TSTP Solution File: SEV465^1 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV465^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n020.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 16:03:59 EDT 2024
% Result : Theorem 0.19s 0.38s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 511 ( 144 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 791 ( 94 ~; 90 |; 30 &; 556 @)
% ( 8 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 10 con; 0-5 aty)
% Number of variables : 149 ( 0 ^ 113 !; 36 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK1: $tType ).
thf(type_def_7,type,
sK2: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/IMAGE':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > $o ) > X1 > $o ) ).
thf(func_def_5,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > $o ) > X0 > X1 ) ).
thf(func_def_6,type,
sK3: sK1 > $o ).
thf(func_def_7,type,
sK4: sK2 > sK1 ).
thf(func_def_8,type,
sK5: sK2 > $o ).
thf(func_def_9,type,
sK6: sK1 ).
thf(func_def_10,type,
sK7: sK2 ).
thf(func_def_12,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f91,plain,
$false,
inference(avatar_sat_refutation,[],[f37,f42,f47,f54,f55,f63,f81,f90]) ).
thf(f90,plain,
( spl8_5
| ~ spl8_6 ),
inference(avatar_split_clause,[],[f85,f52,f49]) ).
thf(f49,plain,
( spl8_5
<=> ! [X8: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X8 @ sK5 ) )
| ( $true
= ( sK3 @ ( sK4 @ X8 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
thf(f52,plain,
( spl8_6
<=> ! [X7: sK1] :
( ( $true
= ( sK3 @ X7 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ X7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
thf(f85,plain,
( ! [X0: sK2] :
( ( $true
= ( sK3 @ ( sK4 @ X0 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK5 ) ) )
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f84,plain,
( ! [X0: sK2] :
( ( $true
= ( sK3 @ ( sK4 @ X0 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK5 ) )
| ( $true != $true ) )
| ~ spl8_6 ),
inference(superposition,[],[f53,f28]) ).
thf(f28,plain,
! [X1: $tType,X0: $tType,X3: X1 > $o,X4: X1 > X0,X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X0 @ ( X4 @ X5 ) @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) ) ),
inference(equality_resolution,[],[f22]) ).
thf(f22,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0,X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
| ( ( X4 @ X5 )
!= X2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ! [X5: X1] :
( ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
| ( ( X4 @ X5 )
!= X2 ) ) )
& ( ( ( ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) @ X3 )
= $true )
& ( ( X4 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) )
= X2 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).
thf(f12,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ? [X6: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X6 @ X3 ) )
& ( ( X4 @ X6 )
= X2 ) )
=> ( ( ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) @ X3 )
= $true )
& ( ( X4 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) )
= X2 ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ! [X5: X1] :
( ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
| ( ( X4 @ X5 )
!= X2 ) ) )
& ( ? [X6: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X6 @ X3 ) )
& ( ( X4 @ X6 )
= X2 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ! [X5: X1] :
( ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
| ( ( X4 @ X5 )
!= X2 ) ) )
& ( ? [X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
& ( ( X4 @ X5 )
= X2 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
<=> ? [X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
& ( ( X4 @ X5 )
= X2 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= ( ? [X5: X1] :
( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
& ( ( X4 @ X5 )
= X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X1: $tType,X0: $tType,X2: X1,X3: X0 > $o,X4: X0 > X1] :
( ( 'const/sets/IN' @ X1 @ X2 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X4 @ X3 ) )
= ( ? [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ X3 )
& ( ( X4 @ X5 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_IMAGE_') ).
thf(f53,plain,
( ! [X7: sK1] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ X7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) )
| ( $true
= ( sK3 @ X7 ) ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f81,plain,
( spl8_1
| ~ spl8_4
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f80]) ).
thf(f80,plain,
( $false
| spl8_1
| ~ spl8_4
| ~ spl8_5 ),
inference(subsumption_resolution,[],[f79,f32]) ).
thf(f32,plain,
( ( $true
!= ( sK3 @ sK6 ) )
| spl8_1 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f30,plain,
( spl8_1
<=> ( $true
= ( sK3 @ sK6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
thf(f79,plain,
( ( $true
= ( sK3 @ sK6 ) )
| ~ spl8_4
| ~ spl8_5 ),
inference(forward_demodulation,[],[f77,f67]) ).
thf(f67,plain,
( ( sK6
= ( sK4 @ ( sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK6 ) ) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f65,plain,
( ( $true != $true )
| ( sK6
= ( sK4 @ ( sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK6 ) ) )
| ~ spl8_4 ),
inference(superposition,[],[f20,f46]) ).
thf(f46,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f44,plain,
( spl8_4
<=> ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
thf(f20,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ( ( X4 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) )
= X2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f77,plain,
( ( $true
= ( sK3 @ ( sK4 @ ( sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK6 ) ) ) )
| ~ spl8_4
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f75,plain,
( ( $true
= ( sK3 @ ( sK4 @ ( sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK6 ) ) ) )
| ( $true != $true )
| ~ spl8_4
| ~ spl8_5 ),
inference(superposition,[],[f59,f46]) ).
thf(f59,plain,
( ! [X0: $tType,X2: X0,X1: sK2 > X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK5 ) ) )
| ( $true
= ( sK3 @ ( sK4 @ ( sK0 @ X0 @ sK2 @ X1 @ sK5 @ X2 ) ) ) ) )
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f58,plain,
( ! [X0: $tType,X2: X0,X1: sK2 > X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK5 ) ) )
| ( $true
= ( sK3 @ ( sK4 @ ( sK0 @ X0 @ sK2 @ X1 @ sK5 @ X2 ) ) ) )
| ( $true != $true ) )
| ~ spl8_5 ),
inference(superposition,[],[f50,f21]) ).
thf(f21,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) @ X3 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f50,plain,
( ! [X8: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X8 @ sK5 ) )
| ( $true
= ( sK3 @ ( sK4 @ X8 ) ) ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f63,plain,
( spl8_3
| ~ spl8_2
| ~ spl8_5 ),
inference(avatar_split_clause,[],[f60,f49,f34,f39]) ).
thf(f39,plain,
( spl8_3
<=> ( $true
= ( sK3 @ ( sK4 @ sK7 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
thf(f34,plain,
( spl8_2
<=> ( $true
= ( 'const/sets/IN' @ sK2 @ sK7 @ sK5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
thf(f60,plain,
( ( $true
= ( sK3 @ ( sK4 @ sK7 ) ) )
| ~ spl8_2
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f57,plain,
( ( $true
= ( sK3 @ ( sK4 @ sK7 ) ) )
| ( $true != $true )
| ~ spl8_2
| ~ spl8_5 ),
inference(superposition,[],[f50,f36]) ).
thf(f36,plain,
( ( $true
= ( 'const/sets/IN' @ sK2 @ sK7 @ sK5 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f55,plain,
( spl8_4
| spl8_2 ),
inference(avatar_split_clause,[],[f24,f34,f44]) ).
thf(f24,plain,
( ( $true
= ( 'const/sets/IN' @ sK2 @ sK7 @ sK5 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
( ( ( ( $true
!= ( sK3 @ sK6 ) )
& ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) )
| ( ( $true
!= ( sK3 @ ( sK4 @ sK7 ) ) )
& ( $true
= ( 'const/sets/IN' @ sK2 @ sK7 @ sK5 ) ) ) )
& ( ! [X7: sK1] :
( ( $true
= ( sK3 @ X7 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ X7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) )
| ! [X8: sK2] :
( ( $true
= ( sK3 @ ( sK4 @ X8 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X8 @ sK5 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f15,f18,f17,f16]) ).
thf(f16,plain,
( ? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ( ? [X5: X0] :
( ( $true
!= ( X2 @ X5 ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) ) )
| ? [X6: X1] :
( ( $true
!= ( X2 @ ( X3 @ X6 ) ) )
& ( $true
= ( 'const/sets/IN' @ X1 @ X6 @ X4 ) ) ) )
& ( ! [X7: X0] :
( ( $true
= ( X2 @ X7 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X7 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) ) )
| ! [X8: X1] :
( ( $true
= ( X2 @ ( X3 @ X8 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X8 @ X4 ) ) ) ) )
=> ( ( ? [X5: sK1] :
( ( $true
!= ( sK3 @ X5 ) )
& ( $true
= ( 'const/sets/IN' @ sK1 @ X5 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) )
| ? [X6: sK2] :
( ( $true
!= ( sK3 @ ( sK4 @ X6 ) ) )
& ( $true
= ( 'const/sets/IN' @ sK2 @ X6 @ sK5 ) ) ) )
& ( ! [X7: sK1] :
( ( $true
= ( sK3 @ X7 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ X7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) )
| ! [X8: sK2] :
( ( $true
= ( sK3 @ ( sK4 @ X8 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X8 @ sK5 ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
( ? [X5: sK1] :
( ( $true
!= ( sK3 @ X5 ) )
& ( $true
= ( 'const/sets/IN' @ sK1 @ X5 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) )
=> ( ( $true
!= ( sK3 @ sK6 ) )
& ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f18,plain,
( ? [X6: sK2] :
( ( $true
!= ( sK3 @ ( sK4 @ X6 ) ) )
& ( $true
= ( 'const/sets/IN' @ sK2 @ X6 @ sK5 ) ) )
=> ( ( $true
!= ( sK3 @ ( sK4 @ sK7 ) ) )
& ( $true
= ( 'const/sets/IN' @ sK2 @ sK7 @ sK5 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ( ? [X5: X0] :
( ( $true
!= ( X2 @ X5 ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) ) )
| ? [X6: X1] :
( ( $true
!= ( X2 @ ( X3 @ X6 ) ) )
& ( $true
= ( 'const/sets/IN' @ X1 @ X6 @ X4 ) ) ) )
& ( ! [X7: X0] :
( ( $true
= ( X2 @ X7 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X7 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) ) )
| ! [X8: X1] :
( ( $true
= ( X2 @ ( X3 @ X8 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X8 @ X4 ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f14,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ( ? [X6: X0] :
( ( $true
!= ( X2 @ X6 ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) ) )
| ? [X5: X1] :
( ( $true
!= ( X2 @ ( X3 @ X5 ) ) )
& ( $true
= ( 'const/sets/IN' @ X1 @ X5 @ X4 ) ) ) )
& ( ! [X6: X0] :
( ( $true
= ( X2 @ X6 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) ) )
| ! [X5: X1] :
( ( $true
= ( X2 @ ( X3 @ X5 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X4 ) ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f9,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ! [X5: X1] :
( ( $true
= ( X2 @ ( X3 @ X5 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X4 ) ) )
<~> ! [X6: X0] :
( ( $true
= ( X2 @ X6 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ! [X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X5 @ X4 ) )
=> ( $true
= ( X2 @ ( X3 @ X5 ) ) ) )
<=> ! [X6: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) )
=> ( $true
= ( X2 @ X6 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o,X5: X1] :
( ( ( 'const/sets/IN' @ X1 @ X5 @ X4 )
=> ( X2 @ ( X3 @ X5 ) ) )
= ( ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
=> ( X2 @ X6 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $tType,X2: $tType,X6: X0 > $o,X3: X2 > X0,X4: X2 > $o,X5: X2] :
( ( ( 'const/sets/IN' @ X2 @ X5 @ X4 )
=> ( X6 @ ( X3 @ X5 ) ) )
= ( ! [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X2 @ X0 @ X3 @ X4 ) )
=> ( X6 @ X5 ) ) ) ),
inference(negated_conjecture,[],[f2]) ).
thf(f2,conjecture,
! [X0: $tType,X2: $tType,X6: X0 > $o,X3: X2 > X0,X4: X2 > $o,X5: X2] :
( ( ( 'const/sets/IN' @ X2 @ X5 @ X4 )
=> ( X6 @ ( X3 @ X5 ) ) )
= ( ! [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X2 @ X0 @ X3 @ X4 ) )
=> ( X6 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FORALL_IN_IMAGE_') ).
thf(f54,plain,
( spl8_5
| spl8_6 ),
inference(avatar_split_clause,[],[f23,f52,f49]) ).
thf(f23,plain,
! [X8: sK2,X7: sK1] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X8 @ sK5 ) )
| ( $true
= ( sK3 @ X7 ) )
| ( $true
= ( sK3 @ ( sK4 @ X8 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ X7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f47,plain,
( spl8_4
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f25,f39,f44]) ).
thf(f25,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) )
| ( $true
!= ( sK3 @ ( sK4 @ sK7 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f42,plain,
( ~ spl8_3
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f27,f30,f39]) ).
thf(f27,plain,
( ( $true
!= ( sK3 @ ( sK4 @ sK7 ) ) )
| ( $true
!= ( sK3 @ sK6 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f37,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f26,f34,f30]) ).
thf(f26,plain,
( ( $true
!= ( sK3 @ sK6 ) )
| ( $true
= ( 'const/sets/IN' @ sK2 @ sK7 @ sK5 ) ) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV465^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.11 % Command : run_vampire %s %d THM
% 0.11/0.33 % Computer : n020.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 21 18:54:39 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 This is a TH1_THM_EQU_NAR problem
% 0.11/0.34 Running higher-order theorem proving
% 0.11/0.34 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
% 0.19/0.36 % (10639)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.19/0.36 % (10641)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)
% 0.19/0.36 % (10640)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)
% 0.19/0.36 % (10642)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.36 % (10643)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)
% 0.19/0.36 % (10644)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)
% 0.19/0.36 % (10645)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.36 % Exception at run slice level
% 0.19/0.36 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.19/0.36 % (10642)Instruction limit reached!
% 0.19/0.36 % (10642)------------------------------
% 0.19/0.36 % (10642)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.36 % (10642)Termination reason: Unknown
% 0.19/0.36 % (10642)Termination phase: Saturation
% 0.19/0.36
% 0.19/0.36 % (10642)Memory used [KB]: 5500
% 0.19/0.36 % (10642)Time elapsed: 0.003 s
% 0.19/0.36 % (10642)Instructions burned: 2 (million)
% 0.19/0.36 % (10642)------------------------------
% 0.19/0.36 % (10642)------------------------------
% 0.19/0.37 % (10640)Instruction limit reached!
% 0.19/0.37 % (10640)------------------------------
% 0.19/0.37 % (10640)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.37 % (10640)Termination reason: Unknown
% 0.19/0.37 % (10640)Termination phase: Saturation
% 0.19/0.37
% 0.19/0.37 % (10640)Memory used [KB]: 5500
% 0.19/0.37 % (10640)Time elapsed: 0.005 s
% 0.19/0.37 % (10640)Instructions burned: 4 (million)
% 0.19/0.37 % (10640)------------------------------
% 0.19/0.37 % (10640)------------------------------
% 0.19/0.37 % (10644)First to succeed.
% 0.19/0.37 % (10659)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)
% 0.19/0.37 % Exception at run slice level
% 0.19/0.37 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.19/0.38 % (10644)Refutation found. Thanks to Tanya!
% 0.19/0.38 % SZS status Theorem for theBenchmark
% 0.19/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.38 % (10644)------------------------------
% 0.19/0.38 % (10644)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.38 % (10644)Termination reason: Refutation
% 0.19/0.38
% 0.19/0.38 % (10644)Memory used [KB]: 5628
% 0.19/0.38 % (10644)Time elapsed: 0.013 s
% 0.19/0.38 % (10644)Instructions burned: 12 (million)
% 0.19/0.38 % (10644)------------------------------
% 0.19/0.38 % (10644)------------------------------
% 0.19/0.38 % (10637)Success in time 0.028 s
%------------------------------------------------------------------------------