%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV223^5 : 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 : n014.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 09:40:36 AM UTC 2026
% Result : Theorem 1.39s 1.25s
% Output : Refutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 144 ( 9 unt; 0 typ; 12 def)
% Number of atoms : 1133 ( 399 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1430 ( 160 ~; 260 |; 176 &; 702 @)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 19 con; 0-2 aty)
% ( 0 !!; 120 ??; 0 @@+; 0 @@-)
% Number of variables : 307 ( 202 ^; 90 !; 15 ?; 307 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
f: b > a ).
thf(func_def_3,type,
w: ( b > $o ) > $o ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a ).
thf(func_def_18,type,
sK3: a > $o ).
thf(func_def_19,type,
sK4: b ).
thf(func_def_20,type,
sK5: b > $o ).
thf(func_def_21,type,
sK6: b > $o ).
thf(func_def_22,type,
sK7: b > $o ).
thf(func_def_23,type,
sK8: b > $o ).
thf(func_def_24,type,
sK9: a > b ).
thf(func_def_25,type,
sK10: a > b ).
thf(func_def_26,type,
sK11: a ).
thf(func_def_27,type,
sK12: b ).
thf(func_def_28,type,
sK13: a > b ).
thf(func_def_29,type,
sK14: a > b ).
thf(f362,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f67,f72,f81,f86,f91,f92,f97,f102,f107,f114,f121,f161,f298,f316,f359]) ).
thf(f359,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f358]) ).
thf(f358,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f348]) ).
thf(f348,plain,
( ( sK2 != sK2 )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f347,f96]) ).
thf(f96,plain,
( ( ( sK3 @ sK2 )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f94,definition,
( spl0_8
<=> ( ( sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f347,plain,
( ! [X0: a] :
( ( $false
= ( sK3 @ X0 ) )
| ( sK2 != X0 ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12 ),
inference(duplicate_literal_removal,[status(thm)],[f346]) ).
thf(f346,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( $false
= ( sK3 @ X0 ) )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f337,f252]) ).
thf(f252,plain,
( ! [X1: a] :
( ( ( f @ ( sK13 @ X1 ) )
= X1 )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f250]) ).
thf(f250,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $false )
| ( ( ( f @ ( sK13 @ X1 ) )
= X1 )
= $true ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f249]) ).
thf(f249,plain,
( ! [X1: a] :
( ( $true
= ( ( sK8 @ ( sK13 @ X1 ) )
& ( ( f @ ( sK13 @ X1 ) )
= X1 ) ) )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f248]) ).
thf(f248,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $false )
| ( ( ^ [Y0: b] :
( ( sK8 @ Y0 )
& ( ( f @ Y0 )
= X1 ) )
@ ( sK13 @ X1 ) )
= $true ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f247]) ).
thf(f247,plain,
( ! [X1: a] :
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( sK8 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f245]) ).
thf(f245,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( ?? @ b
@ ^ [Y0: b] :
( ( sK8 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f243]) ).
thf(f243,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK8 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(argument_congruence,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK8 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= sK3 )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f69,definition,
( spl0_3
<=> ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK8 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f337,plain,
( ! [X0: a] :
( ( ( f @ ( sK13 @ X0 ) )
!= sK2 )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f334]) ).
thf(f334,plain,
( ! [X0: a] :
( ( ( f @ ( sK13 @ X0 ) )
!= sK2 )
| ( $false = $true )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f323,f251]) ).
thf(f251,plain,
( ! [X1: a] :
( ( ( sK8 @ ( sK13 @ X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f249]) ).
thf(f323,plain,
( ! [X0: b] :
( ( $false
= ( sK8 @ X0 ) )
| ( ( f @ X0 )
!= sK2 ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f321]) ).
thf(f321,plain,
( ! [X0: b] :
( ( $false
= ( sK8 @ X0 ) )
| ( ( f @ X0 )
!= sK2 )
| ( $false = $true ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f113,f62]) ).
thf(f62,plain,
( ( ( w @ sK8 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl0_1
<=> ( ( w @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f113,plain,
( ! [X1: b,X4: b > $o] :
( ( $false
= ( w @ X4 ) )
| ( ( f @ X1 )
!= sK2 )
| ( $false
= ( X4 @ X1 ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f112]) ).
thf(f112,definition,
( spl0_12
<=> ! [X4: b > $o,X1: b] :
( ( ( f @ X1 )
!= sK2 )
| ( $false
= ( w @ X4 ) )
| ( $false
= ( X4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f316,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f315]) ).
thf(f315,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f309]) ).
thf(f309,plain,
( ( $false = $true )
| ( sK2 != sK2 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f96,f305]) ).
thf(f305,plain,
( ! [X0: a] :
( ( $false
= ( sK3 @ X0 ) )
| ( sK2 != X0 ) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12 ),
inference(duplicate_literal_removal,[status(thm)],[f304]) ).
thf(f304,plain,
( ! [X0: a] :
( ( sK2 != X0 )
| ( $false
= ( sK3 @ X0 ) )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f303,f273]) ).
thf(f273,plain,
( ! [X1: a] :
( ( ( f @ ( sK14 @ X1 ) )
= X1 )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f271]) ).
thf(f271,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $false )
| ( ( ( f @ ( sK14 @ X1 ) )
= X1 )
= $true ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f270]) ).
thf(f270,plain,
( ! [X1: a] :
( ( ( ( sK6 @ ( sK14 @ X1 ) )
& ( ( f @ ( sK14 @ X1 ) )
= X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f269]) ).
thf(f269,plain,
( ! [X1: a] :
( ( ( ^ [Y0: b] :
( ( sK6 @ Y0 )
& ( ( f @ Y0 )
= X1 ) )
@ ( sK14 @ X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f268]) ).
thf(f268,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $false )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( sK6 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) )
= $true ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f266]) ).
thf(f266,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( ?? @ b
@ ^ [Y0: b] :
( ( sK6 @ Y0 )
& ( ( f @ Y0 )
= X1 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f264]) ).
thf(f264,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ X1 ) )
| ~ spl0_6 ),
inference(argument_congruence,[status(thm)],[f85]) ).
thf(f85,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl0_6
<=> ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f303,plain,
( ! [X0: a] :
( ( ( f @ ( sK14 @ X0 ) )
!= sK2 )
| ( $false
= ( sK3 @ X0 ) ) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f300]) ).
thf(f300,plain,
( ! [X0: a] :
( ( ( f @ ( sK14 @ X0 ) )
!= sK2 )
| ( $false
= ( sK3 @ X0 ) )
| ( $false = $true ) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f272,f125]) ).
thf(f125,plain,
( ! [X0: b] :
( ( $false
= ( sK6 @ X0 ) )
| ( ( f @ X0 )
!= sK2 ) )
| ~ spl0_5
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ! [X0: b] :
( ( $false = $true )
| ( $false
= ( sK6 @ X0 ) )
| ( ( f @ X0 )
!= sK2 ) )
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f80,f113]) ).
thf(f80,plain,
( ( $true
= ( w @ sK6 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl0_5
<=> ( $true
= ( w @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f272,plain,
( ! [X1: a] :
( ( ( sK6 @ ( sK14 @ X1 ) )
= $true )
| ( ( sK3 @ X1 )
= $false ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f270]) ).
thf(f298,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f297]) ).
thf(f297,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(subsumption_resolution,[status(thm)],[f293,f66]) ).
thf(f66,plain,
( ( ( f @ sK4 )
= sK2 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl0_2
<=> ( ( f @ sK4 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f293,plain,
( ( ( f @ sK4 )
!= sK2 )
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f291]) ).
thf(f291,plain,
( ( ( f @ sK4 )
!= sK2 )
| ( $false = $true )
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f287,f101]) ).
thf(f101,plain,
( ( ( sK5 @ sK4 )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl0_9
<=> ( ( sK5 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f287,plain,
( ! [X0: b] :
( ( ( sK5 @ X0 )
= $false )
| ( ( f @ X0 )
!= sK2 ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f285]) ).
thf(f285,plain,
( ! [X0: b] :
( ( $false = $true )
| ( ( sK5 @ X0 )
= $false )
| ( ( f @ X0 )
!= sK2 ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f113,f106]) ).
thf(f106,plain,
( ( ( w @ sK5 )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f104,definition,
( spl0_10
<=> ( ( w @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f161,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f155,f112,f88,f74,f64]) ).
thf(f74,definition,
( spl0_4
<=> ( ( sK7 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f88,definition,
( spl0_7
<=> ( ( w @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f155,plain,
( ( ( f @ sK4 )
!= sK2 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
( ( ( f @ sK4 )
!= sK2 )
| ( $false = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f151,f76]) ).
thf(f76,plain,
( ( ( sK7 @ sK4 )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f151,plain,
( ! [X0: b] :
( ( ( sK7 @ X0 )
= $false )
| ( ( f @ X0 )
!= sK2 ) )
| ~ spl0_7
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
( ! [X0: b] :
( ( ( sK7 @ X0 )
= $false )
| ( $false = $true )
| ( ( f @ X0 )
!= sK2 ) )
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f90,f113]) ).
thf(f90,plain,
( ( ( w @ sK7 )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f121,plain,
( spl0_12
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f120,f109,f112]) ).
thf(f109,definition,
( spl0_11
<=> ! [X2: a > $o,X3: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X2 )
| ( ( X2 @ sK2 )
= $false )
| ( $false
= ( w @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f120,plain,
( ! [X0: b > $o,X1: b] :
( ( ( w @ X0 )
= $false )
| ( ( X0 @ X1 )
= $false )
| ( ( f @ X1 )
!= sK2 ) )
| ~ spl0_11 ),
inference(equality_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ! [X0: b > $o,X1: b] :
( ( $false
= ( ( f @ X1 )
= sK2 ) )
| ( ( X0 @ X1 )
= $false )
| ( ( w @ X0 )
= $false ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
( ! [X0: b > $o,X1: b] :
( ( ( ( X0 @ X1 )
& ( ( f @ X1 )
= sK2 ) )
= $false )
| ( ( w @ X0 )
= $false ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f117]) ).
thf(f117,plain,
( ! [X0: b > $o,X1: b] :
( ( ( w @ X0 )
= $false )
| ( ( ^ [Y0: b] :
( ( X0 @ Y0 )
& ( ( f @ Y0 )
= sK2 ) )
@ X1 )
= $false ) )
| ~ spl0_11 ),
inference(pi_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
( ! [X0: b > $o] :
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( X0 @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) ) )
| ( ( w @ X0 )
= $false ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f115]) ).
thf(f115,plain,
( ! [X0: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X0 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK2 )
= $false )
| ( ( w @ X0 )
= $false ) )
| ~ spl0_11 ),
inference(equality_resolution,[status(thm)],[f110]) ).
thf(f110,plain,
( ! [X2: a > $o,X3: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X2 )
| ( ( X2 @ sK2 )
= $false )
| ( $false
= ( w @ X3 ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f109]) ).
thf(f114,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f25,f112,f109]) ).
thf(f25,plain,
! [X2: a > $o,X3: b > $o,X1: b,X4: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= X2 )
| ( $false
= ( w @ X3 ) )
| ( ( f @ X1 )
!= sK2 )
| ( $false
= ( X4 @ X1 ) )
| ( $false
= ( w @ X4 ) )
| ( ( X2 @ sK2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: a > $o,X3: b > $o,X1: b,X4: b > $o] :
( ( $false
= ( w @ X3 ) )
| ( ( X2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $false )
| ( ( X2 @ sK2 )
= $false )
| ( ( f @ X1 )
!= sK2 )
| ( $false
= ( X4 @ X1 ) )
| ( $false
= ( w @ X4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: a > $o,X3: b > $o,X1: b,X4: b > $o] :
( ( $false
= ( ( f @ X1 )
= sK2 ) )
| ( $false
= ( X4 @ X1 ) )
| ( $false
= ( w @ X3 ) )
| ( ( X2 @ sK2 )
= $false )
| ( $false
= ( w @ X4 ) )
| ( ( X2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: a > $o,X3: b > $o,X1: b,X4: b > $o] :
( ( ( ( w @ X4 )
& ( X4 @ X1 ) )
= $false )
| ( $false
= ( ( f @ X1 )
= sK2 ) )
| ( $false
= ( w @ X3 ) )
| ( ( X2 @ sK2 )
= $false )
| ( ( X2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: a > $o,X3: b > $o,X1: b,X4: b > $o] :
( ( ( ( X2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ X3 ) )
= $false )
| ( ( ( w @ X4 )
& ( X4 @ X1 ) )
= $false )
| ( ( X2 @ sK2 )
= $false )
| ( $false
= ( ( f @ X1 )
= sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: a > $o,X3: b > $o,X1: b,X4: b > $o] :
( ( $false
= ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ X1 ) )
@ X4 ) )
| ( ( ( X2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ X3 ) )
= $false )
| ( ( X2 @ sK2 )
= $false )
| ( $false
= ( ( f @ X1 )
= sK2 ) ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: a > $o,X3: b > $o,X1: b] :
( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ X1 ) ) )
= $false )
| ( ( ( X2
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X3 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ X3 ) )
= $false )
| ( $false
= ( ( f @ X1 )
= sK2 ) )
| ( ( X2 @ sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: a > $o,X3: b > $o,X1: b] :
( ( ( X2 @ sK2 )
= $false )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ X1 ) ) )
= $false )
| ( $false
= ( ( f @ X1 )
= sK2 ) )
| ( ( ^ [Y0: b > $o] :
( ( X2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) )
@ X3 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: a > $o,X1: b] :
( ( ( X2 @ sK2 )
= $false )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( X2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) )
= $false )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ X1 ) ) )
= $false )
| ( $false
= ( ( f @ X1 )
= sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: a > $o,X1: b] :
( ( $false
= ( ( X2 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( X2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) ) ) )
| ( $false
= ( ( f @ X1 )
= sK2 ) )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: a > $o,X1: b] :
( ( $false
= ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ X1 ) ) )
& ( ( f @ X1 )
= sK2 ) ) )
| ( $false
= ( ( X2 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( X2
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: a > $o,X1: b] :
( ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) )
& ( w @ Y1 ) ) ) )
@ X2 )
= $false )
| ( $false
= ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ X1 ) ) )
& ( ( f @ X1 )
= sK2 ) ) ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: b] :
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) )
& ( w @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ X1 ) ) )
& ( ( f @ X1 )
= sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: b] :
( ( $false
= ( ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y1 @ Y0 ) ) )
& ( ( f @ Y0 )
= sK2 ) )
@ X1 ) )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) )
& ( w @ Y1 ) ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y1 @ Y0 ) ) )
& ( ( f @ Y0 )
= sK2 ) ) )
= $false )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) )
& ( w @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y1 @ Y0 ) ) )
& ( ( f @ Y0 )
= sK2 ) ) )
!= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) )
& ( w @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y2 @ Y1 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) )
& ( w @ Y2 ) ) ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) )
& ( w @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y2 @ Y1 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) )
& ( w @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y2 @ Y1 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y1
= ( ^ [Y3: a] :
( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( f @ Y4 )
= Y3 ) ) ) ) )
& ( w @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ?? @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( w @ Y2 )
& ( Y2 @ Y1 ) ) )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a] :
? [X1: a > $o] :
( ? [X2: b > $o] :
( ( w @ X2 )
& ( X1
= ( ^ [X3: a] :
? [X4: b] :
( ( ( f @ X4 )
= X3 )
& ( X2 @ X4 ) ) ) ) )
& ( X1 @ X0 ) ) )
!= ( ^ [X5: a] :
? [X6: b] :
( ( ( f @ X6 )
= X5 )
& ? [X7: b > $o] :
( ( X7 @ X6 )
& ( w @ X7 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X3: a] :
? [X2: a > $o] :
( ? [X1: b > $o] :
( ( w @ X1 )
& ( X2
= ( ^ [X0: a] :
? [X4: b] :
( ( ( f @ X4 )
= X0 )
& ( X1 @ X4 ) ) ) ) )
& ( X2 @ X3 ) ) )
!= ( ^ [X0: a] :
? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ? [X2: b > $o] :
( ( X2 @ X1 )
& ( w @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X3: a] :
? [X2: a > $o] :
( ? [X1: b > $o] :
( ( w @ X1 )
& ( X2
= ( ^ [X0: a] :
? [X4: b] :
( ( ( f @ X4 )
= X0 )
& ( X1 @ X4 ) ) ) ) )
& ( X2 @ X3 ) ) )
= ( ^ [X0: a] :
? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ? [X2: b > $o] :
( ( X2 @ X1 )
& ( w @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Yzj215njTM/DTF2THF_5708.p',cX5204_pme) ).
thf(f107,plain,
( spl0_8
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f37,f104,f94]) ).
thf(f37,plain,
( ( ( w @ sK5 )
= $true )
| ( ( sK3 @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( ( ( w @ sK5 )
& ( sK5 @ sK4 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) )
@ sK5 )
= $true )
| ( ( sK3 @ sK2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) ) )
= $true )
| ( ( sK3 @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) ) )
& ( ( f @ sK4 )
= sK2 ) )
= $true )
| ( ( sK3 @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ( sK3 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) ) )
= $true )
| ( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) ) )
& ( ( f @ sK4 )
= sK2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y1 @ Y0 ) ) )
& ( ( f @ Y0 )
= sK2 ) )
@ sK4 )
= $true )
| ( ( ( sK3 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y1 @ Y0 ) ) )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true )
| ( ( ( sK3 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) )
& ( w @ Y1 ) ) ) )
@ sK3 )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y1 @ Y0 ) ) )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
& ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0
= ( ^ [Y2: a] :
( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( f @ Y3 )
= Y2 ) ) ) ) )
& ( w @ Y1 ) ) ) ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ?? @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( w @ Y1 )
& ( Y1 @ Y0 ) ) )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f102,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f36,f94,f99]) ).
thf(f36,plain,
( ( ( sK5 @ sK4 )
= $true )
| ( ( sK3 @ sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f97,plain,
( spl0_8
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f64,f94]) ).
thf(f38,plain,
( ( ( f @ sK4 )
= sK2 )
| ( ( sK3 @ sK2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( sK3 @ sK2 )
= $true )
| ( ( ( f @ sK4 )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f92,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f49,f88,f83]) ).
thf(f49,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( ( w @ sK7 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( w @ sK7 )
= $true )
| ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( w @ sK7 )
= $true )
| ( $true
= ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ sK6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ( w @ sK7 )
& ( sK7 @ sK4 ) )
= $true )
| ( $true
= ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ sK6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) )
@ sK7 )
= $true )
| ( $true
= ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ sK6 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) ) )
= $true )
| ( $true
= ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ sK6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) ) )
= $true )
| ( ( ^ [Y0: b > $o] :
( ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) )
@ sK6 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) )
= $true )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( w @ Y0 )
& ( Y0 @ sK4 ) ) )
& ( ( f @ sK4 )
= sK2 ) )
= $true )
| ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f91,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f47,f78,f88]) ).
thf(f47,plain,
( ( ( w @ sK7 )
= $true )
| ( $true
= ( w @ sK6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f86,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f52,f83,f74]) ).
thf(f52,plain,
( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
| ( ( sK7 @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ( ( sK7 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( sK7 @ sK4 )
= $true )
| ( $true
= ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK6 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ sK6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f81,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f50,f78,f74]) ).
thf(f50,plain,
( ( $true
= ( w @ sK6 ) )
| ( ( sK7 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f72,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f58,f69,f64]) ).
thf(f58,plain,
( ( ( f @ sK4 )
= sK2 )
| ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK8 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= sK3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK8 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ( ( f @ sK4 )
= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK8 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ sK8 ) )
= $true )
| ( ( f @ sK4 )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( ( f @ sK4 )
= sK2 )
= $true )
| ( ( ( sK3
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK8 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( w @ sK8 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( ^ [Y0: b > $o] :
( ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) )
@ sK8 )
= $true )
| ( ( ( f @ sK4 )
= sK2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ?? @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( sK3
= ( ^ [Y1: a] :
( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( f @ Y2 )
= Y1 ) ) ) ) )
& ( w @ Y0 ) ) )
= $true )
| ( ( ( f @ sK4 )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f67,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f56,f64,f60]) ).
thf(f56,plain,
( ( ( w @ sK8 )
= $true )
| ( ( f @ sK4 )
= sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV223^5 : TPTP v9.2.1. Released v4.0.0.
% 0.10/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n014.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:42:12 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.24/0.46 ---- Original DTF file ---
% 0.24/0.46 thf(spec,logic,$$dhol).
% 0.24/0.46 %------------------------------------------------------------------------------
% 0.24/0.46 % File : SEV223^5 : TPTP v9.2.1. Released v4.0.0.
% 0.24/0.46 % Domain : Set Theory (Sets of sets)
% 0.24/0.46 % Problem : TPS problem X5204
% 0.24/0.46 % Version : Especial.
% 0.24/0.46 % English :
% 0.24/0.46
% 0.24/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.24/0.46 % Source : [Bro09]
% 0.24/0.46 % Names : tps_0535 [Bro09]
% 0.24/0.46 % : X5204 [TPS]
% 0.24/0.46
% 0.24/0.46 % Status : Theorem
% 0.24/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.24/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 4 typ; 0 def)
% 0.24/0.46 % Number of atoms : 6 ( 4 equ; 0 cnn)
% 0.24/0.46 % Maximal formula atoms : 1 ( 6 avg)
% 0.24/0.46 % Number of connectives : 12 ( 0 ~; 0 |; 5 &; 7 @)
% 0.24/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.24/0.46 % Maximal formula depth : 1 ( 1 avg)
% 0.24/0.46 % Number of types : 3 ( 2 usr)
% 0.24/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.24/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.24/0.46 % Number of variables : 8 ( 3 ^; 0 !; 5 ?; 8 :)
% 0.24/0.46 % SPC : TH0_THM_EQU_NAR
% 0.24/0.46
% 0.24/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.24/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.24/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.24/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.24/0.46 % : Polymorphic definitions expanded.
% 0.24/0.46 %------------------------------------------------------------------------------
% 0.24/0.46 thf(b_type,type,
% 0.24/0.46 b: $tType ).
% 0.24/0.46
% 0.24/0.46 thf(a_type,type,
% 0.24/0.46 a: $tType ).
% 0.24/0.46
% 0.24/0.46 thf(f,type,
% 0.24/0.46 f: b > a ).
% 0.24/0.46
% 0.24/0.46 thf(w,type,
% 0.24/0.46 w: ( b > $o ) > $o ).
% 0.24/0.46
% 0.24/0.46 thf(cX5204_pme,conjecture,
% 0.24/0.46 ( ( ^ [Xz: a] :
% 0.24/0.46 ? [Xt: b] :
% 0.24/0.46 ( ? [S: b > $o] :
% 0.24/0.46 ( ( w @ S )
% 0.24/0.46 & ( S @ Xt ) )
% 0.24/0.46 & ( Xz
% 0.24/0.46 = ( f @ Xt ) ) ) )
% 0.24/0.46 = ( ^ [Xx: a] :
% 0.24/0.46 ? [S: a > $o] :
% 0.24/0.46 ( ? [Xt: b > $o] :
% 0.24/0.46 ( ( w @ Xt )
% 0.24/0.46 & ( S
% 0.24/0.46 = ( ^ [Xz: a] :
% 0.24/0.46 ? [Xt0: b] :
% 0.24/0.46 ( ( Xt @ Xt0 )
% 0.24/0.46 & ( Xz
% 0.24/0.46 = ( f @ Xt0 ) ) ) ) ) )
% 0.24/0.46 & ( S @ Xx ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 %------------------------------------------------------------------------------
% 0.24/0.46 ------------------------
% 1.39/1.20 ---- Embedded in THF ---
% 1.39/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.20 %%% Generated on Tue Feb 24 12:42:13 EST 2026
% 1.39/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.20 %%% Logic specification used:
% 1.39/1.20 %%% thf(spec, logic, $$dhol).
% 1.39/1.20
% 1.39/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Yzj215njTM/DTF2DTF5708.p
% See solution above
% 1.39/1.20 ------------------------
% 1.39/1.21 ---- Cleaned THF ---
% 1.39/1.21 thf(b_type,type,
% 1.39/1.21 b: $tType ).
% 1.39/1.21
% 1.39/1.21 thf(a_type,type,
% 1.39/1.21 a: $tType ).
% 1.39/1.21
% 1.39/1.21 thf(f,type,
% 1.39/1.21 f: b > a ).
% 1.39/1.21
% 1.39/1.21 thf(w,type,
% 1.39/1.21 w: ( b > $o ) > $o ).
% 1.39/1.21
% 1.39/1.21 thf(cX5204_pme,conjecture,
% 1.39/1.21 ( ( ^ [Xz: a] :
% 1.39/1.21 ? [Xt: b] :
% 1.39/1.21 ( ? [S: b > $o] :
% 1.39/1.21 ( ( w @ S )
% 1.39/1.21 & ( S @ Xt ) )
% 1.39/1.21 & ( Xz
% 1.39/1.21 = ( f @ Xt ) ) ) )
% 1.39/1.21 = ( ^ [Xx: a] :
% 1.39/1.21 ? [S: a > $o] :
% 1.39/1.21 ( ? [Xt: b > $o] :
% 1.39/1.21 ( ( w @ Xt )
% 1.39/1.21 & ( S
% 1.39/1.21 = ( ^ [Xz: a] :
% 1.39/1.21 ? [Xt0: b] :
% 1.39/1.21 ( ( Xt @ Xt0 )
% 1.39/1.21 & ( Xz
% 1.39/1.21 = ( f @ Xt0 ) ) ) ) ) )
% 1.39/1.21 & ( S @ Xx ) ) ) ) ).
% 1.39/1.21 ------------------------
% 1.39/1.23 % (5806)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_5708 for (3000ds/4Mi)
% 1.39/1.23 % (5809)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_5708 for (3000ds/2Mi)
% 1.39/1.23 % (5811)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5708 for (3000ds/18Mi)
% 1.39/1.23 % (5810)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_5708 for (3000ds/275Mi)
% 1.39/1.23 % (5808)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5708 for (3000ds/2Mi)
% 1.39/1.23 % (5807)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_5708 for (3000ds/27Mi)
% 1.39/1.23 % (5805)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5708 for (3000ds/183Mi)
% 1.39/1.23 % (5808)Instruction limit reached!
% 1.39/1.23 % (5808)------------------------------
% 1.39/1.23 % (5808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.23 % (5808)Termination reason: Unknown
% 1.39/1.23 % (5806)Instruction limit reached!
% 1.39/1.23 % (5806)------------------------------
% 1.39/1.23 % (5806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.23 % (5806)Termination reason: Unknown
% 1.39/1.23 % (5808)Termination phase: Saturation
% 1.39/1.23
% 1.39/1.23 % (5806)Termination phase: Saturation
% 1.39/1.23
% 1.39/1.23 % (5806)Memory used [KB]: 5500
% 1.39/1.23 % (5808)Memory used [KB]: 5373
% 1.39/1.23 % (5806)Time elapsed: 0.003 s
% 1.39/1.23 % (5808)Time elapsed: 0.003 s
% 1.39/1.23 % (5806)Instructions burned: 5 (million)
% 1.39/1.23 % (5808)Instructions burned: 2 (million)
% 1.39/1.23 % (5806)------------------------------
% 1.39/1.23 % (5806)------------------------------
% 1.39/1.23 % (5808)------------------------------
% 1.39/1.23 % (5808)------------------------------
% 1.39/1.23 % (5809)Instruction limit reached!
% 1.39/1.23 % (5809)------------------------------
% 1.39/1.23 % (5809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.23 % (5809)Termination reason: Unknown
% 1.39/1.23 % (5809)Termination phase: Saturation
% 1.39/1.23
% 1.39/1.23 % (5809)Memory used [KB]: 5500
% 1.39/1.23 % (5809)Time elapsed: 0.003 s
% 1.39/1.23 % (5809)Instructions burned: 2 (million)
% 1.39/1.23 % (5809)------------------------------
% 1.39/1.23 % (5809)------------------------------
% 1.39/1.24 % (5811)Instruction limit reached!
% 1.39/1.24 % (5811)------------------------------
% 1.39/1.24 % (5811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.24 % (5811)Termination reason: Unknown
% 1.39/1.24 % (5811)Termination phase: Saturation
% 1.39/1.24
% 1.39/1.24 % (5811)Memory used [KB]: 5628
% 1.39/1.24 % (5811)Time elapsed: 0.012 s
% 1.39/1.24 % (5811)Instructions burned: 18 (million)
% 1.39/1.24 % (5811)------------------------------
% 1.39/1.24 % (5811)------------------------------
% 1.39/1.24 % (5814)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_5708 for (2999ds/15Mi)
% 1.39/1.25 % (5807)Instruction limit reached!
% 1.39/1.25 % (5807)------------------------------
% 1.39/1.25 % (5807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.25 % (5807)Termination reason: Unknown
% 1.39/1.25 % (5807)Termination phase: Saturation
% 1.39/1.25
% 1.39/1.25 % (5807)Memory used [KB]: 5628
% 1.39/1.25 % (5807)Time elapsed: 0.017 s
% 1.39/1.25 % (5807)Instructions burned: 27 (million)
% 1.39/1.25 % (5807)------------------------------
% 1.39/1.25 % (5807)------------------------------
% 1.39/1.25 % (5810)First to succeed.
% 1.39/1.25 % (5812)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5708 for (2999ds/3Mi)
% 1.39/1.25 % (5813)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_5708 for (2999ds/37Mi)
% 1.39/1.25 % (5812)Refutation not found, incomplete strategy
% 1.39/1.25 % (5812)------------------------------
% 1.39/1.25 % (5812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.25 % (5812)Termination reason: Refutation not found, incomplete strategy
% 1.39/1.25
% 1.39/1.25
% 1.39/1.25 % (5812)Memory used [KB]: 5500
% 1.39/1.25 % (5812)Time elapsed: 0.002 s
% 1.39/1.25 % (5812)Instructions burned: 1 (million)
% 1.39/1.25 % (5812)------------------------------
% 1.39/1.25 % (5812)------------------------------
% 1.39/1.25 % (5814)Instruction limit reached!
% 1.39/1.25 % (5814)------------------------------
% 1.39/1.25 % (5814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.25 % (5814)Termination reason: Unknown
% 1.39/1.25 % (5814)Termination phase: Saturation
% 1.39/1.25
% 1.39/1.25 % (5814)Memory used [KB]: 5756
% 1.39/1.25 % (5814)Time elapsed: 0.007 s
% 1.39/1.25 % (5814)Instructions burned: 16 (million)
% 1.39/1.25 % (5814)------------------------------
% 1.39/1.25 % (5814)------------------------------
% 1.39/1.25 % (5810)Refutation found. Thanks to Tanya!
% 1.39/1.25 % SZS status Theorem for DTF2THF_5708
% 1.39/1.25 % SZS output start Proof for DTF2THF_5708
% 1.39/1.25 thf(type_def_5, type, b: $tType).
% 1.39/1.25 thf(type_def_6, type, a: $tType).
% 1.39/1.25 thf(func_def_0, type, b: $tType).
% 1.39/1.25 thf(func_def_1, type, a: $tType).
% 1.39/1.25 thf(func_def_2, type, f: b > a).
% 1.39/1.25 thf(func_def_3, type, w: (b > $o) > $o).
% 1.39/1.25 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.39/1.25 thf(func_def_17, type, sK2: a).
% 1.39/1.25 thf(func_def_18, type, sK3: a > $o).
% 1.39/1.25 thf(func_def_19, type, sK4: b).
% 1.39/1.25 thf(func_def_20, type, sK5: b > $o).
% 1.39/1.25 thf(func_def_21, type, sK6: b > $o).
% 1.39/1.25 thf(func_def_22, type, sK7: b > $o).
% 1.39/1.25 thf(func_def_23, type, sK8: b > $o).
% 1.39/1.25 thf(func_def_24, type, sK9: a > b).
% 1.39/1.25 thf(func_def_25, type, sK10: a > b).
% 1.39/1.25 thf(func_def_26, type, sK11: a).
% 1.39/1.25 thf(func_def_27, type, sK12: b).
% 1.39/1.25 thf(func_def_28, type, sK13: a > b).
% 1.39/1.25 thf(func_def_29, type, sK14: a > b).
% 1.39/1.25 thf(f362,plain,(
% 1.39/1.25 $false),
% 1.39/1.25 inference(avatar_sat_refutation,[status(thm)],[f67,f72,f81,f86,f91,f92,f97,f102,f107,f114,f121,f161,f298,f316,f359])).
% 1.39/1.25 thf(f359,plain,(
% 1.39/1.25 ~spl0_1 | ~spl0_3 | ~spl0_8 | ~spl0_12),
% 1.39/1.25 inference(avatar_contradiction_clause,[status(thm)],[f358])).
% 1.39/1.25 thf(f358,plain,(
% 1.39/1.25 $false | (~spl0_1 | ~spl0_3 | ~spl0_8 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f348])).
% 1.39/1.25 thf(f348,plain,(
% 1.39/1.25 (sK2 != sK2) | ($false = $true) | (~spl0_1 | ~spl0_3 | ~spl0_8 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f347,f96])).
% 1.39/1.25 thf(f96,plain,(
% 1.39/1.25 ((sK3 @ sK2) = $true) | ~spl0_8),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.39/1.25 thf(f94,definition,(
% 1.39/1.25 spl0_8 <=> ((sK3 @ sK2) = $true)),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.39/1.25 thf(f347,plain,(
% 1.39/1.25 ( ! [X0 : a] : (($false = (sK3 @ X0)) | (sK2 != X0)) ) | (~spl0_1 | ~spl0_3 | ~spl0_12)),
% 1.39/1.25 inference(duplicate_literal_removal,[status(thm)],[f346])).
% 1.39/1.25 thf(f346,plain,(
% 1.39/1.25 ( ! [X0 : a] : ((sK2 != X0) | ($false = (sK3 @ X0)) | ($false = (sK3 @ X0))) ) | (~spl0_1 | ~spl0_3 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f337,f252])).
% 1.39/1.25 thf(f252,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((f @ (sK13 @ X1)) = X1) | ((sK3 @ X1) = $false)) ) | ~spl0_3),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f250])).
% 1.39/1.25 thf(f250,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK3 @ X1) = $false) | (((f @ (sK13 @ X1)) = X1) = $true)) ) | ~spl0_3),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f249])).
% 1.39/1.25 thf(f249,plain,(
% 1.39/1.25 ( ! [X1 : a] : (($true = ((sK8 @ (sK13 @ X1)) & ((f @ (sK13 @ X1)) = X1))) | ((sK3 @ X1) = $false)) ) | ~spl0_3),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f248])).
% 1.39/1.25 thf(f248,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK3 @ X1) = $false) | (((^[Y0 : b]: ((sK8 @ Y0) & ((f @ Y0) = X1))) @ (sK13 @ X1)) = $true)) ) | ~spl0_3),
% 1.39/1.25 inference(sigma_clausification,[status(thm)],[f247])).
% 1.39/1.25 thf(f247,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((?? @ b @ (^[Y0 : b]: ((sK8 @ Y0) & ((f @ Y0) = X1)))) = $true) | ((sK3 @ X1) = $false)) ) | ~spl0_3),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f245])).
% 1.39/1.25 thf(f245,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK3 @ X1) = (?? @ b @ (^[Y0 : b]: ((sK8 @ Y0) & ((f @ Y0) = X1)))))) ) | ~spl0_3),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f243])).
% 1.39/1.25 thf(f243,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK3 @ X1) = ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK8 @ Y1) & ((f @ Y1) = Y0))))) @ X1))) ) | ~spl0_3),
% 1.39/1.25 inference(argument_congruence,[status(thm)],[f71])).
% 1.39/1.25 thf(f71,plain,(
% 1.39/1.25 ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK8 @ Y1) & ((f @ Y1) = Y0))))) = sK3) | ~spl0_3),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.39/1.25 thf(f69,definition,(
% 1.39/1.25 spl0_3 <=> ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK8 @ Y1) & ((f @ Y1) = Y0))))) = sK3)),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.39/1.25 thf(f337,plain,(
% 1.39/1.25 ( ! [X0 : a] : (((f @ (sK13 @ X0)) != sK2) | ($false = (sK3 @ X0))) ) | (~spl0_1 | ~spl0_3 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f334])).
% 1.39/1.25 thf(f334,plain,(
% 1.39/1.25 ( ! [X0 : a] : (((f @ (sK13 @ X0)) != sK2) | ($false = $true) | ($false = (sK3 @ X0))) ) | (~spl0_1 | ~spl0_3 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f323,f251])).
% 1.39/1.25 thf(f251,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK8 @ (sK13 @ X1)) = $true) | ((sK3 @ X1) = $false)) ) | ~spl0_3),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f249])).
% 1.39/1.25 thf(f323,plain,(
% 1.39/1.25 ( ! [X0 : b] : (($false = (sK8 @ X0)) | ((f @ X0) != sK2)) ) | (~spl0_1 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f321])).
% 1.39/1.25 thf(f321,plain,(
% 1.39/1.25 ( ! [X0 : b] : (($false = (sK8 @ X0)) | ((f @ X0) != sK2) | ($false = $true)) ) | (~spl0_1 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f113,f62])).
% 1.39/1.25 thf(f62,plain,(
% 1.39/1.25 ((w @ sK8) = $true) | ~spl0_1),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.39/1.25 thf(f60,definition,(
% 1.39/1.25 spl0_1 <=> ((w @ sK8) = $true)),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.39/1.25 thf(f113,plain,(
% 1.39/1.25 ( ! [X1 : b,X4 : b > $o] : (($false = (w @ X4)) | ((f @ X1) != sK2) | ($false = (X4 @ X1))) ) | ~spl0_12),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f112])).
% 1.39/1.25 thf(f112,definition,(
% 1.39/1.25 spl0_12 <=> ! [X4 : b > $o,X1 : b] : (((f @ X1) != sK2) | ($false = (w @ X4)) | ($false = (X4 @ X1)))),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.39/1.25 thf(f316,plain,(
% 1.39/1.25 ~spl0_5 | ~spl0_6 | ~spl0_8 | ~spl0_12),
% 1.39/1.25 inference(avatar_contradiction_clause,[status(thm)],[f315])).
% 1.39/1.25 thf(f315,plain,(
% 1.39/1.25 $false | (~spl0_5 | ~spl0_6 | ~spl0_8 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f309])).
% 1.39/1.25 thf(f309,plain,(
% 1.39/1.25 ($false = $true) | (sK2 != sK2) | (~spl0_5 | ~spl0_6 | ~spl0_8 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f96,f305])).
% 1.39/1.25 thf(f305,plain,(
% 1.39/1.25 ( ! [X0 : a] : (($false = (sK3 @ X0)) | (sK2 != X0)) ) | (~spl0_5 | ~spl0_6 | ~spl0_12)),
% 1.39/1.25 inference(duplicate_literal_removal,[status(thm)],[f304])).
% 1.39/1.25 thf(f304,plain,(
% 1.39/1.25 ( ! [X0 : a] : ((sK2 != X0) | ($false = (sK3 @ X0)) | ($false = (sK3 @ X0))) ) | (~spl0_5 | ~spl0_6 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f303,f273])).
% 1.39/1.25 thf(f273,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((f @ (sK14 @ X1)) = X1) | ((sK3 @ X1) = $false)) ) | ~spl0_6),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f271])).
% 1.39/1.25 thf(f271,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK3 @ X1) = $false) | (((f @ (sK14 @ X1)) = X1) = $true)) ) | ~spl0_6),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f270])).
% 1.39/1.25 thf(f270,plain,(
% 1.39/1.25 ( ! [X1 : a] : ((((sK6 @ (sK14 @ X1)) & ((f @ (sK14 @ X1)) = X1)) = $true) | ((sK3 @ X1) = $false)) ) | ~spl0_6),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f269])).
% 1.39/1.25 thf(f269,plain,(
% 1.39/1.25 ( ! [X1 : a] : ((((^[Y0 : b]: ((sK6 @ Y0) & ((f @ Y0) = X1))) @ (sK14 @ X1)) = $true) | ((sK3 @ X1) = $false)) ) | ~spl0_6),
% 1.39/1.25 inference(sigma_clausification,[status(thm)],[f268])).
% 1.39/1.25 thf(f268,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK3 @ X1) = $false) | ((?? @ b @ (^[Y0 : b]: ((sK6 @ Y0) & ((f @ Y0) = X1)))) = $true)) ) | ~spl0_6),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f266])).
% 1.39/1.25 thf(f266,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK3 @ X1) = (?? @ b @ (^[Y0 : b]: ((sK6 @ Y0) & ((f @ Y0) = X1)))))) ) | ~spl0_6),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f264])).
% 1.39/1.25 thf(f264,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK3 @ X1) = ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0))))) @ X1))) ) | ~spl0_6),
% 1.39/1.25 inference(argument_congruence,[status(thm)],[f85])).
% 1.39/1.25 thf(f85,plain,(
% 1.39/1.25 (sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) | ~spl0_6),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.39/1.25 thf(f83,definition,(
% 1.39/1.25 spl0_6 <=> (sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0))))))),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.39/1.25 thf(f303,plain,(
% 1.39/1.25 ( ! [X0 : a] : (((f @ (sK14 @ X0)) != sK2) | ($false = (sK3 @ X0))) ) | (~spl0_5 | ~spl0_6 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f300])).
% 1.39/1.25 thf(f300,plain,(
% 1.39/1.25 ( ! [X0 : a] : (((f @ (sK14 @ X0)) != sK2) | ($false = (sK3 @ X0)) | ($false = $true)) ) | (~spl0_5 | ~spl0_6 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f272,f125])).
% 1.39/1.25 thf(f125,plain,(
% 1.39/1.25 ( ! [X0 : b] : (($false = (sK6 @ X0)) | ((f @ X0) != sK2)) ) | (~spl0_5 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.39/1.25 thf(f122,plain,(
% 1.39/1.25 ( ! [X0 : b] : (($false = $true) | ($false = (sK6 @ X0)) | ((f @ X0) != sK2)) ) | (~spl0_5 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f80,f113])).
% 1.39/1.25 thf(f80,plain,(
% 1.39/1.25 ($true = (w @ sK6)) | ~spl0_5),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.39/1.25 thf(f78,definition,(
% 1.39/1.25 spl0_5 <=> ($true = (w @ sK6))),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.39/1.25 thf(f272,plain,(
% 1.39/1.25 ( ! [X1 : a] : (((sK6 @ (sK14 @ X1)) = $true) | ((sK3 @ X1) = $false)) ) | ~spl0_6),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f270])).
% 1.39/1.25 thf(f298,plain,(
% 1.39/1.25 ~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_12),
% 1.39/1.25 inference(avatar_contradiction_clause,[status(thm)],[f297])).
% 1.39/1.25 thf(f297,plain,(
% 1.39/1.25 $false | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_12)),
% 1.39/1.25 inference(subsumption_resolution,[status(thm)],[f293,f66])).
% 1.39/1.25 thf(f66,plain,(
% 1.39/1.25 ((f @ sK4) = sK2) | ~spl0_2),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.39/1.25 thf(f64,definition,(
% 1.39/1.25 spl0_2 <=> ((f @ sK4) = sK2)),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.39/1.25 thf(f293,plain,(
% 1.39/1.25 ((f @ sK4) != sK2) | (~spl0_9 | ~spl0_10 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f291])).
% 1.39/1.25 thf(f291,plain,(
% 1.39/1.25 ((f @ sK4) != sK2) | ($false = $true) | (~spl0_9 | ~spl0_10 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f287,f101])).
% 1.39/1.25 thf(f101,plain,(
% 1.39/1.25 ((sK5 @ sK4) = $true) | ~spl0_9),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.39/1.25 thf(f99,definition,(
% 1.39/1.25 spl0_9 <=> ((sK5 @ sK4) = $true)),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.39/1.25 thf(f287,plain,(
% 1.39/1.25 ( ! [X0 : b] : (((sK5 @ X0) = $false) | ((f @ X0) != sK2)) ) | (~spl0_10 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f285])).
% 1.39/1.25 thf(f285,plain,(
% 1.39/1.25 ( ! [X0 : b] : (($false = $true) | ((sK5 @ X0) = $false) | ((f @ X0) != sK2)) ) | (~spl0_10 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f113,f106])).
% 1.39/1.25 thf(f106,plain,(
% 1.39/1.25 ((w @ sK5) = $true) | ~spl0_10),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.39/1.25 thf(f104,definition,(
% 1.39/1.25 spl0_10 <=> ((w @ sK5) = $true)),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.39/1.25 thf(f161,plain,(
% 1.39/1.25 ~spl0_2 | ~spl0_4 | ~spl0_7 | ~spl0_12),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f155,f112,f88,f74,f64])).
% 1.39/1.25 thf(f74,definition,(
% 1.39/1.25 spl0_4 <=> ((sK7 @ sK4) = $true)),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.39/1.25 thf(f88,definition,(
% 1.39/1.25 spl0_7 <=> ((w @ sK7) = $true)),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.39/1.25 thf(f155,plain,(
% 1.39/1.25 ((f @ sK4) != sK2) | (~spl0_4 | ~spl0_7 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.39/1.25 thf(f152,plain,(
% 1.39/1.25 ((f @ sK4) != sK2) | ($false = $true) | (~spl0_4 | ~spl0_7 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f151,f76])).
% 1.39/1.25 thf(f76,plain,(
% 1.39/1.25 ((sK7 @ sK4) = $true) | ~spl0_4),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.39/1.25 thf(f151,plain,(
% 1.39/1.25 ( ! [X0 : b] : (((sK7 @ X0) = $false) | ((f @ X0) != sK2)) ) | (~spl0_7 | ~spl0_12)),
% 1.39/1.25 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.39/1.25 thf(f148,plain,(
% 1.39/1.25 ( ! [X0 : b] : (((sK7 @ X0) = $false) | ($false = $true) | ((f @ X0) != sK2)) ) | (~spl0_7 | ~spl0_12)),
% 1.39/1.25 inference(superposition,[status(thm)],[f90,f113])).
% 1.39/1.25 thf(f90,plain,(
% 1.39/1.25 ((w @ sK7) = $true) | ~spl0_7),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.39/1.25 thf(f121,plain,(
% 1.39/1.25 spl0_12 | ~spl0_11),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f120,f109,f112])).
% 1.39/1.25 thf(f109,definition,(
% 1.39/1.25 spl0_11 <=> ! [X2 : a > $o,X3 : b > $o] : (((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0))))) != X2) | ((X2 @ sK2) = $false) | ($false = (w @ X3)))),
% 1.39/1.25 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.39/1.25 thf(f120,plain,(
% 1.39/1.25 ( ! [X0 : b > $o,X1 : b] : (((w @ X0) = $false) | ((X0 @ X1) = $false) | ((f @ X1) != sK2)) ) | ~spl0_11),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f119])).
% 1.39/1.25 thf(f119,plain,(
% 1.39/1.25 ( ! [X0 : b > $o,X1 : b] : (($false = ((f @ X1) = sK2)) | ((X0 @ X1) = $false) | ((w @ X0) = $false)) ) | ~spl0_11),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.39/1.25 thf(f118,plain,(
% 1.39/1.25 ( ! [X0 : b > $o,X1 : b] : ((((X0 @ X1) & ((f @ X1) = sK2)) = $false) | ((w @ X0) = $false)) ) | ~spl0_11),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f117])).
% 1.39/1.25 thf(f117,plain,(
% 1.39/1.25 ( ! [X0 : b > $o,X1 : b] : (((w @ X0) = $false) | (((^[Y0 : b]: ((X0 @ Y0) & ((f @ Y0) = sK2))) @ X1) = $false)) ) | ~spl0_11),
% 1.39/1.25 inference(pi_clausification,[status(thm)],[f116])).
% 1.39/1.25 thf(f116,plain,(
% 1.39/1.25 ( ! [X0 : b > $o] : (($false = (?? @ b @ (^[Y0 : b]: ((X0 @ Y0) & ((f @ Y0) = sK2))))) | ((w @ X0) = $false)) ) | ~spl0_11),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f115])).
% 1.39/1.25 thf(f115,plain,(
% 1.39/1.25 ( ! [X0 : b > $o] : ((((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X0 @ Y1) & ((f @ Y1) = Y0))))) @ sK2) = $false) | ((w @ X0) = $false)) ) | ~spl0_11),
% 1.39/1.25 inference(equality_resolution,[status(thm)],[f110])).
% 1.39/1.25 thf(f110,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o] : (((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0))))) != X2) | ((X2 @ sK2) = $false) | ($false = (w @ X3))) ) | ~spl0_11),
% 1.39/1.25 inference(avatar_component_clause,[status(thm)],[f109])).
% 1.39/1.25 thf(f114,plain,(
% 1.39/1.25 spl0_11 | spl0_12),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f25,f112,f109])).
% 1.39/1.25 thf(f25,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o,X1 : b,X4 : b > $o] : (((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0))))) != X2) | ($false = (w @ X3)) | ((f @ X1) != sK2) | ($false = (X4 @ X1)) | ($false = (w @ X4)) | ((X2 @ sK2) = $false)) )),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.39/1.25 thf(f24,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o,X1 : b,X4 : b > $o] : (($false = (w @ X3)) | ((X2 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0)))))) = $false) | ((X2 @ sK2) = $false) | ((f @ X1) != sK2) | ($false = (X4 @ X1)) | ($false = (w @ X4))) )),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 1.39/1.25 thf(f23,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o,X1 : b,X4 : b > $o] : (($false = ((f @ X1) = sK2)) | ($false = (X4 @ X1)) | ($false = (w @ X3)) | ((X2 @ sK2) = $false) | ($false = (w @ X4)) | ((X2 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0)))))) = $false)) )),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.39/1.25 thf(f22,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o,X1 : b,X4 : b > $o] : ((((w @ X4) & (X4 @ X1)) = $false) | ($false = ((f @ X1) = sK2)) | ($false = (w @ X3)) | ((X2 @ sK2) = $false) | ((X2 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0)))))) = $false)) )),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.39/1.25 thf(f21,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o,X1 : b,X4 : b > $o] : ((((X2 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ X3)) = $false) | (((w @ X4) & (X4 @ X1)) = $false) | ((X2 @ sK2) = $false) | ($false = ((f @ X1) = sK2))) )),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.39/1.25 thf(f20,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o,X1 : b,X4 : b > $o] : (($false = ((^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ X1))) @ X4)) | (((X2 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ X3)) = $false) | ((X2 @ sK2) = $false) | ($false = ((f @ X1) = sK2))) )),
% 1.39/1.25 inference(pi_clausification,[status(thm)],[f19])).
% 1.39/1.25 thf(f19,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o,X1 : b] : (((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ X1)))) = $false) | (((X2 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X3 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ X3)) = $false) | ($false = ((f @ X1) = sK2)) | ((X2 @ sK2) = $false)) )),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.39/1.25 thf(f18,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X3 : b > $o,X1 : b] : (((X2 @ sK2) = $false) | ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ X1)))) = $false) | ($false = ((f @ X1) = sK2)) | (((^[Y0 : b > $o]: ((X2 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0))) @ X3) = $false)) )),
% 1.39/1.25 inference(pi_clausification,[status(thm)],[f17])).
% 1.39/1.25 thf(f17,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X1 : b] : (((X2 @ sK2) = $false) | ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((X2 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0)))) = $false) | ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ X1)))) = $false) | ($false = ((f @ X1) = sK2))) )),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.39/1.25 thf(f16,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X1 : b] : (($false = ((X2 @ sK2) & (?? @ (b > $o) @ (^[Y0 : b > $o]: ((X2 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0)))))) | ($false = ((f @ X1) = sK2)) | ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ X1)))) = $false)) )),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.39/1.25 thf(f15,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X1 : b] : (($false = ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ X1)))) & ((f @ X1) = sK2))) | ($false = ((X2 @ sK2) & (?? @ (b > $o) @ (^[Y0 : b > $o]: ((X2 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0))))))) )),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.39/1.25 thf(f14,plain,(
% 1.39/1.25 ( ! [X2 : a > $o,X1 : b] : ((((^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 = (^[Y2 : a]: (?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((f @ Y3) = Y2)))))) & (w @ Y1)))))) @ X2) = $false) | ($false = ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ X1)))) & ((f @ X1) = sK2)))) )),
% 1.39/1.25 inference(pi_clausification,[status(thm)],[f13])).
% 1.39/1.25 thf(f13,plain,(
% 1.39/1.25 ( ! [X1 : b] : (((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 = (^[Y2 : a]: (?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((f @ Y3) = Y2)))))) & (w @ Y1))))))) = $false) | ($false = ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ X1)))) & ((f @ X1) = sK2)))) )),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.39/1.25 thf(f12,plain,(
% 1.39/1.25 ( ! [X1 : b] : (($false = ((^[Y0 : b]: ((?? @ (b > $o) @ (^[Y1 : b > $o]: ((w @ Y1) & (Y1 @ Y0)))) & ((f @ Y0) = sK2))) @ X1)) | ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 = (^[Y2 : a]: (?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((f @ Y3) = Y2)))))) & (w @ Y1))))))) = $false)) )),
% 1.39/1.25 inference(pi_clausification,[status(thm)],[f11])).
% 1.39/1.25 thf(f11,plain,(
% 1.39/1.25 ((?? @ b @ (^[Y0 : b]: ((?? @ (b > $o) @ (^[Y1 : b > $o]: ((w @ Y1) & (Y1 @ Y0)))) & ((f @ Y0) = sK2)))) = $false) | ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 = (^[Y2 : a]: (?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((f @ Y3) = Y2)))))) & (w @ Y1))))))) = $false)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.39/1.25 thf(f9,plain,(
% 1.39/1.25 ((?? @ b @ (^[Y0 : b]: ((?? @ (b > $o) @ (^[Y1 : b > $o]: ((w @ Y1) & (Y1 @ Y0)))) & ((f @ Y0) = sK2)))) != (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 = (^[Y2 : a]: (?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((f @ Y3) = Y2)))))) & (w @ Y1))))))))),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.39/1.25 thf(f8,plain,(
% 1.39/1.25 (((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((?? @ (b > $o) @ (^[Y2 : b > $o]: ((w @ Y2) & (Y2 @ Y1)))) & ((f @ Y1) = Y0))))) @ sK2) != ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ (b > $o) @ (^[Y2 : b > $o]: ((Y1 = (^[Y3 : a]: (?? @ b @ (^[Y4 : b]: ((Y2 @ Y4) & ((f @ Y4) = Y3)))))) & (w @ Y2)))))))) @ sK2))),
% 1.39/1.25 inference(negative_extensionality,[status(thm)],[f7])).
% 1.39/1.25 thf(f7,plain,(
% 1.39/1.25 ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ (b > $o) @ (^[Y2 : b > $o]: ((Y1 = (^[Y3 : a]: (?? @ b @ (^[Y4 : b]: ((Y2 @ Y4) & ((f @ Y4) = Y3)))))) & (w @ Y2)))))))) != (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((?? @ (b > $o) @ (^[Y2 : b > $o]: ((w @ Y2) & (Y2 @ Y1)))) & ((f @ Y1) = Y0))))))),
% 1.39/1.25 inference(cnf_transformation,[status(thm)],[f6])).
% 1.39/1.25 thf(f6,plain,(
% 1.39/1.25 ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ (b > $o) @ (^[Y2 : b > $o]: ((Y1 = (^[Y3 : a]: (?? @ b @ (^[Y4 : b]: ((Y2 @ Y4) & ((f @ Y4) = Y3)))))) & (w @ Y2)))))))) != (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((?? @ (b > $o) @ (^[Y2 : b > $o]: ((w @ Y2) & (Y2 @ Y1)))) & ((f @ Y1) = Y0))))))),
% 1.39/1.25 inference(flattening,[status(thm)],[f5])).
% 1.39/1.25 thf(f5,plain,(
% 1.39/1.25 ~((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (?? @ (b > $o) @ (^[Y2 : b > $o]: ((Y1 = (^[Y3 : a]: (?? @ b @ (^[Y4 : b]: ((Y2 @ Y4) & ((f @ Y4) = Y3)))))) & (w @ Y2)))))))) = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((?? @ (b > $o) @ (^[Y2 : b > $o]: ((w @ Y2) & (Y2 @ Y1)))) & ((f @ Y1) = Y0))))))),
% 1.39/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.39/1.25 thf(f4,plain,(
% 1.39/1.25 ~((^[X0 : a] : (? [X1 : a > $o] : (? [X2 : b > $o] : ((w @ X2) & (X1 = (^[X3 : a] : (? [X4 : b] : (((f @ X4) = X3) & (X2 @ X4)))))) & (X1 @ X0)))) = (^[X5 : a] : (? [X6 : b] : (((f @ X6) = X5) & ? [X7 : b > $o] : ((X7 @ X6) & (w @ X7))))))),
% 1.39/1.25 inference(rectify,[status(thm)],[f2])).
% 1.39/1.25 thf(f2,negated_conjecture,(
% 1.39/1.25 ~((^[X3 : a] : (? [X2 : a > $o] : (? [X1 : b > $o] : ((w @ X1) & (X2 = (^[X0 : a] : (? [X4 : b] : (((f @ X4) = X0) & (X1 @ X4)))))) & (X2 @ X3)))) = (^[X0 : a] : (? [X1 : b] : (((f @ X1) = X0) & ? [X2 : b > $o] : ((X2 @ X1) & (w @ X2))))))),
% 1.39/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.39/1.25 thf(f1,conjecture,(
% 1.39/1.25 ((^[X3 : a] : (? [X2 : a > $o] : (? [X1 : b > $o] : ((w @ X1) & (X2 = (^[X0 : a] : (? [X4 : b] : (((f @ X4) = X0) & (X1 @ X4)))))) & (X2 @ X3)))) = (^[X0 : a] : (? [X1 : b] : (((f @ X1) = X0) & ? [X2 : b > $o] : ((X2 @ X1) & (w @ X2))))))),
% 1.39/1.25 file('/export/starexec/sandbox2/tmp/tmp.Yzj215njTM/DTF2THF_5708.p',cX5204_pme)).
% 1.39/1.25 thf(f107,plain,(
% 1.39/1.25 spl0_8 | spl0_10),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f37,f104,f94])).
% 1.39/1.25 thf(f37,plain,(
% 1.39/1.25 ((w @ sK5) = $true) | ((sK3 @ sK2) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.39/1.25 thf(f35,plain,(
% 1.39/1.25 ((sK3 @ sK2) = $true) | (((w @ sK5) & (sK5 @ sK4)) = $true)),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.39/1.25 thf(f34,plain,(
% 1.39/1.25 (((^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4))) @ sK5) = $true) | ((sK3 @ sK2) = $true)),
% 1.39/1.25 inference(sigma_clausification,[status(thm)],[f33])).
% 1.39/1.25 thf(f33,plain,(
% 1.39/1.25 ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4)))) = $true) | ((sK3 @ sK2) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.39/1.25 thf(f31,plain,(
% 1.39/1.25 (((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4)))) & ((f @ sK4) = sK2)) = $true) | ((sK3 @ sK2) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.39/1.25 thf(f29,plain,(
% 1.39/1.25 (((sK3 @ sK2) & (?? @ (b > $o) @ (^[Y0 : b > $o]: ((sK3 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0))))) = $true) | (((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4)))) & ((f @ sK4) = sK2)) = $true)),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.39/1.25 thf(f28,plain,(
% 1.39/1.25 (((^[Y0 : b]: ((?? @ (b > $o) @ (^[Y1 : b > $o]: ((w @ Y1) & (Y1 @ Y0)))) & ((f @ Y0) = sK2))) @ sK4) = $true) | (((sK3 @ sK2) & (?? @ (b > $o) @ (^[Y0 : b > $o]: ((sK3 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0))))) = $true)),
% 1.39/1.25 inference(sigma_clausification,[status(thm)],[f27])).
% 1.39/1.25 thf(f27,plain,(
% 1.39/1.25 ((?? @ b @ (^[Y0 : b]: ((?? @ (b > $o) @ (^[Y1 : b > $o]: ((w @ Y1) & (Y1 @ Y0)))) & ((f @ Y0) = sK2)))) = $true) | (((sK3 @ sK2) & (?? @ (b > $o) @ (^[Y0 : b > $o]: ((sK3 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0))))) = $true)),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.39/1.25 thf(f26,plain,(
% 1.39/1.25 (((^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 = (^[Y2 : a]: (?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((f @ Y3) = Y2)))))) & (w @ Y1)))))) @ sK3) = $true) | ((?? @ b @ (^[Y0 : b]: ((?? @ (b > $o) @ (^[Y1 : b > $o]: ((w @ Y1) & (Y1 @ Y0)))) & ((f @ Y0) = sK2)))) = $true)),
% 1.39/1.25 inference(sigma_clausification,[status(thm)],[f10])).
% 1.39/1.25 thf(f10,plain,(
% 1.39/1.25 ((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) & (?? @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 = (^[Y2 : a]: (?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((f @ Y3) = Y2)))))) & (w @ Y1))))))) = $true) | ((?? @ b @ (^[Y0 : b]: ((?? @ (b > $o) @ (^[Y1 : b > $o]: ((w @ Y1) & (Y1 @ Y0)))) & ((f @ Y0) = sK2)))) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.39/1.25 thf(f102,plain,(
% 1.39/1.25 spl0_9 | spl0_8),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f36,f94,f99])).
% 1.39/1.25 thf(f36,plain,(
% 1.39/1.25 ((sK5 @ sK4) = $true) | ((sK3 @ sK2) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.39/1.25 thf(f97,plain,(
% 1.39/1.25 spl0_8 | spl0_2),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f38,f64,f94])).
% 1.39/1.25 thf(f38,plain,(
% 1.39/1.25 ((f @ sK4) = sK2) | ((sK3 @ sK2) = $true)),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f32])).
% 1.39/1.25 thf(f32,plain,(
% 1.39/1.25 ((sK3 @ sK2) = $true) | (((f @ sK4) = sK2) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.39/1.25 thf(f92,plain,(
% 1.39/1.25 spl0_6 | spl0_7),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f49,f88,f83])).
% 1.39/1.25 thf(f49,plain,(
% 1.39/1.25 (sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) | ((w @ sK7) = $true)),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f48])).
% 1.39/1.25 thf(f48,plain,(
% 1.39/1.25 ((w @ sK7) = $true) | ((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.39/1.25 thf(f46,plain,(
% 1.39/1.25 ((w @ sK7) = $true) | ($true = ((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ sK6)))),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.39/1.25 thf(f44,plain,(
% 1.39/1.25 (((w @ sK7) & (sK7 @ sK4)) = $true) | ($true = ((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ sK6)))),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.39/1.25 thf(f43,plain,(
% 1.39/1.25 (((^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4))) @ sK7) = $true) | ($true = ((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ sK6)))),
% 1.39/1.25 inference(sigma_clausification,[status(thm)],[f42])).
% 1.39/1.25 thf(f42,plain,(
% 1.39/1.25 ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4)))) = $true) | ($true = ((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ sK6)))),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.39/1.25 thf(f41,plain,(
% 1.39/1.25 ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4)))) = $true) | (((^[Y0 : b > $o]: ((sK3 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0))) @ sK6) = $true)),
% 1.39/1.25 inference(sigma_clausification,[status(thm)],[f40])).
% 1.39/1.25 thf(f40,plain,(
% 1.39/1.25 ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((sK3 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0)))) = $true) | ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4)))) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.39/1.25 thf(f30,plain,(
% 1.39/1.25 (((?? @ (b > $o) @ (^[Y0 : b > $o]: ((w @ Y0) & (Y0 @ sK4)))) & ((f @ sK4) = sK2)) = $true) | ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((sK3 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0)))) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.39/1.25 thf(f91,plain,(
% 1.39/1.25 spl0_7 | spl0_5),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f47,f78,f88])).
% 1.39/1.25 thf(f47,plain,(
% 1.39/1.25 ((w @ sK7) = $true) | ($true = (w @ sK6))),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.39/1.25 thf(f86,plain,(
% 1.39/1.25 spl0_4 | spl0_6),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f52,f83,f74])).
% 1.39/1.25 thf(f52,plain,(
% 1.39/1.25 (sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) | ((sK7 @ sK4) = $true)),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 1.39/1.25 thf(f51,plain,(
% 1.39/1.25 ((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) = $true) | ((sK7 @ sK4) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.39/1.25 thf(f45,plain,(
% 1.39/1.25 ((sK7 @ sK4) = $true) | ($true = ((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK6 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ sK6)))),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.39/1.25 thf(f81,plain,(
% 1.39/1.25 spl0_4 | spl0_5),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f50,f78,f74])).
% 1.39/1.25 thf(f50,plain,(
% 1.39/1.25 ($true = (w @ sK6)) | ((sK7 @ sK4) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.39/1.25 thf(f72,plain,(
% 1.39/1.25 spl0_2 | spl0_3),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f58,f69,f64])).
% 1.39/1.25 thf(f58,plain,(
% 1.39/1.25 ((f @ sK4) = sK2) | ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK8 @ Y1) & ((f @ Y1) = Y0))))) = sK3)),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f57])).
% 1.39/1.25 thf(f57,plain,(
% 1.39/1.25 ((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK8 @ Y1) & ((f @ Y1) = Y0)))))) = $true) | ((f @ sK4) = sK2)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.39/1.25 thf(f55,plain,(
% 1.39/1.25 (((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK8 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ sK8)) = $true) | ((f @ sK4) = sK2)),
% 1.39/1.25 inference(equality_proxy_clausification,[status(thm)],[f54])).
% 1.39/1.25 thf(f54,plain,(
% 1.39/1.25 (((f @ sK4) = sK2) = $true) | (((sK3 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK8 @ Y1) & ((f @ Y1) = Y0)))))) & (w @ sK8)) = $true)),
% 1.39/1.25 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.39/1.25 thf(f53,plain,(
% 1.39/1.25 (((^[Y0 : b > $o]: ((sK3 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0))) @ sK8) = $true) | (((f @ sK4) = sK2) = $true)),
% 1.39/1.25 inference(sigma_clausification,[status(thm)],[f39])).
% 1.39/1.25 thf(f39,plain,(
% 1.39/1.25 ((?? @ (b > $o) @ (^[Y0 : b > $o]: ((sK3 = (^[Y1 : a]: (?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((f @ Y2) = Y1)))))) & (w @ Y0)))) = $true) | (((f @ sK4) = sK2) = $true)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.39/1.25 thf(f67,plain,(
% 1.39/1.25 spl0_1 | spl0_2),
% 1.39/1.25 inference(avatar_split_clause,[status(thm)],[f56,f64,f60])).
% 1.39/1.25 thf(f56,plain,(
% 1.39/1.25 ((w @ sK8) = $true) | ((f @ sK4) = sK2)),
% 1.39/1.25 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.39/1.25 % SZS output end Proof for DTF2THF_5708
% 1.39/1.25 % (5810)------------------------------
% 1.39/1.25 % (5810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.25 % (5810)Termination reason: Refutation
% 1.39/1.25
% 1.39/1.25 % (5810)Memory used [KB]: 5756
% 1.39/1.25 % (5810)Time elapsed: 0.022 s
% 1.39/1.25 % (5810)Instructions burned: 28 (million)
% 1.39/1.25 % (5810)------------------------------
% 1.39/1.25 % (5810)------------------------------
% 1.39/1.25 % (5804)Success in time 0.035 s
%------------------------------------------------------------------------------