%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV058^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 09:40:11 AM UTC 2026
% Result : Theorem 0.98s 0.94s
% Output : Refutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 91 ( 8 unt; 0 typ; 6 def)
% Number of atoms : 1059 ( 395 equ; 0 cnn)
% Maximal formula atoms : 5 ( 11 avg)
% Number of connectives : 1398 ( 59 ~; 151 |; 52 &; 895 @)
% ( 6 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 716 ( 716 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 11 con; 0-2 aty)
% ( 151 !!; 3 ??; 0 @@+; 0 @@-)
% Number of variables : 541 ( 494 ^; 44 !; 3 ?; 541 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_16,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_17,type,
sK4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_18,type,
sK5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_19,type,
sK6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_20,type,
sK7: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_22,type,
sK8: $i > $o ).
thf(func_def_25,type,
sK11: $i > $o ).
thf(func_def_26,type,
sK12: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i ).
thf(f404,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f69,f83,f101,f173,f184,f355,f389,f403]) ).
thf(f403,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f402]) ).
thf(f402,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f401]) ).
thf(f401,plain,
( ( $true = $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f400]) ).
thf(f400,plain,
( ( $false
= ( ^ [Y0: $i] : $true
@ sK14 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] : $true ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl0_7
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] : $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f389,plain,
( spl0_3
| spl0_2
| ~ spl0_1
| ~ spl0_19 ),
inference(avatar_split_clause,[status(thm)],[f388,f353,f61,f64,f67]) ).
thf(f67,definition,
( spl0_3
<=> ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f64,definition,
( spl0_2
<=> ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f61,definition,
( spl0_1
<=> ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f353,definition,
( spl0_19
<=> ( $true
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f388,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f387]) ).
thf(f387,plain,
( ( $true = $false )
| ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ~ spl0_1
| ~ spl0_19 ),
inference(forward_demodulation,[status(thm)],[f386,f358]) ).
thf(f358,plain,
( ( $false
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_19 ),
inference(backward_demodulation,[status(thm)],[f62,f356]) ).
thf(f356,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl0_19 ),
inference(equality_proxy_clausification,[status(thm)],[f354]) ).
thf(f354,plain,
( ( $true
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f353]) ).
thf(f62,plain,
( ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f386,plain,
( ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f385]) ).
thf(f385,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& $true ) )
| ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f384]) ).
thf(f384,plain,
( ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f383]) ).
thf(f383,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false )
| ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ~ spl0_19 ),
inference(beta_eta_normalization,[status(thm)],[f366]) ).
thf(f366,plain,
( ( $true
= ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0
@ Y0 ) ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f160,f356]) ).
thf(f160,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) )
| ( $true
= ( X1 @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( X1 @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK6 @ X1 @ Y0 )
=> ( sK5 @ X1 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f155]) ).
thf(f155,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( X1 @ Y0 @ ( sK5 @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK5 @ X1 @ Y1 ) ) ) )
@ ( sK6 @ X1 ) ) )
| ( $true
= ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( X1 @ Y0 @ ( sK5 @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK5 @ X1 @ Y1 ) ) ) ) ) )
| ( $true
= ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f147]) ).
thf(f147,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) )
| ( $true
= ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) )
@ ( sK5 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) )
| ( $true
= ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) )
=> ( X1 @ ( sK2 @ X1 ) @ ( sK4 @ X1 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ Y0 ) )
=> ( X1 @ ( sK2 @ X1 ) @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( X1 @ ( sK2 @ X1 ) @ ( sK3 @ X1 ) )
& ( X1 @ ( sK3 @ X1 ) @ Y0 ) )
=> ( X1 @ ( sK2 @ X1 ) @ Y0 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X1 @ ( sK2 @ X1 ) @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ ( sK2 @ X1 ) @ Y1 ) ) )
@ ( sK3 @ X1 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X1 @ ( sK2 @ X1 ) @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ ( sK2 @ X1 ) @ Y1 ) ) ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( $false
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( $false
= ( ^ [Y0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ?? @ ( ( $i > $o ) > ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $o ) > ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $o ) > ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
& ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X4 @ X3 ) )
=> ( X0 @ X4 @ X2 ) )
& ! [X5: $i > $o,X6: $i > $o] :
( ( X0 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X5 @ X7 )
=> ( X6 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X4: $i > $o] : ( X0 @ X4 @ X4 )
& ! [X3: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X5 @ X3 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X4 @ X3 ) )
& ! [X1: $i > $o,X2: $i > $o] :
( ( X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X4: $i > $o] : ( X0 @ X4 @ X4 )
& ! [X3: $i > $o,X5: $i > $o,X4: $i > $o] :
( ( ( X0 @ X5 @ X3 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X4 @ X3 ) )
& ! [X1: $i > $o,X2: $i > $o] :
( ( X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kj3Ft1QIMf/DTF2THF_11559.p',cTHM122_pme) ).
thf(f355,plain,
( spl0_19
| spl0_3
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f337,f64,f67,f353]) ).
thf(f337,plain,
( ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) ) ),
inference(boolean_simplification,[status(thm)],[f336]) ).
thf(f336,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false )
| ( $true
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f326]) ).
thf(f326,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0
@ Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f262]) ).
thf(f262,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X1 @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) ) )
| ( $true
= ( X1 @ ( sK3 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f160]) ).
thf(f184,plain,
( ~ spl0_1
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[status(thm)],[f183]) ).
thf(f183,plain,
( $false
| ~ spl0_1
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f182]) ).
thf(f182,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f175,f180]) ).
thf(f180,plain,
( ( $false
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f62,f178]) ).
thf(f178,plain,
( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl0_16 ),
inference(equality_proxy_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
( ( $true
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $true
= ( $true
& ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f172,f175]) ).
thf(f172,plain,
( ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f171]) ).
thf(f171,definition,
( spl0_16
<=> ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f175,plain,
( ( $true
= ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f172]) ).
thf(f173,plain,
( spl0_16
| spl0_7
| spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f167,f67,f64,f99,f171]) ).
thf(f167,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] : $true ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f166]) ).
thf(f166,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] : $true ) )
| ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] : $true ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false )
| ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f164]) ).
thf(f164,plain,
( ( $false
= ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] : $true ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false )
| ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f163]) ).
thf(f163,plain,
( ( $false
= ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5
@ ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0 )
=> ( sK5
@ ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0 ) ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false )
| ( $true
= ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f161]) ).
thf(f161,plain,
( ( $true
= ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
& ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) )
| ( $false
= ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5
@ ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0 )
=> ( sK5
@ ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0
@ Y0 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f156,f84]) ).
thf(f84,plain,
( ( ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f101,plain,
( spl0_1
| spl0_7
| spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f94,f67,f64,f99,f61]) ).
thf(f94,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] : $true ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] : $true ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] : $true ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false )
| ( $false
= ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] : $true ) ) )
| ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $false
= ( ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5
@ ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0 )
=> ( sK5
@ ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0 ) ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false )
| ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $false
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5
@ ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0 )
=> ( sK5
@ ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0 ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0
@ Y0 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f39,f84]) ).
thf(f39,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( X1 @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK6 @ X1 @ Y0 )
=> ( sK5 @ X1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( X1 @ ( sK2 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( ^ [Y0: $i > $o] :
( ( X1 @ Y0 @ ( sK5 @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK5 @ X1 @ Y1 ) ) ) )
@ ( sK6 @ X1 ) ) )
| ( $false
= ( X1 @ ( sK2 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( X1 @ Y0 @ ( sK5 @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( sK5 @ X1 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) )
| ( $false
= ( X1 @ ( sK2 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $false
= ( X1 @ ( sK2 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) )
@ ( sK5 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( X1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( X1 @ ( sK2 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f83,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f82]) ).
thf(f82,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $false
= ( ^ [Y0: $i > $o] : $true
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f69,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f58,f67,f64,f61]) ).
thf(f58,plain,
( ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) )
| ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true
= ( ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( Y0 = Y0 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK6
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK4
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] : ( Y2 = Y1 )
@ Y0
@ Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X1 @ ( sK6 @ X1 ) @ ( sK5 @ X1 ) ) )
| ( $false
= ( X1 @ ( sK2 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV058^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:39:30 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SEV058^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.31 % Domain : Set Theory (Relations)
% 0.07/0.31 % Problem : TPS problem THM122
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Bro09]
% 0.07/0.31 % Names : tps_0324 [Bro09]
% 0.07/0.31 % : THM122 [TPS]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : 0.17 v9.1.0, 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.5.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.33 v4.0.0
% 0.07/0.31 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.07/0.31 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 0 ( 0 avg)
% 0.07/0.31 % Number of connectives : 18 ( 0 ~; 0 |; 3 &; 12 @)
% 0.07/0.31 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 11 ( 11 avg)
% 0.07/0.31 % Number of types : 2 ( 0 usr)
% 0.07/0.31 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.07/0.31 % Number of variables : 8 ( 0 ^; 7 !; 1 ?; 8 :)
% 0.07/0.31 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.31 % : Polymorphic definitions expanded.
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(cTHM122_pme,conjecture,
% 0.07/0.31 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.07/0.31 ( ! [Xu: $i > $o,Xv: $i > $o] :
% 0.07/0.31 ( ( R @ Xu @ Xv )
% 0.07/0.31 => ! [Xz: $i] :
% 0.07/0.31 ( ( Xu @ Xz )
% 0.07/0.31 => ( Xv @ Xz ) ) )
% 0.07/0.31 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.07/0.31 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.07/0.31 ( ( ( R @ Xx @ Xy )
% 0.07/0.31 & ( R @ Xy @ Xz ) )
% 0.07/0.31 => ( R @ Xx @ Xz ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.82/0.87 ---- Embedded in THF ---
% 0.82/0.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.82/0.87 %%% Generated on Tue Feb 24 12:39:31 EST 2026
% 0.82/0.87 %%% using '$$dhol' embedding, version 1.3.0.
% 0.82/0.87 %%% Logic specification used:
% 0.82/0.87 %%% thf(spec, logic, $$dhol).
% 0.82/0.87
% 0.82/0.87 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.kj3Ft1QIMf/DTF2DTF11559.p
% See solution above
% 0.82/0.87 ------------------------
% 0.82/0.88 ---- Cleaned THF ---
% 0.82/0.88 thf(cTHM122_pme,conjecture,
% 0.82/0.88 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.82/0.88 ( ! [Xu: $i > $o,Xv: $i > $o] :
% 0.82/0.88 ( ( R @ Xu @ Xv )
% 0.82/0.88 => ! [Xz: $i] :
% 0.82/0.88 ( ( Xu @ Xz )
% 0.82/0.88 => ( Xv @ Xz ) ) )
% 0.82/0.88 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.82/0.88 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.82/0.88 ( ( ( R @ Xx @ Xy )
% 0.82/0.88 & ( R @ Xy @ Xz ) )
% 0.82/0.88 => ( R @ Xx @ Xz ) ) ) ).
% 0.82/0.88 ------------------------
% 0.82/0.89 % (11659)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11559 for (3000ds/2Mi)
% 0.82/0.89 % (11656)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11559 for (3000ds/183Mi)
% 0.82/0.89 % (11658)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_11559 for (3000ds/27Mi)
% 0.82/0.89 % (11661)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_11559 for (3000ds/275Mi)
% 0.82/0.89 % (11662)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11559 for (3000ds/18Mi)
% 0.82/0.89 % (11660)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_11559 for (3000ds/2Mi)
% 0.82/0.89 % (11657)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_11559 for (3000ds/4Mi)
% 0.82/0.89 % (11659)Instruction limit reached!
% 0.82/0.89 % (11659)------------------------------
% 0.82/0.89 % (11659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.82/0.89 % (11659)Termination reason: Unknown
% 0.82/0.89 % (11659)Termination phase: Saturation
% 0.82/0.89
% 0.82/0.89 % (11659)Memory used [KB]: 5500
% 0.82/0.89 % (11660)Instruction limit reached!
% 0.82/0.89 % (11660)------------------------------
% 0.82/0.89 % (11660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.82/0.89 % (11659)Time elapsed: 0.002 s
% 0.82/0.89 % (11659)Instructions burned: 2 (million)
% 0.82/0.89 % (11659)------------------------------
% 0.82/0.89 % (11659)------------------------------
% 0.82/0.89 % (11660)Termination reason: Unknown
% 0.82/0.89 % (11660)Termination phase: Saturation
% 0.82/0.89
% 0.82/0.89 % (11660)Memory used [KB]: 5500
% 0.82/0.89 % (11660)Time elapsed: 0.002 s
% 0.82/0.89 % (11660)Instructions burned: 2 (million)
% 0.82/0.89 % (11660)------------------------------
% 0.82/0.89 % (11660)------------------------------
% 0.82/0.89 % (11657)Instruction limit reached!
% 0.82/0.89 % (11657)------------------------------
% 0.82/0.89 % (11657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.82/0.89 % (11657)Termination reason: Unknown
% 0.82/0.89 % (11657)Termination phase: Saturation
% 0.82/0.89
% 0.82/0.89 % (11657)Memory used [KB]: 5500
% 0.82/0.89 % (11658)Refutation not found, incomplete strategy
% 0.82/0.89 % (11658)------------------------------
% 0.82/0.89 % (11658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.82/0.89 % (11657)Time elapsed: 0.003 s
% 0.82/0.89 % (11657)Instructions burned: 4 (million)
% 0.82/0.89 % (11657)------------------------------
% 0.82/0.89 % (11657)------------------------------
% 0.82/0.89 % (11658)Termination reason: Refutation not found, incomplete strategy
% 0.82/0.89
% 0.82/0.89
% 0.82/0.89 % (11658)Memory used [KB]: 5500
% 0.82/0.89 % (11658)Time elapsed: 0.003 s
% 0.82/0.89 % (11658)Instructions burned: 2 (million)
% 0.82/0.89 % (11658)------------------------------
% 0.82/0.89 % (11658)------------------------------
% 0.82/0.89 % (11662)Instruction limit reached!
% 0.82/0.89 % (11662)------------------------------
% 0.82/0.89 % (11662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.82/0.89 % (11662)Termination reason: Unknown
% 0.82/0.89 % (11662)Termination phase: Saturation
% 0.82/0.89
% 0.82/0.89 % (11662)Memory used [KB]: 5628
% 0.82/0.89 % (11662)Time elapsed: 0.007 s
% 0.82/0.89 % (11662)Instructions burned: 20 (million)
% 0.82/0.89 % (11662)------------------------------
% 0.82/0.89 % (11662)------------------------------
% 0.98/0.90 % (11661)Refutation not found, incomplete strategy
% 0.98/0.90 % (11661)------------------------------
% 0.98/0.90 % (11661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (11661)Termination reason: Refutation not found, incomplete strategy
% 0.98/0.90
% 0.98/0.90
% 0.98/0.90 % (11661)Memory used [KB]: 5628
% 0.98/0.90 % (11661)Time elapsed: 0.009 s
% 0.98/0.90 % (11661)Instructions burned: 25 (million)
% 0.98/0.90 % (11661)------------------------------
% 0.98/0.90 % (11661)------------------------------
% 0.98/0.90 % (11663)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/3Mi)
% 0.98/0.90 % (11664)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_11559 for (2999ds/37Mi)
% 0.98/0.90 % (11665)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_11559 for (2999ds/15Mi)
% 0.98/0.90 % (11663)Instruction limit reached!
% 0.98/0.90 % (11663)------------------------------
% 0.98/0.90 % (11663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (11663)Termination reason: Unknown
% 0.98/0.90 % (11663)Termination phase: Saturation
% 0.98/0.90
% 0.98/0.90 % (11663)Memory used [KB]: 5500
% 0.98/0.90 % (11663)Time elapsed: 0.002 s
% 0.98/0.90 % (11663)Instructions burned: 3 (million)
% 0.98/0.90 % (11663)------------------------------
% 0.98/0.90 % (11663)------------------------------
% 0.98/0.90 % (11666)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_11559 for (2999ds/3Mi)
% 0.98/0.90 % (11666)Instruction limit reached!
% 0.98/0.90 % (11666)------------------------------
% 0.98/0.90 % (11666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (11666)Termination reason: Unknown
% 0.98/0.90 % (11666)Termination phase: Saturation
% 0.98/0.90
% 0.98/0.90 % (11666)Memory used [KB]: 5500
% 0.98/0.90 % (11666)Time elapsed: 0.002 s
% 0.98/0.90 % (11666)Instructions burned: 3 (million)
% 0.98/0.90 % (11666)------------------------------
% 0.98/0.90 % (11666)------------------------------
% 0.98/0.90 % (11667)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_11559 for (2999ds/1041Mi)
% 0.98/0.90 % (11665)Instruction limit reached!
% 0.98/0.90 % (11665)------------------------------
% 0.98/0.90 % (11665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (11665)Termination reason: Unknown
% 0.98/0.91 % (11665)Termination phase: Saturation
% 0.98/0.91
% 0.98/0.91 % (11665)Memory used [KB]: 5628
% 0.98/0.91 % (11665)Time elapsed: 0.006 s
% 0.98/0.91 % (11665)Instructions burned: 15 (million)
% 0.98/0.91 % (11665)------------------------------
% 0.98/0.91 % (11665)------------------------------
% 0.98/0.91 % (11668)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/7Mi)
% 0.98/0.91 % (11669)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/16Mi)
% 0.98/0.91 % (11668)Instruction limit reached!
% 0.98/0.91 % (11668)------------------------------
% 0.98/0.91 % (11668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.91 % (11668)Termination reason: Unknown
% 0.98/0.91 % (11668)Termination phase: Saturation
% 0.98/0.91
% 0.98/0.91 % (11668)Memory used [KB]: 1023
% 0.98/0.91 % (11668)Time elapsed: 0.004 s
% 0.98/0.91 % (11668)Instructions burned: 9 (million)
% 0.98/0.91 % (11668)------------------------------
% 0.98/0.91 % (11668)------------------------------
% 0.98/0.91 % (11664)Instruction limit reached!
% 0.98/0.91 % (11664)------------------------------
% 0.98/0.91 % (11664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.91 % (11664)Termination reason: Unknown
% 0.98/0.91 % (11664)Termination phase: Saturation
% 0.98/0.91
% 0.98/0.91 % (11664)Memory used [KB]: 6012
% 0.98/0.91 % (11664)Time elapsed: 0.012 s
% 0.98/0.91 % (11664)Instructions burned: 40 (million)
% 0.98/0.91 % (11664)------------------------------
% 0.98/0.91 % (11664)------------------------------
% 0.98/0.91 % (11670)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_11559 for (2999ds/3Mi)
% 0.98/0.91 % (11670)Instruction limit reached!
% 0.98/0.91 % (11670)------------------------------
% 0.98/0.91 % (11670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.91 % (11670)Termination reason: Unknown
% 0.98/0.91 % (11670)Termination phase: Saturation
% 0.98/0.91
% 0.98/0.91 % (11670)Memory used [KB]: 5500
% 0.98/0.91 % (11670)Time elapsed: 0.002 s
% 0.98/0.91 % (11670)Instructions burned: 3 (million)
% 0.98/0.91 % (11670)------------------------------
% 0.98/0.91 % (11670)------------------------------
% 0.98/0.91 % (11671)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_11559 for (2999ds/3Mi)
% 0.98/0.91 % (11669)Instruction limit reached!
% 0.98/0.91 % (11669)------------------------------
% 0.98/0.91 % (11669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.91 % (11669)Termination reason: Unknown
% 0.98/0.91 % (11669)Termination phase: Saturation
% 0.98/0.91
% 0.98/0.91 % (11669)Memory used [KB]: 5628
% 0.98/0.91 % (11669)Time elapsed: 0.006 s
% 0.98/0.91 % (11669)Instructions burned: 16 (million)
% 0.98/0.91 % (11669)------------------------------
% 0.98/0.91 % (11669)------------------------------
% 0.98/0.92 % (11671)Instruction limit reached!
% 0.98/0.92 % (11671)------------------------------
% 0.98/0.92 % (11671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.92 % (11671)Termination reason: Unknown
% 0.98/0.92 % (11671)Termination phase: Saturation
% 0.98/0.92
% 0.98/0.92 % (11671)Memory used [KB]: 1023
% 0.98/0.92 % (11671)Time elapsed: 0.002 s
% 0.98/0.92 % (11671)Instructions burned: 3 (million)
% 0.98/0.92 % (11671)------------------------------
% 0.98/0.92 % (11671)------------------------------
% 0.98/0.92 % (11672)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/7Mi)
% 0.98/0.92 % (11673)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/3Mi)
% 0.98/0.92 % (11673)Instruction limit reached!
% 0.98/0.92 % (11673)------------------------------
% 0.98/0.92 % (11673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.92 % (11673)Termination reason: Unknown
% 0.98/0.92 % (11673)Termination phase: Saturation
% 0.98/0.92
% 0.98/0.92 % (11673)Memory used [KB]: 5500
% 0.98/0.92 % (11673)Time elapsed: 0.002 s
% 0.98/0.92 % (11673)Instructions burned: 3 (million)
% 0.98/0.92 % (11673)------------------------------
% 0.98/0.92 % (11673)------------------------------
% 0.98/0.92 % (11674)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/4Mi)
% 0.98/0.92 % (11672)Instruction limit reached!
% 0.98/0.92 % (11672)------------------------------
% 0.98/0.92 % (11672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.92 % (11672)Termination reason: Unknown
% 0.98/0.92 % (11672)Termination phase: Saturation
% 0.98/0.92
% 0.98/0.92 % (11672)Memory used [KB]: 5500
% 0.98/0.92 % (11672)Time elapsed: 0.004 s
% 0.98/0.92 % (11672)Instructions burned: 10 (million)
% 0.98/0.92 % (11672)------------------------------
% 0.98/0.92 % (11672)------------------------------
% 0.98/0.92 % (11674)Instruction limit reached!
% 0.98/0.92 % (11674)------------------------------
% 0.98/0.92 % (11674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.92 % (11674)Termination reason: Unknown
% 0.98/0.92 % (11674)Termination phase: Saturation
% 0.98/0.92
% 0.98/0.92 % (11674)Memory used [KB]: 5500
% 0.98/0.92 % (11674)Time elapsed: 0.003 s
% 0.98/0.92 % (11674)Instructions burned: 6 (million)
% 0.98/0.92 % (11674)------------------------------
% 0.98/0.92 % (11674)------------------------------
% 0.98/0.92 % (11675)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/18Mi)
% 0.98/0.92 % (11676)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/710Mi)
% 0.98/0.93 % (11675)Refutation not found, incomplete strategy
% 0.98/0.93 % (11675)------------------------------
% 0.98/0.93 % (11675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.93 % (11675)Termination reason: Refutation not found, incomplete strategy
% 0.98/0.93
% 0.98/0.93
% 0.98/0.93 % (11675)Memory used [KB]: 5500
% 0.98/0.93 % (11675)Time elapsed: 0.002 s
% 0.98/0.93 % (11675)Instructions burned: 3 (million)
% 0.98/0.93 % (11675)------------------------------
% 0.98/0.93 % (11675)------------------------------
% 0.98/0.93 % (11677)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/6Mi)
% 0.98/0.93 % (11678)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_11559 for (2999ds/902Mi)
% 0.98/0.93 % (11677)Instruction limit reached!
% 0.98/0.93 % (11677)------------------------------
% 0.98/0.93 % (11677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.93 % (11677)Termination reason: Unknown
% 0.98/0.93 % (11677)Termination phase: Saturation
% 0.98/0.93
% 0.98/0.93 % (11677)Memory used [KB]: 5500
% 0.98/0.93 % (11677)Time elapsed: 0.003 s
% 0.98/0.93 % (11677)Instructions burned: 6 (million)
% 0.98/0.93 % (11677)------------------------------
% 0.98/0.93 % (11677)------------------------------
% 0.98/0.93 % (11679)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_11559 for (2999ds/21Mi)
% 0.98/0.93 % (11680)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11559 for (2999ds/5Mi)
% 0.98/0.94 % (11667)First to succeed.
% 0.98/0.94 % (11680)Instruction limit reached!
% 0.98/0.94 % (11680)------------------------------
% 0.98/0.94 % (11680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.94 % (11680)Termination reason: Unknown
% 0.98/0.94 % (11680)Termination phase: Saturation
% 0.98/0.94
% 0.98/0.94 % (11680)Memory used [KB]: 5500
% 0.98/0.94 % (11680)Time elapsed: 0.003 s
% 0.98/0.94 % (11680)Instructions burned: 6 (million)
% 0.98/0.94 % (11680)------------------------------
% 0.98/0.94 % (11680)------------------------------
% 0.98/0.94 % (11656)Instruction limit reached!
% 0.98/0.94 % (11656)------------------------------
% 0.98/0.94 % (11656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.94 % (11656)Termination reason: Unknown
% 0.98/0.94 % (11656)Termination phase: Saturation
% 0.98/0.94
% 0.98/0.94 % (11656)Memory used [KB]: 7419
% 0.98/0.94 % (11656)Time elapsed: 0.050 s
% 0.98/0.94 % (11656)Instructions burned: 186 (million)
% 0.98/0.94 % (11656)------------------------------
% 0.98/0.94 % (11656)------------------------------
% 0.98/0.94 % (11667)Refutation found. Thanks to Tanya!
% 0.98/0.94 % SZS status Theorem for DTF2THF_11559
% 0.98/0.94 % SZS output start Proof for DTF2THF_11559
% 0.98/0.94 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 0.98/0.94 thf(func_def_15, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.98/0.94 thf(func_def_16, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.98/0.94 thf(func_def_17, type, sK4: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.98/0.94 thf(func_def_18, type, sK5: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.98/0.94 thf(func_def_19, type, sK6: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.98/0.94 thf(func_def_20, type, sK7: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.98/0.94 thf(func_def_22, type, sK8: $i > $o).
% 0.98/0.94 thf(func_def_25, type, sK11: $i > $o).
% 0.98/0.94 thf(func_def_26, type, sK12: (($i > $o) > ($i > $o) > $o) > $i).
% 0.98/0.94 thf(f404,plain,(
% 0.98/0.94 $false),
% 0.98/0.94 inference(avatar_sat_refutation,[status(thm)],[f69,f83,f101,f173,f184,f355,f389,f403])).
% 0.98/0.94 thf(f403,plain,(
% 0.98/0.94 ~spl0_7),
% 0.98/0.94 inference(avatar_contradiction_clause,[status(thm)],[f402])).
% 0.98/0.94 thf(f402,plain,(
% 0.98/0.94 $false | ~spl0_7),
% 0.98/0.94 inference(trivial_inequality_removal,[status(thm)],[f401])).
% 0.98/0.94 thf(f401,plain,(
% 0.98/0.94 ($true = $false) | ~spl0_7),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f400])).
% 0.98/0.94 thf(f400,plain,(
% 0.98/0.94 ($false = ((^[Y0 : $i]: ($true)) @ sK14)) | ~spl0_7),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f100])).
% 0.98/0.94 thf(f100,plain,(
% 0.98/0.94 ($false = (!! @ $i @ (^[Y0 : $i]: ($true)))) | ~spl0_7),
% 0.98/0.94 inference(avatar_component_clause,[status(thm)],[f99])).
% 0.98/0.94 thf(f99,definition,(
% 0.98/0.94 spl0_7 <=> ($false = (!! @ $i @ (^[Y0 : $i]: ($true))))),
% 0.98/0.94 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 0.98/0.94 thf(f389,plain,(
% 0.98/0.94 spl0_3 | spl0_2 | ~spl0_1 | ~spl0_19),
% 0.98/0.94 inference(avatar_split_clause,[status(thm)],[f388,f353,f61,f64,f67])).
% 0.98/0.94 thf(f67,definition,(
% 0.98/0.94 spl0_3 <=> ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 0.98/0.94 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 0.98/0.94 thf(f64,definition,(
% 0.98/0.94 spl0_2 <=> ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))))),
% 0.98/0.94 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 0.98/0.94 thf(f61,definition,(
% 0.98/0.94 spl0_1 <=> ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 0.98/0.94 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 0.98/0.94 thf(f353,definition,(
% 0.98/0.94 spl0_19 <=> ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 0.98/0.94 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 0.98/0.94 thf(f388,plain,(
% 0.98/0.94 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (~spl0_1 | ~spl0_19)),
% 0.98/0.94 inference(trivial_inequality_removal,[status(thm)],[f387])).
% 0.98/0.94 thf(f387,plain,(
% 0.98/0.94 ($true = $false) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | (~spl0_1 | ~spl0_19)),
% 0.98/0.94 inference(forward_demodulation,[status(thm)],[f386,f358])).
% 0.98/0.94 thf(f358,plain,(
% 0.98/0.94 ($false = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (~spl0_1 | ~spl0_19)),
% 0.98/0.94 inference(backward_demodulation,[status(thm)],[f62,f356])).
% 0.98/0.94 thf(f356,plain,(
% 0.98/0.94 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl0_19),
% 0.98/0.94 inference(equality_proxy_clausification,[status(thm)],[f354])).
% 0.98/0.94 thf(f354,plain,(
% 0.98/0.94 ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_19),
% 0.98/0.94 inference(avatar_component_clause,[status(thm)],[f353])).
% 0.98/0.94 thf(f62,plain,(
% 0.98/0.94 ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_1),
% 0.98/0.94 inference(avatar_component_clause,[status(thm)],[f61])).
% 0.98/0.94 thf(f386,plain,(
% 0.98/0.94 ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($true = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_19),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f385])).
% 0.98/0.94 thf(f385,plain,(
% 0.98/0.94 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & $true)) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_19),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f384])).
% 0.98/0.94 thf(f384,plain,(
% 0.98/0.94 ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_19),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f383])).
% 0.98/0.94 thf(f383,plain,(
% 0.98/0.94 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ~spl0_19),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f366])).
% 0.98/0.94 thf(f366,plain,(
% 0.98/0.94 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0 @ Y0)))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_19),
% 0.98/0.94 inference(superposition,[status(thm)],[f160,f356])).
% 0.98/0.94 thf(f160,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($true = ((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ (sK4 @ X1)))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))) | ($true = (X1 @ (sK6 @ X1) @ (sK5 @ X1)))) )),
% 0.98/0.94 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 0.98/0.94 thf(f156,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : ((((X1 @ (sK6 @ X1) @ (sK5 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((sK6 @ X1 @ Y0) => (sK5 @ X1 @ Y0))))) = $false) | ($true = ((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ (sK4 @ X1)))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f155])).
% 0.98/0.94 thf(f155,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))) | ($false = ((^[Y0 : $i > $o]: ((X1 @ Y0 @ (sK5 @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK5 @ X1 @ Y1)))))) @ (sK6 @ X1))) | ($true = ((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ (sK4 @ X1))))) )),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f150])).
% 0.98/0.94 thf(f150,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((X1 @ Y0 @ (sK5 @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK5 @ X1 @ Y1)))))))) | ($true = ((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ (sK4 @ X1)))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f147])).
% 0.98/0.94 thf(f147,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))) | ($true = ((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ (sK4 @ X1)))) | ($false = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2)))))))) @ (sK5 @ X1)))) )),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f29])).
% 0.98/0.94 thf(f29,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))) | ($true = ((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ (sK4 @ X1))))) )),
% 0.98/0.94 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 0.98/0.94 thf(f27,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ (sK4 @ X1))) => (X1 @ (sK2 @ X1) @ (sK4 @ X1)))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f26])).
% 0.98/0.94 thf(f26,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))) | ($false = ((^[Y0 : $i > $o]: (((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ Y0)) => (X1 @ (sK2 @ X1) @ Y0))) @ (sK4 @ X1))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false)) )),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f25])).
% 0.98/0.94 thf(f25,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((X1 @ (sK2 @ X1) @ (sK3 @ X1)) & (X1 @ (sK3 @ X1) @ Y0)) => (X1 @ (sK2 @ X1) @ Y0))))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f24])).
% 0.98/0.94 thf(f24,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false) | ($false = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((X1 @ (sK2 @ X1) @ Y0) & (X1 @ Y0 @ Y1)) => (X1 @ (sK2 @ X1) @ Y1))))) @ (sK3 @ X1))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f19])).
% 0.98/0.94 thf(f19,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((X1 @ (sK2 @ X1) @ Y0) & (X1 @ Y0 @ Y1)) => (X1 @ (sK2 @ X1) @ Y1)))))) = $false) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f16])).
% 0.98/0.94 thf(f16,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false) | ($false = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((X1 @ Y0 @ Y1) & (X1 @ Y1 @ Y2)) => (X1 @ Y0 @ Y2))))))) @ (sK2 @ X1)))) )),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f13])).
% 0.98/0.94 thf(f13,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((X1 @ Y0 @ Y1) & (X1 @ Y1 @ Y2)) => (X1 @ Y0 @ Y2))))))))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 0.98/0.94 thf(f12,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((X1 @ Y0 @ Y1) & (X1 @ Y1 @ Y2)) => (X1 @ Y0 @ Y2)))))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 0.98/0.94 thf(f11,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((X1 @ Y0 @ Y1) & (X1 @ Y1 @ Y2)) => (X1 @ Y0 @ Y2))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))))) )),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f10])).
% 0.98/0.94 thf(f10,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = ((^[Y0 : ($i > $o) > ($i > $o) > $o]: (((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3))))))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (Y0 @ Y1 @ Y1))))) @ X1))) )),
% 0.98/0.94 inference(pi_clausification,[status(thm)],[f7])).
% 0.98/0.94 thf(f7,plain,(
% 0.98/0.94 ($false = (?? @ (($i > $o) > ($i > $o) > $o) @ (^[Y0 : ($i > $o) > ($i > $o) > $o]: (((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3))))))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (Y0 @ Y1 @ Y1)))))))),
% 0.98/0.94 inference(not_proxy_clausification,[status(thm)],[f6])).
% 0.98/0.94 thf(f6,plain,(
% 0.98/0.94 ($true = (~ (?? @ (($i > $o) > ($i > $o) > $o) @ (^[Y0 : ($i > $o) > ($i > $o) > $o]: (((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3))))))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (Y0 @ Y1 @ Y1))))))))),
% 0.98/0.94 inference(cnf_transformation,[status(thm)],[f5])).
% 0.98/0.94 thf(f5,plain,(
% 0.98/0.94 ($true = (~ (?? @ (($i > $o) > ($i > $o) > $o) @ (^[Y0 : ($i > $o) > ($i > $o) > $o]: (((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3))))))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (Y0 @ Y1 @ Y1))))))))),
% 0.98/0.94 inference(fool_elimination,[status(thm)],[f4])).
% 0.98/0.94 thf(f4,plain,(
% 0.98/0.94 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o] : (X0 @ X1 @ X1) & ! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (((X0 @ X3 @ X2) & (X0 @ X4 @ X3)) => (X0 @ X4 @ X2)) & ! [X5 : $i > $o,X6 : $i > $o] : ((X0 @ X5 @ X6) => ! [X7 : $i] : ((X5 @ X7) => (X6 @ X7))))),
% 0.98/0.94 inference(rectify,[status(thm)],[f2])).
% 0.98/0.94 thf(f2,negated_conjecture,(
% 0.98/0.94 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X4 : $i > $o] : (X0 @ X4 @ X4) & ! [X3 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (((X0 @ X5 @ X3) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X3)) & ! [X1 : $i > $o,X2 : $i > $o] : ((X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => (X2 @ X3))))),
% 0.98/0.94 inference(negated_conjecture,[status(cth)],[f1])).
% 0.98/0.94 thf(f1,conjecture,(
% 0.98/0.94 ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X4 : $i > $o] : (X0 @ X4 @ X4) & ! [X3 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (((X0 @ X5 @ X3) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X3)) & ! [X1 : $i > $o,X2 : $i > $o] : ((X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => (X2 @ X3))))),
% 0.98/0.94 file('/export/starexec/sandbox2/tmp/tmp.kj3Ft1QIMf/DTF2THF_11559.p',cTHM122_pme)).
% 0.98/0.94 thf(f355,plain,(
% 0.98/0.94 spl0_19 | spl0_3 | spl0_2),
% 0.98/0.94 inference(avatar_split_clause,[status(thm)],[f337,f64,f67,f353])).
% 0.98/0.94 thf(f337,plain,(
% 0.98/0.94 ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))))),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f336])).
% 0.98/0.94 thf(f336,plain,(
% 0.98/0.94 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false) | ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f326])).
% 0.98/0.94 thf(f326,plain,(
% 0.98/0.94 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0 @ Y0))))),
% 0.98/0.94 inference(primitive_instantiation,[status(thm)],[f262])).
% 0.98/0.94 thf(f262,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($true = (X1 @ (sK6 @ X1) @ (sK5 @ X1))) | ($true = (X1 @ (sK3 @ X1) @ (sK4 @ X1))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(binary_proxy_clausification,[status(thm)],[f160])).
% 0.98/0.94 thf(f184,plain,(
% 0.98/0.94 ~spl0_1 | ~spl0_16),
% 0.98/0.94 inference(avatar_contradiction_clause,[status(thm)],[f183])).
% 0.98/0.94 thf(f183,plain,(
% 0.98/0.94 $false | (~spl0_1 | ~spl0_16)),
% 0.98/0.94 inference(trivial_inequality_removal,[status(thm)],[f182])).
% 0.98/0.94 thf(f182,plain,(
% 0.98/0.94 ($true = $false) | (~spl0_1 | ~spl0_16)),
% 0.98/0.94 inference(backward_demodulation,[status(thm)],[f175,f180])).
% 0.98/0.94 thf(f180,plain,(
% 0.98/0.94 ($false = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | (~spl0_1 | ~spl0_16)),
% 0.98/0.94 inference(backward_demodulation,[status(thm)],[f62,f178])).
% 0.98/0.94 thf(f178,plain,(
% 0.98/0.94 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl0_16),
% 0.98/0.94 inference(equality_proxy_clausification,[status(thm)],[f177])).
% 0.98/0.94 thf(f177,plain,(
% 0.98/0.94 ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_16),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f176])).
% 0.98/0.94 thf(f176,plain,(
% 0.98/0.94 ($true = ($true & ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ~spl0_16),
% 0.98/0.94 inference(backward_demodulation,[status(thm)],[f172,f175])).
% 0.98/0.94 thf(f172,plain,(
% 0.98/0.94 ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ~spl0_16),
% 0.98/0.94 inference(avatar_component_clause,[status(thm)],[f171])).
% 0.98/0.94 thf(f171,definition,(
% 0.98/0.94 spl0_16 <=> ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))))),
% 0.98/0.94 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 0.98/0.94 thf(f175,plain,(
% 0.98/0.94 ($true = ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_16),
% 0.98/0.94 inference(binary_proxy_clausification,[status(thm)],[f172])).
% 0.98/0.94 thf(f173,plain,(
% 0.98/0.94 spl0_16 | spl0_7 | spl0_2 | ~spl0_3),
% 0.98/0.94 inference(avatar_split_clause,[status(thm)],[f167,f67,f64,f99,f171])).
% 0.98/0.94 thf(f167,plain,(
% 0.98/0.94 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ($true)))) | ~spl0_3),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f166])).
% 0.98/0.94 thf(f166,plain,(
% 0.98/0.94 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ($true)))) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ~spl0_3),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f165])).
% 0.98/0.94 thf(f165,plain,(
% 0.98/0.94 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: ($true))))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ~spl0_3),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f164])).
% 0.98/0.94 thf(f164,plain,(
% 0.98/0.94 ($false = (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) => (!! @ $i @ (^[Y0 : $i]: ($true))))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ~spl0_3),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f163])).
% 0.98/0.94 thf(f163,plain,(
% 0.98/0.94 ($false = (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) => (!! @ $i @ (^[Y0 : $i]: ((sK5 @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0) => (sK5 @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0)))))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false) | ($true = (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ~spl0_3),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f161])).
% 0.98/0.94 thf(f161,plain,(
% 0.98/0.94 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) & ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))) | ($false = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) => (!! @ $i @ (^[Y0 : $i]: ((sK5 @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0) => (sK5 @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0)))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0 @ Y0)))) | ~spl0_3),
% 0.98/0.94 inference(superposition,[status(thm)],[f156,f84])).
% 0.98/0.94 thf(f84,plain,(
% 0.98/0.94 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl0_3),
% 0.98/0.94 inference(equality_proxy_clausification,[status(thm)],[f68])).
% 0.98/0.94 thf(f68,plain,(
% 0.98/0.94 ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_3),
% 0.98/0.94 inference(avatar_component_clause,[status(thm)],[f67])).
% 0.98/0.94 thf(f101,plain,(
% 0.98/0.94 spl0_1 | spl0_7 | spl0_2 | ~spl0_3),
% 0.98/0.94 inference(avatar_split_clause,[status(thm)],[f94,f67,f64,f99,f61])).
% 0.98/0.94 thf(f94,plain,(
% 0.98/0.94 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ($true)))) | ~spl0_3),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f93])).
% 0.98/0.94 thf(f93,plain,(
% 0.98/0.94 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = ($true => (!! @ $i @ (^[Y0 : $i]: ($true))))) | ~spl0_3),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f92])).
% 0.98/0.94 thf(f92,plain,(
% 0.98/0.94 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) => (!! @ $i @ (^[Y0 : $i]: ($true))))) | ~spl0_3),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f91])).
% 0.98/0.94 thf(f91,plain,(
% 0.98/0.94 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false) | ($false = (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) => (!! @ $i @ (^[Y0 : $i]: ($true))))) | ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_3),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f90])).
% 0.98/0.94 thf(f90,plain,(
% 0.98/0.94 ($false = (((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) => (!! @ $i @ (^[Y0 : $i]: ((sK5 @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0) => (sK5 @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0)))))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false) | ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl0_3),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f88])).
% 0.98/0.94 thf(f88,plain,(
% 0.98/0.94 ($false = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) => (!! @ $i @ (^[Y0 : $i]: ((sK5 @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0) => (sK5 @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0)))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0 @ Y0)))) | ~spl0_3),
% 0.98/0.94 inference(superposition,[status(thm)],[f39,f84])).
% 0.98/0.94 thf(f39,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : ((((X1 @ (sK6 @ X1) @ (sK5 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((sK6 @ X1 @ Y0) => (sK5 @ X1 @ Y0))))) = $false) | ($false = (X1 @ (sK2 @ X1) @ (sK4 @ X1))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f38])).
% 0.98/0.94 thf(f38,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = ((^[Y0 : $i > $o]: ((X1 @ Y0 @ (sK5 @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK5 @ X1 @ Y1)))))) @ (sK6 @ X1))) | ($false = (X1 @ (sK2 @ X1) @ (sK4 @ X1))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f35])).
% 0.98/0.94 thf(f35,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((X1 @ Y0 @ (sK5 @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK5 @ X1 @ Y1)))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))) | ($false = (X1 @ (sK2 @ X1) @ (sK4 @ X1)))) )),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f30])).
% 0.98/0.94 thf(f30,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($false = (X1 @ (sK2 @ X1) @ (sK4 @ X1))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0)))) | ($false = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2)))))))) @ (sK5 @ X1)))) )),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f28])).
% 0.98/0.94 thf(f28,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((X1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2))))))))) = $false) | ($false = (X1 @ (sK2 @ X1) @ (sK4 @ X1))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 0.98/0.94 thf(f83,plain,(
% 0.98/0.94 ~spl0_2),
% 0.98/0.94 inference(avatar_contradiction_clause,[status(thm)],[f82])).
% 0.98/0.94 thf(f82,plain,(
% 0.98/0.94 $false | ~spl0_2),
% 0.98/0.94 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 0.98/0.94 thf(f81,plain,(
% 0.98/0.94 ($true = $false) | ~spl0_2),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f80])).
% 0.98/0.94 thf(f80,plain,(
% 0.98/0.94 ($false = ((^[Y0 : $i > $o]: ($true)) @ sK8)) | ~spl0_2),
% 0.98/0.94 inference(sigma_clausification,[status(thm)],[f65])).
% 0.98/0.94 thf(f65,plain,(
% 0.98/0.94 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ~spl0_2),
% 0.98/0.94 inference(avatar_component_clause,[status(thm)],[f64])).
% 0.98/0.94 thf(f69,plain,(
% 0.98/0.94 spl0_1 | spl0_2 | spl0_3),
% 0.98/0.94 inference(avatar_split_clause,[status(thm)],[f58,f67,f64,f61])).
% 0.98/0.94 thf(f58,plain,(
% 0.98/0.94 ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))) | ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))),
% 0.98/0.94 inference(boolean_simplification,[status(thm)],[f57])).
% 0.98/0.94 thf(f57,plain,(
% 0.98/0.94 ($true = ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (Y0 = Y0))) = $false)),
% 0.98/0.94 inference(beta_eta_normalization,[status(thm)],[f43])).
% 0.98/0.94 thf(f43,plain,(
% 0.98/0.94 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (Y2 = Y1)))) @ Y0 @ Y0))))),
% 0.98/0.94 inference(primitive_instantiation,[status(thm)],[f41])).
% 0.98/0.94 thf(f41,plain,(
% 0.98/0.94 ( ! [X1 : ($i > $o) > ($i > $o) > $o] : (($true = (X1 @ (sK6 @ X1) @ (sK5 @ X1))) | ($false = (X1 @ (sK2 @ X1) @ (sK4 @ X1))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (X1 @ Y0 @ Y0))))) )),
% 0.98/0.94 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 0.98/0.94 % SZS output end Proof for DTF2THF_11559
% 0.98/0.94 % (11667)------------------------------
% 0.98/0.94 % (11667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.94 % (11667)Termination reason: Refutation
% 0.98/0.94
% 0.98/0.94 % (11667)Memory used [KB]: 5884
% 0.98/0.94 % (11667)Time elapsed: 0.035 s
% 0.98/0.94 % (11667)Instructions burned: 100 (million)
% 0.98/0.94 % (11667)------------------------------
% 0.98/0.94 % (11667)------------------------------
% 0.98/0.94 % (11655)Success in time 0.065 s
%------------------------------------------------------------------------------