TSTP Solution File: SEV221^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV221^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n028.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 16:02:20 EDT 2024
% Result : Theorem 0.16s 0.33s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 88 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 702 ( 200 equ; 0 cnn)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 699 ( 169 ~; 175 |; 95 &; 241 @)
% ( 14 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 114 ( 30 ^ 41 !; 43 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cZ: a > $o ).
thf(func_def_2,type,
cW: ( a > $o ) > $o ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_12,type,
sK3: a > $o ).
thf(func_def_15,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK6: a ).
thf(f165,plain,
$false,
inference(avatar_sat_refutation,[],[f37,f51,f52,f57,f58,f59,f60,f61,f72,f98,f104,f117,f127,f134,f164]) ).
thf(f164,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f163]) ).
thf(f163,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f159]) ).
thf(f159,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(superposition,[],[f136,f32]) ).
thf(f32,plain,
( ( ( sK1 @ sK0 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f30,plain,
( spl4_1
<=> ( ( sK1 @ sK0 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
thf(f136,plain,
( ( $false
= ( sK1 @ sK0 ) )
| ~ spl4_4
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f135]) ).
thf(f135,plain,
( ( $true != $true )
| ( $false
= ( sK1 @ sK0 ) )
| ~ spl4_4
| ~ spl4_8 ),
inference(superposition,[],[f68,f46]) ).
thf(f46,plain,
( ( ( cW @ sK1 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f44,plain,
( spl4_4
<=> ( ( cW @ sK1 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
thf(f68,plain,
( ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( $false
= ( X3 @ sK0 ) ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f67,plain,
( spl4_8
<=> ! [X3: a > $o] :
( ( $false
= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
thf(f134,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f133]) ).
thf(f133,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f132,f32]) ).
thf(f132,plain,
( ( ( sK1 @ sK0 )
!= $true )
| ~ spl4_4
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f129,plain,
( ( ( sK1 @ sK0 )
!= $true )
| ( $true != $true )
| ~ spl4_4
| ~ spl4_9 ),
inference(superposition,[],[f71,f46]) ).
thf(f71,plain,
( ! [X1: a > $o] :
( ( ( cW @ X1 )
!= $true )
| ( ( X1 @ sK0 )
!= $true ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f70,plain,
( spl4_9
<=> ! [X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
thf(f127,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_6
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f126]) ).
thf(f126,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f123,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6
| ~ spl4_9 ),
inference(superposition,[],[f56,f121]) ).
thf(f121,plain,
( ( ( sK2 @ sK0 )
= $false )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f120,plain,
( ( ( sK2 @ sK0 )
= $false )
| ( $true != $true )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(superposition,[],[f119,f78]) ).
thf(f78,plain,
( ! [X1: a] :
( ( ( sK3 @ X1 )
= $true )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl4_5 ),
inference(binary_proxy_clausification,[],[f77]) ).
thf(f77,plain,
( ! [X1: a] :
( ( ( ( cZ @ X1 )
& ( sK3 @ X1 ) )
= $true )
| ( ( sK2 @ X1 )
= $false ) )
| ~ spl4_5 ),
inference(binary_proxy_clausification,[],[f75]) ).
thf(f75,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ( cZ @ X1 )
& ( sK3 @ X1 ) ) )
| ~ spl4_5 ),
inference(beta_eta_normalization,[],[f73]) ).
thf(f73,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK3 @ Y0 ) )
@ X1 ) )
| ~ spl4_5 ),
inference(argument_congruence,[],[f50]) ).
thf(f50,plain,
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f48,plain,
( spl4_5
<=> ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
thf(f119,plain,
( ( ( sK3 @ sK0 )
!= $true )
| ~ spl4_2
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f118,plain,
( ( ( sK3 @ sK0 )
!= $true )
| ( $true != $true )
| ~ spl4_2
| ~ spl4_9 ),
inference(superposition,[],[f71,f36]) ).
thf(f36,plain,
( ( $true
= ( cW @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f34,plain,
( spl4_2
<=> ( $true
= ( cW @ sK3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
thf(f56,plain,
( ( ( sK2 @ sK0 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f54,plain,
( spl4_6
<=> ( ( sK2 @ sK0 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
thf(f117,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f116]) ).
thf(f116,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f113,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[],[f56,f111]) ).
thf(f111,plain,
( ( ( sK2 @ sK0 )
= $false )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f108,plain,
( ( ( sK2 @ sK0 )
= $false )
| ( $false = $true )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[],[f107,f78]) ).
thf(f107,plain,
( ( $false
= ( sK3 @ sK0 ) )
| ~ spl4_2
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f106,plain,
( ( $true != $true )
| ( $false
= ( sK3 @ sK0 ) )
| ~ spl4_2
| ~ spl4_8 ),
inference(superposition,[],[f68,f36]) ).
thf(f104,plain,
( ~ spl4_3
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f103]) ).
thf(f103,plain,
( $false
| ~ spl4_3
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f100,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_7 ),
inference(superposition,[],[f41,f65]) ).
thf(f65,plain,
( ( $false
= ( cZ @ sK0 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f63,plain,
( spl4_7
<=> ( $false
= ( cZ @ sK0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
thf(f41,plain,
( ( $true
= ( cZ @ sK0 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f39,plain,
( spl4_3
<=> ( $true
= ( cZ @ sK0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
thf(f98,plain,
( spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f93,f54,f48,f39]) ).
thf(f93,plain,
( ( $true
= ( cZ @ sK0 ) )
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f90,plain,
( ( $false = $true )
| ( $true
= ( cZ @ sK0 ) )
| ~ spl4_5
| ~ spl4_6 ),
inference(superposition,[],[f79,f56]) ).
thf(f79,plain,
( ! [X1: a] :
( ( ( sK2 @ X1 )
= $false )
| ( ( cZ @ X1 )
= $true ) )
| ~ spl4_5 ),
inference(binary_proxy_clausification,[],[f77]) ).
thf(f72,plain,
( spl4_7
| ~ spl4_3
| spl4_8
| spl4_9 ),
inference(avatar_split_clause,[],[f28,f70,f67,f39,f63]) ).
thf(f28,plain,
! [X3: a > $o,X1: a > $o] :
( ( $true
!= ( cZ @ sK0 ) )
| ( ( X1 @ sK0 )
!= $true )
| ( $false
= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true )
| ( $false
= ( cZ @ sK0 ) )
| ( ( cW @ X1 )
!= $true ) ),
inference(binary_proxy_clausification,[],[f27]) ).
thf(f27,plain,
! [X3: a > $o,X1: a > $o] :
( ( ( ( cZ @ sK0 )
& ( X3 @ sK0 ) )
!= $true )
| ( ( cW @ X1 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) )
| ( ( X1 @ sK0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
! [X3: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) )
@ sK0 )
!= $true )
| ( ( X1 @ sK0 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) )
| ( ( cW @ X3 )
!= $true )
| ( ( cW @ X1 )
!= $true ) ),
inference(equality_resolution,[],[f25]) ).
thf(f25,plain,
! [X2: a > $o,X3: a > $o,X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
| ( ( cW @ X1 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) )
| ( ( X2 @ sK0 )
!= $true )
| ( ( cW @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
( ( ! [X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) )
| ( $true
!= ( cZ @ sK0 ) )
| ! [X2: a > $o] :
( ( ( X2 @ sK0 )
!= $true )
| ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 ) ) ) )
& ( ( ( ( sK1 @ sK0 )
= $true )
& ( ( cW @ sK1 )
= $true )
& ( $true
= ( cZ @ sK0 ) ) )
| ( ( ( sK2 @ sK0 )
= $true )
& ( $true
= ( cW @ sK3 ) )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f14,f13,f12,f11]) ).
thf(f11,plain,
( ? [X0: a] :
( ( ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X2: a > $o] :
( ( $true
!= ( X2 @ X0 ) )
| ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 ) ) ) )
& ( ( ? [X4: a > $o] :
( ( $true
= ( X4 @ X0 ) )
& ( ( cW @ X4 )
= $true ) )
& ( ( cZ @ X0 )
= $true ) )
| ? [X5: a > $o] :
( ( ( X5 @ X0 )
= $true )
& ? [X6: a > $o] :
( ( ( cW @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X6 @ Y0 ) ) )
= X5 ) ) ) ) )
=> ( ( ! [X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) )
| ( $true
!= ( cZ @ sK0 ) )
| ! [X2: a > $o] :
( ( ( X2 @ sK0 )
!= $true )
| ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 ) ) ) )
& ( ( ? [X4: a > $o] :
( ( ( X4 @ sK0 )
= $true )
& ( ( cW @ X4 )
= $true ) )
& ( $true
= ( cZ @ sK0 ) ) )
| ? [X5: a > $o] :
( ( ( X5 @ sK0 )
= $true )
& ? [X6: a > $o] :
( ( ( cW @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X6 @ Y0 ) ) )
= X5 ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
( ? [X4: a > $o] :
( ( ( X4 @ sK0 )
= $true )
& ( ( cW @ X4 )
= $true ) )
=> ( ( ( sK1 @ sK0 )
= $true )
& ( ( cW @ sK1 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X5: a > $o] :
( ( ( X5 @ sK0 )
= $true )
& ? [X6: a > $o] :
( ( ( cW @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X6 @ Y0 ) ) )
= X5 ) ) )
=> ( ( ( sK2 @ sK0 )
= $true )
& ? [X6: a > $o] :
( ( ( cW @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X6 @ Y0 ) ) )
= sK2 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
( ? [X6: a > $o] :
( ( ( cW @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X6 @ Y0 ) ) )
= sK2 ) )
=> ( ( $true
= ( cW @ sK3 ) )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
? [X0: a] :
( ( ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X2: a > $o] :
( ( $true
!= ( X2 @ X0 ) )
| ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 ) ) ) )
& ( ( ? [X4: a > $o] :
( ( $true
= ( X4 @ X0 ) )
& ( ( cW @ X4 )
= $true ) )
& ( ( cZ @ X0 )
= $true ) )
| ? [X5: a > $o] :
( ( ( X5 @ X0 )
= $true )
& ? [X6: a > $o] :
( ( ( cW @ X6 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X6 @ Y0 ) ) )
= X5 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,plain,
? [X0: a] :
( ( ! [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ! [X2: a > $o] :
( ( ( cW @ X2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 ) ) ) )
& ( ( ? [X3: a > $o] :
( ( ( X3 @ X0 )
= $true )
& ( ( cW @ X3 )
= $true ) )
& ( ( cZ @ X0 )
= $true ) )
| ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ? [X2: a > $o] :
( ( ( cW @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
= X1 ) ) ) ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
? [X0: a] :
( ( ! [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
| ( ( cW @ X3 )
!= $true ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ! [X2: a > $o] :
( ( ( cW @ X2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 ) ) ) )
& ( ( ? [X3: a > $o] :
( ( ( X3 @ X0 )
= $true )
& ( ( cW @ X3 )
= $true ) )
& ( ( cZ @ X0 )
= $true ) )
| ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ? [X2: a > $o] :
( ( ( cW @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
= X1 ) ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f7,plain,
? [X0: a] :
( ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ? [X2: a > $o] :
( ( ( cW @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
= X1 ) ) )
<~> ( ? [X3: a > $o] :
( ( ( X3 @ X0 )
= $true )
& ( ( cW @ X3 )
= $true ) )
& ( ( cZ @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: a] :
( ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ? [X2: a > $o] :
( ( ( cW @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
= X1 ) ) )
<=> ( ? [X3: a > $o] :
( ( ( X3 @ X0 )
= $true )
& ( ( cW @ X3 )
= $true ) )
& ( ( cZ @ X0 )
= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ? [X2: a > $o] :
( ( ( cW @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
= X1 ) ) )
<=> ( ( ( cZ @ X0 )
= $true )
& ? [X4: a > $o] :
( ( ( cW @ X4 )
= $true )
& ( $true
= ( X4 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a > $o] :
( ( cW @ X2 )
& ( X1
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( cZ @ X3 ) ) ) ) ) )
<=> ( ( cZ @ X0 )
& ? [X4: a > $o] :
( ( cW @ X4 )
& ( X4 @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a > $o] :
( ( cW @ X2 )
& ( X1
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( cZ @ X3 ) ) ) ) ) )
<=> ( ( cZ @ X0 )
& ? [X1: a > $o] :
( ( cW @ X1 )
& ( X1 @ X0 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a > $o] :
( ( cW @ X2 )
& ( X1
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( cZ @ X3 ) ) ) ) ) )
<=> ( ( cZ @ X0 )
& ? [X1: a > $o] :
( ( cW @ X1 )
& ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM61_pme) ).
thf(f61,plain,
( spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f16,f39,f48]) ).
thf(f16,plain,
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f60,plain,
( spl4_6
| spl4_3 ),
inference(avatar_split_clause,[],[f18,f39,f54]) ).
thf(f18,plain,
( ( $true
= ( cZ @ sK0 ) )
| ( ( sK2 @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f59,plain,
( spl4_4
| spl4_6 ),
inference(avatar_split_clause,[],[f21,f54,f44]) ).
thf(f21,plain,
( ( ( sK2 @ sK0 )
= $true )
| ( ( cW @ sK1 )
= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f58,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f20,f34,f44]) ).
thf(f20,plain,
( ( ( cW @ sK1 )
= $true )
| ( $true
= ( cW @ sK3 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f57,plain,
( spl4_6
| spl4_1 ),
inference(avatar_split_clause,[],[f24,f30,f54]) ).
thf(f24,plain,
( ( ( sK2 @ sK0 )
= $true )
| ( ( sK1 @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f52,plain,
( spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f22,f30,f48]) ).
thf(f22,plain,
( ( ( sK1 @ sK0 )
= $true )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f51,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f19,f48,f44]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK3 @ Y0 ) ) )
= sK2 )
| ( ( cW @ sK1 )
= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f37,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f23,f34,f30]) ).
thf(f23,plain,
( ( $true
= ( cW @ sK3 ) )
| ( ( sK1 @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV221^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire %s %d THM
% 0.09/0.29 % Computer : n028.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri Jun 21 19:05:54 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.31 This is a TH0_THM_EQU_NAR problem
% 0.09/0.31 Running higher-order theorem proving
% 0.09/0.31 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
% 0.16/0.33 % (17637)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.33 % (17642)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)
% 0.16/0.33 % (17640)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.33 % (17641)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)
% 0.16/0.33 % (17643)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.33 % (17638)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)
% 0.16/0.33 % (17640)Instruction limit reached!
% 0.16/0.33 % (17640)------------------------------
% 0.16/0.33 % (17640)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.33 % (17640)Termination reason: Unknown
% 0.16/0.33 % (17640)Termination phase: Saturation
% 0.16/0.33
% 0.16/0.33 % (17640)Memory used [KB]: 5500
% 0.16/0.33 % (17640)Time elapsed: 0.003 s
% 0.16/0.33 % (17640)Instructions burned: 2 (million)
% 0.16/0.33 % (17640)------------------------------
% 0.16/0.33 % (17640)------------------------------
% 0.16/0.33 % (17641)Instruction limit reached!
% 0.16/0.33 % (17641)------------------------------
% 0.16/0.33 % (17641)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.33 % (17641)Termination reason: Unknown
% 0.16/0.33 % (17641)Termination phase: Saturation
% 0.16/0.33
% 0.16/0.33 % (17641)Memory used [KB]: 5500
% 0.16/0.33 % (17641)Time elapsed: 0.003 s
% 0.16/0.33 % (17641)Instructions burned: 2 (million)
% 0.16/0.33 % (17641)------------------------------
% 0.16/0.33 % (17641)------------------------------
% 0.16/0.33 % (17638)Instruction limit reached!
% 0.16/0.33 % (17638)------------------------------
% 0.16/0.33 % (17638)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.33 % (17638)Termination reason: Unknown
% 0.16/0.33 % (17638)Termination phase: Saturation
% 0.16/0.33
% 0.16/0.33 % (17638)Memory used [KB]: 5500
% 0.16/0.33 % (17638)Time elapsed: 0.004 s
% 0.16/0.33 % (17638)Instructions burned: 4 (million)
% 0.16/0.33 % (17638)------------------------------
% 0.16/0.33 % (17638)------------------------------
% 0.16/0.33 % (17637)First to succeed.
% 0.16/0.33 % (17642)Also succeeded, but the first one will report.
% 0.16/0.33 % (17637)Refutation found. Thanks to Tanya!
% 0.16/0.33 % SZS status Theorem for theBenchmark
% 0.16/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33 % (17637)------------------------------
% 0.16/0.33 % (17637)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.33 % (17637)Termination reason: Refutation
% 0.16/0.33
% 0.16/0.33 % (17637)Memory used [KB]: 5628
% 0.16/0.33 % (17637)Time elapsed: 0.008 s
% 0.16/0.33 % (17637)Instructions burned: 6 (million)
% 0.16/0.33 % (17637)------------------------------
% 0.16/0.33 % (17637)------------------------------
% 0.16/0.33 % (17636)Success in time 0.019 s
%------------------------------------------------------------------------------