TSTP Solution File: SEV497^1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV497^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n032.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 16:04:08 EDT 2024
% Result : Theorem 0.13s 0.30s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 373 ( 98 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1250 ( 58 ~; 47 |; 23 &;1099 @)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 6 con; 0-6 aty)
% Number of variables : 161 ( 0 ^ 137 !; 24 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(type_def_8,type,
sK2: $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/iterate/support':
!>[X0: $tType,X1: $tType] : ( ( X0 > X0 > X0 ) > ( X1 > X0 ) > ( X1 > $o ) > X1 > $o ) ).
thf(func_def_5,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_6,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_7,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_8,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_10,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK3: sK2 > sK2 > sK2 ).
thf(func_def_14,type,
sK4: sK1 > sK2 ).
thf(func_def_15,type,
sK5: sK1 ).
thf(func_def_16,type,
sK6: sK1 > $o ).
thf(func_def_17,type,
sK7: sK0 > sK2 ).
thf(func_def_19,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f70,plain,
$false,
inference(avatar_sat_refutation,[],[f36,f41,f46,f69]) ).
thf(f69,plain,
( spl8_2
| ~ spl8_3 ),
inference(avatar_contradiction_clause,[],[f68]) ).
thf(f68,plain,
( $false
| spl8_2
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f67,plain,
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 ) )
| spl8_2
| ~ spl8_3 ),
inference(superposition,[],[f35,f58]) ).
thf(f58,plain,
( ! [X0: sK1,X1: sK1 > sK2] :
( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ X0 @ sK6 ) @ X1 )
= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ X0 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ X1 ) @ ( sK3 @ ( X1 @ X0 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ X1 ) ) ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f57,plain,
( ! [X0: sK1,X1: sK1 > sK2] :
( ( $true != $true )
| ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ X0 @ sK6 ) @ X1 )
= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ X0 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ X1 ) @ ( sK3 @ ( X1 @ X0 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ X1 ) ) ) ) )
| ~ spl8_3 ),
inference(superposition,[],[f52,f25]) ).
thf(f25,plain,
( $true
= ( 'const/iterate/monoidal' @ sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
( ( $true
= ( 'const/iterate/monoidal' @ sK2 @ sK3 ) )
& ( ( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) )
& ( ( 'const/sets/FINITE' @ sK1 @ sK6 )
= $true ) )
| ( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f14,f19,f18,f17]) ).
thf(f17,plain,
( ? [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( $true
= ( 'const/iterate/monoidal' @ X2 @ X3 ) )
& ( ? [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
!= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X1 @ X6 ) ) )
| ? [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
!= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ) )
=> ( ( $true
= ( 'const/iterate/monoidal' @ sK2 @ sK3 ) )
& ( ? [X6: sK1 > $o,X5: sK1,X4: sK1 > sK2] :
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ X5 @ X6 ) @ X4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X6 @ X4 ) @ ( sK3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X6 @ X4 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK1 @ X6 ) ) )
| ? [X7: sK0 > sK2] :
( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ X7 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f18,plain,
( ? [X6: sK1 > $o,X5: sK1,X4: sK1 > sK2] :
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ X5 @ X6 ) @ X4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X6 @ X4 ) @ ( sK3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X6 @ X4 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK1 @ X6 ) ) )
=> ( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) )
& ( ( 'const/sets/FINITE' @ sK1 @ sK6 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f19,plain,
( ? [X7: sK0 > sK2] :
( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ X7 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
=> ( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
? [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( $true
= ( 'const/iterate/monoidal' @ X2 @ X3 ) )
& ( ? [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
!= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X1 @ X6 ) ) )
| ? [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
!= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( $true
= ( 'const/iterate/monoidal' @ X2 @ X3 ) )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( $true
= ( 'const/sets/FINITE' @ X1 @ X6 ) )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) ) )
& ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X6 )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) ) )
& ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X2: $tType,X3: $tType,X4: X3 > X3 > X3] :
( ( 'const/iterate/monoidal' @ X3 @ X4 )
=> ( ! [X5: X2 > X3,X6: X2,X7: X2 > $o] :
( ( 'const/sets/FINITE' @ X2 @ X7 )
=> ( ( 'const/iterate/iterate' @ X2 @ X3 @ X4 @ ( 'const/sets/INSERT' @ X2 @ X6 @ X7 ) @ X5 )
= ( 'const/class/COND' @ X3 @ ( 'const/sets/IN' @ X2 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X2 @ X3 @ X4 @ X7 @ X5 ) @ ( X4 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X2 @ X3 @ X4 @ X7 @ X5 ) ) ) ) )
& ! [X5: X0 > X3] :
( ( 'const/iterate/iterate' @ X0 @ X3 @ X4 @ 'const/sets/EMPTY' @ X0 @ X5 )
= ( 'const/iterate/neutral' @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X2: $tType,X3: $tType,X4: X3 > X3 > X3] :
( ( 'const/iterate/monoidal' @ X3 @ X4 )
=> ( ! [X5: X2 > X3,X6: X2,X7: X2 > $o] :
( ( 'const/sets/FINITE' @ X2 @ X7 )
=> ( ( 'const/iterate/iterate' @ X2 @ X3 @ X4 @ ( 'const/sets/INSERT' @ X2 @ X6 @ X7 ) @ X5 )
= ( 'const/class/COND' @ X3 @ ( 'const/sets/IN' @ X2 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X2 @ X3 @ X4 @ X7 @ X5 ) @ ( X4 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X2 @ X3 @ X4 @ X7 @ X5 ) ) ) ) )
& ! [X5: X0 > X3] :
( ( 'const/iterate/iterate' @ X0 @ X3 @ X4 @ 'const/sets/EMPTY' @ X0 @ X5 )
= ( 'const/iterate/neutral' @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(f52,plain,
( ! [X0: $tType,X2: sK1 > X0,X3: sK1,X1: X0 > X0 > X0] :
( ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X1 ) )
| ( ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK1 @ X3 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ sK6 @ X2 ) @ ( X1 @ ( X2 @ X3 ) @ ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ sK6 @ X2 ) ) )
= ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ ( 'const/sets/INSERT' @ sK1 @ X3 @ sK6 ) @ X2 ) ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f49,plain,
( ! [X0: $tType,X2: sK1 > X0,X3: sK1,X1: X0 > X0 > X0] :
( ( $true != $true )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X1 ) )
| ( ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK1 @ X3 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ sK6 @ X2 ) @ ( X1 @ ( X2 @ X3 ) @ ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ sK6 @ X2 ) ) )
= ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ ( 'const/sets/INSERT' @ sK1 @ X3 @ sK6 ) @ X2 ) ) )
| ~ spl8_3 ),
inference(superposition,[],[f27,f48]) ).
thf(f48,plain,
( ! [X0: $tType,X2: sK1 > X0,X1: X0 > X0 > X0] :
( $true
= ( 'const/sets/FINITE' @ sK1 @ ( 'const/iterate/support' @ X0 @ sK1 @ X1 @ X2 @ sK6 ) ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f47,plain,
( ! [X0: $tType,X2: sK1 > X0,X1: X0 > X0 > X0] :
( ( $true != $true )
| ( $true
= ( 'const/sets/FINITE' @ sK1 @ ( 'const/iterate/support' @ X0 @ sK1 @ X1 @ X2 @ sK6 ) ) ) )
| ~ spl8_3 ),
inference(superposition,[],[f26,f40]) ).
thf(f40,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ sK6 )
= $true )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f38,plain,
( spl8_3
<=> ( ( 'const/sets/FINITE' @ sK1 @ sK6 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
thf(f26,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ X1 @ X4 ) )
| ( ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= $true )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X4 ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( $true
= ( 'const/sets/FINITE' @ X1 @ X4 ) )
=> ( ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X4 )
=> ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: $tType,X3: X0 > X0 > X0,X4: X2 > X0,X5: X2 > $o] :
( ( 'const/sets/FINITE' @ X2 @ X5 )
=> ( 'const/sets/FINITE' @ X2 @ ( 'const/iterate/support' @ X0 @ X2 @ X3 @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_SUPPORT_') ).
thf(f27,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X6: X0 > $o,X4: X0 > X1,X5: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X6 @ X4 ) @ ( X2 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X6 @ X4 ) ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X5 @ X6 ) @ X4 ) ) ),
inference(duplicate_literal_removal,[],[f21]) ).
thf(f21,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X6: X0 > $o,X4: X0 > X1,X5: X0] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) )
!= $true )
| ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X6 @ X4 ) @ ( X2 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X6 @ X4 ) ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X5 @ X6 ) @ X4 ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) )
& ! [X4: X0 > X1,X5: X0,X6: X0 > $o] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X6 @ X4 ) @ ( X2 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X6 @ X4 ) ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X5 @ X6 ) @ X4 ) )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) )
!= $true ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ! [X6: X0 > X1] :
( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) )
& ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ ( X3 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
!= $true ) ) ) ),
inference(flattening,[],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ ( X3 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) )
& ! [X6: X0 > X1] :
( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ( ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
= $true )
& ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ ( X3 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) )
& ! [X6: X0 > X1] :
( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ( ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
& ( 'const/iterate/monoidal' @ X1 @ X2 ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ ( X3 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) )
& ! [X6: X0 > X1] :
( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ( ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
& ( 'const/iterate/monoidal' @ X1 @ X2 ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ ( X3 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) )
& ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_GEN_') ).
thf(f35,plain,
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) )
| spl8_2 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f33,plain,
( spl8_2
<=> ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
thf(f46,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f45]) ).
thf(f45,plain,
( $false
| spl8_1 ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f44,plain,
( ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
| spl8_1 ),
inference(superposition,[],[f31,f43]) ).
thf(f43,plain,
! [X0: $tType,X1: X0 > sK2] :
( ( 'const/iterate/iterate' @ X0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ X0 @ X1 )
= ( 'const/iterate/neutral' @ sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f42,plain,
! [X0: $tType,X1: X0 > sK2] :
( ( ( 'const/iterate/iterate' @ X0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ X0 @ X1 )
= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
| ( $true != $true ) ),
inference(superposition,[],[f22,f25]) ).
thf(f22,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f31,plain,
( ( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
| spl8_1 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f29,plain,
( spl8_1
<=> ( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
= ( 'const/iterate/neutral' @ sK2 @ sK3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
thf(f41,plain,
( ~ spl8_1
| spl8_3 ),
inference(avatar_split_clause,[],[f23,f38,f29]) ).
thf(f23,plain,
( ( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
| ( ( 'const/sets/FINITE' @ sK1 @ sK6 )
= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f36,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f24,f33,f29]) ).
thf(f24,plain,
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) )
| ( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEV497^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.08 % Command : run_vampire %s %d THM
% 0.08/0.26 % Computer : n032.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Fri Jun 21 18:49:38 EDT 2024
% 0.08/0.26 % CPUTime :
% 0.13/0.28 This is a TH1_THM_EQU_NAR problem
% 0.13/0.28 Running higher-order theorem proving
% 0.13/0.28 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.13/0.29 % (26700)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.29 % (26702)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)
% 0.13/0.29 % (26703)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.29 % (26701)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)
% 0.13/0.29 % (26703)Instruction limit reached!
% 0.13/0.29 % (26703)------------------------------
% 0.13/0.29 % (26703)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.29 % (26703)Termination reason: Unknown
% 0.13/0.29 % (26703)Termination phase: Property scanning
% 0.13/0.29
% 0.13/0.29 % (26703)Memory used [KB]: 1023
% 0.13/0.29 % (26703)Time elapsed: 0.002 s
% 0.13/0.29 % (26703)Instructions burned: 3 (million)
% 0.13/0.29 % (26703)------------------------------
% 0.13/0.29 % (26703)------------------------------
% 0.13/0.29 % (26705)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)
% 0.13/0.29 % (26701)Instruction limit reached!
% 0.13/0.29 % (26701)------------------------------
% 0.13/0.29 % (26701)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.29 % (26701)Termination reason: Unknown
% 0.13/0.29 % (26701)Termination phase: Saturation
% 0.13/0.29
% 0.13/0.29 % (26701)Memory used [KB]: 5500
% 0.13/0.29 % (26701)Time elapsed: 0.003 s
% 0.13/0.29 % (26701)Instructions burned: 5 (million)
% 0.13/0.29 % (26701)------------------------------
% 0.13/0.29 % (26701)------------------------------
% 0.13/0.30 % (26704)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)
% 0.13/0.30 % (26706)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.30 % Exception at run slice level
% 0.13/0.30 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
% 0.13/0.30 % (26702)First to succeed.
% 0.13/0.30 % (26705)Also succeeded, but the first one will report.
% 0.13/0.30 % (26707)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)
% 0.13/0.30 % (26702)Refutation found. Thanks to Tanya!
% 0.13/0.30 % SZS status Theorem for theBenchmark
% 0.13/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.30 % (26702)------------------------------
% 0.13/0.30 % (26702)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.30 % (26702)Termination reason: Refutation
% 0.13/0.30
% 0.13/0.30 % (26702)Memory used [KB]: 5756
% 0.13/0.30 % (26702)Time elapsed: 0.011 s
% 0.13/0.30 % (26702)Instructions burned: 19 (million)
% 0.13/0.30 % (26702)------------------------------
% 0.13/0.30 % (26702)------------------------------
% 0.13/0.30 % (26699)Success in time 0.018 s
%------------------------------------------------------------------------------