TSTP Solution File: SYO244^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYO244^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n023.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 : Mon Jun 24 21:01:26 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of formulae : 114 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 991 ( 231 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 1393 ( 152 ~; 241 |; 94 &; 739 @)
% ( 8 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 658 ( 658 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 13 con; 0-2 aty)
% ( 37 !!; 42 ??; 0 @@+; 0 @@-)
% Number of variables : 257 ( 112 ^ 103 !; 42 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_12,type,
sK0: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_13,type,
sK1: ( ( a > $o ) > $o ) > $o ).
thf(func_def_14,type,
sK2: ( a > $o ) > $o ).
thf(func_def_15,type,
sK3: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_17,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK6: a ).
thf(func_def_21,type,
sK7: ( a > $o ) > $o ).
thf(func_def_22,type,
sK8: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(func_def_23,type,
sK9: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_24,type,
sK10: ( ( a > $o ) > $o ) > a > $o ).
thf(f434,plain,
$false,
inference(avatar_sat_refutation,[],[f86,f90,f94,f95,f102,f107,f111,f112,f251,f352,f392,f433]) ).
thf(f433,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f432]) ).
thf(f432,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f429,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(superposition,[],[f106,f426]) ).
thf(f426,plain,
( ( ( sK1 @ sK7 )
= $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f423]) ).
thf(f423,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_7 ),
inference(superposition,[],[f89,f415]) ).
thf(f415,plain,
( ( ( sK9 @ sK7 @ sK6 )
= $false )
| ~ spl4_1
| ~ spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f414]) ).
thf(f414,plain,
( ( ( sK9 @ sK7 @ sK6 )
= $false )
| ( $true = $false )
| ~ spl4_1
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_demodulation,[],[f407,f106]) ).
thf(f407,plain,
( ( ( sK9 @ sK7 @ sK6 )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f395]) ).
thf(f395,plain,
( ( $true = $false )
| ( ( sK9 @ sK7 @ sK6 )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl4_1
| ~ spl4_6 ),
inference(superposition,[],[f101,f82]) ).
thf(f82,plain,
( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK9 @ X2 ) )
= $true )
| ( ( sK1 @ X2 )
= $false ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f81]) ).
thf(f81,plain,
( spl4_1
<=> ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK9 @ X2 ) )
= $true )
| ( ( sK1 @ X2 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
thf(f101,plain,
( ! [X2: a > $o] :
( ( ( sK7 @ X2 )
= $false )
| ( ( X2 @ sK6 )
= $false ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f100,plain,
( spl4_6
<=> ! [X2: a > $o] :
( ( ( sK7 @ X2 )
= $false )
| ( ( X2 @ sK6 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
thf(f89,plain,
( ! [X2: ( a > $o ) > $o] :
( ( ( sK9 @ X2 @ sK6 )
= $true )
| ( ( sK1 @ X2 )
= $false ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f88,plain,
( spl4_3
<=> ! [X2: ( a > $o ) > $o] :
( ( ( sK9 @ X2 @ sK6 )
= $true )
| ( ( sK1 @ X2 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
thf(f106,plain,
( ( ( sK1 @ sK7 )
= $true )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f104,plain,
( spl4_7
<=> ( ( sK1 @ sK7 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
thf(f392,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f391]) ).
thf(f391,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f388,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[],[f110,f373]) ).
thf(f373,plain,
( ( ( sK1 @ ( sK8 @ sK9 ) )
= $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f369,plain,
( ( ( sK1 @ ( sK8 @ sK9 ) )
= $false )
| ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[],[f89,f366]) ).
thf(f366,plain,
( ( ( sK9 @ ( sK8 @ sK9 ) @ sK6 )
= $false )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f365,plain,
( ( ( sK9 @ ( sK8 @ sK9 ) @ sK6 )
= $false )
| ( $true = $false )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_8 ),
inference(forward_demodulation,[],[f364,f110]) ).
thf(f364,plain,
( ( ( sK9 @ ( sK8 @ sK9 ) @ sK6 )
= $false )
| ( ( sK1 @ ( sK8 @ sK9 ) )
= $false )
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f357]) ).
thf(f357,plain,
( ( ( sK9 @ ( sK8 @ sK9 ) @ sK6 )
= $false )
| ( ( sK1 @ ( sK8 @ sK9 ) )
= $false )
| ( $true = $false )
| ~ spl4_1
| ~ spl4_5 ),
inference(superposition,[],[f98,f82]) ).
thf(f98,plain,
( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
= $false ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f97,plain,
( spl4_5
<=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
= $false )
| ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
thf(f110,plain,
( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( sK1 @ ( sK8 @ X1 ) )
= $true )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f109,plain,
( spl4_8
<=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( sK1 @ ( sK8 @ X1 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
thf(f352,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f351]) ).
thf(f351,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f347,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[],[f346,f110]) ).
thf(f346,plain,
( ( ( sK1 @ ( sK8 @ sK10 ) )
= $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f340]) ).
thf(f340,plain,
( ( $true = $false )
| ( ( sK1 @ ( sK8 @ sK10 ) )
= $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[],[f291,f85]) ).
thf(f85,plain,
( ! [X1: ( a > $o ) > $o] :
( ( $true
= ( sK10 @ X1 @ sK6 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f84]) ).
thf(f84,plain,
( spl4_2
<=> ! [X1: ( a > $o ) > $o] :
( ( $true
= ( sK10 @ X1 @ sK6 ) )
| ( ( sK1 @ X1 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
thf(f291,plain,
( ( ( sK10 @ ( sK8 @ sK10 ) @ sK6 )
= $false )
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f290]) ).
thf(f290,plain,
( ( $true = $false )
| ( ( sK10 @ ( sK8 @ sK10 ) @ sK6 )
= $false )
| ~ spl4_4
| ~ spl4_5
| ~ spl4_8 ),
inference(forward_demodulation,[],[f278,f110]) ).
thf(f278,plain,
( ( ( sK10 @ ( sK8 @ sK10 ) @ sK6 )
= $false )
| ( ( sK1 @ ( sK8 @ sK10 ) )
= $false )
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f267,plain,
( ( $true = $false )
| ( ( sK10 @ ( sK8 @ sK10 ) @ sK6 )
= $false )
| ( ( sK1 @ ( sK8 @ sK10 ) )
= $false )
| ~ spl4_4
| ~ spl4_5 ),
inference(superposition,[],[f98,f93]) ).
thf(f93,plain,
( ! [X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK10 @ X1 ) ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f92,plain,
( spl4_4
<=> ! [X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK10 @ X1 ) ) )
| ( ( sK1 @ X1 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
thf(f251,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f250]) ).
thf(f250,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f247]) ).
thf(f247,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7 ),
inference(superposition,[],[f106,f245]) ).
thf(f245,plain,
( ( ( sK1 @ sK7 )
= $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f239,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7 ),
inference(superposition,[],[f237,f85]) ).
thf(f237,plain,
( ( ( sK10 @ sK7 @ sK6 )
= $false )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f236,plain,
( ( $true = $false )
| ( ( sK10 @ sK7 @ sK6 )
= $false )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7 ),
inference(forward_demodulation,[],[f235,f106]) ).
thf(f235,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( ( sK10 @ sK7 @ sK6 )
= $false )
| ~ spl4_4
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f227,plain,
( ( $true = $false )
| ( ( sK10 @ sK7 @ sK6 )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl4_4
| ~ spl4_6 ),
inference(superposition,[],[f93,f101]) ).
thf(f112,plain,
( spl4_8
| spl4_7 ),
inference(avatar_split_clause,[],[f53,f104,f109]) ).
thf(f53,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK1 @ sK7 )
= $true )
| ( ( sK1 @ ( sK8 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f51]) ).
thf(f51,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ( sK1 @ sK7 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $false )
| ( ( sK1 @ ( sK8 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f49]) ).
thf(f49,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ( sK1 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK7 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f48]) ).
thf(f48,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( X1 @ Y0 @ sK6 )
& ( Y0 @ ( X1 @ Y0 ) ) ) )
@ ( sK8 @ X1 ) )
= $false )
| ( ( ( sK1 @ sK7 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $false ) ),
inference(sigma_clausification,[],[f47]) ).
thf(f47,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( X1 @ Y0 @ sK6 )
& ( Y0 @ ( X1 @ Y0 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK7 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f46]) ).
thf(f46,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( X1 @ Y0 @ sK6 )
& ( Y0 @ ( X1 @ Y0 ) ) ) ) )
= $false )
| ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) )
@ sK7 )
= $false ) ),
inference(sigma_clausification,[],[f45]) ).
thf(f45,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $false )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( X1 @ Y0 @ sK6 )
& ( Y0 @ ( X1 @ Y0 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y0 @ Y1 @ sK6 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
@ X1 )
= $false )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $false ) ),
inference(pi_clausification,[],[f43]) ).
thf(f43,plain,
( ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y0 @ Y1 @ sK6 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f41,plain,
( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y0 @ Y1 @ sK6 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
!= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK1 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) )
@ sK6 )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) )
@ sK6 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK1 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ! [X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK0 @ X1 ) ) )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) )
& ( $true
= ( sK1 @ sK2 ) )
& ! [X5: ( a > $o ) > $o] :
( ( ( sK1 @ X5 )
!= $true )
| ( $true
= ( X5 @ ( sK3 @ X5 ) ) ) )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK1 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) )
=> ! [X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK0 @ X1 ) ) )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ? [X3: ( ( a > $o ) > $o ) > $o] :
( ? [X4: ( a > $o ) > $o] :
( $true
= ( X3 @ X4 ) )
& ! [X5: ( a > $o ) > $o] :
( ( $true
!= ( X3 @ X5 ) )
| ? [X6: a > $o] :
( $true
= ( X5 @ X6 ) ) )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ? [X4: ( a > $o ) > $o] :
( $true
= ( sK1 @ X4 ) )
& ! [X5: ( a > $o ) > $o] :
( ( ( sK1 @ X5 )
!= $true )
| ? [X6: a > $o] :
( $true
= ( X5 @ X6 ) ) )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK1 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
( ? [X4: ( a > $o ) > $o] :
( $true
= ( sK1 @ X4 ) )
=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X5: ( a > $o ) > $o] :
( ? [X6: a > $o] :
( $true
= ( X5 @ X6 ) )
=> ( $true
= ( X5 @ ( sK3 @ X5 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f8,plain,
( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) )
& ? [X3: ( ( a > $o ) > $o ) > $o] :
( ? [X4: ( a > $o ) > $o] :
( $true
= ( X3 @ X4 ) )
& ! [X5: ( a > $o ) > $o] :
( ( $true
!= ( X3 @ X5 ) )
| ? [X6: a > $o] :
( $true
= ( X5 @ X6 ) ) )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,plain,
( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) )
& ? [X3: ( ( a > $o ) > $o ) > $o] :
( ? [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
= $true )
& ! [X4: ( a > $o ) > $o] :
( ( $true
!= ( X3 @ X4 ) )
| ? [X5: a > $o] :
( ( X4 @ X5 )
= $true ) )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
( ? [X3: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ? [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
= $true )
& ! [X4: ( a > $o ) > $o] :
( ( $true
!= ( X3 @ X4 ) )
| ? [X5: a > $o] :
( ( X4 @ X5 )
= $true ) ) )
& ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,plain,
~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o] :
( ( X1 @ X2 )
= $true )
=> ( ( X1 @ ( X0 @ X1 ) )
= $true ) )
=> ! [X3: ( ( a > $o ) > $o ) > $o] :
( ( ? [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
= $true )
& ! [X4: ( a > $o ) > $o] :
( ( $true
= ( X3 @ X4 ) )
=> ? [X5: a > $o] :
( ( X4 @ X5 )
= $true ) ) )
=> ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ! [X3: ( ( a > $o ) > $o ) > $o] :
( ( ! [X4: ( a > $o ) > $o] :
( ( X3 @ X4 )
=> ? [X5: a > $o] : ( X4 @ X5 ) )
& ? [X6: ( a > $o ) > $o] : ( X3 @ X6 ) )
=> ( ( ^ [X7: a] :
! [X8: ( a > $o ) > $o] :
( ( X3 @ X8 )
=> ? [X9: a > $o] :
( ( X9 @ X7 )
& ( X8 @ X9 ) ) ) )
= ( ^ [X10: a] :
? [X11: ( ( a > $o ) > $o ) > a > $o] :
! [X12: ( a > $o ) > $o] :
( ( X3 @ X12 )
=> ( ( X12 @ ( X11 @ X12 ) )
& ( X11 @ X12 @ X10 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ! [X3: ( ( a > $o ) > $o ) > $o] :
( ( ! [X1: ( a > $o ) > $o] :
( ( X3 @ X1 )
=> ? [X4: a > $o] : ( X1 @ X4 ) )
& ? [X1: ( a > $o ) > $o] : ( X3 @ X1 ) )
=> ( ( ^ [X5: a] :
! [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
=> ? [X7: a > $o] :
( ( X7 @ X5 )
& ( X6 @ X7 ) ) ) )
= ( ^ [X5: a] :
? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
=> ( ( X6 @ ( X0 @ X6 ) )
& ( X0 @ X6 @ X5 ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ! [X3: ( ( a > $o ) > $o ) > $o] :
( ( ! [X1: ( a > $o ) > $o] :
( ( X3 @ X1 )
=> ? [X4: a > $o] : ( X1 @ X4 ) )
& ? [X1: ( a > $o ) > $o] : ( X3 @ X1 ) )
=> ( ( ^ [X5: a] :
! [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
=> ? [X7: a > $o] :
( ( X7 @ X5 )
& ( X6 @ X7 ) ) ) )
= ( ^ [X5: a] :
? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
=> ( ( X6 @ ( X0 @ X6 ) )
& ( X0 @ X6 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM535B) ).
thf(f111,plain,
( spl4_8
| spl4_6 ),
inference(avatar_split_clause,[],[f56,f100,f109]) ).
thf(f56,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK1 @ ( sK8 @ X1 ) )
= $true )
| ( ( X2 @ sK6 )
= $false )
| ( ( sK7 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f55]) ).
thf(f55,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK7 @ X2 )
& ( X2 @ sK6 ) ) )
| ( ( sK1 @ ( sK8 @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f54]) ).
thf(f54,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK1 @ ( sK8 @ X1 ) )
= $true )
| ( ( ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[],[f52]) ).
thf(f52,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) ) )
= $false )
| ( ( sK1 @ ( sK8 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f51]) ).
thf(f107,plain,
( spl4_7
| spl4_5 ),
inference(avatar_split_clause,[],[f59,f97,f104]) ).
thf(f59,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
= $false )
| ( ( sK1 @ sK7 )
= $true ) ),
inference(binary_proxy_clausification,[],[f57]) ).
thf(f57,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
= $false )
| ( ( ( sK1 @ sK7 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f50]) ).
thf(f50,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) )
| ( ( ( sK1 @ sK7 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f49]) ).
thf(f102,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f62,f100,f97]) ).
thf(f62,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
= $false )
| ( ( sK7 @ X2 )
= $false )
| ( ( X2 @ sK6 )
= $false )
| ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f61]) ).
thf(f61,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
= $false )
| ( $false
= ( ( sK7 @ X2 )
& ( X2 @ sK6 ) ) )
| ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f60]) ).
thf(f60,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
= $false )
| ( ( ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) )
@ X2 )
= $false )
| ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
= $false ) ),
inference(pi_clausification,[],[f58]) ).
thf(f58,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( X1 @ ( sK8 @ X1 ) @ sK6 )
= $false )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK7 @ Y0 )
& ( Y0 @ sK6 ) ) )
= $false )
| ( ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f57]) ).
thf(f95,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f76,f92,f88]) ).
thf(f76,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK10 @ X1 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK9 @ X2 @ sK6 )
= $true ) ),
inference(binary_proxy_clausification,[],[f74]) ).
thf(f74,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ ( sK10 @ X1 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( ( sK9 @ X2 @ sK6 )
& ( X2 @ ( sK9 @ X2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f73]) ).
thf(f73,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ( sK1 @ X2 )
=> ( ( sK9 @ X2 @ sK6 )
& ( X2 @ ( sK9 @ X2 ) ) ) )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ ( sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f71]) ).
thf(f71,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ( X1 @ ( sK10 @ X1 ) )
& ( sK10 @ X1 @ sK6 ) )
= $true )
| ( ( ( sK1 @ X2 )
=> ( ( sK9 @ X2 @ sK6 )
& ( X2 @ ( sK9 @ X2 ) ) ) )
= $true )
| ( ( sK1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f70]) ).
thf(f70,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK6 ) )
@ ( sK10 @ X1 ) )
= $true )
| ( ( ( sK1 @ X2 )
=> ( ( sK9 @ X2 @ sK6 )
& ( X2 @ ( sK9 @ X2 ) ) ) )
= $true )
| ( ( sK1 @ X1 )
= $false ) ),
inference(sigma_clausification,[],[f69]) ).
thf(f69,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK6 ) ) )
= $true )
| ( ( ( sK1 @ X2 )
=> ( ( sK9 @ X2 @ sK6 )
& ( X2 @ ( sK9 @ X2 ) ) ) )
= $true )
| ( ( sK1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( sK9 @ Y0 @ sK6 )
& ( Y0 @ ( sK9 @ Y0 ) ) ) )
@ X2 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK6 ) ) )
= $true ) ),
inference(pi_clausification,[],[f67]) ).
thf(f67,plain,
! [X1: ( a > $o ) > $o] :
( ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( sK9 @ Y0 @ sK6 )
& ( Y0 @ ( sK9 @ Y0 ) ) ) ) ) )
| ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK6 ) ) )
= $true )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f66]) ).
thf(f66,plain,
! [X1: ( a > $o ) > $o] :
( ( ( ( sK1 @ X1 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $true )
| ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( sK9 @ Y0 @ sK6 )
& ( Y0 @ ( sK9 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f65]) ).
thf(f65,plain,
! [X1: ( a > $o ) > $o] :
( ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( sK9 @ Y0 @ sK6 )
& ( Y0 @ ( sK9 @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[],[f64]) ).
thf(f64,plain,
( ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) ) )
| ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( sK9 @ Y0 @ sK6 )
& ( Y0 @ ( sK9 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f63]) ).
thf(f63,plain,
( ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y0 @ Y1 @ sK6 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
@ sK9 ) ) ),
inference(sigma_clausification,[],[f42]) ).
thf(f42,plain,
( ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y0 @ Y1 @ sK6 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f94,plain,
( spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f75,f81,f92]) ).
thf(f75,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK10 @ X1 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( ( X2 @ ( sK9 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f74]) ).
thf(f90,plain,
( spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f79,f88,f84]) ).
thf(f79,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK9 @ X2 @ sK6 )
= $true )
| ( $true
= ( sK10 @ X1 @ sK6 ) )
| ( ( sK1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f77]) ).
thf(f77,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ( sK9 @ X2 @ sK6 )
& ( X2 @ ( sK9 @ X2 ) ) )
= $true )
| ( $true
= ( sK10 @ X1 @ sK6 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f72]) ).
thf(f72,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( sK10 @ X1 @ sK6 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X2 )
=> ( ( sK9 @ X2 @ sK6 )
& ( X2 @ ( sK9 @ X2 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f71]) ).
thf(f86,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f78,f84,f81]) ).
thf(f78,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( sK10 @ X1 @ sK6 ) )
| ( ( X2 @ ( sK9 @ X2 ) )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO244^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Jun 23 08:57:54 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running higher-order theorem proving
% 0.13/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.22/0.37 % (25821)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.37 % (25817)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.37 % (25820)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.37 % (25819)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 theBenchmark for (2999ds/27Mi)
% 0.22/0.37 % (25818)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 theBenchmark for (2999ds/4Mi)
% 0.22/0.37 % (25822)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.22/0.37 % (25823)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38 % (25820)Instruction limit reached!
% 0.22/0.38 % (25820)------------------------------
% 0.22/0.38 % (25820)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (25820)Termination reason: Unknown
% 0.22/0.38 % (25820)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (25820)Memory used [KB]: 5500
% 0.22/0.38 % (25820)Time elapsed: 0.004 s
% 0.22/0.38 % (25820)Instructions burned: 2 (million)
% 0.22/0.38 % (25820)------------------------------
% 0.22/0.38 % (25820)------------------------------
% 0.22/0.38 % (25821)Instruction limit reached!
% 0.22/0.38 % (25821)------------------------------
% 0.22/0.38 % (25821)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (25821)Termination reason: Unknown
% 0.22/0.38 % (25821)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (25821)Memory used [KB]: 5500
% 0.22/0.38 % (25821)Time elapsed: 0.004 s
% 0.22/0.38 % (25821)Instructions burned: 2 (million)
% 0.22/0.38 % (25821)------------------------------
% 0.22/0.38 % (25821)------------------------------
% 0.22/0.38 % (25818)Instruction limit reached!
% 0.22/0.38 % (25818)------------------------------
% 0.22/0.38 % (25818)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (25818)Termination reason: Unknown
% 0.22/0.38 % (25818)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (25818)Memory used [KB]: 5500
% 0.22/0.38 % (25818)Time elapsed: 0.006 s
% 0.22/0.38 % (25818)Instructions burned: 4 (million)
% 0.22/0.38 % (25818)------------------------------
% 0.22/0.38 % (25818)------------------------------
% 0.22/0.39 % (25823)Instruction limit reached!
% 0.22/0.39 % (25823)------------------------------
% 0.22/0.39 % (25823)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (25823)Termination reason: Unknown
% 0.22/0.39 % (25823)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (25823)Memory used [KB]: 5628
% 0.22/0.39 % (25823)Time elapsed: 0.014 s
% 0.22/0.39 % (25823)Instructions burned: 18 (million)
% 0.22/0.39 % (25823)------------------------------
% 0.22/0.39 % (25823)------------------------------
% 0.22/0.39 % (25824)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.39 % (25825)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 theBenchmark for (2999ds/37Mi)
% 0.22/0.39 % (25826)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 theBenchmark for (2999ds/15Mi)
% 0.22/0.39 % (25819)Instruction limit reached!
% 0.22/0.39 % (25819)------------------------------
% 0.22/0.39 % (25819)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (25819)Termination reason: Unknown
% 0.22/0.39 % (25819)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (25819)Memory used [KB]: 5628
% 0.22/0.39 % (25819)Time elapsed: 0.022 s
% 0.22/0.39 % (25819)Instructions burned: 27 (million)
% 0.22/0.39 % (25819)------------------------------
% 0.22/0.39 % (25819)------------------------------
% 0.22/0.39 % (25824)Instruction limit reached!
% 0.22/0.39 % (25824)------------------------------
% 0.22/0.39 % (25824)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (25824)Termination reason: Unknown
% 0.22/0.39 % (25824)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (25824)Memory used [KB]: 5500
% 0.22/0.39 % (25824)Time elapsed: 0.005 s
% 0.22/0.39 % (25824)Instructions burned: 4 (million)
% 0.22/0.39 % (25824)------------------------------
% 0.22/0.39 % (25824)------------------------------
% 0.22/0.40 % (25822)First to succeed.
% 0.22/0.40 % (25827)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40 % (25822)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (25822)------------------------------
% 0.22/0.40 % (25822)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (25822)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (25822)Memory used [KB]: 5756
% 0.22/0.40 % (25822)Time elapsed: 0.029 s
% 0.22/0.40 % (25822)Instructions burned: 32 (million)
% 0.22/0.40 % (25822)------------------------------
% 0.22/0.40 % (25822)------------------------------
% 0.22/0.40 % (25816)Success in time 0.042 s
%------------------------------------------------------------------------------