%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV204^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 09:40:33 AM UTC 2026
% Result : Theorem 1.67s 1.52s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 7
% Syntax : Number of formulae : 128 ( 24 unt; 0 typ; 6 def)
% Number of atoms : 1418 ( 552 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 3488 ( 141 ~; 286 |; 250 &;2461 @)
% ( 6 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 101 ( 101 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 14 usr; 13 con; 0-3 aty)
% ( 126 !!; 138 ??; 0 @@+; 0 @@-)
% Number of variables : 877 ( 502 ^; 357 !; 18 ?; 877 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
iS: $tType ).
thf(func_def_0,type,
iS: $tType ).
thf(func_def_1,type,
y: iS ).
thf(func_def_2,type,
x: iS ).
thf(func_def_3,type,
cP: iS > iS > iS ).
thf(func_def_4,type,
c0: iS ).
thf(func_def_27,type,
sK1: iS > iS > iS > $o ).
thf(func_def_28,type,
sK2: ( iS > $o ) > iS ).
thf(func_def_29,type,
sK3: ( iS > $o ) > iS ).
thf(func_def_30,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f633,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f197,f270,f352,f422,f442,f483,f624]) ).
thf(f624,plain,
( spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f623]) ).
thf(f623,plain,
( $false
| spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f619]) ).
thf(f619,plain,
( ( $true = $false )
| spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f557,f612]) ).
thf(f612,plain,
( ! [X0: iS] :
( $true
= ( sK1 @ X0 @ X0 @ X0 ) )
| spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[status(thm)],[f611,f259]) ).
thf(f259,plain,
( ( ( sK1 @ c0 @ c0 @ c0 )
!= $false )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f258]) ).
thf(f258,definition,
( spl0_3
<=> ( ( sK1 @ c0 @ c0 @ c0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f611,plain,
( ! [X0: iS] :
( ( ( sK1 @ c0 @ c0 @ c0 )
= $false )
| ( $true
= ( sK1 @ X0 @ X0 @ X0 ) ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f610]) ).
thf(f610,plain,
( ! [X0: iS] :
( ( $true
= ( sK1 @ X0 @ X0 @ X0 ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( sK1 @ c0 @ c0 @ c0 )
= $false ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f609]) ).
thf(f609,plain,
( ! [X0: iS] :
( ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
| ( $false
= ( sK1 @ c0
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 ) ) )
| ( $true
= ( sK1 @ X0
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 ) ) ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f608]) ).
thf(f608,plain,
( ! [X0: iS] :
( ( $true
= ( sK1 @ X0
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
| ( $false
= ( sK1 @ c0
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 ) ) ) )
| ~ spl0_6 ),
inference(duplicate_literal_removal,[status(thm)],[f605]) ).
thf(f605,plain,
( ! [X0: iS] :
( ( $false
= ( sK1 @ c0
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 ) ) )
| ( $true
= ( sK1 @ X0
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) ) )
| ~ spl0_6 ),
inference(equality_resolution,[status(thm)],[f569]) ).
thf(f569,plain,
( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
( ( ( X1
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) )
!= ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
| ( $false
= ( sK1 @ c0 @ ( X0 @ c0 ) @ ( X1 @ c0 ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= X1 )
| ( ( ^ [Y0: iS] : Y0 )
!= X0 )
| ( $true
= ( sK1 @ X2 @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) )
| ( ( X0
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) )
!= ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f568]) ).
thf(f568,plain,
( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
( ( ( X1
@ ( sK2
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) ) ) )
!= ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( $true
= ( ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : ( X1 @ Y0 ) ) )
| ( ( X0
@ ( sK2
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) ) ) )
!= ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) )
@ c0 )
= $false ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f563]) ).
thf(f563,plain,
( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
( ( $true
= ( ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) )
@ c0 )
= $false )
| ( ( X1
@ ( sK2
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) ) ) )
!= ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
| ( $true = $false )
| ( ( X0
@ ( sK2
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X0 @ Y0 )
@ ( X1 @ Y0 ) ) ) )
!= ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : ( X1 @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(constrained_superposition,[status(thm)],[f81,f557]) ).
thf(f81,plain,
! [X2: iS,X1: iS > $o] :
( ( $true
= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( X1 @ c0 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: iS,X1: iS > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( X1 @ c0 )
= $false )
| ( $true
= ( ( X1 @ ( sK3 @ X1 ) )
& ( X1 @ ( sK2 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: iS,X1: iS > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( X1 @ c0 )
= $false )
| ( $false
= ( ( ( X1 @ ( sK3 @ X1 ) )
& ( X1 @ ( sK2 @ X1 ) ) )
=> ( X1 @ ( cP @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: iS,X1: iS > $o] :
( ( ( ^ [Y0: iS] :
( ( ( X1 @ Y0 )
& ( X1 @ ( sK2 @ X1 ) ) )
=> ( X1 @ ( cP @ Y0 @ ( sK2 @ X1 ) ) ) )
@ ( sK3 @ X1 ) )
= $false )
| ( ( X1 @ X2 )
= $true )
| ( ( X1 @ c0 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: iS,X1: iS > $o] :
( ( ( X1 @ c0 )
= $false )
| ( ( !! @ iS
@ ^ [Y0: iS] :
( ( ( X1 @ Y0 )
& ( X1 @ ( sK2 @ X1 ) ) )
=> ( X1 @ ( cP @ Y0 @ ( sK2 @ X1 ) ) ) ) )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: iS,X1: iS > $o] :
( ( ( X1 @ c0 )
= $false )
| ( ( X1 @ X2 )
= $true )
| ( ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) )
@ ( sK2 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: iS,X1: iS > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: iS,X1: iS > $o] :
( ( $false
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) )
& ( X1 @ c0 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: iS > $o] :
( ( $true
= ( !! @ iS @ X1 ) )
| ( $false
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) )
& ( X1 @ c0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: iS > $o] :
( $true
= ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( X1 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) )
& ( X1 @ c0 ) )
=> ( !! @ iS @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: iS > $o] :
( $true
= ( ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( $true
= ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y1 )
= ( cP @ Y0 @ Y2 ) )
=> ( ( Y3 = Y0 )
& ( Y2 = Y1 ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y1 )
= ( cP @ Y0 @ Y2 ) )
=> ( ( Y3 = Y0 )
& ( Y2 = Y1 ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( cP @ Y1 @ Y0 )
!= c0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y1 )
= ( cP @ Y0 @ Y2 ) )
=> ( ( Y3 = Y0 )
& ( Y2 = Y1 ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( cP @ Y1 @ Y0 )
!= c0 ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ( Y3 = Y1 )
& ( c0 = Y2 ) )
| ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( ( cP @ Y6 @ Y5 )
= Y3 )
& ( Y0 @ Y8 @ Y7 @ Y5 )
& ( ( cP @ Y4 @ Y8 )
= Y1 )
& ( Y0 @ Y4 @ Y9 @ Y6 )
& ( ( cP @ Y9 @ Y7 )
= Y2 ) ) ) ) ) ) ) )
| ( ( c0 = Y1 )
& ( Y3 = Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y1 )
= ( cP @ Y0 @ Y2 ) )
=> ( ( Y3 = Y0 )
& ( Y2 = Y1 ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( cP @ Y1 @ Y0 )
!= c0 ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ( Y3 = Y1 )
& ( c0 = Y2 ) )
| ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( ( cP @ Y6 @ Y5 )
= Y3 )
& ( Y0 @ Y8 @ Y7 @ Y5 )
& ( ( cP @ Y4 @ Y8 )
= Y1 )
& ( Y0 @ Y4 @ Y9 @ Y6 )
& ( ( cP @ Y9 @ Y7 )
= Y2 ) ) ) ) ) ) ) )
| ( ( c0 = Y1 )
& ( Y3 = Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y1 )
= ( cP @ Y0 @ Y2 ) )
=> ( ( Y3 = Y0 )
& ( Y2 = Y1 ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS @ Y0 ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( cP @ Y1 @ Y0 )
!= c0 ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( $true
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ( Y3 = Y1 )
& ( c0 = Y2 ) )
| ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( ( cP @ Y6 @ Y5 )
= Y3 )
& ( Y0 @ Y8 @ Y7 @ Y5 )
& ( ( cP @ Y4 @ Y8 )
= Y1 )
& ( Y0 @ Y4 @ Y9 @ Y6 )
& ( ( cP @ Y9 @ Y7 )
= Y2 ) ) ) ) ) ) ) )
| ( ( c0 = Y1 )
& ( Y3 = Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y1 )
= ( cP @ Y0 @ Y2 ) )
=> ( ( Y3 = Y0 )
& ( Y2 = Y1 ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( cP @ Y1 @ Y0 )
!= c0 ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( $true
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ( Y3 = Y1 )
& ( c0 = Y2 ) )
| ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( ( cP @ Y6 @ Y5 )
= Y3 )
& ( Y0 @ Y8 @ Y7 @ Y5 )
& ( ( cP @ Y4 @ Y8 )
= Y1 )
& ( Y0 @ Y4 @ Y9 @ Y6 )
& ( ( cP @ Y9 @ Y7 )
= Y2 ) ) ) ) ) ) ) )
| ( ( c0 = Y1 )
& ( Y3 = Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y3 @ Y1 )
= ( cP @ Y0 @ Y2 ) )
=> ( ( Y3 = Y0 )
& ( Y2 = Y1 ) ) ) ) ) ) )
& ( !! @ ( iS > $o )
@ ^ [Y0: iS > $o] :
( ( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ iS
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) )
& ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( cP @ Y1 @ Y0 )
!= c0 ) ) ) )
=> ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( $true
& ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ( Y3 = Y1 )
& ( c0 = Y2 ) )
| ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( ( cP @ Y6 @ Y5 )
= Y3 )
& ( Y0 @ Y8 @ Y7 @ Y5 )
& ( ( cP @ Y4 @ Y8 )
= Y1 )
& ( Y0 @ Y4 @ Y9 @ Y6 )
& ( ( cP @ Y9 @ Y7 )
= Y2 ) ) ) ) ) ) ) )
| ( ( c0 = Y1 )
& ( Y3 = Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 )
& ! [X2: iS > $o] :
( ( ( X2 @ c0 )
& ! [X3: iS,X4: iS] :
( ( ( X2 @ X4 )
& ( X2 @ X3 ) )
=> ( X2 @ ( cP @ X3 @ X4 ) ) ) )
=> ! [X5: iS] : ( X2 @ X5 ) )
& ! [X6: iS,X7: iS,X8: iS,X9: iS] :
( ( ( cP @ X6 @ X8 )
= ( cP @ X9 @ X7 ) )
=> ( ( X7 = X8 )
& ( X6 = X9 ) ) ) )
=> ! [X10: iS > iS > iS > $o] :
( ( ! [X11: iS,X12: iS,X13: iS] :
( ( ( ( X11 = X12 )
& ( c0 = X13 ) )
| ? [X14: iS,X15: iS,X16: iS,X17: iS,X18: iS,X19: iS] :
( ( ( cP @ X14 @ X16 )
= X12 )
& ( X10 @ X19 @ X14 @ X17 )
& ( ( cP @ X19 @ X15 )
= X13 )
& ( X10 @ X15 @ X16 @ X18 )
& ( ( cP @ X17 @ X18 )
= X11 ) )
| ( ( c0 = X12 )
& ( X11 = X13 ) ) )
=> ( X10 @ X13 @ X12 @ X11 ) )
& $true )
=> ( X10 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 )
& ! [X4: iS > $o] :
( ( ( X4 @ c0 )
& ! [X0: iS,X1: iS] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X0: iS,X3: iS,X2: iS,X1: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) ) )
=> ! [X5: iS > iS > iS > $o] :
( ( ! [X8: iS,X7: iS,X6: iS] :
( ( ( ( X7 = X8 )
& ( c0 = X6 ) )
| ? [X11: iS,X10: iS,X12: iS,X13: iS,X14: iS,X9: iS] :
( ( ( cP @ X11 @ X12 )
= X7 )
& ( X5 @ X9 @ X11 @ X13 )
& ( ( cP @ X9 @ X10 )
= X6 )
& ( X5 @ X10 @ X12 @ X14 )
& ( ( cP @ X13 @ X14 )
= X8 ) )
| ( ( c0 = X7 )
& ( X6 = X8 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
& $true )
=> ( X5 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 )
& ! [X4: iS > $o] :
( ( ( X4 @ c0 )
& ! [X0: iS,X1: iS] :
( ( ( X4 @ X1 )
& ( X4 @ X0 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X0: iS,X3: iS,X2: iS,X1: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) ) )
=> ! [X5: iS > iS > iS > $o] :
( ( ! [X8: iS,X7: iS,X6: iS] :
( ( ( ( X7 = X8 )
& ( c0 = X6 ) )
| ? [X11: iS,X10: iS,X12: iS,X13: iS,X14: iS,X9: iS] :
( ( ( cP @ X11 @ X12 )
= X7 )
& ( X5 @ X9 @ X11 @ X13 )
& ( ( cP @ X9 @ X10 )
= X6 )
& ( X5 @ X10 @ X12 @ X14 )
& ( ( cP @ X13 @ X14 )
= X8 ) )
| ( ( c0 = X7 )
& ( X6 = X8 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
& $true )
=> ( X5 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OInPMZid53/DTF2THF_12262.p',cS_INCL_LEM4_pme) ).
thf(f557,plain,
( ( ( sK1
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ~ spl0_6 ),
inference(equality_resolution,[status(thm)],[f269]) ).
thf(f269,plain,
( ! [X0: iS] :
( ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= X0 )
| ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ X0
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f268]) ).
thf(f268,definition,
( spl0_6
<=> ! [X0: iS] :
( ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= X0 )
| ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ X0
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f483,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f482]) ).
thf(f482,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f455]) ).
thf(f455,plain,
( ( $true = $false )
| ( y != y )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f93,f191]) ).
thf(f191,plain,
( ( ( sK1 @ c0 @ y @ y )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f189]) ).
thf(f189,definition,
( spl0_1
<=> ( ( sK1 @ c0 @ y @ y )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f93,plain,
! [X0: iS,X1: iS] :
( ( $true
= ( sK1 @ c0 @ X0 @ X1 ) )
| ( X0 != X1 ) ),
inference(equality_resolution,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( c0 != X1 )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( c0 != X1 )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( X3 = X2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( c0 = X1 )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( X3 = X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( $false
= ( ( c0 = X1 )
& ( X3 = X2 ) ) )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( ( ( X3 = X1 )
& ( c0 = X2 ) )
| ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( ( cP @ Y2 @ Y1 )
= X3 )
& ( sK1 @ Y4 @ Y3 @ Y1 )
& ( ( cP @ Y0 @ Y4 )
= X1 )
& ( sK1 @ Y0 @ Y5 @ Y2 )
& ( ( cP @ Y5 @ Y3 )
= X2 ) ) ) ) ) ) ) )
| ( ( c0 = X1 )
& ( X3 = X2 ) ) )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: iS,X3: iS,X1: iS] :
( $true
= ( ( ( ( X3 = X1 )
& ( c0 = X2 ) )
| ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( ( cP @ Y2 @ Y1 )
= X3 )
& ( sK1 @ Y4 @ Y3 @ Y1 )
& ( ( cP @ Y0 @ Y4 )
= X1 )
& ( sK1 @ Y0 @ Y5 @ Y2 )
& ( ( cP @ Y5 @ Y3 )
= X2 ) ) ) ) ) ) ) )
| ( ( c0 = X1 )
& ( X3 = X2 ) ) )
=> ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: iS,X3: iS,X1: iS] :
( $true
= ( ^ [Y0: iS] :
( ( ( ( Y0 = X1 )
& ( c0 = X2 ) )
| ( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ( ( cP @ Y3 @ Y2 )
= Y0 )
& ( sK1 @ Y5 @ Y4 @ Y2 )
& ( ( cP @ Y1 @ Y5 )
= X1 )
& ( sK1 @ Y1 @ Y6 @ Y3 )
& ( ( cP @ Y6 @ Y4 )
= X2 ) ) ) ) ) ) ) )
| ( ( c0 = X1 )
& ( Y0 = X2 ) ) )
=> ( sK1 @ X1 @ X2 @ Y0 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: iS,X1: iS] :
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( ( ( ( Y0 = X1 )
& ( c0 = X2 ) )
| ( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ( ( cP @ Y3 @ Y2 )
= Y0 )
& ( sK1 @ Y5 @ Y4 @ Y2 )
& ( ( cP @ Y1 @ Y5 )
= X1 )
& ( sK1 @ Y1 @ Y6 @ Y3 )
& ( ( cP @ Y6 @ Y4 )
= X2 ) ) ) ) ) ) ) )
| ( ( c0 = X1 )
& ( Y0 = X2 ) ) )
=> ( sK1 @ X1 @ X2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: iS,X1: iS] :
( $true
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( ( Y1 = X1 )
& ( c0 = Y0 ) )
| ( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ( ( cP @ Y4 @ Y3 )
= Y1 )
& ( sK1 @ Y6 @ Y5 @ Y3 )
& ( ( cP @ Y2 @ Y6 )
= X1 )
& ( sK1 @ Y2 @ Y7 @ Y4 )
& ( ( cP @ Y7 @ Y5 )
= Y0 ) ) ) ) ) ) ) )
| ( ( c0 = X1 )
& ( Y1 = Y0 ) ) )
=> ( sK1 @ X1 @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: iS] :
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( ( ( ( Y1 = X1 )
& ( c0 = Y0 ) )
| ( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ( ( cP @ Y4 @ Y3 )
= Y1 )
& ( sK1 @ Y6 @ Y5 @ Y3 )
& ( ( cP @ Y2 @ Y6 )
= X1 )
& ( sK1 @ Y2 @ Y7 @ Y4 )
& ( ( cP @ Y7 @ Y5 )
= Y0 ) ) ) ) ) ) ) )
| ( ( c0 = X1 )
& ( Y1 = Y0 ) ) )
=> ( sK1 @ X1 @ Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: iS] :
( $true
= ( ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( ( Y2 = Y0 )
& ( c0 = Y1 ) )
| ( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ( ( cP @ Y5 @ Y4 )
= Y2 )
& ( sK1 @ Y7 @ Y6 @ Y4 )
& ( ( cP @ Y3 @ Y7 )
= Y0 )
& ( sK1 @ Y3 @ Y8 @ Y5 )
& ( ( cP @ Y8 @ Y6 )
= Y1 ) ) ) ) ) ) ) )
| ( ( c0 = Y0 )
& ( Y2 = Y1 ) ) )
=> ( sK1 @ Y0 @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( ( Y2 = Y0 )
& ( c0 = Y1 ) )
| ( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ( ( cP @ Y5 @ Y4 )
= Y2 )
& ( sK1 @ Y7 @ Y6 @ Y4 )
& ( ( cP @ Y3 @ Y7 )
= Y0 )
& ( sK1 @ Y3 @ Y8 @ Y5 )
& ( ( cP @ Y8 @ Y6 )
= Y1 ) ) ) ) ) ) ) )
| ( ( c0 = Y0 )
& ( Y2 = Y1 ) ) )
=> ( sK1 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( !! @ iS
@ ^ [Y0: iS] :
( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( ( ( ( Y2 = Y0 )
& ( c0 = Y1 ) )
| ( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ( ( cP @ Y5 @ Y4 )
= Y2 )
& ( sK1 @ Y7 @ Y6 @ Y4 )
& ( ( cP @ Y3 @ Y7 )
= Y0 )
& ( sK1 @ Y3 @ Y8 @ Y5 )
& ( ( cP @ Y8 @ Y6 )
= Y1 ) ) ) ) ) ) ) )
| ( ( c0 = Y0 )
& ( Y2 = Y1 ) ) )
=> ( sK1 @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( sK1 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ( Y3 = Y1 )
& ( c0 = Y2 ) )
| ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( ( cP @ Y6 @ Y5 )
= Y3 )
& ( Y0 @ Y8 @ Y7 @ Y5 )
& ( ( cP @ Y4 @ Y8 )
= Y1 )
& ( Y0 @ Y4 @ Y9 @ Y6 )
& ( ( cP @ Y9 @ Y7 )
= Y2 ) ) ) ) ) ) ) )
| ( ( c0 = Y1 )
& ( Y3 = Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( !! @ ( iS > iS > iS > $o )
@ ^ [Y0: iS > iS > iS > $o] :
( ( !! @ iS
@ ^ [Y1: iS] :
( !! @ iS
@ ^ [Y2: iS] :
( !! @ iS
@ ^ [Y3: iS] :
( ( ( ( Y3 = Y1 )
& ( c0 = Y2 ) )
| ( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ?? @ iS
@ ^ [Y6: iS] :
( ?? @ iS
@ ^ [Y7: iS] :
( ?? @ iS
@ ^ [Y8: iS] :
( ?? @ iS
@ ^ [Y9: iS] :
( ( ( cP @ Y6 @ Y5 )
= Y3 )
& ( Y0 @ Y8 @ Y7 @ Y5 )
& ( ( cP @ Y4 @ Y8 )
= Y1 )
& ( Y0 @ Y4 @ Y9 @ Y6 )
& ( ( cP @ Y9 @ Y7 )
= Y2 ) ) ) ) ) ) ) )
| ( ( c0 = Y1 )
& ( Y3 = Y2 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f442,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f441]) ).
thf(f441,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f427]) ).
thf(f427,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f195,f266]) ).
thf(f266,plain,
( ! [X2: iS] :
( $true
= ( sK1 @ X2 @ X2 @ X2 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f265]) ).
thf(f265,definition,
( spl0_5
<=> ! [X2: iS] :
( $true
= ( sK1 @ X2 @ X2 @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f195,plain,
( ( $false
= ( sK1 @ x @ x @ x ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f193]) ).
thf(f193,definition,
( spl0_2
<=> ( $false
= ( sK1 @ x @ x @ x ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f422,plain,
( spl0_5
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f421,f262,f258,f265]) ).
thf(f262,definition,
( spl0_4
<=> ! [X1: iS] :
( ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= X1 )
| ( $false
= ( sK1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ X1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f421,plain,
( ! [X0: iS] :
( $true
= ( sK1 @ X0 @ X0 @ X0 ) )
| spl0_3
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f419,f259]) ).
thf(f419,plain,
( ! [X0: iS] :
( ( $true
= ( sK1 @ X0 @ X0 @ X0 ) )
| ( ( sK1 @ c0 @ c0 @ c0 )
= $false ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f418]) ).
thf(f418,plain,
( ! [X0: iS] :
( ( $true
= ( sK1 @ X0 @ X0 @ X0 ) )
| ( ( sK1 @ c0 @ c0 @ c0 )
= $false )
| ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f417]) ).
thf(f417,plain,
( ! [X0: iS] :
( ( ( sK1
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ c0 )
= $false )
| ( $true
= ( sK1
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ X0 ) )
| ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK3
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f416]) ).
thf(f416,plain,
( ! [X0: iS] :
( ( $true
= ( sK1
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ X0 ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( sK1
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ c0 )
= $false )
| ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK3
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[status(thm)],[f414]) ).
thf(f414,plain,
( ! [X0: iS] :
( ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0
@ ( sK3
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0 ) ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) )
| ( $true
= ( sK1
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ ( ^ [Y0: iS] : Y0
@ X0 )
@ X0 ) )
| ( ( sK1
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ c0 )
= $false )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : Y0 ) ) )
| ~ spl0_4 ),
inference(equality_resolution,[status(thm)],[f408]) ).
thf(f408,plain,
( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
( ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( X1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) @ Y0 ) ) ) )
| ( $true
= ( sK1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) @ X2 ) )
| ( ( X0
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) @ Y0 ) ) )
!= ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= X1 )
| ( ( ^ [Y0: iS] : Y0 )
!= X0 )
| ( $false
= ( sK1 @ ( X0 @ c0 ) @ ( X1 @ c0 ) @ c0 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f407]) ).
thf(f407,plain,
( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
( ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : ( X1 @ Y0 ) ) )
| ( ( ^ [Y0: iS] :
( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) )
@ c0 )
= $false )
| ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( X1
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: iS] :
( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( X0
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) )
!= ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f398]) ).
thf(f398,plain,
( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
( ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= ( X1
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
| ( ( ^ [Y0: iS] : Y0 )
!= ( ^ [Y0: iS] : ( X1 @ Y0 ) ) )
| ( ( ^ [Y0: iS] :
( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) )
@ c0 )
= $false )
| ( $true
= ( ^ [Y0: iS] :
( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
!= ( ^ [Y0: iS] : Y0 ) )
| ( ( X0
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X0 @ Y0 ) @ ( X1 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) )
!= ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
| ( $true = $false ) )
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f82,f393]) ).
thf(f393,plain,
( ( ( sK1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
= $false )
| ~ spl0_4 ),
inference(equality_resolution,[status(thm)],[f263]) ).
thf(f263,plain,
( ! [X1: iS] :
( ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= X1 )
| ( $false
= ( sK1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ X1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f262]) ).
thf(f82,plain,
! [X2: iS,X1: iS > $o] :
( ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( ( X1 @ c0 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f352,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f351]) ).
thf(f351,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f281]) ).
thf(f281,plain,
( ( $true = $false )
| ( c0 != c0 )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f260,f95]) ).
thf(f95,plain,
! [X0: iS,X1: iS] :
( ( $true
= ( sK1 @ X0 @ c0 @ X1 ) )
| ( X0 != X1 ) ),
inference(equality_resolution,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( c0 != X2 )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( X1 != X3 )
| ( ( c0 = X2 )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( X3 = X1 )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( c0 = X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( ( X3 = X1 )
& ( c0 = X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( ( ( ( X3 = X1 )
& ( c0 = X2 ) )
| ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( ( cP @ Y2 @ Y1 )
= X3 )
& ( sK1 @ Y4 @ Y3 @ Y1 )
& ( ( cP @ Y0 @ Y4 )
= X1 )
& ( sK1 @ Y0 @ Y5 @ Y2 )
& ( ( cP @ Y5 @ Y3 )
= X2 ) ) ) ) ) ) ) ) )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f260,plain,
( ( ( sK1 @ c0 @ c0 @ c0 )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f258]) ).
thf(f270,plain,
( spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f256,f268,f265,f262,f258]) ).
thf(f256,plain,
! [X2: iS,X0: iS,X1: iS] :
( ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= X0 )
| ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
!= X1 )
| ( $true
= ( sK1 @ X2 @ X2 @ X2 ) )
| ( ( sK1 @ c0 @ c0 @ c0 )
= $false )
| ( $false
= ( sK1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ X1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) )
| ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
@ X0
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f253]) ).
thf(f253,plain,
! [X2: iS,X0: iS,X1: iS] :
( ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ Y0 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
@ X0
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ Y0 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
| ( $true
= ( sK1 @ X2 @ X2
@ ( ^ [Y0: iS] : Y0
@ X2 ) ) )
| ( ( sK2
@ ^ [Y0: iS] :
( sK1 @ Y0 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
!= X0 )
| ( ( sK3
@ ^ [Y0: iS] :
( sK1 @ Y0 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
!= X1 )
| ( $false
= ( sK1
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ Y0 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) )
@ X1
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ Y0 @ Y0
@ ( ^ [Y1: iS] : Y1
@ Y0 ) ) ) ) )
| ( $false
= ( sK1 @ c0 @ c0
@ ( ^ [Y0: iS] : Y0
@ c0 ) ) ) ),
inference(equality_resolution,[status(thm)],[f243]) ).
thf(f243,plain,
! [X2: iS,X3: iS,X0: iS > iS,X1: iS,X4: iS,X5: iS] :
( ( ( cP @ X4 @ X2 )
!= ( X0
@ ( cP
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ ( X0 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ ( X0 @ Y0 ) ) ) ) ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ ( X0 @ Y0 ) ) )
!= X1 )
| ( $false
= ( sK1
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ ( X0 @ Y0 ) ) )
@ X3
@ X4 ) )
| ( ( sK1 @ c0 @ c0 @ ( X0 @ c0 ) )
= $false )
| ( $true
= ( sK1 @ X5 @ X5 @ ( X0 @ X5 ) ) )
| ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ ( X0 @ Y0 ) ) )
!= X3 )
| ( ( sK1
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ ( X0 @ Y0 ) ) )
@ X1
@ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f240]) ).
thf(f240,plain,
! [X2: iS,X3: iS,X0: iS > iS,X1: iS,X4: iS,X5: iS] :
( ( ( sK1
@ ( ^ [Y0: iS] : Y0
@ c0 )
@ c0
@ ( X0 @ c0 ) )
= $false )
| ( ( sK1
@ ( sK3
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( X0 @ Y0 ) ) )
@ X3
@ X4 )
= $false )
| ( ( X0
@ ( cP
@ ( sK3
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( X0 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( X0 @ Y0 ) ) ) ) )
!= ( cP @ X4 @ X2 ) )
| ( $true
= ( sK1
@ ( ^ [Y0: iS] : Y0
@ X5 )
@ X5
@ ( X0 @ X5 ) ) )
| ( $false
= ( sK1
@ ( sK2
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( X0 @ Y0 ) ) )
@ X1
@ X2 ) )
| ( ( sK2
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( X0 @ Y0 ) ) )
!= X1 )
| ( ( sK3
@ ^ [Y0: iS] :
( sK1
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ Y0
@ ( X0 @ Y0 ) ) )
!= X3 ) ),
inference(equality_resolution,[status(thm)],[f182]) ).
thf(f182,plain,
! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( cP @ X0 @ X1 )
!= ( X2
@ ( cP
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) ) ) ) )
| ( ( sK1 @ X1 @ X6 @ X5 )
= $false )
| ( ( sK1 @ X0 @ X7 @ X4 )
= $false )
| ( ( sK3
@ ^ [Y0: iS] : ( sK1 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) )
!= X7 )
| ( $true
= ( sK1 @ ( X2 @ X8 ) @ X8 @ ( X3 @ X8 ) ) )
| ( ( X3
@ ( cP
@ ( sK3
@ ^ [Y0: iS] : ( sK1 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: iS] : ( sK1 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) ) ) )
!= ( cP @ X4 @ X5 ) )
| ( ( sK2
@ ^ [Y0: iS] : ( sK1 @ ( X2 @ Y0 ) @ Y0 @ ( X3 @ Y0 ) ) )
!= X6 )
| ( ( sK1 @ ( X2 @ c0 ) @ c0 @ ( X3 @ c0 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f181]) ).
thf(f181,plain,
! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( X3
@ ( cP
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) ) ) )
!= ( cP @ X4 @ X5 ) )
| ( ( sK1 @ X0 @ X7 @ X4 )
= $false )
| ( ( sK2
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
!= X6 )
| ( ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
!= X7 )
| ( $true
= ( ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) )
@ X8 ) )
| ( ( sK1 @ X1 @ X6 @ X5 )
= $false )
| ( $false
= ( ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) )
@ c0 ) )
| ( ( cP @ X0 @ X1 )
!= ( X2
@ ( cP
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f173]) ).
thf(f173,plain,
! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( cP @ X0 @ X1 )
!= ( X2
@ ( cP
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) ) ) ) )
| ( ( sK1 @ X0 @ X7 @ X4 )
= $false )
| ( $true
= ( ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) )
@ X8 ) )
| ( ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
!= X7 )
| ( $true = $false )
| ( ( sK1 @ X1 @ X6 @ X5 )
= $false )
| ( ( sK2
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
!= X6 )
| ( ( X3
@ ( cP
@ ( sK3
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) )
@ ( sK2
@ ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) ) ) ) )
!= ( cP @ X4 @ X5 ) )
| ( $false
= ( ^ [Y0: iS] :
( sK1 @ ( X2 @ Y0 )
@ ( ^ [Y1: iS] : Y1
@ Y0 )
@ ( X3 @ Y0 ) )
@ c0 ) ) ),
inference(constrained_superposition,[status(thm)],[f170,f79]) ).
thf(f79,plain,
! [X2: iS,X1: iS > $o] :
( ( ( X1 @ ( cP @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) ) )
= $false )
| ( ( X1 @ c0 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f170,plain,
! [X2: iS,X3: iS,X0: iS,X1: iS,X4: iS,X5: iS] :
( ( $true
= ( sK1 @ ( cP @ X0 @ X1 ) @ ( cP @ X2 @ X3 ) @ ( cP @ X4 @ X5 ) ) )
| ( ( sK1 @ X1 @ X3 @ X5 )
= $false )
| ( ( sK1 @ X0 @ X2 @ X4 )
= $false ) ),
inference(equality_resolution,[status(thm)],[f169]) ).
thf(f169,plain,
! [X2: iS,X3: iS,X0: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
( ( ( cP @ X6 @ X0 )
!= X3 )
| ( $true
= ( sK1 @ X3 @ ( cP @ X4 @ X1 ) @ ( cP @ X5 @ X2 ) ) )
| ( ( sK1 @ X6 @ X4 @ X5 )
= $false )
| ( ( sK1 @ X0 @ X1 @ X2 )
= $false ) ),
inference(equality_resolution,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: iS,X3: iS,X0: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( cP @ X5 @ X6 )
!= X3 )
| ( ( sK1 @ X7 @ X2 @ X6 )
= $false )
| ( $true
= ( sK1 @ X0 @ ( cP @ X1 @ X2 ) @ X3 ) )
| ( ( cP @ X4 @ X7 )
!= X0 )
| ( $false
= ( sK1 @ X4 @ X1 @ X5 ) ) ),
inference(equality_resolution,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( cP @ X9 @ X7 )
!= X2 )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( sK1 @ X4 @ X9 @ X6 )
= $false )
| ( ( cP @ X6 @ X5 )
!= X3 )
| ( ( cP @ X4 @ X8 )
!= X1 )
| ( ( sK1 @ X8 @ X7 @ X5 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( sK1 @ X8 @ X7 @ X5 )
= $false )
| ( $false
= ( ( cP @ X9 @ X7 )
= X2 ) )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( sK1 @ X4 @ X9 @ X6 )
= $false )
| ( ( cP @ X4 @ X8 )
!= X1 )
| ( ( cP @ X6 @ X5 )
!= X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( sK1 @ X8 @ X7 @ X5 )
= $false )
| ( ( cP @ X6 @ X5 )
!= X3 )
| ( ( ( cP @ X4 @ X8 )
= X1 )
= $false )
| ( ( sK1 @ X4 @ X9 @ X6 )
= $false )
| ( $false
= ( ( cP @ X9 @ X7 )
= X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ( cP @ X6 @ X5 )
= X3 )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( sK1 @ X4 @ X9 @ X6 )
= $false )
| ( ( sK1 @ X8 @ X7 @ X5 )
= $false )
| ( ( ( cP @ X4 @ X8 )
= X1 )
= $false )
| ( $false
= ( ( cP @ X9 @ X7 )
= X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ X8 @ X7 @ X5 ) )
= $false )
| ( ( ( cP @ X4 @ X8 )
= X1 )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( sK1 @ X4 @ X9 @ X6 )
= $false )
| ( $false
= ( ( cP @ X9 @ X7 )
= X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ X8 @ X7 @ X5 )
& ( ( cP @ X4 @ X8 )
= X1 ) )
= $false )
| ( ( sK1 @ X4 @ X9 @ X6 )
= $false )
| ( $false
= ( ( cP @ X9 @ X7 )
= X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ X8 @ X7 @ X5 )
& ( ( cP @ X4 @ X8 )
= X1 )
& ( sK1 @ X4 @ X9 @ X6 ) )
= $false )
| ( $false
= ( ( cP @ X9 @ X7 )
= X2 ) )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( $false
= ( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ X8 @ X7 @ X5 )
& ( ( cP @ X4 @ X8 )
= X1 )
& ( sK1 @ X4 @ X9 @ X6 )
& ( ( cP @ X9 @ X7 )
= X2 ) ) )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ^ [Y0: iS] :
( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ X8 @ X7 @ X5 )
& ( ( cP @ X4 @ X8 )
= X1 )
& ( sK1 @ X4 @ Y0 @ X6 )
& ( ( cP @ Y0 @ X7 )
= X2 ) )
@ X9 )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( ?? @ iS
@ ^ [Y0: iS] :
( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ X8 @ X7 @ X5 )
& ( ( cP @ X4 @ X8 )
= X1 )
& ( sK1 @ X4 @ Y0 @ X6 )
& ( ( cP @ Y0 @ X7 )
= X2 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ Y0 @ X7 @ X5 )
& ( ( cP @ X4 @ Y0 )
= X1 )
& ( sK1 @ X4 @ Y1 @ X6 )
& ( ( cP @ Y1 @ X7 )
= X2 ) ) )
@ X8 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( $false
= ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ Y0 @ X7 @ X5 )
& ( ( cP @ X4 @ Y0 )
= X1 )
& ( sK1 @ X4 @ Y1 @ X6 )
& ( ( cP @ Y1 @ X7 )
= X2 ) ) ) ) )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
( ( ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ Y1 @ Y0 @ X5 )
& ( ( cP @ X4 @ Y1 )
= X1 )
& ( sK1 @ X4 @ Y2 @ X6 )
& ( ( cP @ Y2 @ Y0 )
= X2 ) ) ) )
@ X7 )
= $false )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
( ( $false
= ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ( ( cP @ X6 @ X5 )
= X3 )
& ( sK1 @ Y1 @ Y0 @ X5 )
& ( ( cP @ X4 @ Y1 )
= X1 )
& ( sK1 @ X4 @ Y2 @ X6 )
& ( ( cP @ Y2 @ Y0 )
= X2 ) ) ) ) ) )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: iS,X3: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y0 @ X5 )
= X3 )
& ( sK1 @ Y2 @ Y1 @ X5 )
& ( ( cP @ X4 @ Y2 )
= X1 )
& ( sK1 @ X4 @ Y3 @ Y0 )
& ( ( cP @ Y3 @ Y1 )
= X2 ) ) ) ) )
@ X6 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS,X5: iS] :
( ( $false
= ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ( ( cP @ Y0 @ X5 )
= X3 )
& ( sK1 @ Y2 @ Y1 @ X5 )
& ( ( cP @ X4 @ Y2 )
= X1 )
& ( sK1 @ X4 @ Y3 @ Y0 )
& ( ( cP @ Y3 @ Y1 )
= X2 ) ) ) ) ) ) )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS,X5: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( $false
= ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ( ( cP @ Y1 @ Y0 )
= X3 )
& ( sK1 @ Y3 @ Y2 @ Y0 )
& ( ( cP @ X4 @ Y3 )
= X1 )
& ( sK1 @ X4 @ Y4 @ Y1 )
& ( ( cP @ Y4 @ Y2 )
= X2 ) ) ) ) ) )
@ X5 ) ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( $false
= ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ( ( cP @ Y1 @ Y0 )
= X3 )
& ( sK1 @ Y3 @ Y2 @ Y0 )
& ( ( cP @ X4 @ Y3 )
= X1 )
& ( sK1 @ X4 @ Y4 @ Y1 )
& ( ( cP @ Y4 @ Y2 )
= X2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: iS,X3: iS,X1: iS,X4: iS] :
( ( $true
= ( sK1 @ X1 @ X2 @ X3 ) )
| ( ( ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( ( cP @ Y2 @ Y1 )
= X3 )
& ( sK1 @ Y4 @ Y3 @ Y1 )
& ( ( cP @ Y0 @ Y4 )
= X1 )
& ( sK1 @ Y0 @ Y5 @ Y2 )
& ( ( cP @ Y5 @ Y3 )
= X2 ) ) ) ) ) ) )
@ X4 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: iS,X3: iS,X1: iS] :
( ( $false
= ( ?? @ iS
@ ^ [Y0: iS] :
( ?? @ iS
@ ^ [Y1: iS] :
( ?? @ iS
@ ^ [Y2: iS] :
( ?? @ iS
@ ^ [Y3: iS] :
( ?? @ iS
@ ^ [Y4: iS] :
( ?? @ iS
@ ^ [Y5: iS] :
( ( ( cP @ Y2 @ Y1 )
= X3 )
& ( sK1 @ Y4 @ Y3 @ Y1 )
& ( ( cP @ Y0 @ Y4 )
= X1 )
& ( sK1 @ Y0 @ Y5 @ Y2 )
& ( ( cP @ Y5 @ Y3 )
= X2 ) ) ) ) ) ) ) ) )
| ( $true
= ( sK1 @ X1 @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f197,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f180,f193,f189]) ).
thf(f180,plain,
( ( $false
= ( sK1 @ x @ x @ x ) )
| ( ( sK1 @ c0 @ y @ y )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( $false
= ( sK1 @ x @ x @ x ) )
| ( $true = $false )
| ( ( sK1 @ c0 @ y @ y )
= $false ) ),
inference(superposition,[status(thm)],[f14,f170]) ).
thf(f14,plain,
( $false
= ( sK1 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV204^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n007.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 12:42:08 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEV204^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.45 % Domain : Set Theory (Sets of sets)
% 0.20/0.45 % Problem : TPS problem from S-THMS
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Bro09]
% 0.20/0.45 % Names : tps_1157 [Bro09]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0, 0.71 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 1.00 v4.0.0
% 0.20/0.45 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.20/0.45 % Number of atoms : 12 ( 11 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 12 ( 12 avg)
% 0.20/0.45 % Number of connectives : 58 ( 1 ~; 2 |; 12 &; 37 @)
% 0.20/0.45 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 24 ( 24 avg)
% 0.20/0.45 % Number of types : 2 ( 1 usr)
% 0.20/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% 0.20/0.45 % Number of variables : 20 ( 0 ^; 14 !; 6 ?; 20 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(iS_type,type,
% 0.20/0.45 iS: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(y,type,
% 0.20/0.45 y: iS ).
% 0.20/0.45
% 0.20/0.45 thf(x,type,
% 0.20/0.45 x: iS ).
% 0.20/0.45
% 0.20/0.45 thf(cP,type,
% 0.20/0.45 cP: iS > iS > iS ).
% 0.20/0.45
% 0.20/0.45 thf(c0,type,
% 0.20/0.45 c0: iS ).
% 0.20/0.45
% 0.20/0.45 thf(cS_INCL_LEM4_pme,conjecture,
% 0.20/0.45 ( ( ! [Xx0: iS,Xy0: iS] :
% 0.20/0.45 ( ( cP @ Xx0 @ Xy0 )
% 0.20/0.45 != c0 )
% 0.20/0.45 & ! [Xx0: iS,Xy0: iS,Xu: iS,Xv: iS] :
% 0.20/0.45 ( ( ( cP @ Xx0 @ Xu )
% 0.20/0.45 = ( cP @ Xy0 @ Xv ) )
% 0.20/0.45 => ( ( Xx0 = Xy0 )
% 0.20/0.45 & ( Xu = Xv ) ) )
% 0.20/0.45 & ! [X: iS > $o] :
% 0.20/0.45 ( ( ( X @ c0 )
% 0.20/0.45 & ! [Xx0: iS,Xy0: iS] :
% 0.20/0.45 ( ( ( X @ Xx0 )
% 0.20/0.45 & ( X @ Xy0 ) )
% 0.20/0.45 => ( X @ ( cP @ Xx0 @ Xy0 ) ) ) )
% 0.20/0.45 => ! [Xx0: iS] : ( X @ Xx0 ) ) )
% 0.20/0.45 => ! [R: iS > iS > iS > $o] :
% 0.20/0.45 ( ( $true
% 0.20/0.45 & ! [Xa: iS,Xb: iS,Xc: iS] :
% 0.20/0.45 ( ( ( ( Xa = c0 )
% 0.20/0.45 & ( Xb = Xc ) )
% 0.20/0.45 | ( ( Xb = c0 )
% 0.20/0.45 & ( Xa = Xc ) )
% 0.20/0.45 | ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
% 0.20/0.45 ( ( Xa
% 0.20/0.45 = ( cP @ Xx1 @ Xx2 ) )
% 0.20/0.45 & ( Xb
% 0.20/0.45 = ( cP @ Xy1 @ Xy2 ) )
% 0.20/0.45 & ( Xc
% 0.20/0.45 = ( cP @ Xz1 @ Xz2 ) )
% 0.20/0.45 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.20/0.45 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.20/0.45 => ( R @ Xa @ Xb @ Xc ) ) )
% 0.20/0.45 => ( R @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.48/1.29 ---- Embedded in THF ---
% 1.48/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.29 %%% Generated on Tue Feb 24 12:42:09 EST 2026
% 1.48/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.29 %%% Logic specification used:
% 1.48/1.29 %%% thf(spec, logic, $$dhol).
% 1.48/1.29
% 1.48/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OInPMZid53/DTF2DTF12262.p
% See solution above
% 1.48/1.29 ------------------------
% 1.48/1.30 ---- Cleaned THF ---
% 1.67/1.30 thf(iS_type,type,
% 1.67/1.30 iS: $tType ).
% 1.67/1.30
% 1.67/1.30 thf(y,type,
% 1.67/1.30 y: iS ).
% 1.67/1.30
% 1.67/1.30 thf(x,type,
% 1.67/1.30 x: iS ).
% 1.67/1.30
% 1.67/1.30 thf(cP,type,
% 1.67/1.30 cP: iS > iS > iS ).
% 1.67/1.30
% 1.67/1.30 thf(c0,type,
% 1.67/1.30 c0: iS ).
% 1.67/1.30
% 1.67/1.30 thf(cS_INCL_LEM4_pme,conjecture,
% 1.67/1.30 ( ( ! [Xx0: iS,Xy0: iS] :
% 1.67/1.30 ( ( cP @ Xx0 @ Xy0 )
% 1.67/1.30 != c0 )
% 1.67/1.30 & ! [Xx0: iS,Xy0: iS,Xu: iS,Xv: iS] :
% 1.67/1.30 ( ( ( cP @ Xx0 @ Xu )
% 1.67/1.30 = ( cP @ Xy0 @ Xv ) )
% 1.67/1.30 => ( ( Xx0 = Xy0 )
% 1.67/1.30 & ( Xu = Xv ) ) )
% 1.67/1.30 & ! [X: iS > $o] :
% 1.67/1.30 ( ( ( X @ c0 )
% 1.67/1.30 & ! [Xx0: iS,Xy0: iS] :
% 1.67/1.30 ( ( ( X @ Xx0 )
% 1.67/1.30 & ( X @ Xy0 ) )
% 1.67/1.30 => ( X @ ( cP @ Xx0 @ Xy0 ) ) ) )
% 1.67/1.30 => ! [Xx0: iS] : ( X @ Xx0 ) ) )
% 1.67/1.30 => ! [R: iS > iS > iS > $o] :
% 1.67/1.30 ( ( $true
% 1.67/1.30 & ! [Xa: iS,Xb: iS,Xc: iS] :
% 1.67/1.30 ( ( ( ( Xa = c0 )
% 1.67/1.30 & ( Xb = Xc ) )
% 1.67/1.30 | ( ( Xb = c0 )
% 1.67/1.30 & ( Xa = Xc ) )
% 1.67/1.30 | ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
% 1.67/1.30 ( ( Xa
% 1.67/1.30 = ( cP @ Xx1 @ Xx2 ) )
% 1.67/1.30 & ( Xb
% 1.67/1.30 = ( cP @ Xy1 @ Xy2 ) )
% 1.67/1.30 & ( Xc
% 1.67/1.30 = ( cP @ Xz1 @ Xz2 ) )
% 1.67/1.30 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 1.67/1.30 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 1.67/1.30 => ( R @ Xa @ Xb @ Xc ) ) )
% 1.67/1.30 => ( R @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ).
% 1.67/1.30 ------------------------
% 1.67/1.31 % (12456)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_12262 for (3000ds/275Mi)
% 1.67/1.31 % (12451)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12262 for (3000ds/183Mi)
% 1.67/1.31 % (12453)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_12262 for (3000ds/27Mi)
% 1.67/1.32 % (12454)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12262 for (3000ds/2Mi)
% 1.67/1.32 % (12454)Instruction limit reached!
% 1.67/1.32 % (12454)------------------------------
% 1.67/1.32 % (12454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (12454)Termination reason: Unknown
% 1.67/1.32 % (12454)Termination phase: Property scanning
% 1.67/1.32
% 1.67/1.32 % (12454)Memory used [KB]: 1023
% 1.67/1.32 % (12454)Time elapsed: 0.002 s
% 1.67/1.32 % (12454)Instructions burned: 3 (million)
% 1.67/1.32 % (12454)------------------------------
% 1.67/1.32 % (12454)------------------------------
% 1.67/1.32 % (12452)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_12262 for (3000ds/4Mi)
% 1.67/1.32 % (12455)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_12262 for (3000ds/2Mi)
% 1.67/1.32 % (12457)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12262 for (3000ds/18Mi)
% 1.67/1.32 % (12455)Instruction limit reached!
% 1.67/1.32 % (12455)------------------------------
% 1.67/1.32 % (12455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (12455)Termination reason: Unknown
% 1.67/1.32 % (12455)Termination phase: shuffling
% 1.67/1.32
% 1.67/1.32 % (12455)Memory used [KB]: 1023
% 1.67/1.32 % (12455)Time elapsed: 0.003 s
% 1.67/1.32 % (12455)Instructions burned: 2 (million)
% 1.67/1.32 % (12455)------------------------------
% 1.67/1.32 % (12455)------------------------------
% 1.67/1.32 % (12452)Instruction limit reached!
% 1.67/1.32 % (12452)------------------------------
% 1.67/1.32 % (12452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (12452)Termination reason: Unknown
% 1.67/1.32 % (12452)Termination phase: Saturation
% 1.67/1.32
% 1.67/1.32 % (12452)Memory used [KB]: 5500
% 1.67/1.32 % (12452)Time elapsed: 0.005 s
% 1.67/1.32 % (12452)Instructions burned: 4 (million)
% 1.67/1.32 % (12452)------------------------------
% 1.67/1.32 % (12452)------------------------------
% 1.67/1.33 % (12453)Instruction limit reached!
% 1.67/1.33 % (12453)------------------------------
% 1.67/1.33 % (12453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (12453)Termination reason: Unknown
% 1.67/1.33 % (12453)Termination phase: Saturation
% 1.67/1.33
% 1.67/1.33 % (12453)Memory used [KB]: 5628
% 1.67/1.33 % (12453)Time elapsed: 0.015 s
% 1.67/1.33 % (12453)Instructions burned: 27 (million)
% 1.67/1.33 % (12453)------------------------------
% 1.67/1.33 % (12453)------------------------------
% 1.67/1.33 % (12458)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/3Mi)
% 1.67/1.33 % (12458)Instruction limit reached!
% 1.67/1.33 % (12458)------------------------------
% 1.67/1.33 % (12458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (12458)Termination reason: Unknown
% 1.67/1.33 % (12458)Termination phase: Saturation
% 1.67/1.33
% 1.67/1.33 % (12458)Memory used [KB]: 5500
% 1.67/1.33 % (12458)Time elapsed: 0.003 s
% 1.67/1.33 % (12458)Instructions burned: 4 (million)
% 1.67/1.33 % (12458)------------------------------
% 1.67/1.33 % (12458)------------------------------
% 1.67/1.33 % (12457)Instruction limit reached!
% 1.67/1.33 % (12457)------------------------------
% 1.67/1.33 % (12457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (12457)Termination reason: Unknown
% 1.67/1.33 % (12457)Termination phase: Saturation
% 1.67/1.33
% 1.67/1.33 % (12457)Memory used [KB]: 5628
% 1.67/1.33 % (12457)Time elapsed: 0.014 s
% 1.67/1.33 % (12457)Instructions burned: 19 (million)
% 1.67/1.33 % (12457)------------------------------
% 1.67/1.33 % (12457)------------------------------
% 1.67/1.34 % (12461)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_12262 for (2999ds/3Mi)
% 1.67/1.34 % (12459)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_12262 for (2999ds/37Mi)
% 1.67/1.34 % (12461)Instruction limit reached!
% 1.67/1.34 % (12461)------------------------------
% 1.67/1.34 % (12461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (12461)Termination reason: Unknown
% 1.67/1.34 % (12461)Termination phase: Saturation
% 1.67/1.34
% 1.67/1.34 % (12461)Memory used [KB]: 1023
% 1.67/1.34 % (12461)Time elapsed: 0.002 s
% 1.67/1.34 % (12461)Instructions burned: 3 (million)
% 1.67/1.34 % (12461)------------------------------
% 1.67/1.34 % (12461)------------------------------
% 1.67/1.34 % (12460)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_12262 for (2999ds/15Mi)
% 1.67/1.34 % (12462)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_12262 for (2999ds/1041Mi)
% 1.67/1.35 % (12460)Instruction limit reached!
% 1.67/1.35 % (12460)------------------------------
% 1.67/1.35 % (12460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (12460)Termination reason: Unknown
% 1.67/1.35 % (12460)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (12460)Memory used [KB]: 5628
% 1.67/1.35 % (12460)Time elapsed: 0.012 s
% 1.67/1.35 % (12460)Instructions burned: 16 (million)
% 1.67/1.35 % (12460)------------------------------
% 1.67/1.35 % (12460)------------------------------
% 1.67/1.35 % (12464)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/16Mi)
% 1.67/1.36 % (12463)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/7Mi)
% 1.67/1.36 % (12459)Instruction limit reached!
% 1.67/1.36 % (12459)------------------------------
% 1.67/1.36 % (12459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (12459)Termination reason: Unknown
% 1.67/1.36 % (12459)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (12459)Memory used [KB]: 5756
% 1.67/1.36 % (12459)Time elapsed: 0.023 s
% 1.67/1.36 % (12459)Instructions burned: 38 (million)
% 1.67/1.36 % (12459)------------------------------
% 1.67/1.36 % (12459)------------------------------
% 1.67/1.36 % (12464)Instruction limit reached!
% 1.67/1.36 % (12464)------------------------------
% 1.67/1.36 % (12464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (12464)Termination reason: Unknown
% 1.67/1.36 % (12464)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (12464)Memory used [KB]: 5628
% 1.67/1.36 % (12464)Time elapsed: 0.010 s
% 1.67/1.36 % (12464)Instructions burned: 16 (million)
% 1.67/1.36 % (12464)------------------------------
% 1.67/1.36 % (12464)------------------------------
% 1.67/1.36 % (12463)Instruction limit reached!
% 1.67/1.36 % (12463)------------------------------
% 1.67/1.36 % (12463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (12463)Termination reason: Unknown
% 1.67/1.36 % (12463)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (12463)Memory used [KB]: 1023
% 1.67/1.36 % (12463)Time elapsed: 0.009 s
% 1.67/1.36 % (12463)Instructions burned: 7 (million)
% 1.67/1.36 % (12463)------------------------------
% 1.67/1.36 % (12463)------------------------------
% 1.67/1.37 % (12465)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_12262 for (2999ds/3Mi)
% 1.67/1.37 % (12465)Instruction limit reached!
% 1.67/1.37 % (12465)------------------------------
% 1.67/1.37 % (12465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (12465)Termination reason: Unknown
% 1.67/1.37 % (12465)Termination phase: Twee Goal Transformation
% 1.67/1.37
% 1.67/1.37 % (12465)Memory used [KB]: 1023
% 1.67/1.37 % (12465)Time elapsed: 0.004 s
% 1.67/1.37 % (12465)Instructions burned: 4 (million)
% 1.67/1.37 % (12465)------------------------------
% 1.67/1.37 % (12465)------------------------------
% 1.67/1.37 % (12451)Instruction limit reached!
% 1.67/1.37 % (12451)------------------------------
% 1.67/1.37 % (12451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (12451)Termination reason: Unknown
% 1.67/1.37 % (12451)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (12451)Memory used [KB]: 6268
% 1.67/1.37 % (12451)Time elapsed: 0.063 s
% 1.67/1.37 % (12451)Instructions burned: 185 (million)
% 1.67/1.37 % (12451)------------------------------
% 1.67/1.37 % (12451)------------------------------
% 1.67/1.37 % (12467)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/7Mi)
% 1.67/1.37 % (12466)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_12262 for (2999ds/3Mi)
% 1.67/1.38 % (12467)Instruction limit reached!
% 1.67/1.38 % (12467)------------------------------
% 1.67/1.38 % (12467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (12467)Termination reason: Unknown
% 1.67/1.38 % (12467)Termination phase: Saturation
% 1.67/1.38
% 1.67/1.38 % (12467)Memory used [KB]: 5500
% 1.67/1.38 % (12467)Time elapsed: 0.004 s
% 1.67/1.38 % (12467)Instructions burned: 8 (million)
% 1.67/1.38 % (12467)------------------------------
% 1.67/1.38 % (12467)------------------------------
% 1.67/1.38 % (12466)Instruction limit reached!
% 1.67/1.38 % (12466)------------------------------
% 1.67/1.38 % (12466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (12466)Termination reason: Unknown
% 1.67/1.38 % (12466)Termination phase: Saturation
% 1.67/1.38
% 1.67/1.38 % (12466)Memory used [KB]: 1023
% 1.67/1.38 % (12466)Time elapsed: 0.004 s
% 1.67/1.38 % (12466)Instructions burned: 4 (million)
% 1.67/1.38 % (12466)------------------------------
% 1.67/1.38 % (12466)------------------------------
% 1.67/1.38 % (12470)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/18Mi)
% 1.67/1.38 % (12471)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/710Mi)
% 1.67/1.39 % (12469)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/4Mi)
% 1.67/1.39 % (12470)Refutation not found, incomplete strategy
% 1.67/1.39 % (12470)------------------------------
% 1.67/1.39 % (12470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (12470)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.39
% 1.67/1.39
% 1.67/1.39 % (12470)Memory used [KB]: 5500
% 1.67/1.39 % (12470)Time elapsed: 0.005 s
% 1.67/1.39 % (12470)Instructions burned: 9 (million)
% 1.67/1.39 % (12470)------------------------------
% 1.67/1.39 % (12470)------------------------------
% 1.67/1.39 % (12468)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/3Mi)
% 1.67/1.39 % (12469)Instruction limit reached!
% 1.67/1.39 % (12469)------------------------------
% 1.67/1.39 % (12469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (12469)Termination reason: Unknown
% 1.67/1.39 % (12469)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (12469)Memory used [KB]: 5500
% 1.67/1.39 % (12469)Time elapsed: 0.005 s
% 1.67/1.39 % (12469)Instructions burned: 5 (million)
% 1.67/1.39 % (12469)------------------------------
% 1.67/1.39 % (12469)------------------------------
% 1.67/1.39 % (12468)Instruction limit reached!
% 1.67/1.39 % (12468)------------------------------
% 1.67/1.39 % (12468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (12468)Termination reason: Unknown
% 1.67/1.39 % (12468)Termination phase: Property scanning
% 1.67/1.39
% 1.67/1.39 % (12468)Memory used [KB]: 1023
% 1.67/1.39 % (12468)Time elapsed: 0.004 s
% 1.67/1.39 % (12468)Instructions burned: 3 (million)
% 1.67/1.39 % (12468)------------------------------
% 1.67/1.39 % (12468)------------------------------
% 1.67/1.39 % (12456)Instruction limit reached!
% 1.67/1.39 % (12456)------------------------------
% 1.67/1.39 % (12456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (12456)Termination reason: Unknown
% 1.67/1.39 % (12456)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (12456)Memory used [KB]: 6140
% 1.67/1.39 % (12456)Time elapsed: 0.084 s
% 1.67/1.39 % (12456)Instructions burned: 275 (million)
% 1.67/1.39 % (12456)------------------------------
% 1.67/1.39 % (12456)------------------------------
% 1.67/1.39 % (12472)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/6Mi)
% 1.67/1.40 % (12473)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_12262 for (2999ds/902Mi)
% 1.67/1.40 % (12472)Instruction limit reached!
% 1.67/1.40 % (12472)------------------------------
% 1.67/1.40 % (12472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (12472)Termination reason: Unknown
% 1.67/1.40 % (12472)Termination phase: Saturation
% 1.67/1.40
% 1.67/1.40 % (12472)Memory used [KB]: 5500
% 1.67/1.40 % (12472)Time elapsed: 0.006 s
% 1.67/1.40 % (12472)Instructions burned: 6 (million)
% 1.67/1.40 % (12472)------------------------------
% 1.67/1.40 % (12472)------------------------------
% 1.67/1.40 % (12476)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_12262 for (2999ds/6Mi)
% 1.67/1.40 % (12476)Instruction limit reached!
% 1.67/1.40 % (12476)------------------------------
% 1.67/1.40 % (12476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (12476)Termination reason: Unknown
% 1.67/1.40 % (12476)Termination phase: Saturation
% 1.67/1.40
% 1.67/1.40 % (12476)Memory used [KB]: 5500
% 1.67/1.40 % (12476)Time elapsed: 0.003 s
% 1.67/1.40 % (12476)Instructions burned: 7 (million)
% 1.67/1.40 % (12476)------------------------------
% 1.67/1.40 % (12476)------------------------------
% 1.67/1.41 % (12474)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_12262 for (2999ds/21Mi)
% 1.67/1.41 % (12475)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12262 for (2999ds/5Mi)
% 1.67/1.41 % (12475)Instruction limit reached!
% 1.67/1.41 % (12475)------------------------------
% 1.67/1.41 % (12475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (12475)Termination reason: Unknown
% 1.67/1.41 % (12475)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (12475)Memory used [KB]: 5500
% 1.67/1.41 % (12475)Time elapsed: 0.004 s
% 1.67/1.41 % (12475)Instructions burned: 5 (million)
% 1.67/1.41 % (12475)------------------------------
% 1.67/1.41 % (12475)------------------------------
% 1.67/1.41 % (12478)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_12262 for (2998ds/779Mi)
% 1.67/1.42 % (12477)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12262 for (2998ds/377Mi)
% 1.67/1.42 % (12474)Instruction limit reached!
% 1.67/1.42 % (12474)------------------------------
% 1.67/1.42 % (12474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (12474)Termination reason: Unknown
% 1.67/1.42 % (12474)Termination phase: Saturation
% 1.67/1.42
% 1.67/1.42 % (12474)Memory used [KB]: 5628
% 1.67/1.42 % (12474)Time elapsed: 0.015 s
% 1.67/1.42 % (12474)Instructions burned: 21 (million)
% 1.67/1.42 % (12474)------------------------------
% 1.67/1.42 % (12474)------------------------------
% 1.67/1.43 % (12479)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_12262 for (2998ds/19Mi)
% 1.67/1.43 % (12479)Instruction limit reached!
% 1.67/1.43 % (12479)------------------------------
% 1.67/1.43 % (12479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (12479)Termination reason: Unknown
% 1.67/1.43 % (12479)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (12479)Memory used [KB]: 5628
% 1.67/1.43 % (12479)Time elapsed: 0.009 s
% 1.67/1.43 % (12479)Instructions burned: 21 (million)
% 1.67/1.43 % (12479)------------------------------
% 1.67/1.43 % (12479)------------------------------
% 1.67/1.44 % (12480)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12262 for (2998ds/879Mi)
% 1.67/1.45 % (12486)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12262 for (2998ds/17Mi)
% 1.67/1.46 % (12486)Instruction limit reached!
% 1.67/1.46 % (12486)------------------------------
% 1.67/1.46 % (12486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (12486)Termination reason: Unknown
% 1.67/1.46 % (12486)Termination phase: Saturation
% 1.67/1.46
% 1.67/1.46 % (12486)Memory used [KB]: 5628
% 1.67/1.46 % (12486)Time elapsed: 0.012 s
% 1.67/1.46 % (12486)Instructions burned: 18 (million)
% 1.67/1.46 % (12486)------------------------------
% 1.67/1.46 % (12486)------------------------------
% 1.67/1.47 % (12496)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12262 for (2998ds/3Mi)
% 1.67/1.48 % (12496)Instruction limit reached!
% 1.67/1.48 % (12496)------------------------------
% 1.67/1.48 % (12496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (12496)Termination reason: Unknown
% 1.67/1.48 % (12496)Termination phase: Property scanning
% 1.67/1.48
% 1.67/1.48 % (12496)Memory used [KB]: 1023
% 1.67/1.48 % (12496)Time elapsed: 0.003 s
% 1.67/1.48 % (12496)Instructions burned: 3 (million)
% 1.67/1.48 % (12496)------------------------------
% 1.67/1.48 % (12496)------------------------------
% 1.67/1.49 % (12502)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12262 for (2998ds/30Mi)
% 1.67/1.51 % (12502)Instruction limit reached!
% 1.67/1.51 % (12502)------------------------------
% 1.67/1.51 % (12502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.51 % (12502)Termination reason: Unknown
% 1.67/1.51 % (12502)Termination phase: Saturation
% 1.67/1.51
% 1.67/1.51 % (12502)Memory used [KB]: 5756
% 1.67/1.51 % (12502)Time elapsed: 0.018 s
% 1.67/1.51 % (12502)Instructions burned: 31 (million)
% 1.67/1.51 % (12502)------------------------------
% 1.67/1.51 % (12502)------------------------------
% 1.67/1.51 % (12478)First to succeed.
% 1.67/1.52 % (12478)Refutation found. Thanks to Tanya!
% 1.67/1.52 % SZS status Theorem for DTF2THF_12262
% 1.67/1.52 % SZS output start Proof for DTF2THF_12262
% 1.67/1.52 thf(type_def_5, type, iS: $tType).
% 1.67/1.52 thf(func_def_0, type, iS: $tType).
% 1.67/1.52 thf(func_def_1, type, y: iS).
% 1.67/1.52 thf(func_def_2, type, x: iS).
% 1.67/1.52 thf(func_def_3, type, cP: iS > iS > iS).
% 1.67/1.52 thf(func_def_4, type, c0: iS).
% 1.67/1.52 thf(func_def_27, type, sK1: iS > iS > iS > $o).
% 1.67/1.52 thf(func_def_28, type, sK2: (iS > $o) > iS).
% 1.67/1.52 thf(func_def_29, type, sK3: (iS > $o) > iS).
% 1.67/1.52 thf(func_def_30, type, ph4: !>[X0: $tType]:(X0)).
% 1.67/1.52 thf(f633,plain,(
% 1.67/1.52 $false),
% 1.67/1.52 inference(avatar_sat_refutation,[status(thm)],[f197,f270,f352,f422,f442,f483,f624])).
% 1.67/1.52 thf(f624,plain,(
% 1.67/1.52 spl0_3 | ~spl0_6),
% 1.67/1.52 inference(avatar_contradiction_clause,[status(thm)],[f623])).
% 1.67/1.52 thf(f623,plain,(
% 1.67/1.52 $false | (spl0_3 | ~spl0_6)),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f619])).
% 1.67/1.52 thf(f619,plain,(
% 1.67/1.52 ($true = $false) | (spl0_3 | ~spl0_6)),
% 1.67/1.52 inference(superposition,[status(thm)],[f557,f612])).
% 1.67/1.52 thf(f612,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (($true = (sK1 @ X0 @ X0 @ X0))) ) | (spl0_3 | ~spl0_6)),
% 1.67/1.52 inference(subsumption_resolution,[status(thm)],[f611,f259])).
% 1.67/1.52 thf(f259,plain,(
% 1.67/1.52 ((sK1 @ c0 @ c0 @ c0) != $false) | spl0_3),
% 1.67/1.52 inference(avatar_component_clause,[status(thm)],[f258])).
% 1.67/1.52 thf(f258,definition,(
% 1.67/1.52 spl0_3 <=> ((sK1 @ c0 @ c0 @ c0) = $false)),
% 1.67/1.52 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.67/1.52 thf(f611,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (((sK1 @ c0 @ c0 @ c0) = $false) | ($true = (sK1 @ X0 @ X0 @ X0))) ) | ~spl0_6),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f610])).
% 1.67/1.52 thf(f610,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (($true = (sK1 @ X0 @ X0 @ X0)) | ((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) | ((sK1 @ c0 @ c0 @ c0) = $false)) ) | ~spl0_6),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f609])).
% 1.67/1.52 thf(f609,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) | ($false = (sK1 @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0))) | ($true = (sK1 @ X0 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0)))) ) | ~spl0_6),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f608])).
% 1.67/1.52 thf(f608,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (($true = (sK1 @ X0 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0))) | ((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) | ($false = (sK1 @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0)))) ) | ~spl0_6),
% 1.67/1.52 inference(duplicate_literal_removal,[status(thm)],[f605])).
% 1.67/1.52 thf(f605,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (($false = (sK1 @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0))) | ($true = (sK1 @ X0 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0))) | ((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0)))) ) | ~spl0_6),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f569])).
% 1.67/1.52 thf(f569,plain,(
% 1.67/1.52 ( ! [X2 : iS,X0 : iS > iS,X1 : iS > iS] : (((X1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ (X0 @ Y0) @ (X1 @ Y0))))) != (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) | ($false = (sK1 @ c0 @ (X0 @ c0) @ (X1 @ c0))) | ((^[Y0 : iS]: (Y0)) != X1) | ((^[Y0 : iS]: (Y0)) != X0) | ($true = (sK1 @ X2 @ (X0 @ X2) @ (X1 @ X2))) | ((X0 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ (X0 @ Y0) @ (X1 @ Y0))))) != (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))))) ) | ~spl0_6),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f568])).
% 1.67/1.52 thf(f568,plain,(
% 1.67/1.52 ( ! [X2 : iS,X0 : iS > iS,X1 : iS > iS] : (((X1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))))) != (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) | ((^[Y0 : iS]: (X0 @ Y0)) != (^[Y0 : iS]: (Y0))) | ($true = ((^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))) @ X2)) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (X1 @ Y0))) | ((X0 @ (sK2 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))))) != (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) | (((^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))) @ c0) = $false)) ) | ~spl0_6),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f563])).
% 1.67/1.52 thf(f563,plain,(
% 1.67/1.52 ( ! [X2 : iS,X0 : iS > iS,X1 : iS > iS] : (($true = ((^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))) @ X2)) | (((^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))) @ c0) = $false) | ((X1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))))) != (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) | ($true = $false) | ((X0 @ (sK2 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X0 @ Y0) @ (X1 @ Y0))))) != (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) | ((^[Y0 : iS]: (X0 @ Y0)) != (^[Y0 : iS]: (Y0))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (X1 @ Y0)))) ) | ~spl0_6),
% 1.67/1.52 inference(constrained_superposition,[status(thm)],[f81,f557])).
% 1.67/1.52 thf(f81,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (($true = (X1 @ (sK2 @ X1))) | ((X1 @ c0) = $false) | ((X1 @ X2) = $true)) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.67/1.52 thf(f80,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (((X1 @ X2) = $true) | ((X1 @ c0) = $false) | ($true = ((X1 @ (sK3 @ X1)) & (X1 @ (sK2 @ X1))))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.67/1.52 thf(f78,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (((X1 @ X2) = $true) | ((X1 @ c0) = $false) | ($false = (((X1 @ (sK3 @ X1)) & (X1 @ (sK2 @ X1))) => (X1 @ (cP @ (sK3 @ X1) @ (sK2 @ X1)))))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.67/1.52 thf(f77,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : ((((^[Y0 : iS]: (((X1 @ Y0) & (X1 @ (sK2 @ X1))) => (X1 @ (cP @ Y0 @ (sK2 @ X1))))) @ (sK3 @ X1)) = $false) | ((X1 @ X2) = $true) | ((X1 @ c0) = $false)) )),
% 1.67/1.52 inference(sigma_clausification,[status(thm)],[f76])).
% 1.67/1.52 thf(f76,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (((X1 @ c0) = $false) | ((!! @ iS @ (^[Y0 : iS]: (((X1 @ Y0) & (X1 @ (sK2 @ X1))) => (X1 @ (cP @ Y0 @ (sK2 @ X1)))))) = $false) | ((X1 @ X2) = $true)) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.67/1.52 thf(f75,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (((X1 @ c0) = $false) | ((X1 @ X2) = $true) | (((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0)))))) @ (sK2 @ X1)) = $false)) )),
% 1.67/1.52 inference(sigma_clausification,[status(thm)],[f74])).
% 1.67/1.52 thf(f74,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (((X1 @ X2) = $true) | ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0))))))) = $false) | ((X1 @ c0) = $false)) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.67/1.52 thf(f73,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (($false = ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0))))))) & (X1 @ c0))) | ((X1 @ X2) = $true)) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f72])).
% 1.67/1.52 thf(f72,plain,(
% 1.67/1.52 ( ! [X1 : iS > $o] : (($true = (!! @ iS @ X1)) | ($false = ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0))))))) & (X1 @ c0)))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.67/1.52 thf(f71,plain,(
% 1.67/1.52 ( ! [X1 : iS > $o] : (($true = (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((X1 @ Y1) & (X1 @ Y0)) => (X1 @ (cP @ Y1 @ Y0))))))) & (X1 @ c0)) => (!! @ iS @ X1)))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.67/1.52 thf(f70,plain,(
% 1.67/1.52 ( ! [X1 : iS > $o] : (($true = ((^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))) @ X1))) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f54])).
% 1.67/1.52 thf(f54,plain,(
% 1.67/1.52 ($true = (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ Y0)))))),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.67/1.52 thf(f53,plain,(
% 1.67/1.52 ($true = ((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y1) = (cP @ Y0 @ Y2)) => ((Y3 = Y0) & (Y2 = Y1))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))))),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.67/1.52 thf(f11,plain,(
% 1.67/1.52 ($true = (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y1) = (cP @ Y0 @ Y2)) => ((Y3 = Y0) & (Y2 = Y1))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ ((cP @ Y1 @ Y0) = c0))))))))),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.67/1.52 thf(f9,plain,(
% 1.67/1.52 (((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y1) = (cP @ Y0 @ Y2)) => ((Y3 = Y0) & (Y2 = Y1))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ ((cP @ Y1 @ Y0) = c0))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: ((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((((Y3 = Y1) & (c0 = Y2)) | (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: ((((((cP @ Y6 @ Y5) = Y3) & (Y0 @ Y8 @ Y7 @ Y5)) & ((cP @ Y4 @ Y8) = Y1)) & (Y0 @ Y4 @ Y9 @ Y6)) & ((cP @ Y9 @ Y7) = Y2))))))))))))))) | ((c0 = Y1) & (Y3 = Y2))) => (Y0 @ Y1 @ Y2 @ Y3)))))))) => (Y0 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y)))))) = $false)),
% 1.67/1.52 inference(not_proxy_clausification,[status(thm)],[f8])).
% 1.67/1.52 thf(f8,plain,(
% 1.67/1.52 ($true = (~ ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y1) = (cP @ Y0 @ Y2)) => ((Y3 = Y0) & (Y2 = Y1))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ ((cP @ Y1 @ Y0) = c0))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: ((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((((Y3 = Y1) & (c0 = Y2)) | (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: ((((((cP @ Y6 @ Y5) = Y3) & (Y0 @ Y8 @ Y7 @ Y5)) & ((cP @ Y4 @ Y8) = Y1)) & (Y0 @ Y4 @ Y9 @ Y6)) & ((cP @ Y9 @ Y7) = Y2))))))))))))))) | ((c0 = Y1) & (Y3 = Y2))) => (Y0 @ Y1 @ Y2 @ Y3)))))))) => (Y0 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y))))))))),
% 1.67/1.52 inference(boolean_simplification,[status(thm)],[f7])).
% 1.67/1.52 thf(f7,plain,(
% 1.67/1.52 ($true = (~ ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y1) = (cP @ Y0 @ Y2)) => ((Y3 = Y0) & (Y2 = Y1))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ Y0))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ ((cP @ Y1 @ Y0) = c0))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: (($true & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((((Y3 = Y1) & (c0 = Y2)) | (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: ((((((cP @ Y6 @ Y5) = Y3) & (Y0 @ Y8 @ Y7 @ Y5)) & ((cP @ Y4 @ Y8) = Y1)) & (Y0 @ Y4 @ Y9 @ Y6)) & ((cP @ Y9 @ Y7) = Y2))))))))))))))) | ((c0 = Y1) & (Y3 = Y2))) => (Y0 @ Y1 @ Y2 @ Y3))))))))) => (Y0 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y))))))))),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f6])).
% 1.67/1.52 thf(f6,plain,(
% 1.67/1.52 ($true = (~ ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y1) = (cP @ Y0 @ Y2)) => ((Y3 = Y0) & (Y2 = Y1))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ (^[Y1 : iS]: (Y0 @ Y1))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ ((cP @ Y1 @ Y0) = c0))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: (($true & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((((Y3 = Y1) & (c0 = Y2)) | (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: ((((((cP @ Y6 @ Y5) = Y3) & (Y0 @ Y8 @ Y7 @ Y5)) & ((cP @ Y4 @ Y8) = Y1)) & (Y0 @ Y4 @ Y9 @ Y6)) & ((cP @ Y9 @ Y7) = Y2))))))))))))))) | ((c0 = Y1) & (Y3 = Y2))) => (Y0 @ Y1 @ Y2 @ Y3))))))))) => (Y0 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y))))))))),
% 1.67/1.52 inference(cnf_transformation,[status(thm)],[f5])).
% 1.67/1.52 thf(f5,plain,(
% 1.67/1.52 ($true = (~ ((((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((cP @ Y3 @ Y1) = (cP @ Y0 @ Y2)) => ((Y3 = Y0) & (Y2 = Y1))))))))))) & (!! @ (iS > $o) @ (^[Y0 : iS > $o]: (((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((Y0 @ Y2) & (Y0 @ Y1)) => (Y0 @ (cP @ Y2 @ Y1))))))) & (Y0 @ c0)) => (!! @ iS @ (^[Y1 : iS]: (Y0 @ Y1))))))) & (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (~ ((cP @ Y1 @ Y0) = c0))))))) => (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: (($true & (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((((Y3 = Y1) & (c0 = Y2)) | (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: ((((((cP @ Y6 @ Y5) = Y3) & (Y0 @ Y8 @ Y7 @ Y5)) & ((cP @ Y4 @ Y8) = Y1)) & (Y0 @ Y4 @ Y9 @ Y6)) & ((cP @ Y9 @ Y7) = Y2))))))))))))))) | ((c0 = Y1) & (Y3 = Y2))) => (Y0 @ Y1 @ Y2 @ Y3))))))))) => (Y0 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y))))))))),
% 1.67/1.52 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.52 thf(f4,plain,(
% 1.67/1.52 ~((! [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) != c0) & ! [X2 : iS > $o] : (((X2 @ c0) & ! [X3 : iS,X4 : iS] : (((X2 @ X4) & (X2 @ X3)) => (X2 @ (cP @ X3 @ X4)))) => ! [X5 : iS] : (X2 @ X5)) & ! [X6 : iS,X7 : iS,X8 : iS,X9 : iS] : (((cP @ X6 @ X8) = (cP @ X9 @ X7)) => ((X7 = X8) & (X6 = X9)))) => ! [X10 : iS > iS > iS > $o] : ((! [X11 : iS,X12 : iS,X13 : iS] : ((((X11 = X12) & (c0 = X13)) | ? [X14 : iS,X15 : iS,X16 : iS,X17 : iS,X18 : iS,X19 : iS] : (((cP @ X14 @ X16) = X12) & (X10 @ X19 @ X14 @ X17) & ((cP @ X19 @ X15) = X13) & (X10 @ X15 @ X16 @ X18) & ((cP @ X17 @ X18) = X11)) | ((c0 = X12) & (X11 = X13))) => (X10 @ X13 @ X12 @ X11)) & $true) => (X10 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y))))),
% 1.67/1.52 inference(rectify,[status(thm)],[f2])).
% 1.67/1.52 thf(f2,negated_conjecture,(
% 1.67/1.52 ~((! [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) != c0) & ! [X4 : iS > $o] : (((X4 @ c0) & ! [X0 : iS,X1 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : iS] : (X4 @ X0)) & ! [X0 : iS,X3 : iS,X2 : iS,X1 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1)))) => ! [X5 : iS > iS > iS > $o] : ((! [X8 : iS,X7 : iS,X6 : iS] : ((((X7 = X8) & (c0 = X6)) | ? [X11 : iS,X10 : iS,X12 : iS,X13 : iS,X14 : iS,X9 : iS] : (((cP @ X11 @ X12) = X7) & (X5 @ X9 @ X11 @ X13) & ((cP @ X9 @ X10) = X6) & (X5 @ X10 @ X12 @ X14) & ((cP @ X13 @ X14) = X8)) | ((c0 = X7) & (X6 = X8))) => (X5 @ X6 @ X7 @ X8)) & $true) => (X5 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y))))),
% 1.67/1.52 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.52 thf(f1,conjecture,(
% 1.67/1.52 (! [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) != c0) & ! [X4 : iS > $o] : (((X4 @ c0) & ! [X0 : iS,X1 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : iS] : (X4 @ X0)) & ! [X0 : iS,X3 : iS,X2 : iS,X1 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1)))) => ! [X5 : iS > iS > iS > $o] : ((! [X8 : iS,X7 : iS,X6 : iS] : ((((X7 = X8) & (c0 = X6)) | ? [X11 : iS,X10 : iS,X12 : iS,X13 : iS,X14 : iS,X9 : iS] : (((cP @ X11 @ X12) = X7) & (X5 @ X9 @ X11 @ X13) & ((cP @ X9 @ X10) = X6) & (X5 @ X10 @ X12 @ X14) & ((cP @ X13 @ X14) = X8)) | ((c0 = X7) & (X6 = X8))) => (X5 @ X6 @ X7 @ X8)) & $true) => (X5 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y)))),
% 1.67/1.52 file('/export/starexec/sandbox/tmp/tmp.OInPMZid53/DTF2THF_12262.p',cS_INCL_LEM4_pme)).
% 1.67/1.52 thf(f557,plain,(
% 1.67/1.52 ((sK1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) = $false) | ~spl0_6),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f269])).
% 1.67/1.52 thf(f269,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != X0) | ($false = (sK1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ X0 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))))) ) | ~spl0_6),
% 1.67/1.52 inference(avatar_component_clause,[status(thm)],[f268])).
% 1.67/1.52 thf(f268,definition,(
% 1.67/1.52 spl0_6 <=> ! [X0 : iS] : (((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != X0) | ($false = (sK1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ X0 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))))))),
% 1.67/1.52 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.67/1.52 thf(f483,plain,(
% 1.67/1.52 ~spl0_1),
% 1.67/1.52 inference(avatar_contradiction_clause,[status(thm)],[f482])).
% 1.67/1.52 thf(f482,plain,(
% 1.67/1.52 $false | ~spl0_1),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f455])).
% 1.67/1.52 thf(f455,plain,(
% 1.67/1.52 ($true = $false) | (y != y) | ~spl0_1),
% 1.67/1.52 inference(superposition,[status(thm)],[f93,f191])).
% 1.67/1.52 thf(f191,plain,(
% 1.67/1.52 ((sK1 @ c0 @ y @ y) = $false) | ~spl0_1),
% 1.67/1.52 inference(avatar_component_clause,[status(thm)],[f189])).
% 1.67/1.52 thf(f189,definition,(
% 1.67/1.52 spl0_1 <=> ((sK1 @ c0 @ y @ y) = $false)),
% 1.67/1.52 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.67/1.52 thf(f93,plain,(
% 1.67/1.52 ( ! [X0 : iS,X1 : iS] : (($true = (sK1 @ c0 @ X0 @ X1)) | (X0 != X1)) )),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f51])).
% 1.67/1.52 thf(f51,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((c0 != X1) | ($true = (sK1 @ X1 @ X2 @ X3)) | (X2 != X3)) )),
% 1.67/1.52 inference(equality_proxy_clausification,[status(thm)],[f50])).
% 1.67/1.52 thf(f50,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((c0 != X1) | ($true = (sK1 @ X1 @ X2 @ X3)) | ((X3 = X2) = $false)) )),
% 1.67/1.52 inference(equality_proxy_clausification,[status(thm)],[f49])).
% 1.67/1.52 thf(f49,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : (((c0 = X1) = $false) | ($true = (sK1 @ X1 @ X2 @ X3)) | ((X3 = X2) = $false)) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.67/1.52 thf(f23,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($false = ((c0 = X1) & (X3 = X2))) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.67/1.52 thf(f22,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((((((X3 = X1) & (c0 = X2)) | (?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: ((((((cP @ Y2 @ Y1) = X3) & (sK1 @ Y4 @ Y3 @ Y1)) & ((cP @ Y0 @ Y4) = X1)) & (sK1 @ Y0 @ Y5 @ Y2)) & ((cP @ Y5 @ Y3) = X2))))))))))))))) | ((c0 = X1) & (X3 = X2))) = $false) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.67/1.52 thf(f21,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($true = (((((X3 = X1) & (c0 = X2)) | (?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: ((((((cP @ Y2 @ Y1) = X3) & (sK1 @ Y4 @ Y3 @ Y1)) & ((cP @ Y0 @ Y4) = X1)) & (sK1 @ Y0 @ Y5 @ Y2)) & ((cP @ Y5 @ Y3) = X2))))))))))))))) | ((c0 = X1) & (X3 = X2))) => (sK1 @ X1 @ X2 @ X3)))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.67/1.52 thf(f20,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($true = ((^[Y0 : iS]: (((((Y0 = X1) & (c0 = X2)) | (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: ((((((cP @ Y3 @ Y2) = Y0) & (sK1 @ Y5 @ Y4 @ Y2)) & ((cP @ Y1 @ Y5) = X1)) & (sK1 @ Y1 @ Y6 @ Y3)) & ((cP @ Y6 @ Y4) = X2))))))))))))))) | ((c0 = X1) & (Y0 = X2))) => (sK1 @ X1 @ X2 @ Y0))) @ X3))) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f19])).
% 1.67/1.52 thf(f19,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS] : (($true = (!! @ iS @ (^[Y0 : iS]: (((((Y0 = X1) & (c0 = X2)) | (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: ((((((cP @ Y3 @ Y2) = Y0) & (sK1 @ Y5 @ Y4 @ Y2)) & ((cP @ Y1 @ Y5) = X1)) & (sK1 @ Y1 @ Y6 @ Y3)) & ((cP @ Y6 @ Y4) = X2))))))))))))))) | ((c0 = X1) & (Y0 = X2))) => (sK1 @ X1 @ X2 @ Y0)))))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.67/1.52 thf(f18,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS] : (($true = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((((Y1 = X1) & (c0 = Y0)) | (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: ((((((cP @ Y4 @ Y3) = Y1) & (sK1 @ Y6 @ Y5 @ Y3)) & ((cP @ Y2 @ Y6) = X1)) & (sK1 @ Y2 @ Y7 @ Y4)) & ((cP @ Y7 @ Y5) = Y0))))))))))))))) | ((c0 = X1) & (Y1 = Y0))) => (sK1 @ X1 @ Y0 @ Y1))))) @ X2))) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f17])).
% 1.67/1.52 thf(f17,plain,(
% 1.67/1.52 ( ! [X1 : iS] : (($true = (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (((((Y1 = X1) & (c0 = Y0)) | (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: ((((((cP @ Y4 @ Y3) = Y1) & (sK1 @ Y6 @ Y5 @ Y3)) & ((cP @ Y2 @ Y6) = X1)) & (sK1 @ Y2 @ Y7 @ Y4)) & ((cP @ Y7 @ Y5) = Y0))))))))))))))) | ((c0 = X1) & (Y1 = Y0))) => (sK1 @ X1 @ Y0 @ Y1)))))))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.67/1.52 thf(f16,plain,(
% 1.67/1.52 ( ! [X1 : iS] : (($true = ((^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((((Y2 = Y0) & (c0 = Y1)) | (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: ((((((cP @ Y5 @ Y4) = Y2) & (sK1 @ Y7 @ Y6 @ Y4)) & ((cP @ Y3 @ Y7) = Y0)) & (sK1 @ Y3 @ Y8 @ Y5)) & ((cP @ Y8 @ Y6) = Y1))))))))))))))) | ((c0 = Y0) & (Y2 = Y1))) => (sK1 @ Y0 @ Y1 @ Y2))))))) @ X1))) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f15])).
% 1.67/1.52 thf(f15,plain,(
% 1.67/1.52 ($true = (!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((((Y2 = Y0) & (c0 = Y1)) | (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: ((((((cP @ Y5 @ Y4) = Y2) & (sK1 @ Y7 @ Y6 @ Y4)) & ((cP @ Y3 @ Y7) = Y0)) & (sK1 @ Y3 @ Y8 @ Y5)) & ((cP @ Y8 @ Y6) = Y1))))))))))))))) | ((c0 = Y0) & (Y2 = Y1))) => (sK1 @ Y0 @ Y1 @ Y2)))))))))),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.67/1.52 thf(f13,plain,(
% 1.67/1.52 (((!! @ iS @ (^[Y0 : iS]: (!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (((((Y2 = Y0) & (c0 = Y1)) | (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: ((((((cP @ Y5 @ Y4) = Y2) & (sK1 @ Y7 @ Y6 @ Y4)) & ((cP @ Y3 @ Y7) = Y0)) & (sK1 @ Y3 @ Y8 @ Y5)) & ((cP @ Y8 @ Y6) = Y1))))))))))))))) | ((c0 = Y0) & (Y2 = Y1))) => (sK1 @ Y0 @ Y1 @ Y2)))))))) => (sK1 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y))) = $false)),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.67/1.52 thf(f12,plain,(
% 1.67/1.52 ($false = ((^[Y0 : iS > iS > iS > $o]: ((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((((Y3 = Y1) & (c0 = Y2)) | (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: ((((((cP @ Y6 @ Y5) = Y3) & (Y0 @ Y8 @ Y7 @ Y5)) & ((cP @ Y4 @ Y8) = Y1)) & (Y0 @ Y4 @ Y9 @ Y6)) & ((cP @ Y9 @ Y7) = Y2))))))))))))))) | ((c0 = Y1) & (Y3 = Y2))) => (Y0 @ Y1 @ Y2 @ Y3)))))))) => (Y0 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y)))) @ sK1))),
% 1.67/1.52 inference(sigma_clausification,[status(thm)],[f10])).
% 1.67/1.52 thf(f10,plain,(
% 1.67/1.52 ($false = (!! @ (iS > iS > iS > $o) @ (^[Y0 : iS > iS > iS > $o]: ((!! @ iS @ (^[Y1 : iS]: (!! @ iS @ (^[Y2 : iS]: (!! @ iS @ (^[Y3 : iS]: (((((Y3 = Y1) & (c0 = Y2)) | (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: (?? @ iS @ (^[Y6 : iS]: (?? @ iS @ (^[Y7 : iS]: (?? @ iS @ (^[Y8 : iS]: (?? @ iS @ (^[Y9 : iS]: ((((((cP @ Y6 @ Y5) = Y3) & (Y0 @ Y8 @ Y7 @ Y5)) & ((cP @ Y4 @ Y8) = Y1)) & (Y0 @ Y4 @ Y9 @ Y6)) & ((cP @ Y9 @ Y7) = Y2))))))))))))))) | ((c0 = Y1) & (Y3 = Y2))) => (Y0 @ Y1 @ Y2 @ Y3)))))))) => (Y0 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y))))))),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.67/1.52 thf(f442,plain,(
% 1.67/1.52 ~spl0_2 | ~spl0_5),
% 1.67/1.52 inference(avatar_contradiction_clause,[status(thm)],[f441])).
% 1.67/1.52 thf(f441,plain,(
% 1.67/1.52 $false | (~spl0_2 | ~spl0_5)),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f427])).
% 1.67/1.52 thf(f427,plain,(
% 1.67/1.52 ($true = $false) | (~spl0_2 | ~spl0_5)),
% 1.67/1.52 inference(superposition,[status(thm)],[f195,f266])).
% 1.67/1.52 thf(f266,plain,(
% 1.67/1.52 ( ! [X2 : iS] : (($true = (sK1 @ X2 @ X2 @ X2))) ) | ~spl0_5),
% 1.67/1.52 inference(avatar_component_clause,[status(thm)],[f265])).
% 1.67/1.52 thf(f265,definition,(
% 1.67/1.52 spl0_5 <=> ! [X2 : iS] : ($true = (sK1 @ X2 @ X2 @ X2))),
% 1.67/1.52 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.67/1.52 thf(f195,plain,(
% 1.67/1.52 ($false = (sK1 @ x @ x @ x)) | ~spl0_2),
% 1.67/1.52 inference(avatar_component_clause,[status(thm)],[f193])).
% 1.67/1.52 thf(f193,definition,(
% 1.67/1.52 spl0_2 <=> ($false = (sK1 @ x @ x @ x))),
% 1.67/1.52 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.67/1.52 thf(f422,plain,(
% 1.67/1.52 spl0_5 | spl0_3 | ~spl0_4),
% 1.67/1.52 inference(avatar_split_clause,[status(thm)],[f421,f262,f258,f265])).
% 1.67/1.52 thf(f262,definition,(
% 1.67/1.52 spl0_4 <=> ! [X1 : iS] : (((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != X1) | ($false = (sK1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ X1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))))))),
% 1.67/1.52 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.67/1.52 thf(f421,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (($true = (sK1 @ X0 @ X0 @ X0))) ) | (spl0_3 | ~spl0_4)),
% 1.67/1.52 inference(subsumption_resolution,[status(thm)],[f419,f259])).
% 1.67/1.52 thf(f419,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (($true = (sK1 @ X0 @ X0 @ X0)) | ((sK1 @ c0 @ c0 @ c0) = $false)) ) | ~spl0_4),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f418])).
% 1.67/1.52 thf(f418,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (($true = (sK1 @ X0 @ X0 @ X0)) | ((sK1 @ c0 @ c0 @ c0) = $false) | ((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))))) ) | ~spl0_4),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f417])).
% 1.67/1.52 thf(f417,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (((sK1 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0) @ c0) = $false) | ($true = (sK1 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0) @ X0)) | ((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK3 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0)))))) ) | ~spl0_4),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f416])).
% 1.67/1.52 thf(f416,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (($true = (sK1 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0) @ X0)) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0))) | ((sK1 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0) @ c0) = $false) | ((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK3 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0)))))) ) | ~spl0_4),
% 1.67/1.52 inference(duplicate_literal_removal,[status(thm)],[f414])).
% 1.67/1.52 thf(f414,plain,(
% 1.67/1.52 ( ! [X0 : iS] : (((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != ((^[Y0 : iS]: (Y0)) @ (sK3 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0))))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0))) | ($true = (sK1 @ ((^[Y0 : iS]: (Y0)) @ X0) @ ((^[Y0 : iS]: (Y0)) @ X0) @ X0)) | ((sK1 @ ((^[Y0 : iS]: (Y0)) @ c0) @ ((^[Y0 : iS]: (Y0)) @ c0) @ c0) = $false) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (Y0)))) ) | ~spl0_4),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f408])).
% 1.67/1.52 thf(f408,plain,(
% 1.67/1.52 ( ! [X2 : iS,X0 : iS > iS,X1 : iS > iS] : (((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != (X1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ Y0))))) | ($true = (sK1 @ (X0 @ X2) @ (X1 @ X2) @ X2)) | ((X0 @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ Y0)))) != (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) | ((^[Y0 : iS]: (Y0)) != X1) | ((^[Y0 : iS]: (Y0)) != X0) | ($false = (sK1 @ (X0 @ c0) @ (X1 @ c0) @ c0))) ) | ~spl0_4),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f407])).
% 1.67/1.52 thf(f407,plain,(
% 1.67/1.52 ( ! [X2 : iS,X0 : iS > iS,X1 : iS > iS] : (((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (X1 @ Y0))) | (((^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0))) @ c0) = $false) | ((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != (X1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) | ($true = ((^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0))) @ X2)) | ((^[Y0 : iS]: (X0 @ Y0)) != (^[Y0 : iS]: (Y0))) | ((X0 @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0))))) != (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))))) ) | ~spl0_4),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f398])).
% 1.67/1.52 thf(f398,plain,(
% 1.67/1.52 ( ! [X2 : iS,X0 : iS > iS,X1 : iS > iS] : (((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != (X1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) | ((^[Y0 : iS]: (Y0)) != (^[Y0 : iS]: (X1 @ Y0))) | (((^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0))) @ c0) = $false) | ($true = ((^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0))) @ X2)) | ((^[Y0 : iS]: (X0 @ Y0)) != (^[Y0 : iS]: (Y0))) | ((X0 @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X0 @ Y0) @ (X1 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0))))) != (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) | ($true = $false)) ) | ~spl0_4),
% 1.67/1.52 inference(constrained_superposition,[status(thm)],[f82,f393])).
% 1.67/1.52 thf(f393,plain,(
% 1.67/1.52 ((sK1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))) = $false) | ~spl0_4),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f263])).
% 1.67/1.52 thf(f263,plain,(
% 1.67/1.52 ( ! [X1 : iS] : (((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != X1) | ($false = (sK1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ X1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))))) ) | ~spl0_4),
% 1.67/1.52 inference(avatar_component_clause,[status(thm)],[f262])).
% 1.67/1.52 thf(f82,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (($true = (X1 @ (sK3 @ X1))) | ((X1 @ c0) = $false) | ((X1 @ X2) = $true)) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.67/1.52 thf(f352,plain,(
% 1.67/1.52 ~spl0_3),
% 1.67/1.52 inference(avatar_contradiction_clause,[status(thm)],[f351])).
% 1.67/1.52 thf(f351,plain,(
% 1.67/1.52 $false | ~spl0_3),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f281])).
% 1.67/1.52 thf(f281,plain,(
% 1.67/1.52 ($true = $false) | (c0 != c0) | ~spl0_3),
% 1.67/1.52 inference(superposition,[status(thm)],[f260,f95])).
% 1.67/1.52 thf(f95,plain,(
% 1.67/1.52 ( ! [X0 : iS,X1 : iS] : (($true = (sK1 @ X0 @ c0 @ X1)) | (X0 != X1)) )),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f29])).
% 1.67/1.52 thf(f29,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((c0 != X2) | ($true = (sK1 @ X1 @ X2 @ X3)) | (X1 != X3)) )),
% 1.67/1.52 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.67/1.52 thf(f28,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : ((X1 != X3) | ((c0 = X2) = $false) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(equality_proxy_clausification,[status(thm)],[f27])).
% 1.67/1.52 thf(f27,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : (((X3 = X1) = $false) | ($true = (sK1 @ X1 @ X2 @ X3)) | ((c0 = X2) = $false)) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.67/1.52 thf(f26,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | (((X3 = X1) & (c0 = X2)) = $false)) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.67/1.52 thf(f24,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : (((((X3 = X1) & (c0 = X2)) | (?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: ((((((cP @ Y2 @ Y1) = X3) & (sK1 @ Y4 @ Y3 @ Y1)) & ((cP @ Y0 @ Y4) = X1)) & (sK1 @ Y0 @ Y5 @ Y2)) & ((cP @ Y5 @ Y3) = X2))))))))))))))) = $false) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.67/1.52 thf(f260,plain,(
% 1.67/1.52 ((sK1 @ c0 @ c0 @ c0) = $false) | ~spl0_3),
% 1.67/1.52 inference(avatar_component_clause,[status(thm)],[f258])).
% 1.67/1.52 thf(f270,plain,(
% 1.67/1.52 spl0_3 | spl0_4 | spl0_5 | spl0_6),
% 1.67/1.52 inference(avatar_split_clause,[status(thm)],[f256,f268,f265,f262,f258])).
% 1.67/1.52 thf(f256,plain,(
% 1.67/1.52 ( ! [X2 : iS,X0 : iS,X1 : iS] : (((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != X0) | ((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) != X1) | ($true = (sK1 @ X2 @ X2 @ X2)) | ((sK1 @ c0 @ c0 @ c0) = $false) | ($false = (sK1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ X1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))))) | ($false = (sK1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0))) @ X0 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ Y0)))))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f253])).
% 1.67/1.52 thf(f253,plain,(
% 1.67/1.52 ( ! [X2 : iS,X0 : iS,X1 : iS] : (($false = (sK1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) @ X0 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) | ($true = (sK1 @ X2 @ X2 @ ((^[Y0 : iS]: (Y0)) @ X2))) | ((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) != X0) | ((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) != X1) | ($false = (sK1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))) @ X1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ ((^[Y1 : iS]: (Y1)) @ Y0)))))) | ($false = (sK1 @ c0 @ c0 @ ((^[Y0 : iS]: (Y0)) @ c0)))) )),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f243])).
% 1.67/1.52 thf(f243,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS,X4 : iS,X5 : iS] : (((cP @ X4 @ X2) != (X0 @ (cP @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ (X0 @ Y0)))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ (X0 @ Y0))))))) | ((sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ (X0 @ Y0)))) != X1) | ($false = (sK1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ (X0 @ Y0)))) @ X3 @ X4)) | ((sK1 @ c0 @ c0 @ (X0 @ c0)) = $false) | ($true = (sK1 @ X5 @ X5 @ (X0 @ X5))) | ((sK3 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ (X0 @ Y0)))) != X3) | ((sK1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ Y0 @ Y0 @ (X0 @ Y0)))) @ X1 @ X2) = $false)) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f240])).
% 1.67/1.52 thf(f240,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X0 : iS > iS,X1 : iS,X4 : iS,X5 : iS] : (((sK1 @ ((^[Y0 : iS]: (Y0)) @ c0) @ c0 @ (X0 @ c0)) = $false) | ((sK1 @ (sK3 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ (X0 @ Y0)))) @ X3 @ X4) = $false) | ((X0 @ (cP @ (sK3 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ (X0 @ Y0)))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ (X0 @ Y0)))))) != (cP @ X4 @ X2)) | ($true = (sK1 @ ((^[Y0 : iS]: (Y0)) @ X5) @ X5 @ (X0 @ X5))) | ($false = (sK1 @ (sK2 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ (X0 @ Y0)))) @ X1 @ X2)) | ((sK2 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ (X0 @ Y0)))) != X1) | ((sK3 @ (^[Y0 : iS]: (sK1 @ ((^[Y1 : iS]: (Y1)) @ Y0) @ Y0 @ (X0 @ Y0)))) != X3)) )),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f182])).
% 1.67/1.52 thf(f182,plain,(
% 1.67/1.52 ( ! [X2 : iS > iS,X3 : iS > iS,X0 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (((cP @ X0 @ X1) != (X2 @ (cP @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0))))))) | ((sK1 @ X1 @ X6 @ X5) = $false) | ((sK1 @ X0 @ X7 @ X4) = $false) | ((sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))) != X7) | ($true = (sK1 @ (X2 @ X8) @ X8 @ (X3 @ X8))) | ((X3 @ (cP @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))))) != (cP @ X4 @ X5)) | ((sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ Y0 @ (X3 @ Y0)))) != X6) | ((sK1 @ (X2 @ c0) @ c0 @ (X3 @ c0)) = $false)) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f181])).
% 1.67/1.52 thf(f181,plain,(
% 1.67/1.52 ( ! [X2 : iS > iS,X3 : iS > iS,X0 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (((X3 @ (cP @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))))) != (cP @ X4 @ X5)) | ((sK1 @ X0 @ X7 @ X4) = $false) | ((sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) != X6) | ((sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) != X7) | ($true = ((^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))) @ X8)) | ((sK1 @ X1 @ X6 @ X5) = $false) | ($false = ((^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))) @ c0)) | ((cP @ X0 @ X1) != (X2 @ (cP @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))))))) )),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f173])).
% 1.67/1.52 thf(f173,plain,(
% 1.67/1.52 ( ! [X2 : iS > iS,X3 : iS > iS,X0 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (((cP @ X0 @ X1) != (X2 @ (cP @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))))))) | ((sK1 @ X0 @ X7 @ X4) = $false) | ($true = ((^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))) @ X8)) | ((sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) != X7) | ($true = $false) | ((sK1 @ X1 @ X6 @ X5) = $false) | ((sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) != X6) | ((X3 @ (cP @ (sK3 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))) @ (sK2 @ (^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0)))))) != (cP @ X4 @ X5)) | ($false = ((^[Y0 : iS]: (sK1 @ (X2 @ Y0) @ ((^[Y1 : iS]: (Y1)) @ Y0) @ (X3 @ Y0))) @ c0))) )),
% 1.67/1.52 inference(constrained_superposition,[status(thm)],[f170,f79])).
% 1.67/1.52 thf(f79,plain,(
% 1.67/1.52 ( ! [X2 : iS,X1 : iS > $o] : (((X1 @ (cP @ (sK3 @ X1) @ (sK2 @ X1))) = $false) | ((X1 @ c0) = $false) | ((X1 @ X2) = $true)) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.67/1.52 thf(f170,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X0 : iS,X1 : iS,X4 : iS,X5 : iS] : (($true = (sK1 @ (cP @ X0 @ X1) @ (cP @ X2 @ X3) @ (cP @ X4 @ X5))) | ((sK1 @ X1 @ X3 @ X5) = $false) | ((sK1 @ X0 @ X2 @ X4) = $false)) )),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f169])).
% 1.67/1.52 thf(f169,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X0 : iS,X1 : iS,X6 : iS,X4 : iS,X5 : iS] : (((cP @ X6 @ X0) != X3) | ($true = (sK1 @ X3 @ (cP @ X4 @ X1) @ (cP @ X5 @ X2))) | ((sK1 @ X6 @ X4 @ X5) = $false) | ((sK1 @ X0 @ X1 @ X2) = $false)) )),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f168])).
% 1.67/1.52 thf(f168,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X0 : iS,X1 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (((cP @ X5 @ X6) != X3) | ((sK1 @ X7 @ X2 @ X6) = $false) | ($true = (sK1 @ X0 @ (cP @ X1 @ X2) @ X3)) | ((cP @ X4 @ X7) != X0) | ($false = (sK1 @ X4 @ X1 @ X5))) )),
% 1.67/1.52 inference(equality_resolution,[status(thm)],[f48])).
% 1.67/1.52 thf(f48,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (((cP @ X9 @ X7) != X2) | ($true = (sK1 @ X1 @ X2 @ X3)) | ((sK1 @ X4 @ X9 @ X6) = $false) | ((cP @ X6 @ X5) != X3) | ((cP @ X4 @ X8) != X1) | ((sK1 @ X8 @ X7 @ X5) = $false)) )),
% 1.67/1.52 inference(equality_proxy_clausification,[status(thm)],[f47])).
% 1.67/1.52 thf(f47,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (((sK1 @ X8 @ X7 @ X5) = $false) | ($false = ((cP @ X9 @ X7) = X2)) | ($true = (sK1 @ X1 @ X2 @ X3)) | ((sK1 @ X4 @ X9 @ X6) = $false) | ((cP @ X4 @ X8) != X1) | ((cP @ X6 @ X5) != X3)) )),
% 1.67/1.52 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.67/1.52 thf(f46,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | ((sK1 @ X8 @ X7 @ X5) = $false) | ((cP @ X6 @ X5) != X3) | (((cP @ X4 @ X8) = X1) = $false) | ((sK1 @ X4 @ X9 @ X6) = $false) | ($false = ((cP @ X9 @ X7) = X2))) )),
% 1.67/1.52 inference(equality_proxy_clausification,[status(thm)],[f45])).
% 1.67/1.52 thf(f45,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : ((((cP @ X6 @ X5) = X3) = $false) | ($true = (sK1 @ X1 @ X2 @ X3)) | ((sK1 @ X4 @ X9 @ X6) = $false) | ((sK1 @ X8 @ X7 @ X5) = $false) | (((cP @ X4 @ X8) = X1) = $false) | ($false = ((cP @ X9 @ X7) = X2))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.67/1.52 thf(f44,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (((((cP @ X6 @ X5) = X3) & (sK1 @ X8 @ X7 @ X5)) = $false) | (((cP @ X4 @ X8) = X1) = $false) | ($true = (sK1 @ X1 @ X2 @ X3)) | ((sK1 @ X4 @ X9 @ X6) = $false) | ($false = ((cP @ X9 @ X7) = X2))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.67/1.52 thf(f43,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | (((((cP @ X6 @ X5) = X3) & (sK1 @ X8 @ X7 @ X5)) & ((cP @ X4 @ X8) = X1)) = $false) | ((sK1 @ X4 @ X9 @ X6) = $false) | ($false = ((cP @ X9 @ X7) = X2))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.67/1.52 thf(f42,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (((((((cP @ X6 @ X5) = X3) & (sK1 @ X8 @ X7 @ X5)) & ((cP @ X4 @ X8) = X1)) & (sK1 @ X4 @ X9 @ X6)) = $false) | ($false = ((cP @ X9 @ X7) = X2)) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.67/1.52 thf(f41,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : (($false = ((((((cP @ X6 @ X5) = X3) & (sK1 @ X8 @ X7 @ X5)) & ((cP @ X4 @ X8) = X1)) & (sK1 @ X4 @ X9 @ X6)) & ((cP @ X9 @ X7) = X2))) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.67/1.52 thf(f40,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X9 : iS,X7 : iS,X4 : iS,X5 : iS] : ((((^[Y0 : iS]: ((((((cP @ X6 @ X5) = X3) & (sK1 @ X8 @ X7 @ X5)) & ((cP @ X4 @ X8) = X1)) & (sK1 @ X4 @ Y0 @ X6)) & ((cP @ Y0 @ X7) = X2))) @ X9) = $false) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f39])).
% 1.67/1.52 thf(f39,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | ((?? @ iS @ (^[Y0 : iS]: ((((((cP @ X6 @ X5) = X3) & (sK1 @ X8 @ X7 @ X5)) & ((cP @ X4 @ X8) = X1)) & (sK1 @ X4 @ Y0 @ X6)) & ((cP @ Y0 @ X7) = X2)))) = $false)) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.67/1.52 thf(f38,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X8 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | (((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: ((((((cP @ X6 @ X5) = X3) & (sK1 @ Y0 @ X7 @ X5)) & ((cP @ X4 @ Y0) = X1)) & (sK1 @ X4 @ Y1 @ X6)) & ((cP @ Y1 @ X7) = X2))))) @ X8) = $false)) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f37])).
% 1.67/1.52 thf(f37,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : (($false = (?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: ((((((cP @ X6 @ X5) = X3) & (sK1 @ Y0 @ X7 @ X5)) & ((cP @ X4 @ Y0) = X1)) & (sK1 @ X4 @ Y1 @ X6)) & ((cP @ Y1 @ X7) = X2))))))) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.67/1.52 thf(f36,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X7 : iS,X4 : iS,X5 : iS] : ((((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: ((((((cP @ X6 @ X5) = X3) & (sK1 @ Y1 @ Y0 @ X5)) & ((cP @ X4 @ Y1) = X1)) & (sK1 @ X4 @ Y2 @ X6)) & ((cP @ Y2 @ Y0) = X2))))))) @ X7) = $false) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f35])).
% 1.67/1.52 thf(f35,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X4 : iS,X5 : iS] : (($false = (?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: ((((((cP @ X6 @ X5) = X3) & (sK1 @ Y1 @ Y0 @ X5)) & ((cP @ X4 @ Y1) = X1)) & (sK1 @ X4 @ Y2 @ X6)) & ((cP @ Y2 @ Y0) = X2))))))))) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.67/1.52 thf(f34,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X6 : iS,X4 : iS,X5 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | (((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: ((((((cP @ Y0 @ X5) = X3) & (sK1 @ Y2 @ Y1 @ X5)) & ((cP @ X4 @ Y2) = X1)) & (sK1 @ X4 @ Y3 @ Y0)) & ((cP @ Y3 @ Y1) = X2))))))))) @ X6) = $false)) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f33])).
% 1.67/1.52 thf(f33,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS,X5 : iS] : (($false = (?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: ((((((cP @ Y0 @ X5) = X3) & (sK1 @ Y2 @ Y1 @ X5)) & ((cP @ X4 @ Y2) = X1)) & (sK1 @ X4 @ Y3 @ Y0)) & ((cP @ Y3 @ Y1) = X2))))))))))) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.67/1.52 thf(f32,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS,X5 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | ($false = ((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: ((((((cP @ Y1 @ Y0) = X3) & (sK1 @ Y3 @ Y2 @ Y0)) & ((cP @ X4 @ Y3) = X1)) & (sK1 @ X4 @ Y4 @ Y1)) & ((cP @ Y4 @ Y2) = X2))))))))))) @ X5))) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f31])).
% 1.67/1.52 thf(f31,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | ($false = (?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: ((((((cP @ Y1 @ Y0) = X3) & (sK1 @ Y3 @ Y2 @ Y0)) & ((cP @ X4 @ Y3) = X1)) & (sK1 @ X4 @ Y4 @ Y1)) & ((cP @ Y4 @ Y2) = X2)))))))))))))) )),
% 1.67/1.52 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.67/1.52 thf(f30,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS,X4 : iS] : (($true = (sK1 @ X1 @ X2 @ X3)) | (((^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: ((((((cP @ Y2 @ Y1) = X3) & (sK1 @ Y4 @ Y3 @ Y1)) & ((cP @ Y0 @ Y4) = X1)) & (sK1 @ Y0 @ Y5 @ Y2)) & ((cP @ Y5 @ Y3) = X2))))))))))))) @ X4) = $false)) )),
% 1.67/1.52 inference(pi_clausification,[status(thm)],[f25])).
% 1.67/1.52 thf(f25,plain,(
% 1.67/1.52 ( ! [X2 : iS,X3 : iS,X1 : iS] : (($false = (?? @ iS @ (^[Y0 : iS]: (?? @ iS @ (^[Y1 : iS]: (?? @ iS @ (^[Y2 : iS]: (?? @ iS @ (^[Y3 : iS]: (?? @ iS @ (^[Y4 : iS]: (?? @ iS @ (^[Y5 : iS]: ((((((cP @ Y2 @ Y1) = X3) & (sK1 @ Y4 @ Y3 @ Y1)) & ((cP @ Y0 @ Y4) = X1)) & (sK1 @ Y0 @ Y5 @ Y2)) & ((cP @ Y5 @ Y3) = X2))))))))))))))) | ($true = (sK1 @ X1 @ X2 @ X3))) )),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.67/1.52 thf(f197,plain,(
% 1.67/1.52 spl0_1 | spl0_2),
% 1.67/1.52 inference(avatar_split_clause,[status(thm)],[f180,f193,f189])).
% 1.67/1.52 thf(f180,plain,(
% 1.67/1.52 ($false = (sK1 @ x @ x @ x)) | ((sK1 @ c0 @ y @ y) = $false)),
% 1.67/1.52 inference(trivial_inequality_removal,[status(thm)],[f175])).
% 1.67/1.52 thf(f175,plain,(
% 1.67/1.52 ($false = (sK1 @ x @ x @ x)) | ($true = $false) | ((sK1 @ c0 @ y @ y) = $false)),
% 1.67/1.52 inference(superposition,[status(thm)],[f14,f170])).
% 1.67/1.52 thf(f14,plain,(
% 1.67/1.52 ($false = (sK1 @ (cP @ x @ c0) @ (cP @ x @ y) @ (cP @ x @ y)))),
% 1.67/1.52 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.67/1.52 % SZS output end Proof for DTF2THF_12262
% 1.67/1.52 % (12478)------------------------------
% 1.67/1.52 % (12478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.52 % (12478)Termination reason: Refutation
% 1.67/1.52
% 1.67/1.52 % (12478)Memory used [KB]: 6396
% 1.67/1.52 % (12478)Time elapsed: 0.106 s
% 1.67/1.52 % (12478)Instructions burned: 237 (million)
% 1.67/1.52 % (12478)------------------------------
% 1.67/1.52 % (12478)------------------------------
% 1.67/1.52 % (12450)Success in time 0.222 s
%------------------------------------------------------------------------------