% 1.63/1.34 % (19831)Instruction limit reached!
% 1.63/1.34 % (19831)------------------------------
% 1.63/1.34 % (19831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19831)Termination reason: Unknown
% 1.63/1.34 % (19831)Termination phase: Property scanning
% 1.63/1.34
% 1.63/1.34 % (19831)Memory used [KB]: 1023
% 1.63/1.34 % (19831)Time elapsed: 0.004 s
% 1.63/1.34 % (19831)Instructions burned: 4 (million)
% 1.63/1.34 % (19831)------------------------------
% 1.63/1.34 % (19831)------------------------------
% 1.63/1.34 % (19833)Instruction limit reached!
% 1.63/1.34 % (19833)------------------------------
% 1.63/1.34 % (19833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19833)Termination reason: Unknown
% 1.63/1.34 % (19833)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (19833)Memory used [KB]: 5500
% 1.63/1.34 % (19833)Time elapsed: 0.003 s
% 1.63/1.34 % (19833)Instructions burned: 4 (million)
% 1.63/1.34 % (19833)------------------------------
% 1.63/1.34 % (19833)------------------------------
% 1.63/1.34 % (19834)Instruction limit reached!
% 1.63/1.34 % (19834)------------------------------
% 1.63/1.34 % (19834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19834)Termination reason: Unknown
% 1.63/1.34 % (19834)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (19834)Memory used [KB]: 5500
% 1.63/1.34 % (19834)Time elapsed: 0.003 s
% 1.63/1.34 % (19834)Instructions burned: 4 (million)
% 1.63/1.34 % (19834)------------------------------
% 1.63/1.34 % (19834)------------------------------
% 1.63/1.34 % (19832)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/7Mi)
% 1.63/1.34 % (19832)Instruction limit reached!
% 1.63/1.34 % (19832)------------------------------
% 1.63/1.34 % (19832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19832)Termination reason: Unknown
% 1.63/1.34 % (19832)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (19832)Memory used [KB]: 5500
% 1.63/1.34 % (19832)Time elapsed: 0.006 s
% 1.63/1.34 % (19832)Instructions burned: 8 (million)
% 1.63/1.34 % (19832)------------------------------
% 1.63/1.34 % (19832)------------------------------
% 1.63/1.35 % (19835)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/18Mi)
% 1.63/1.35 % (19835)Instruction limit reached!
% 1.63/1.35 % (19835)------------------------------
% 1.63/1.35 % (19835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (19835)Termination reason: Unknown
% 1.63/1.35 % (19835)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (19835)Memory used [KB]: 5500
% 1.63/1.35 % (19835)Time elapsed: 0.007 s
% 1.63/1.35 % (19835)Instructions burned: 18 (million)
% 1.63/1.35 % (19835)------------------------------
% 1.63/1.35 % (19835)------------------------------
% 1.63/1.36 % (19838)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_19563 for (2999ds/902Mi)
% 1.63/1.36 % (19836)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/710Mi)
% 1.63/1.36 % (19837)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/6Mi)
% 1.63/1.36 % (19837)Instruction limit reached!
% 1.63/1.36 % (19837)------------------------------
% 1.63/1.36 % (19837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (19837)Termination reason: Unknown
% 1.63/1.36 % (19837)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (19837)Memory used [KB]: 5500
% 1.63/1.36 % (19837)Time elapsed: 0.006 s
% 1.63/1.36 % (19837)Instructions burned: 7 (million)
% 1.63/1.36 % (19837)------------------------------
% 1.63/1.36 % (19837)------------------------------
% 1.63/1.36 % (19839)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_19563 for (2999ds/21Mi)
% 1.63/1.37 % (19839)Instruction limit reached!
% 1.63/1.37 % (19839)------------------------------
% 1.63/1.37 % (19839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (19839)Termination reason: Unknown
% 1.63/1.37 % (19839)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (19839)Memory used [KB]: 5628
% 1.63/1.37 % (19839)Time elapsed: 0.010 s
% 1.63/1.37 % (19839)Instructions burned: 22 (million)
% 1.63/1.37 % (19839)------------------------------
% 1.63/1.37 % (19839)------------------------------
% 1.63/1.38 % (19840)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/5Mi)
% 1.63/1.38 % (19840)Instruction limit reached!
% 1.63/1.38 % (19840)------------------------------
% 1.63/1.38 % (19840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (19840)Termination reason: Unknown
% 1.63/1.38 % (19840)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (19840)Memory used [KB]: 5500
% 1.63/1.38 % (19840)Time elapsed: 0.005 s
% 1.63/1.38 % (19840)Instructions burned: 5 (million)
% 1.63/1.38 % (19840)------------------------------
% 1.63/1.38 % (19840)------------------------------
% 1.63/1.38 % (19815)Instruction limit reached!
% 1.63/1.38 % (19815)------------------------------
% 1.63/1.38 % (19815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (19815)Termination reason: Unknown
% 1.63/1.38 % (19815)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (19815)Memory used [KB]: 7803
% 1.63/1.38 % (19815)Time elapsed: 0.093 s
% 1.63/1.38 % (19815)Instructions burned: 183 (million)
% 1.63/1.38 % (19815)------------------------------
% 1.63/1.38 % (19815)------------------------------
% 1.63/1.38 % (19841)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_19563 for (2999ds/6Mi)
% 1.63/1.39 % (19841)Instruction limit reached!
% 1.63/1.39 % (19841)------------------------------
% 1.63/1.39 % (19841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (19841)Termination reason: Unknown
% 1.63/1.39 % (19841)Termination phase: Saturation
% 1.63/1.39
% 1.63/1.39 % (19841)Memory used [KB]: 5500
% 1.63/1.39 % (19841)Time elapsed: 0.004 s
% 1.63/1.39 % (19841)Instructions burned: 7 (million)
% 1.63/1.39 % (19841)------------------------------
% 1.63/1.39 % (19841)------------------------------
% 1.63/1.40 % (19844)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_19563 for (2999ds/19Mi)
% 1.63/1.40 % (19842)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19563 for (2999ds/377Mi)
% 1.63/1.40 % (19843)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_19563 for (2999ds/779Mi)
% 1.63/1.40 % (19844)Instruction limit reached!
% 1.63/1.40 % (19844)------------------------------
% 1.63/1.40 % (19844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.40 % (19844)Termination reason: Unknown
% 1.63/1.40 % (19844)Termination phase: Saturation
% 1.63/1.40
% 1.63/1.40 % (19844)Memory used [KB]: 5500
% 1.63/1.40 % (19844)Time elapsed: 0.008 s
% 1.63/1.40 % (19844)Instructions burned: 20 (million)
% 1.63/1.40 % (19844)------------------------------
% 1.63/1.40 % (19844)------------------------------
% 1.63/1.41 % (19845)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19563 for (2998ds/879Mi)
% 1.63/1.43 % (19820)Instruction limit reached!
% 1.63/1.43 % (19820)------------------------------
% 1.63/1.43 % (19820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.43 % (19820)Termination reason: Unknown
% 1.63/1.43 % (19820)Termination phase: Saturation
% 1.63/1.43
% 1.63/1.43 % (19820)Memory used [KB]: 6524
% 1.63/1.43 % (19820)Time elapsed: 0.143 s
% 1.63/1.43 % (19820)Instructions burned: 277 (million)
% 1.63/1.43 % (19820)------------------------------
% 1.63/1.43 % (19820)------------------------------
% 1.63/1.44 % (19846)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19563 for (2998ds/17Mi)
% 1.63/1.45 % (19846)Instruction limit reached!
% 1.63/1.45 % (19846)------------------------------
% 1.63/1.45 % (19846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (19846)Termination reason: Unknown
% 1.63/1.45 % (19846)Termination phase: Saturation
% 1.63/1.45
% 1.63/1.45 % (19846)Memory used [KB]: 5628
% 1.63/1.45 % (19846)Time elapsed: 0.007 s
% 1.63/1.45 % (19846)Instructions burned: 17 (million)
% 1.63/1.45 % (19846)------------------------------
% 1.63/1.45 % (19846)------------------------------
% 1.63/1.46 % (19847)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19563 for (2998ds/3Mi)
% 1.63/1.46 % (19847)Instruction limit reached!
% 1.63/1.46 % (19847)------------------------------
% 1.63/1.46 % (19847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.46 % (19847)Termination reason: Unknown
% 1.63/1.46 % (19847)Termination phase: Saturation
% 1.63/1.46
% 1.63/1.46 % (19847)Memory used [KB]: 1023
% 1.63/1.46 % (19847)Time elapsed: 0.003 s
% 1.63/1.46 % (19847)Instructions burned: 4 (million)
% 1.63/1.46 % (19847)------------------------------
% 1.63/1.46 % (19847)------------------------------
% 1.63/1.47 % (19848)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19563 for (2998ds/30Mi)
% 1.63/1.47 % (19848)Refutation not found, incomplete strategy
% 1.63/1.47 % (19848)------------------------------
% 1.63/1.47 % (19848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (19848)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.47
% 1.63/1.47
% 1.63/1.47 % (19848)Memory used [KB]: 5500
% 1.63/1.47 % (19848)Time elapsed: 0.004 s
% 1.63/1.47 % (19848)Instructions burned: 7 (million)
% 1.63/1.47 % (19848)------------------------------
% 1.63/1.47 % (19848)------------------------------
% 1.63/1.48 % (19849)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19563 for (2998ds/127Mi)
% 1.63/1.52 % (19849)Instruction limit reached!
% 1.63/1.52 % (19849)------------------------------
% 1.63/1.52 % (19849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.52 % (19849)Termination reason: Unknown
% 1.63/1.52 % (19849)Termination phase: Saturation
% 1.63/1.52
% 1.63/1.52 % (19849)Memory used [KB]: 6012
% 1.63/1.52 % (19849)Time elapsed: 0.041 s
% 1.63/1.52 % (19849)Instructions burned: 128 (million)
% 1.63/1.52 % (19849)------------------------------
% 1.63/1.52 % (19849)------------------------------
% 1.63/1.53 % (19850)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19563 for (2997ds/100Mi)
% 1.63/1.55 % (19842)Instruction limit reached!
% 1.63/1.55 % (19842)------------------------------
% 1.63/1.55 % (19842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.55 % (19842)Termination reason: Unknown
% 1.63/1.55 % (19842)Termination phase: Saturation
% 1.63/1.55
% 1.63/1.55 % (19842)Memory used [KB]: 6780
% 1.63/1.55 % (19842)Time elapsed: 0.153 s
% 1.63/1.55 % (19842)Instructions burned: 377 (million)
% 1.63/1.55 % (19842)------------------------------
% 1.63/1.55 % (19842)------------------------------
% 1.63/1.56 % (19851)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_19563 for (2997ds/3Mi)
% 1.63/1.56 % (19851)Instruction limit reached!
% 1.63/1.56 % (19851)------------------------------
% 1.63/1.56 % (19851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.56 % (19851)Termination reason: Unknown
% 1.63/1.56 % (19851)Termination phase: Saturation
% 1.63/1.56
% 1.63/1.56 % (19851)Memory used [KB]: 5500
% 1.63/1.56 % (19851)Time elapsed: 0.003 s
% 1.63/1.56 % (19851)Instructions burned: 4 (million)
% 1.63/1.56 % (19851)------------------------------
% 1.63/1.56 % (19851)------------------------------
% 1.63/1.56 % (19850)Instruction limit reached!
% 1.63/1.56 % (19850)------------------------------
% 1.63/1.56 % (19850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.56 % (19850)Termination reason: Unknown
% 1.63/1.56 % (19850)Termination phase: Saturation
% 1.63/1.56
% 1.63/1.56 % (19850)Memory used [KB]: 5884
% 1.63/1.56 % (19850)Time elapsed: 0.055 s
% 1.63/1.56 % (19850)Instructions burned: 100 (million)
% 1.63/1.56 % (19850)------------------------------
% 1.63/1.56 % (19850)------------------------------
% 1.63/1.57 % (19852)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_19563 for (2997ds/20Mi)
% 1.63/1.57 % (19852)Refutation not found, incomplete strategy
% 1.63/1.57 % (19852)------------------------------
% 1.63/1.57 % (19852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.57 % (19852)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.57
% 1.63/1.57
% 1.63/1.57 % (19852)Memory used [KB]: 5500
% 1.63/1.57 % (19852)Time elapsed: 0.003 s
% 1.63/1.57 % (19852)Instructions burned: 4 (million)
% 1.63/1.57 % (19852)------------------------------
% 1.63/1.57 % (19852)------------------------------
% 1.63/1.58 % (19853)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_19563 for (2997ds/86Mi)
% 1.63/1.58 % (19854)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_19563 for (2997ds/107Mi)
% 1.63/1.60 % (19853)Instruction limit reached!
% 1.63/1.60 % (19853)------------------------------
% 1.63/1.60 % (19853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.60 % (19853)Termination reason: Unknown
% 1.63/1.60 % (19853)Termination phase: Saturation
% 1.63/1.60
% 1.63/1.60 % (19853)Memory used [KB]: 6140
% 1.63/1.60 % (19853)Time elapsed: 0.050 s
% 1.63/1.60 % (19853)Instructions burned: 88 (million)
% 1.63/1.60 % (19853)------------------------------
% 1.63/1.60 % (19853)------------------------------
% 1.63/1.61 % (19855)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/39Mi)
% 1.63/1.61 % (19836)Instruction limit reached!
% 1.63/1.61 % (19836)------------------------------
% 1.63/1.61 % (19836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.61 % (19836)Termination reason: Unknown
% 1.63/1.61 % (19836)Termination phase: Saturation
% 1.63/1.61
% 1.63/1.61 % (19836)Memory used [KB]: 8059
% 1.63/1.61 % (19836)Time elapsed: 0.258 s
% 1.63/1.61 % (19836)Instructions burned: 712 (million)
% 1.63/1.61 % (19836)------------------------------
% 1.63/1.61 % (19836)------------------------------
% 1.63/1.62 % (19854)Instruction limit reached!
% 1.63/1.62 % (19854)------------------------------
% 1.63/1.62 % (19854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.62 % (19854)Termination reason: Unknown
% 1.63/1.62 % (19854)Termination phase: Saturation
% 1.63/1.62
% 1.63/1.62 % (19854)Memory used [KB]: 6012
% 1.63/1.62 % (19854)Time elapsed: 0.059 s
% 1.63/1.62 % (19854)Instructions burned: 108 (million)
% 1.63/1.62 % (19854)------------------------------
% 1.63/1.62 % (19854)------------------------------
% 1.63/1.62 % (19856)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/448Mi)
% 1.63/1.62 % (19855)Instruction limit reached!
% 1.63/1.62 % (19855)------------------------------
% 1.63/1.62 % (19855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.62 % (19855)Termination reason: Unknown
% 1.63/1.62 % (19855)Termination phase: Saturation
% 1.63/1.62
% 1.63/1.62 % (19855)Memory used [KB]: 5884
% 1.63/1.62 % (19855)Time elapsed: 0.014 s
% 1.63/1.62 % (19855)Instructions burned: 41 (million)
% 1.63/1.62 % (19855)------------------------------
% 1.63/1.62 % (19855)------------------------------
% 1.63/1.63 % (19827)Instruction limit reached!
% 1.63/1.63 % (19827)------------------------------
% 1.63/1.63 % (19827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.63 % (19827)Termination reason: Unknown
% 1.63/1.63 % (19827)Termination phase: Saturation
% 1.63/1.63
% 1.63/1.63 % (19827)Memory used [KB]: 7291
% 1.63/1.63 % (19827)Time elapsed: 0.321 s
% 1.63/1.63 % (19827)Instructions burned: 1043 (million)
% 1.63/1.63 % (19827)------------------------------
% 1.63/1.63 % (19827)------------------------------
% 1.63/1.63 % (19857)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/46Mi)
% 1.63/1.63 % (19859)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/507Mi)
% 1.63/1.63 % (19858)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/98Mi)
% 1.63/1.63 % (19838)Instruction limit reached!
% 1.63/1.63 % (19838)------------------------------
% 1.63/1.63 % (19838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.63 % (19838)Termination reason: Unknown
% 1.63/1.63 % (19838)Termination phase: Saturation
% 1.63/1.63
% 1.63/1.63 % (19838)Memory used [KB]: 6908
% 1.63/1.63 % (19838)Time elapsed: 0.280 s
% 1.63/1.63 % (19838)Instructions burned: 902 (million)
% 1.63/1.63 % (19838)------------------------------
% 1.63/1.63 % (19838)------------------------------
% 1.63/1.65 % (19860)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/149Mi)
% 1.63/1.65 % (19857)Instruction limit reached!
% 1.63/1.65 % (19857)------------------------------
% 1.63/1.65 % (19857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.65 % (19857)Termination reason: Unknown
% 1.63/1.65 % (19857)Termination phase: Saturation
% 1.63/1.65
% 1.63/1.65 % (19857)Memory used [KB]: 5628
% 1.63/1.65 % (19857)Time elapsed: 0.019 s
% 1.63/1.65 % (19857)Instructions burned: 48 (million)
% 1.63/1.65 % (19857)------------------------------
% 1.63/1.65 % (19857)------------------------------
% 1.63/1.66 % (19843)Instruction limit reached!
% 1.63/1.66 % (19843)------------------------------
% 1.63/1.66 % (19843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.66 % (19843)Termination reason: Unknown
% 1.63/1.66 % (19843)Termination phase: Saturation
% 1.63/1.66
% 1.63/1.66 % (19843)Memory used [KB]: 8059
% 1.63/1.66 % (19843)Time elapsed: 0.257 s
% 1.63/1.66 % (19843)Instructions burned: 779 (million)
% 1.63/1.66 % (19843)------------------------------
% 1.63/1.66 % (19843)------------------------------
% 1.63/1.66 % (19861)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/39Mi)
% 1.63/1.67 % (19862)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/6Mi)
% 1.63/1.67 % (19858)Instruction limit reached!
% 1.63/1.67 % (19858)------------------------------
% 1.63/1.67 % (19858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.67 % (19858)Termination reason: Unknown
% 1.63/1.67 % (19858)Termination phase: Saturation
% 1.63/1.67
% 1.63/1.67 % (19858)Memory used [KB]: 1279
% 1.63/1.67 % (19858)Time elapsed: 0.034 s
% 1.63/1.67 % (19858)Instructions burned: 99 (million)
% 1.63/1.67 % (19858)------------------------------
% 1.63/1.67 % (19858)------------------------------
% 1.63/1.67 % (19861)Instruction limit reached!
% 1.63/1.67 % (19861)------------------------------
% 1.63/1.67 % (19861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.67 % (19861)Termination reason: Unknown
% 1.63/1.67 % (19861)Termination phase: Saturation
% 1.63/1.67
% 1.63/1.67 % (19861)Memory used [KB]: 5756
% 1.63/1.67 % (19861)Time elapsed: 0.014 s
% 1.63/1.67 % (19861)Instructions burned: 39 (million)
% 1.63/1.67 % (19861)------------------------------
% 1.63/1.67 % (19861)------------------------------
% 1.63/1.67 % (19862)Instruction limit reached!
% 1.63/1.67 % (19862)------------------------------
% 1.63/1.67 % (19862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.67 % (19862)Termination reason: Unknown
% 1.63/1.67 % (19862)Termination phase: Saturation
% 1.63/1.67
% 1.63/1.67 % (19862)Memory used [KB]: 9978
% 1.63/1.67 % (19862)Time elapsed: 0.005 s
% 1.63/1.67 % (19862)Instructions burned: 9 (million)
% 1.63/1.67 % (19862)------------------------------
% 1.63/1.67 % (19862)------------------------------
% 1.63/1.68 % (19863)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/1087Mi)
% 1.63/1.68 % (19864)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/47Mi)
% 1.63/1.68 % (19865)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_19563 for (2996ds/44Mi)
% 1.63/1.69 % (19845)Instruction limit reached!
% 1.63/1.69 % (19845)------------------------------
% 1.63/1.69 % (19845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.69 % (19845)Termination reason: Unknown
% 1.63/1.69 % (19845)Termination phase: Saturation
% 1.63/1.69
% 1.63/1.69 % (19845)Memory used [KB]: 7675
% 1.63/1.69 % (19845)Time elapsed: 0.276 s
% 1.63/1.69 % (19845)Instructions burned: 881 (million)
% 1.63/1.69 % (19845)------------------------------
% 1.63/1.69 % (19845)------------------------------
% 1.63/1.69 % (19864)Instruction limit reached!
% 1.63/1.69 % (19864)------------------------------
% 1.63/1.69 % (19864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.69 % (19864)Termination reason: Unknown
% 1.63/1.69 % (19864)Termination phase: Saturation
% 1.63/1.69
% 1.63/1.69 % (19860)Instruction limit reached!
% 1.63/1.69 % (19860)------------------------------
% 1.63/1.69 % (19860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.69 % (19864)Memory used [KB]: 5628
% 1.63/1.69 % (19864)Time elapsed: 0.016 s
% 1.63/1.69 % (19860)Termination reason: Unknown
% 1.63/1.69 % (19864)Instructions burned: 48 (million)
% 1.63/1.69 % (19860)Termination phase: Saturation
% 1.63/1.69
% 1.63/1.69 % (19864)------------------------------
% 1.63/1.69 % (19864)------------------------------
% 1.63/1.69 % (19860)Memory used [KB]: 5756
% 1.63/1.69 % (19860)Time elapsed: 0.049 s
% 1.63/1.69 % (19860)Instructions burned: 150 (million)
% 1.63/1.69 % (19860)------------------------------
% 1.63/1.69 % (19860)------------------------------
% 1.63/1.69 % (19865)Instruction limit reached!
% 1.63/1.69 % (19865)------------------------------
% 1.63/1.69 % (19865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.69 % (19865)Termination reason: Unknown
% 1.63/1.69 % (19865)Termination phase: Saturation
% 1.63/1.69
% 1.63/1.69 % (19865)Memory used [KB]: 1151
% 1.63/1.69 % (19865)Time elapsed: 0.016 s
% 1.63/1.69 % (19865)Instructions burned: 45 (million)
% 1.63/1.69 % (19865)------------------------------
% 1.63/1.69 % (19865)------------------------------
% 1.63/1.70 % (19866)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_19563 for (2995ds/432Mi)
% 1.63/1.70 % (19867)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_19563 for (2995ds/62Mi)
% 1.63/1.70 % (19869)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_19563 for (2995ds/96Mi)
% 1.63/1.71 % (19868)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19563 for (2995ds/31Mi)
% 1.63/1.72 % (19867)Instruction limit reached!
% 1.63/1.72 % (19867)------------------------------
% 1.63/1.72 % (19867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.72 % (19867)Termination reason: Unknown
% 1.63/1.72 % (19867)Termination phase: Saturation
% 1.63/1.72
% 1.63/1.72 % (19867)Memory used [KB]: 5884
% 1.63/1.72 % (19867)Time elapsed: 0.020 s
% 1.63/1.72 % (19867)Instructions burned: 65 (million)
% 1.63/1.72 % (19867)------------------------------
% 1.63/1.72 % (19867)------------------------------
% 1.63/1.73 % (19868)Instruction limit reached!
% 1.63/1.73 % (19868)------------------------------
% 1.63/1.73 % (19868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.73 % (19868)Termination reason: Unknown
% 1.63/1.73 % (19868)Termination phase: Saturation
% 1.63/1.73
% 1.63/1.73 % (19868)Memory used [KB]: 5628
% 1.63/1.73 % (19868)Time elapsed: 0.019 s
% 1.63/1.73 % (19868)Instructions burned: 32 (million)
% 1.63/1.73 % (19868)------------------------------
% 1.63/1.73 % (19868)------------------------------
% 1.63/1.73 % (19870)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_19563 for (2995ds/453Mi)
% 1.63/1.73 % (19869)Instruction limit reached!
% 1.63/1.73 % (19869)------------------------------
% 1.63/1.73 % (19869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.73 % (19869)Termination reason: Unknown
% 1.63/1.73 % (19869)Termination phase: Saturation
% 1.63/1.73
% 1.63/1.73 % (19869)Memory used [KB]: 6012
% 1.63/1.73 % (19869)Time elapsed: 0.032 s
% 1.63/1.73 % (19869)Instructions burned: 96 (million)
% 1.63/1.73 % (19869)------------------------------
% 1.63/1.73 % (19869)------------------------------
% 1.63/1.74 % (19872)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_19563 for (2995ds/83Mi)
% 1.63/1.75 % (19871)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_19563 for (2995ds/71Mi)
% 1.63/1.76 % (19856)Instruction limit reached!
% 1.63/1.76 % (19856)------------------------------
% 1.63/1.76 % (19856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.76 % (19856)Termination reason: Unknown
% 1.63/1.76 % (19856)Termination phase: Saturation
% 1.63/1.76
% 1.63/1.76 % (19856)Memory used [KB]: 6908
% 1.63/1.76 % (19856)Time elapsed: 0.165 s
% 1.63/1.76 % (19856)Instructions burned: 449 (million)
% 1.63/1.76 % (19856)------------------------------
% 1.63/1.76 % (19856)------------------------------
% 1.63/1.77 % (19870)First to succeed.
% 1.63/1.77 % (19872)Instruction limit reached!
% 1.63/1.77 % (19872)------------------------------
% 1.63/1.77 % (19872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.77 % (19872)Termination reason: Unknown
% 1.63/1.77 % (19872)Termination phase: Saturation
% 1.63/1.77
% 1.63/1.77 % (19872)Memory used [KB]: 5884
% 1.63/1.77 % (19872)Time elapsed: 0.027 s
% 1.63/1.77 % (19872)Instructions burned: 83 (million)
% 1.63/1.77 % (19872)------------------------------
% 1.63/1.77 % (19872)------------------------------
% 1.63/1.77 % (19873)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_19563 for (2995ds/11Mi)
% 1.63/1.78 % (19870)Refutation found. Thanks to Tanya!
% 1.63/1.78 % SZS status Theorem for DTF2THF_19563
% 1.63/1.78 % SZS output start Proof for DTF2THF_19563
% 1.63/1.78 thf(type_def_5, type, a: $tType).
% 1.63/1.78 thf(func_def_0, type, a: $tType).
% 1.63/1.78 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.63/1.78 thf(func_def_21, type, sK2: (a > a > $o) > $o).
% 1.63/1.78 thf(func_def_22, type, sK3: (a > a > $o) > $o).
% 1.63/1.78 thf(func_def_23, type, sK4: a).
% 1.63/1.78 thf(func_def_24, type, sK5: a).
% 1.63/1.78 thf(func_def_25, type, sK6: (a > a > $o) > a).
% 1.63/1.78 thf(func_def_26, type, sK7: (a > a > $o) > a).
% 1.63/1.78 thf(func_def_27, type, sK8: (a > a > $o) > a > a > $o).
% 1.63/1.78 thf(func_def_28, type, sK9: a > a > $o).
% 1.63/1.78 thf(func_def_29, type, sK10: a > a > (a > a > $o) > a > a > $o).
% 1.63/1.78 thf(func_def_30, type, sK11: a > a > $o).
% 1.63/1.78 thf(func_def_31, type, sK12: (a > a > $o) > a).
% 1.63/1.78 thf(func_def_32, type, sK13: (a > a > $o) > a).
% 1.63/1.78 thf(func_def_33, type, sK14: (a > a > $o) > a > a > $o).
% 1.63/1.78 thf(func_def_34, type, sK15: (a > a > $o) > a > a > $o).
% 1.63/1.78 thf(func_def_35, type, sK16: (a > a > $o) > (a > a > $o) > a).
% 1.63/1.78 thf(func_def_36, type, sK17: (a > a > $o) > (a > a > $o) > a).
% 1.63/1.78 thf(f363,plain,(
% 1.63/1.78 $false),
% 1.63/1.78 inference(avatar_sat_refutation,[status(thm)],[f27,f130,f362])).
% 1.63/1.78 thf(f362,plain,(
% 1.63/1.78 ~spl0_1 | spl0_2),
% 1.63/1.78 inference(avatar_contradiction_clause,[status(thm)],[f361])).
% 1.63/1.78 thf(f361,plain,(
% 1.63/1.78 $false | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f360])).
% 1.63/1.78 thf(f360,plain,(
% 1.63/1.78 ($true = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(backward_demodulation,[status(thm)],[f136,f359])).
% 1.63/1.78 thf(f359,plain,(
% 1.63/1.78 ((sK2 @ sK11) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f358])).
% 1.63/1.78 thf(f358,plain,(
% 1.63/1.78 ($true = $false) | ((sK2 @ sK11) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f351,f133])).
% 1.63/1.78 thf(f133,plain,(
% 1.63/1.78 ((sK11 @ sK4 @ sK5) = $false) | spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.63/1.78 thf(f132,plain,(
% 1.63/1.78 ($false = (((sK2 @ sK11) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & (Y2 @ Y0 @ Y1)))) => (sK11 @ Y0 @ Y1))))))) => (sK11 @ sK4 @ sK5))) | spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.63/1.78 thf(f131,plain,(
% 1.63/1.78 ($false = ((^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))) @ sK11)) | spl0_2),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f25])).
% 1.63/1.78 thf(f25,plain,(
% 1.63/1.78 ($true != (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))))) | spl0_2),
% 1.63/1.78 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.63/1.78 thf(f24,definition,(
% 1.63/1.78 spl0_2 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))))),
% 1.63/1.78 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.63/1.78 thf(f351,plain,(
% 1.63/1.78 ($true = (sK11 @ sK4 @ sK5)) | ((sK2 @ sK11) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f350])).
% 1.63/1.78 thf(f350,plain,(
% 1.63/1.78 ((sK2 @ sK11) = $false) | ($true = $false) | ($true = (sK11 @ sK4 @ sK5)) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(superposition,[status(thm)],[f207,f321])).
% 1.63/1.78 thf(f321,plain,(
% 1.63/1.78 ((sK3 @ (sK15 @ sK11)) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f320])).
% 1.63/1.78 thf(f320,plain,(
% 1.63/1.78 ((sK3 @ (sK15 @ sK11)) = $false) | ($true = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f319,f136])).
% 1.63/1.78 thf(f319,plain,(
% 1.63/1.78 ((sK2 @ sK11) = $false) | ((sK3 @ (sK15 @ sK11)) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f318])).
% 1.63/1.78 thf(f318,plain,(
% 1.63/1.78 ($true = $false) | ((sK3 @ (sK15 @ sK11)) = $false) | ((sK2 @ sK11) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f317,f133])).
% 1.63/1.78 thf(f317,plain,(
% 1.63/1.78 ($true = (sK11 @ sK4 @ sK5)) | ((sK3 @ (sK15 @ sK11)) = $false) | ((sK2 @ sK11) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f316])).
% 1.63/1.78 thf(f316,plain,(
% 1.63/1.78 ($true = (sK11 @ sK4 @ sK5)) | ($true = $false) | ((sK3 @ (sK15 @ sK11)) = $false) | ((sK2 @ sK11) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(duplicate_literal_removal,[status(thm)],[f311])).
% 1.63/1.78 thf(f311,plain,(
% 1.63/1.78 ($true = (sK11 @ sK4 @ sK5)) | ($true = $false) | ((sK3 @ (sK15 @ sK11)) = $false) | ((sK2 @ sK11) = $false) | ($true = (sK11 @ sK4 @ sK5)) | ((sK2 @ sK11) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(superposition,[status(thm)],[f162,f307])).
% 1.63/1.78 thf(f307,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (($true = (sK11 @ (sK12 @ X0) @ (sK13 @ X0))) | ((sK3 @ (sK15 @ X0)) = $false) | ((sK2 @ X0) = $false) | ((X0 @ sK4 @ sK5) = $true)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f306])).
% 1.63/1.78 thf(f306,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (($true = $false) | ($true = (sK11 @ (sK12 @ X0) @ (sK13 @ X0))) | ((sK2 @ X0) = $false) | ((X0 @ sK4 @ sK5) = $true) | ((sK3 @ (sK15 @ X0)) = $false)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(duplicate_literal_removal,[status(thm)],[f300])).
% 1.63/1.78 thf(f300,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (((X0 @ sK4 @ sK5) = $true) | ($true = $false) | ($true = (sK11 @ (sK12 @ X0) @ (sK13 @ X0))) | ((X0 @ sK4 @ sK5) = $true) | ((sK2 @ X0) = $false) | ((sK2 @ X0) = $false) | ((sK3 @ (sK15 @ X0)) = $false)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(superposition,[status(thm)],[f178,f291])).
% 1.63/1.78 thf(f291,plain,(
% 1.63/1.78 ( ! [X2 : a,X0 : a > a > $o,X1 : a] : (((sK14 @ X0 @ X1 @ X2) = $false) | ((sK2 @ X0) = $false) | ((sK3 @ (sK15 @ X0)) = $false) | ((X0 @ sK4 @ sK5) = $true) | ($true = (sK11 @ X1 @ X2))) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f290])).
% 1.63/1.78 thf(f290,plain,(
% 1.63/1.78 ( ! [X2 : a,X0 : a > a > $o,X1 : a] : (($false != $false) | ($true = (sK11 @ X1 @ X2)) | ((sK14 @ X0 @ X1 @ X2) = $false) | ((sK2 @ X0) = $false) | ((sK3 @ (sK15 @ X0)) = $false) | ((X0 @ sK4 @ sK5) = $true)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(duplicate_literal_removal,[status(thm)],[f289])).
% 1.63/1.78 thf(f289,plain,(
% 1.63/1.78 ( ! [X2 : a,X0 : a > a > $o,X1 : a] : (((X0 @ sK4 @ sK5) = $true) | ((sK14 @ X0 @ X1 @ X2) = $false) | ((sK2 @ X0) = $false) | ($true = (sK11 @ X1 @ X2)) | ($true = (sK11 @ X1 @ X2)) | ($false != $false) | ((sK3 @ (sK15 @ X0)) = $false)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(equality_factoring,[status(thm)],[f284])).
% 1.63/1.78 thf(f284,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (($false = (sK14 @ X0 @ X3 @ X4)) | ((sK14 @ X0 @ X1 @ X2) = $false) | ((sK3 @ (sK15 @ X0)) = $false) | ($true = (sK11 @ X1 @ X2)) | ((sK2 @ X0) = $false) | ((X0 @ sK4 @ sK5) = $true) | ($true = (sK11 @ X3 @ X4))) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f283])).
% 1.63/1.78 thf(f283,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (($true = (sK11 @ X1 @ X2)) | ((sK3 @ (sK15 @ X0)) = $false) | ((X0 @ sK4 @ sK5) = $true) | ((sK14 @ X0 @ X1 @ X2) = $false) | ($true = $false) | ($false = (sK14 @ X0 @ X3 @ X4)) | ($true = (sK11 @ X3 @ X4)) | ((sK2 @ X0) = $false)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f281,f136])).
% 1.63/1.78 thf(f281,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (((sK3 @ (sK15 @ X0)) = $false) | ((X0 @ sK4 @ sK5) = $true) | ((sK2 @ sK11) = $false) | ((sK2 @ X0) = $false) | ($true = (sK11 @ X1 @ X2)) | ((sK14 @ X0 @ X1 @ X2) = $false) | ($false = (sK14 @ X0 @ X3 @ X4)) | ($true = (sK11 @ X3 @ X4))) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f280])).
% 1.63/1.78 thf(f280,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (((sK2 @ sK11) = $false) | ($false = (sK14 @ X0 @ X3 @ X4)) | ((X0 @ sK4 @ sK5) = $true) | ($true = (sK11 @ X3 @ X4)) | ((sK3 @ (sK15 @ X0)) = $false) | ($true = $false) | ($true = (sK11 @ X1 @ X2)) | ((sK14 @ X0 @ X1 @ X2) = $false) | ((sK2 @ X0) = $false)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(duplicate_literal_removal,[status(thm)],[f272])).
% 1.63/1.78 thf(f272,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a,X4 : a] : (((sK2 @ X0) = $false) | ((sK2 @ X0) = $false) | ((sK3 @ (sK15 @ X0)) = $false) | ($true = $false) | ($false = (sK14 @ X0 @ X3 @ X4)) | ($true = (sK11 @ X1 @ X2)) | ((sK14 @ X0 @ X1 @ X2) = $false) | ($true = (sK11 @ X3 @ X4)) | ((X0 @ sK4 @ sK5) = $true) | ((X0 @ sK4 @ sK5) = $true) | ((sK2 @ sK11) = $false)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(superposition,[status(thm)],[f224,f258])).
% 1.63/1.78 thf(f258,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (((X1 @ (sK16 @ X0 @ sK11) @ (sK17 @ X0 @ sK11)) = $false) | ((sK14 @ X0 @ X2 @ X3) = $false) | ((X0 @ sK4 @ sK5) = $true) | ((sK2 @ X0) = $false) | ($true = (sK11 @ X2 @ X3)) | ($false = (sK3 @ X1))) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f257])).
% 1.63/1.78 thf(f257,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (($false = (sK3 @ X1)) | ($true = (sK11 @ X2 @ X3)) | ($true = $false) | ((sK14 @ X0 @ X2 @ X3) = $false) | ((sK2 @ X0) = $false) | ((X0 @ sK4 @ sK5) = $true) | ((X1 @ (sK16 @ X0 @ sK11) @ (sK17 @ X0 @ sK11)) = $false)) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f256,f136])).
% 1.63/1.78 thf(f256,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (((sK2 @ sK11) = $false) | ((X0 @ sK4 @ sK5) = $true) | ($true = (sK11 @ X2 @ X3)) | ((sK2 @ X0) = $false) | ((X1 @ (sK16 @ X0 @ sK11) @ (sK17 @ X0 @ sK11)) = $false) | ((sK14 @ X0 @ X2 @ X3) = $false) | ($false = (sK3 @ X1))) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f249])).
% 1.63/1.78 thf(f249,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (((sK14 @ X0 @ X2 @ X3) = $false) | ((sK2 @ X0) = $false) | ($false = (sK3 @ X1)) | ((X0 @ sK4 @ sK5) = $true) | ((sK2 @ sK11) = $false) | ($true = $false) | ((X1 @ (sK16 @ X0 @ sK11) @ (sK17 @ X0 @ sK11)) = $false) | ($true = (sK11 @ X2 @ X3))) ) | (~spl0_1 | spl0_2)),
% 1.63/1.78 inference(superposition,[status(thm)],[f148,f223])).
% 1.63/1.78 thf(f223,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (((X4 @ (sK16 @ X1 @ X4) @ (sK17 @ X1 @ X4)) = $false) | ((sK2 @ X4) = $false) | ($true = (X1 @ sK4 @ sK5)) | ((X4 @ X2 @ X3) = $true) | ((sK2 @ X1) = $false) | ($false = (sK14 @ X1 @ X2 @ X3))) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f222])).
% 1.63/1.78 thf(f222,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (((sK2 @ X4) = $false) | ((X4 @ X2 @ X3) = $true) | ($false = (sK14 @ X1 @ X2 @ X3)) | (((sK15 @ X1 @ (sK16 @ X1 @ X4) @ (sK17 @ X1 @ X4)) => (X4 @ (sK16 @ X1 @ X4) @ (sK17 @ X1 @ X4))) = $false) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f221])).
% 1.63/1.78 thf(f221,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false) | ((X4 @ X2 @ X3) = $true) | ($false = (sK14 @ X1 @ X2 @ X3)) | ((sK2 @ X4) = $false) | (((^[Y0 : a]: ((sK15 @ X1 @ (sK16 @ X1 @ X4) @ Y0) => (X4 @ (sK16 @ X1 @ X4) @ Y0))) @ (sK17 @ X1 @ X4)) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f220])).
% 1.63/1.78 thf(f220,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (((!! @ a @ (^[Y0 : a]: ((sK15 @ X1 @ (sK16 @ X1 @ X4) @ Y0) => (X4 @ (sK16 @ X1 @ X4) @ Y0)))) = $false) | ($true = (X1 @ sK4 @ sK5)) | ((X4 @ X2 @ X3) = $true) | ((sK2 @ X1) = $false) | ((sK2 @ X4) = $false) | ($false = (sK14 @ X1 @ X2 @ X3))) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f219])).
% 1.63/1.78 thf(f219,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (((sK2 @ X1) = $false) | ((X4 @ X2 @ X3) = $true) | ((sK2 @ X4) = $false) | ($true = (X1 @ sK4 @ sK5)) | ($false = (sK14 @ X1 @ X2 @ X3)) | (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ X1 @ Y0 @ Y1) => (X4 @ Y0 @ Y1))))) @ (sK16 @ X1 @ X4)) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f218])).
% 1.63/1.78 thf(f218,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ X1 @ Y0 @ Y1) => (X4 @ Y0 @ Y1)))))) = $false) | ($true = (X1 @ sK4 @ sK5)) | ((X4 @ X2 @ X3) = $true) | ($false = (sK14 @ X1 @ X2 @ X3)) | ((sK2 @ X1) = $false) | ((sK2 @ X4) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f217])).
% 1.63/1.78 thf(f217,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | (((sK2 @ X4) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ X1 @ Y0 @ Y1) => (X4 @ Y0 @ Y1))))))) = $false) | ($false = (sK14 @ X1 @ X2 @ X3)) | ((X4 @ X2 @ X3) = $true) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f216])).
% 1.63/1.78 thf(f216,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | ($false = (sK14 @ X1 @ X2 @ X3)) | ($true = (((sK2 @ X4) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ X1 @ Y0 @ Y1) => (X4 @ Y0 @ Y1))))))) => (X4 @ X2 @ X3))) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f215])).
% 1.63/1.78 thf(f215,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK15 @ X1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X2 @ X3))) @ X4) = $true) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5)) | ($false = (sK14 @ X1 @ X2 @ X3))) ) | ~spl0_1),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f213])).
% 1.63/1.78 thf(f213,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o] : (($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK15 @ X1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X2 @ X3))))) | ($false = (sK14 @ X1 @ X2 @ X3)) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f212])).
% 1.63/1.78 thf(f212,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o] : (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK15 @ X1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X2 @ X3)))) = (sK14 @ X1 @ X2 @ X3)) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f211])).
% 1.63/1.78 thf(f211,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false) | (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK15 @ X1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ X2 @ Y0))))) @ X3) = (sK14 @ X1 @ X2 @ X3))) ) | ~spl0_1),
% 1.63/1.78 inference(argument_congruence,[status(thm)],[f210])).
% 1.63/1.78 thf(f210,plain,(
% 1.63/1.78 ( ! [X2 : a,X1 : a > a > $o] : (((sK14 @ X1 @ X2) = (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK15 @ X1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ X2 @ Y0)))))) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f209])).
% 1.63/1.78 thf(f209,plain,(
% 1.63/1.78 ( ! [X2 : a,X1 : a > a > $o] : ((((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK15 @ X1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) @ X2) = (sK14 @ X1 @ X2)) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(argument_congruence,[status(thm)],[f208])).
% 1.63/1.78 thf(f208,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK15 @ X1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = (sK14 @ X1)) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(equality_proxy_clausification,[status(thm)],[f206])).
% 1.63/1.78 thf(f206,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | ($true = ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK15 @ X1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = (sK14 @ X1))) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f205])).
% 1.63/1.78 thf(f205,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false) | ($true = ((sK3 @ (sK15 @ X1)) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK15 @ X1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = (sK14 @ X1))))) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f204])).
% 1.63/1.78 thf(f204,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((sK2 @ X1) = $false) | ($true = ((^[Y0 : a > a > $o]: ((sK3 @ Y0) & ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = (sK14 @ X1)))) @ (sK15 @ X1))) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f179])).
% 1.63/1.78 thf(f179,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((sK3 @ Y0) & ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = (sK14 @ X1)))))) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f177])).
% 1.63/1.78 thf(f177,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = ((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((sK3 @ Y0) & ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = (sK14 @ X1))))) & (sK14 @ X1 @ (sK12 @ X1) @ (sK13 @ X1)))) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f176])).
% 1.63/1.78 thf(f176,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false) | ($true = ((^[Y0 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((sK2 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = Y0)))) & (Y0 @ (sK12 @ X1) @ (sK13 @ X1)))) @ (sK14 @ X1)))) ) | ~spl0_1),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f163])).
% 1.63/1.78 thf(f163,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((sK2 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = Y0)))) & (Y0 @ (sK12 @ X1) @ (sK13 @ X1)))))) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 1.63/1.78 thf(f161,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((sK2 @ X1) = $false) | ($false = ((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((sK2 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = Y0)))) & (Y0 @ (sK12 @ X1) @ (sK13 @ X1))))) => (X1 @ (sK12 @ X1) @ (sK13 @ X1)))) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f160])).
% 1.63/1.78 thf(f160,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | (((^[Y0 : a]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & ((^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((sK2 @ Y5) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4))))))) = Y1)))) & (Y1 @ (sK12 @ X1) @ Y0)))) => (X1 @ (sK12 @ X1) @ Y0))) @ (sK13 @ X1)) = $false) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f159])).
% 1.63/1.78 thf(f159,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($false = (!! @ a @ (^[Y0 : a]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & ((^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((sK2 @ Y5) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4))))))) = Y1)))) & (Y1 @ (sK12 @ X1) @ Y0)))) => (X1 @ (sK12 @ X1) @ Y0))))) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f158])).
% 1.63/1.78 thf(f158,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((sK2 @ X1) = $false) | (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & ((^[Y4 : a]: ((^[Y5 : a]: (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((sK2 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5))))))) = Y2)))) & (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1))))) @ (sK12 @ X1)) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f145])).
% 1.63/1.78 thf(f145,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & ((^[Y4 : a]: ((^[Y5 : a]: (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((sK2 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5))))))) = Y2)))) & (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1)))))) = $false) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.63/1.78 thf(f144,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | (((sK2 @ X1) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & ((^[Y4 : a]: ((^[Y5 : a]: (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((sK2 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5))))))) = Y2)))) & (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1))))))) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.63/1.78 thf(f143,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (((sK2 @ X1) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & ((^[Y4 : a]: ((^[Y5 : a]: (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((sK2 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5))))))) = Y2)))) & (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK4 @ sK5)))) ) | ~spl0_1),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f142])).
% 1.63/1.78 thf(f142,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))) @ X1) = $true)) ) | ~spl0_1),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f22])).
% 1.63/1.78 thf(f22,plain,(
% 1.63/1.78 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))))) | ~spl0_1),
% 1.63/1.78 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.63/1.78 thf(f20,definition,(
% 1.63/1.78 spl0_1 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))))),
% 1.63/1.78 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.63/1.78 thf(f148,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a] : (($true = (sK11 @ X1 @ X2)) | ((sK3 @ X3) = $false) | ((X3 @ X1 @ X2) = $false)) ) | spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.63/1.78 thf(f147,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a] : (($false = ((sK3 @ X3) & (X3 @ X1 @ X2))) | ($true = (sK11 @ X1 @ X2))) ) | spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f146])).
% 1.63/1.78 thf(f146,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a] : ((((^[Y0 : a > a > $o]: ((sK3 @ Y0) & (Y0 @ X1 @ X2))) @ X3) = $false) | ($true = (sK11 @ X1 @ X2))) ) | spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f141])).
% 1.63/1.78 thf(f141,plain,(
% 1.63/1.78 ( ! [X2 : a,X1 : a] : (((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((sK3 @ Y0) & (Y0 @ X1 @ X2)))) = $false) | ($true = (sK11 @ X1 @ X2))) ) | spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.63/1.78 thf(f140,plain,(
% 1.63/1.78 ( ! [X2 : a,X1 : a] : ((((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((sK3 @ Y0) & (Y0 @ X1 @ X2)))) => (sK11 @ X1 @ X2)) = $true)) ) | spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.63/1.78 thf(f139,plain,(
% 1.63/1.78 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & (Y1 @ X1 @ Y0)))) => (sK11 @ X1 @ Y0))) @ X2) = $true)) ) | spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f138])).
% 1.63/1.78 thf(f138,plain,(
% 1.63/1.78 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & (Y1 @ X1 @ Y0)))) => (sK11 @ X1 @ Y0)))) = $true)) ) | spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f137])).
% 1.63/1.78 thf(f137,plain,(
% 1.63/1.78 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & (Y2 @ Y0 @ Y1)))) => (sK11 @ Y0 @ Y1))))) @ X1) = $true)) ) | spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f135])).
% 1.63/1.78 thf(f135,plain,(
% 1.63/1.78 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & (Y2 @ Y0 @ Y1)))) => (sK11 @ Y0 @ Y1))))))) | spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.63/1.78 thf(f134,plain,(
% 1.63/1.78 (((sK2 @ sK11) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & (Y2 @ Y0 @ Y1)))) => (sK11 @ Y0 @ Y1))))))) = $true) | spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.63/1.78 thf(f224,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a,X1 : a > a > $o,X4 : a > a > $o] : (($true = (sK15 @ X1 @ (sK16 @ X1 @ X4) @ (sK17 @ X1 @ X4))) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5)) | ((X4 @ X2 @ X3) = $true) | ($false = (sK14 @ X1 @ X2 @ X3)) | ((sK2 @ X4) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f222])).
% 1.63/1.78 thf(f178,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (sK14 @ X1 @ (sK12 @ X1) @ (sK13 @ X1))) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f177])).
% 1.63/1.78 thf(f162,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($false = (X1 @ (sK12 @ X1) @ (sK13 @ X1))) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 1.63/1.78 thf(f207,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (sK3 @ (sK15 @ X1))) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_1),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f205])).
% 1.63/1.78 thf(f136,plain,(
% 1.63/1.78 ((sK2 @ sK11) = $true) | spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.63/1.78 thf(f130,plain,(
% 1.63/1.78 ~spl0_2),
% 1.63/1.78 inference(avatar_contradiction_clause,[status(thm)],[f129])).
% 1.63/1.78 thf(f129,plain,(
% 1.63/1.78 $false | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.63/1.78 thf(f128,plain,(
% 1.63/1.78 ($true = $false) | ~spl0_2),
% 1.63/1.78 inference(backward_demodulation,[status(thm)],[f49,f127])).
% 1.63/1.78 thf(f127,plain,(
% 1.63/1.78 ($false = (sK2 @ sK9)) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.63/1.78 thf(f126,plain,(
% 1.63/1.78 ($true = $false) | ($false = (sK2 @ sK9)) | ~spl0_2),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f125,f46])).
% 1.63/1.78 thf(f46,plain,(
% 1.63/1.78 ($false = (sK9 @ sK4 @ sK5)) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.63/1.78 thf(f45,plain,(
% 1.63/1.78 ($false = (((sK2 @ sK9) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & ((^[Y4 : a]: ((^[Y5 : a]: (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((sK2 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5))))))) = Y2)))) & (Y2 @ Y0 @ Y1)))) => (sK9 @ Y0 @ Y1))))))) => (sK9 @ sK4 @ sK5))) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.63/1.78 thf(f44,plain,(
% 1.63/1.78 (((^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))) @ sK9) = $false) | ~spl0_2),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f29])).
% 1.63/1.78 thf(f29,plain,(
% 1.63/1.78 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))))) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.63/1.78 thf(f28,plain,(
% 1.63/1.78 ($true = $false) | ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))))) | ~spl0_2),
% 1.63/1.78 inference(backward_demodulation,[status(thm)],[f18,f26])).
% 1.63/1.78 thf(f26,plain,(
% 1.63/1.78 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))))) | ~spl0_2),
% 1.63/1.78 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.63/1.78 thf(f18,plain,(
% 1.63/1.78 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))) = $false) | ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))))),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.63/1.78 thf(f16,plain,(
% 1.63/1.78 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))) != (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))))),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.63/1.78 thf(f15,plain,(
% 1.63/1.78 (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & (Y4 @ Y2 @ Y3)))) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ Y0))))) @ sK5) != ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: ((sK3 @ Y5) & ((^[Y6 : a]: ((^[Y7 : a]: (!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((sK2 @ Y8) & (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y5 @ Y9 @ Y10) => (Y8 @ Y9 @ Y10))))))) => (Y8 @ Y6 @ Y7))))))) = Y4)))) & (Y4 @ Y2 @ Y3)))) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ Y0))))) @ sK5))),
% 1.63/1.78 inference(negative_extensionality,[status(thm)],[f14])).
% 1.63/1.78 thf(f14,plain,(
% 1.63/1.78 ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: ((sK3 @ Y5) & ((^[Y6 : a]: ((^[Y7 : a]: (!! @ (a > a > $o) @ (^[Y8 : a > a > $o]: (((sK2 @ Y8) & (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: ((Y5 @ Y9 @ Y10) => (Y8 @ Y9 @ Y10))))))) => (Y8 @ Y6 @ Y7))))))) = Y4)))) & (Y4 @ Y2 @ Y3)))) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ Y0))))) != (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((sK2 @ Y1) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & (Y4 @ Y2 @ Y3)))) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ Y0))))))),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.63/1.78 thf(f13,plain,(
% 1.63/1.78 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y6 : a > a > $o]: ((sK3 @ Y6) & ((^[Y7 : a]: ((^[Y8 : a]: (!! @ (a > a > $o) @ (^[Y9 : a > a > $o]: (((sK2 @ Y9) & (!! @ a @ (^[Y10 : a]: (!! @ a @ (^[Y11 : a]: ((Y6 @ Y10 @ Y11) => (Y9 @ Y10 @ Y11))))))) => (Y9 @ Y7 @ Y8))))))) = Y5)))) & (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) @ sK4) != ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: ((sK3 @ Y5) & (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) @ sK4))),
% 1.63/1.78 inference(negative_extensionality,[status(thm)],[f12])).
% 1.63/1.78 thf(f12,plain,(
% 1.63/1.78 ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: ((sK3 @ Y5) & (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y6 : a > a > $o]: ((sK3 @ Y6) & ((^[Y7 : a]: ((^[Y8 : a]: (!! @ (a > a > $o) @ (^[Y9 : a > a > $o]: (((sK2 @ Y9) & (!! @ a @ (^[Y10 : a]: (!! @ a @ (^[Y11 : a]: ((Y6 @ Y10 @ Y11) => (Y9 @ Y10 @ Y11))))))) => (Y9 @ Y7 @ Y8))))))) = Y5)))) & (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))),
% 1.63/1.78 inference(equality_proxy_clausification,[status(thm)],[f11])).
% 1.63/1.78 thf(f11,plain,(
% 1.63/1.78 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: ((sK3 @ Y5) & (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((?? @ (a > a > $o) @ (^[Y5 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y6 : a > a > $o]: ((sK3 @ Y6) & ((^[Y7 : a]: ((^[Y8 : a]: (!! @ (a > a > $o) @ (^[Y9 : a > a > $o]: (((sK2 @ Y9) & (!! @ a @ (^[Y10 : a]: (!! @ a @ (^[Y11 : a]: ((Y6 @ Y10 @ Y11) => (Y9 @ Y10 @ Y11))))))) => (Y9 @ Y7 @ Y8))))))) = Y5)))) & (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))))))) = $false)),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.63/1.78 thf(f10,plain,(
% 1.63/1.78 (((^[Y0 : (a > a > $o) > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((?? @ (a > a > $o) @ (^[Y6 : a > a > $o]: ((Y0 @ Y6) & (Y6 @ Y4 @ Y5)))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((?? @ (a > a > $o) @ (^[Y6 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((Y0 @ Y7) & ((^[Y8 : a]: ((^[Y9 : a]: (!! @ (a > a > $o) @ (^[Y10 : a > a > $o]: (((sK2 @ Y10) & (!! @ a @ (^[Y11 : a]: (!! @ a @ (^[Y12 : a]: ((Y7 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))) => (Y10 @ Y8 @ Y9))))))) = Y6)))) & (Y6 @ Y4 @ Y5)))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))))) @ sK3) = $false)),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f9])).
% 1.63/1.78 thf(f9,plain,(
% 1.63/1.78 ($false = (!! @ ((a > a > $o) > $o) @ (^[Y0 : (a > a > $o) > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((?? @ (a > a > $o) @ (^[Y6 : a > a > $o]: ((Y0 @ Y6) & (Y6 @ Y4 @ Y5)))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((?? @ (a > a > $o) @ (^[Y6 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((Y0 @ Y7) & ((^[Y8 : a]: ((^[Y9 : a]: (!! @ (a > a > $o) @ (^[Y10 : a > a > $o]: (((sK2 @ Y10) & (!! @ a @ (^[Y11 : a]: (!! @ a @ (^[Y12 : a]: ((Y7 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))) => (Y10 @ Y8 @ Y9))))))) = Y6)))) & (Y6 @ Y4 @ Y5)))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))))))))))),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.63/1.78 thf(f8,plain,(
% 1.63/1.78 (((^[Y0 : (a > a > $o) > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y1 : (a > a > $o) > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((Y0 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((Y1 @ Y7) & (Y7 @ Y5 @ Y6)))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((Y0 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y8 : a > a > $o]: ((Y1 @ Y8) & ((^[Y9 : a]: ((^[Y10 : a]: (!! @ (a > a > $o) @ (^[Y11 : a > a > $o]: (((Y0 @ Y11) & (!! @ a @ (^[Y12 : a]: (!! @ a @ (^[Y13 : a]: ((Y8 @ Y12 @ Y13) => (Y11 @ Y12 @ Y13))))))) => (Y11 @ Y9 @ Y10))))))) = Y7)))) & (Y7 @ Y5 @ Y6)))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))))))) @ sK2) = $false)),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f7])).
% 1.63/1.78 thf(f7,plain,(
% 1.63/1.78 ($false = (!! @ ((a > a > $o) > $o) @ (^[Y0 : (a > a > $o) > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y1 : (a > a > $o) > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((Y0 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((Y1 @ Y7) & (Y7 @ Y5 @ Y6)))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((Y0 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y8 : a > a > $o]: ((Y1 @ Y8) & ((^[Y9 : a]: ((^[Y10 : a]: (!! @ (a > a > $o) @ (^[Y11 : a > a > $o]: (((Y0 @ Y11) & (!! @ a @ (^[Y12 : a]: (!! @ a @ (^[Y13 : a]: ((Y8 @ Y12 @ Y13) => (Y11 @ Y12 @ Y13))))))) => (Y11 @ Y9 @ Y10))))))) = Y7)))) & (Y7 @ Y5 @ Y6)))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))))))))))))),
% 1.63/1.78 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.63/1.78 thf(f6,plain,(
% 1.63/1.78 ((~ (!! @ ((a > a > $o) > $o) @ (^[Y0 : (a > a > $o) > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y1 : (a > a > $o) > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((Y0 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((Y1 @ Y7) & (Y7 @ Y5 @ Y6)))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((Y0 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y8 : a > a > $o]: ((Y1 @ Y8) & ((^[Y9 : a]: ((^[Y10 : a]: (!! @ (a > a > $o) @ (^[Y11 : a > a > $o]: (((Y0 @ Y11) & (!! @ a @ (^[Y12 : a]: (!! @ a @ (^[Y13 : a]: ((Y8 @ Y12 @ Y13) => (Y11 @ Y12 @ Y13))))))) => (Y11 @ Y9 @ Y10))))))) = Y7)))) & (Y7 @ Y5 @ Y6)))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))))))))) = $true)),
% 1.63/1.78 inference(cnf_transformation,[status(thm)],[f5])).
% 1.63/1.78 thf(f5,plain,(
% 1.63/1.78 ((~ (!! @ ((a > a > $o) > $o) @ (^[Y0 : (a > a > $o) > $o]: (!! @ ((a > a > $o) > $o) @ (^[Y1 : (a > a > $o) > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((Y0 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((Y1 @ Y7) & (Y7 @ Y5 @ Y6)))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((Y0 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((?? @ (a > a > $o) @ (^[Y7 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y8 : a > a > $o]: ((Y1 @ Y8) & ((^[Y9 : a]: ((^[Y10 : a]: (!! @ (a > a > $o) @ (^[Y11 : a > a > $o]: (((Y0 @ Y11) & (!! @ a @ (^[Y12 : a]: (!! @ a @ (^[Y13 : a]: ((Y8 @ Y12 @ Y13) => (Y11 @ Y12 @ Y13))))))) => (Y11 @ Y9 @ Y10))))))) = Y7)))) & (Y7 @ Y5 @ Y6)))) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))))))))) = $true)),
% 1.63/1.78 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.78 thf(f4,plain,(
% 1.63/1.78 ~! [X0 : (a > a > $o) > $o,X1 : (a > a > $o) > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : (? [X7 : a > a > $o] : ((X7 @ X6 @ X5) & (X0 @ X7)) => (X4 @ X6 @ X5)) & (X1 @ X4)) => (X4 @ X2 @ X3)))) = (^[X8 : a, X9 : a] : (! [X10 : a > a > $o] : ((! [X11 : a,X12 : a] : (? [X13 : a > a > $o] : ((X13 @ X12 @ X11) & ? [X14 : a > a > $o] : (((^[X15 : a, X16 : a] : (! [X17 : a > a > $o] : ((! [X18 : a,X19 : a] : ((X14 @ X19 @ X18) => (X17 @ X19 @ X18)) & (X1 @ X17)) => (X17 @ X15 @ X16)))) = X13) & (X0 @ X14))) => (X10 @ X12 @ X11)) & (X1 @ X10)) => (X10 @ X8 @ X9)))))),
% 1.63/1.78 inference(rectify,[status(thm)],[f2])).
% 1.63/1.78 thf(f2,negated_conjecture,(
% 1.63/1.78 ~! [X1 : (a > a > $o) > $o,X0 : (a > a > $o) > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : ((X7 @ X5 @ X6) & (X1 @ X7)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : ((X7 @ X5 @ X6) & ? [X8 : a > a > $o] : (((^[X9 : a, X10 : a] : (! [X11 : a > a > $o] : ((! [X13 : a,X12 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13)) & (X0 @ X11)) => (X11 @ X9 @ X10)))) = X7) & (X1 @ X8))) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))))),
% 1.63/1.78 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.78 thf(f1,conjecture,(
% 1.63/1.78 ! [X1 : (a > a > $o) > $o,X0 : (a > a > $o) > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : ((X7 @ X5 @ X6) & (X1 @ X7)) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (? [X7 : a > a > $o] : ((X7 @ X5 @ X6) & ? [X8 : a > a > $o] : (((^[X9 : a, X10 : a] : (! [X11 : a > a > $o] : ((! [X13 : a,X12 : a] : ((X8 @ X12 @ X13) => (X11 @ X12 @ X13)) & (X0 @ X11)) => (X11 @ X9 @ X10)))) = X7) & (X1 @ X8))) => (X4 @ X5 @ X6)) & (X0 @ X4)) => (X4 @ X2 @ X3)))))),
% 1.63/1.78 file('/export/starexec/sandbox2/tmp/tmp.iE0IFtsIlX/DTF2THF_19563.p',cTHM254_pme)).
% 1.63/1.78 thf(f125,plain,(
% 1.63/1.78 ($true = (sK9 @ sK4 @ sK5)) | ($false = (sK2 @ sK9)) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.63/1.78 thf(f122,plain,(
% 1.63/1.78 ($true = (sK9 @ sK4 @ sK5)) | ($true = $false) | ($false = (sK2 @ sK9)) | ~spl0_2),
% 1.63/1.78 inference(superposition,[status(thm)],[f121,f43])).
% 1.63/1.78 thf(f43,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (sK3 @ (sK8 @ X1))) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.63/1.78 thf(f41,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5)) | ($true = ((sK3 @ (sK8 @ X1)) & (sK8 @ X1 @ (sK6 @ X1) @ (sK7 @ X1))))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.63/1.78 thf(f40,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false) | ($true = ((^[Y0 : a > a > $o]: ((sK3 @ Y0) & (Y0 @ (sK6 @ X1) @ (sK7 @ X1)))) @ (sK8 @ X1)))) ) | ~spl0_2),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f39])).
% 1.63/1.78 thf(f39,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((sK3 @ Y0) & (Y0 @ (sK6 @ X1) @ (sK7 @ X1))))) = $true) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.63/1.78 thf(f37,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5)) | (((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((sK3 @ Y0) & (Y0 @ (sK6 @ X1) @ (sK7 @ X1))))) => (X1 @ (sK6 @ X1) @ (sK7 @ X1))) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.63/1.78 thf(f36,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5)) | (((^[Y0 : a]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & (Y1 @ (sK6 @ X1) @ Y0)))) => (X1 @ (sK6 @ X1) @ Y0))) @ (sK7 @ X1)) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f35])).
% 1.63/1.78 thf(f35,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((!! @ a @ (^[Y0 : a]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & (Y1 @ (sK6 @ X1) @ Y0)))) => (X1 @ (sK6 @ X1) @ Y0)))) = $false) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.63/1.78 thf(f34,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1))))) @ (sK6 @ X1)) = $false) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_2),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f33])).
% 1.63/1.78 thf(f33,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1))))))) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.63/1.78 thf(f32,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (X1 @ sK4 @ sK5)) | ($false = ((sK2 @ X1) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1))))))))) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.63/1.78 thf(f31,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = (((sK2 @ X1) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK4 @ sK5)))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.63/1.78 thf(f30,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))) @ X1))) ) | ~spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f26])).
% 1.63/1.78 thf(f121,plain,(
% 1.63/1.78 ((sK3 @ (sK8 @ sK9)) = $false) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.63/1.78 thf(f120,plain,(
% 1.63/1.78 ((sK3 @ (sK8 @ sK9)) = $false) | ($true = $false) | ~spl0_2),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f119,f49])).
% 1.63/1.78 thf(f119,plain,(
% 1.63/1.78 ((sK3 @ (sK8 @ sK9)) = $false) | ($false = (sK2 @ sK9)) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.63/1.78 thf(f118,plain,(
% 1.63/1.78 ($true = $false) | ((sK3 @ (sK8 @ sK9)) = $false) | ($false = (sK2 @ sK9)) | ~spl0_2),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f117,f46])).
% 1.63/1.78 thf(f117,plain,(
% 1.63/1.78 ($true = (sK9 @ sK4 @ sK5)) | ($false = (sK2 @ sK9)) | ((sK3 @ (sK8 @ sK9)) = $false) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.63/1.78 thf(f111,plain,(
% 1.63/1.78 ((sK3 @ (sK8 @ sK9)) = $false) | ($true = (sK9 @ sK4 @ sK5)) | ($true = $false) | ($false = (sK2 @ sK9)) | ~spl0_2),
% 1.63/1.78 inference(superposition,[status(thm)],[f42,f97])).
% 1.63/1.78 thf(f97,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (($false = (X0 @ (sK6 @ sK9) @ (sK7 @ sK9))) | ((sK3 @ X0) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.63/1.78 thf(f96,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (($true = $false) | ((sK3 @ X0) = $false) | ($false = (X0 @ (sK6 @ sK9) @ (sK7 @ sK9)))) ) | ~spl0_2),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f95,f49])).
% 1.63/1.78 thf(f95,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (((sK3 @ X0) = $false) | ($false = (sK2 @ sK9)) | ($false = (X0 @ (sK6 @ sK9) @ (sK7 @ sK9)))) ) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.63/1.78 thf(f94,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (((sK3 @ X0) = $false) | ($false = (X0 @ (sK6 @ sK9) @ (sK7 @ sK9))) | ($true = $false) | ($false = (sK2 @ sK9))) ) | ~spl0_2),
% 1.63/1.78 inference(forward_demodulation,[status(thm)],[f93,f46])).
% 1.63/1.78 thf(f93,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (((sK3 @ X0) = $false) | ($true = (sK9 @ sK4 @ sK5)) | ($false = (X0 @ (sK6 @ sK9) @ (sK7 @ sK9))) | ($false = (sK2 @ sK9))) ) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.63/1.78 thf(f88,plain,(
% 1.63/1.78 ( ! [X0 : a > a > $o] : (((sK3 @ X0) = $false) | ($true = $false) | ($false = (sK2 @ sK9)) | ($true = (sK9 @ sK4 @ sK5)) | ($false = (X0 @ (sK6 @ sK9) @ (sK7 @ sK9)))) ) | ~spl0_2),
% 1.63/1.78 inference(superposition,[status(thm)],[f38,f84])).
% 1.63/1.78 thf(f84,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (((sK9 @ X1 @ X0) = $true) | ((X2 @ X1 @ X0) = $false) | ($false = (sK3 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.63/1.78 thf(f83,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (((sK9 @ X1 @ X0) = $true) | ($false = (sK3 @ X2)) | ((X2 @ X1 @ X0) = $false) | ($true = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(duplicate_literal_removal,[status(thm)],[f75])).
% 1.63/1.78 thf(f75,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (($false = (sK3 @ X2)) | ((X2 @ X1 @ X0) = $false) | ($false = (sK3 @ X2)) | ((sK9 @ X1 @ X0) = $true) | ($true = $false) | ((sK9 @ X1 @ X0) = $true)) ) | ~spl0_2),
% 1.63/1.78 inference(superposition,[status(thm)],[f74,f66])).
% 1.63/1.78 thf(f66,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (($false = (sK10 @ X1 @ X0 @ X2 @ X0 @ X1)) | ($true = (sK9 @ X0 @ X1)) | ($false = (sK3 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.63/1.78 thf(f65,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (($true = (sK9 @ X0 @ X1)) | ($false = (((sK2 @ (sK10 @ X1 @ X0 @ X2)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X2 @ Y0 @ Y1) => (sK10 @ X1 @ X0 @ X2 @ Y0 @ Y1))))))) => (sK10 @ X1 @ X0 @ X2 @ X0 @ X1))) | ($false = (sK3 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.63/1.78 thf(f64,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (($true = (sK9 @ X0 @ X1)) | ($false = (sK3 @ X2)) | (((^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X0 @ X1))) @ (sK10 @ X1 @ X0 @ X2)) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(sigma_clausification,[status(thm)],[f63])).
% 1.63/1.78 thf(f63,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((X2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X0 @ X1)))) = $false) | ($true = (sK9 @ X0 @ X1)) | ($false = (sK3 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.63/1.78 thf(f62,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (($true = (sK9 @ X0 @ X1)) | (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) @ X0 @ X1) = $false) | ($false = (sK3 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(equality_resolution,[status(thm)],[f61])).
% 1.63/1.78 thf(f61,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a,X4 : a > a > $o] : (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != X3) | ($true = (sK9 @ X1 @ X2)) | ((sK3 @ X4) = $false) | ((X3 @ X1 @ X2) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(equality_proxy_clausification,[status(thm)],[f60])).
% 1.63/1.78 thf(f60,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a,X4 : a > a > $o] : (($false = ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = X3)) | ($true = (sK9 @ X1 @ X2)) | ((sK3 @ X4) = $false) | ((X3 @ X1 @ X2) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.63/1.78 thf(f59,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a,X4 : a > a > $o] : (((X3 @ X1 @ X2) = $false) | (((sK3 @ X4) & ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((sK2 @ Y2) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((X4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = X3)) = $false) | ($true = (sK9 @ X1 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.63/1.78 thf(f58,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a,X4 : a > a > $o] : (($false = ((^[Y0 : a > a > $o]: ((sK3 @ Y0) & ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = X3))) @ X4)) | ($true = (sK9 @ X1 @ X2)) | ((X3 @ X1 @ X2) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f57])).
% 1.63/1.78 thf(f57,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a] : (((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((sK3 @ Y0) & ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = X3)))) = $false) | ($true = (sK9 @ X1 @ X2)) | ((X3 @ X1 @ X2) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.63/1.78 thf(f56,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a] : (($false = ((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((sK3 @ Y0) & ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((sK2 @ Y3) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = X3)))) & (X3 @ X1 @ X2))) | ($true = (sK9 @ X1 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.63/1.78 thf(f55,plain,(
% 1.63/1.78 ( ! [X2 : a,X3 : a > a > $o,X1 : a] : (($false = ((^[Y0 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((sK2 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = Y0)))) & (Y0 @ X1 @ X2))) @ X3)) | ($true = (sK9 @ X1 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f54])).
% 1.63/1.78 thf(f54,plain,(
% 1.63/1.78 ( ! [X2 : a,X1 : a] : (($false = (?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((sK2 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = Y0)))) & (Y0 @ X1 @ X2))))) | ($true = (sK9 @ X1 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.63/1.78 thf(f53,plain,(
% 1.63/1.78 ( ! [X2 : a,X1 : a] : (($true = ((?? @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((sK3 @ Y1) & ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((sK2 @ Y4) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))) = Y0)))) & (Y0 @ X1 @ X2)))) => (sK9 @ X1 @ X2)))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.63/1.78 thf(f52,plain,(
% 1.63/1.78 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & ((^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((sK2 @ Y5) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4))))))) = Y1)))) & (Y1 @ X1 @ Y0)))) => (sK9 @ X1 @ Y0))) @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f51])).
% 1.63/1.78 thf(f51,plain,(
% 1.63/1.78 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((?? @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((sK3 @ Y2) & ((^[Y3 : a]: ((^[Y4 : a]: (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((sK2 @ Y5) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4))))))) = Y1)))) & (Y1 @ X1 @ Y0)))) => (sK9 @ X1 @ Y0)))) = $true)) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.63/1.78 thf(f50,plain,(
% 1.63/1.78 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & ((^[Y4 : a]: ((^[Y5 : a]: (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((sK2 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5))))))) = Y2)))) & (Y2 @ Y0 @ Y1)))) => (sK9 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f48])).
% 1.63/1.78 thf(f48,plain,(
% 1.63/1.78 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & ((^[Y4 : a]: ((^[Y5 : a]: (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((sK2 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5))))))) = Y2)))) & (Y2 @ Y0 @ Y1)))) => (sK9 @ Y0 @ Y1)))))) = $true) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.63/1.78 thf(f47,plain,(
% 1.63/1.78 (((sK2 @ sK9) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((?? @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & ((^[Y4 : a]: ((^[Y5 : a]: (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((sK2 @ Y6) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y3 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5))))))) = Y2)))) & (Y2 @ Y0 @ Y1)))) => (sK9 @ Y0 @ Y1))))))) = $true) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.63/1.78 thf(f74,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X3 : a,X0 : a,X1 : a,X4 : a] : (($true = (sK10 @ X1 @ X0 @ X2 @ X3 @ X4)) | ($false = (sK3 @ X2)) | ($true = (sK9 @ X0 @ X1)) | ((X2 @ X3 @ X4) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.63/1.78 thf(f73,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X3 : a,X0 : a,X1 : a,X4 : a] : (($true = ((X2 @ X3 @ X4) => (sK10 @ X1 @ X0 @ X2 @ X3 @ X4))) | ($false = (sK3 @ X2)) | ($true = (sK9 @ X0 @ X1))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.63/1.78 thf(f72,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X3 : a,X0 : a,X1 : a,X4 : a] : (($true = ((^[Y0 : a]: ((X2 @ X3 @ Y0) => (sK10 @ X1 @ X0 @ X2 @ X3 @ Y0))) @ X4)) | ($false = (sK3 @ X2)) | ($true = (sK9 @ X0 @ X1))) ) | ~spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f71])).
% 1.63/1.78 thf(f71,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X3 : a,X0 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((X2 @ X3 @ Y0) => (sK10 @ X1 @ X0 @ X2 @ X3 @ Y0))))) | ($false = (sK3 @ X2)) | ($true = (sK9 @ X0 @ X1))) ) | ~spl0_2),
% 1.63/1.78 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.63/1.78 thf(f70,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X3 : a,X0 : a,X1 : a] : (($false = (sK3 @ X2)) | ($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X2 @ Y0 @ Y1) => (sK10 @ X1 @ X0 @ X2 @ Y0 @ Y1))))) @ X3)) | ($true = (sK9 @ X0 @ X1))) ) | ~spl0_2),
% 1.63/1.78 inference(pi_clausification,[status(thm)],[f68])).
% 1.63/1.78 thf(f68,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X2 @ Y0 @ Y1) => (sK10 @ X1 @ X0 @ X2 @ Y0 @ Y1))))))) | ($true = (sK9 @ X0 @ X1)) | ($false = (sK3 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.63/1.78 thf(f67,plain,(
% 1.63/1.78 ( ! [X2 : a > a > $o,X0 : a,X1 : a] : (($true = (sK9 @ X0 @ X1)) | (((sK2 @ (sK10 @ X1 @ X0 @ X2)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((X2 @ Y0 @ Y1) => (sK10 @ X1 @ X0 @ X2 @ Y0 @ Y1))))))) = $true) | ($false = (sK3 @ X2))) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.63/1.78 thf(f38,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (($false = (X1 @ (sK6 @ X1) @ (sK7 @ X1))) | ($true = (X1 @ sK4 @ sK5)) | ((sK2 @ X1) = $false)) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.63/1.78 thf(f42,plain,(
% 1.63/1.78 ( ! [X1 : a > a > $o] : (((sK8 @ X1 @ (sK6 @ X1) @ (sK7 @ X1)) = $true) | ((sK2 @ X1) = $false) | ($true = (X1 @ sK4 @ sK5))) ) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.63/1.78 thf(f49,plain,(
% 1.63/1.78 ($true = (sK2 @ sK9)) | ~spl0_2),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.63/1.78 thf(f27,plain,(
% 1.63/1.78 spl0_1 | spl0_2),
% 1.63/1.78 inference(avatar_split_clause,[status(thm)],[f17,f24,f20])).
% 1.63/1.78 thf(f17,plain,(
% 1.63/1.78 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((?? @ (a > a > $o) @ (^[Y4 : a > a > $o]: ((sK3 @ Y4) & ((^[Y5 : a]: ((^[Y6 : a]: (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((sK2 @ Y7) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y4 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y5 @ Y6))))))) = Y3)))) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))))) | ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((sK2 @ Y0) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((?? @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((sK3 @ Y3) & (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))))),
% 1.63/1.78 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.63/1.78 % SZS output end Proof for DTF2THF_19563
% 1.63/1.78 % (19870)------------------------------
% 1.63/1.78 % (19870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.78 % (19870)Termination reason: Refutation
% 1.63/1.78
% 1.63/1.78 % (19870)Memory used [KB]: 6140
% 1.63/1.78 % (19870)Time elapsed: 0.045 s
% 1.63/1.78 % (19870)Instructions burned: 122 (million)
% 1.63/1.78 % (19870)------------------------------
% 1.63/1.78 % (19870)------------------------------
% 1.63/1.78 % (19814)Success in time 0.498 s
%------------------------------------------------------------------------------