%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA095^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:54 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 102 ( 38 unt; 0 typ; 16 def)
% Number of atoms : 470 ( 115 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 779 ( 97 ~; 85 |; 23 &; 555 @)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 18 con; 0-5 aty)
% Number of variables : 71 ( 0 sgn 63 !; 8 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/DISJOINT':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_4,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_5,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_6,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_10,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_11,type,
sK2: sK0 > $o ).
thf(func_def_12,type,
sK3: sK0 > $o ).
thf(func_def_13,type,
sF4: 'type/realax/real' ).
thf(func_def_14,type,
sF5: 'type/realax/real' ).
thf(func_def_15,type,
sF6: 'type/realax/real' ).
thf(func_def_16,type,
sF7: 'type/realax/real' ).
thf(func_def_17,type,
sF8: $o ).
thf(func_def_18,type,
sF9: $o ).
thf(func_def_19,type,
sF10: $o ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(f2,axiom,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X5: X0 > $o,X3: X0 > X1,X4: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X5 )
& ( 'const/sets/DISJOINT' @ X0 @ X4 @ X5 )
& ( 'const/sets/FINITE' @ X0 @ X4 ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_UNION_') ).
thf(f3,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X3: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
& ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X3: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
& ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/sets/DISJOINT' @ X0 @ X3 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X3 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X3 @ X2 ) @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/sets/DISJOINT' @ X0 @ X3 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X3 @ X2 ) @ X1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X2 )
=> ! [X3: X1 > $o,X4: X1 > X0,X5: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X3 )
& ( 'const/sets/DISJOINT' @ X1 @ X5 @ X3 )
& ( 'const/sets/FINITE' @ X1 @ X5 ) )
=> ( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/UNION' @ X1 @ X5 @ X3 ) @ X4 )
= ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X4 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0] :
( ( $true
= ( 'const/iterate/monoidal' @ X0 @ X2 ) )
=> ! [X5: X1 > $o,X3: X1 > $o,X4: X1 > X0] :
( ( ( $true
= ( 'const/sets/FINITE' @ X1 @ X5 ) )
& ( $true
= ( 'const/sets/DISJOINT' @ X1 @ X5 @ X3 ) )
& ( ( 'const/sets/FINITE' @ X1 @ X3 )
= $true ) )
=> ( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/UNION' @ X1 @ X5 @ X3 ) @ X4 )
= ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X4 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[],[f3]) ).
thf(f11,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0] :
( ! [X5: X1 > $o,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/UNION' @ X1 @ X5 @ X3 ) @ X4 )
= ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X4 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4 ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X5 ) )
| ( $true
!= ( 'const/sets/DISJOINT' @ X1 @ X5 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X3 )
!= $true ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X2 ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0] :
( ! [X4: X1 > X0,X5: X1 > $o,X3: X1 > $o] :
( ( $true
!= ( 'const/sets/DISJOINT' @ X1 @ X5 @ X3 ) )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X5 ) )
| ( ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/UNION' @ X1 @ X5 @ X3 ) @ X4 )
= ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X4 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X3 )
!= $true ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X2 ) ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
!= ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X3 @ X2 ) @ X1 ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/sets/DISJOINT' @ X0 @ X3 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f15,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
!= ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X3 @ X2 ) @ X1 ) )
& ( ( 'const/sets/DISJOINT' @ X0 @ X3 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0] :
( ! [X3: X1 > X0,X4: X1 > $o,X5: X1 > $o] :
( ( $true
!= ( 'const/sets/DISJOINT' @ X1 @ X4 @ X5 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true )
| ( ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X3 ) )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/UNION' @ X1 @ X4 @ X5 ) @ X3 ) )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X5 ) ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X2 ) ) ),
inference(rectify,[],[f13]) ).
thf(f17,plain,
( ( ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK3 @ sK2 ) @ sK1 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 ) ) )
& ( ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ sK2 )
= $true )
& ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true )
& ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
thf(f18,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f19,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o,X5: X1 > $o] :
( ( ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X3 ) )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ ( 'const/sets/UNION' @ X1 @ X4 @ X5 ) @ X3 ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X2 ) )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X5 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true )
| ( $true
!= ( 'const/sets/DISJOINT' @ X1 @ X4 @ X5 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f23,plain,
( ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f24,plain,
( ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK3 @ sK2 ) @ sK1 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ sK1 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1 ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/UNION' @ sK0 @ sK3 @ sK2 ) @ sK1 ) ),
inference(definition_unfolding,[],[f24,f18,f18,f18]) ).
thf(f28,definition,
( sF4
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f29,definition,
( sF5
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f30,definition,
( sF6
= ( 'const/realax/real_add' @ sF4 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f31,plain,
( ( 'const/realax/real_add' @ sF4 @ sF5 )
= sF6 ),
inference(reorient_equations,[],[f30]) ).
thf(f32,definition,
( sF7
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/UNION' @ sK0 @ sK3 @ sK2 ) @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f33,plain,
sF7 != sF6,
inference(definition_folding,[],[f27,f32,f31,f29,f28]) ).
thf(f34,definition,
( sF8
= ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f35,plain,
sF8 = $true,
inference(definition_folding,[],[f23,f34]) ).
thf(f36,definition,
( sF9
= ( 'const/sets/FINITE' @ sK0 @ sK3 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f37,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= sF9 ),
inference(reorient_equations,[],[f36]) ).
thf(f38,plain,
$true = sF9,
inference(definition_folding,[],[f22,f37]) ).
thf(f39,definition,
( sF10
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f40,plain,
sF10 = $true,
inference(definition_folding,[],[f21,f39]) ).
thf(f42,plain,
( ( ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ sK2 )
= $true )
| ( sF8 = $false ) ),
inference(iff_proxy_clausification,[],[f34]) ).
thf(f44,plain,
( ( sF10 = $false )
| ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f45,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true )
| ( $false = sF9 ) ),
inference(iff_proxy_clausification,[],[f37]) ).
thf(f48,definition,
( spl11_1
<=> ( ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f50,plain,
( ( ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ sK2 )
= $true )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f52,definition,
( spl11_2
<=> ( sF8 = $false ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f54,plain,
( ( sF8 = $false )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f55,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f42,f52,f48]) ).
thf(f61,definition,
( spl11_4
<=> ( sF8 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f63,plain,
( ( sF8 = $true )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f66,definition,
( spl11_5
<=> ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f68,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f70,definition,
( spl11_6
<=> ( sF10 = $false ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f72,plain,
( ( sF10 = $false )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
( spl11_5
| spl11_6 ),
inference(avatar_split_clause,[],[f44,f70,f66]) ).
thf(f79,definition,
( spl11_8
<=> ( sF10 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f81,plain,
( ( sF10 = $true )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f88,definition,
( spl11_10
<=> ( $true = sF9 ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f90,plain,
( ( $true = sF9 )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f93,definition,
( spl11_11
<=> ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f95,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f97,definition,
( spl11_12
<=> ( $false = sF9 ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f99,plain,
( ( $false = sF9 )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f100,plain,
( spl11_11
| spl11_12 ),
inference(avatar_split_clause,[],[f45,f97,f93]) ).
thf(f101,plain,
spl11_10,
inference(avatar_split_clause,[],[f38,f88]) ).
thf(f102,plain,
spl11_8,
inference(avatar_split_clause,[],[f40,f79]) ).
thf(f103,plain,
spl11_4,
inference(avatar_split_clause,[],[f35,f61]) ).
thf(f104,plain,
( ( $false = $true )
| ~ spl11_2
| ~ spl11_4 ),
inference(forward_demodulation,[],[f63,f54]) ).
thf(f105,plain,
( $false
| ~ spl11_2
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f106,plain,
( ~ spl11_2
| ~ spl11_4 ),
inference(avatar_contradiction_clause,[],[f105]) ).
thf(f126,plain,
! [X0: sK0 > $o] :
( ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ X0 )
!= $true )
| ( ( 'const/realax/real_add' @ sF4 @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ X0 @ sK1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/UNION' @ sK0 @ sK3 @ X0 ) @ sK1 ) )
| ( $true
!= ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ X0 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(constrained_superposition,[],[f20,f28]) ).
thf(f135,plain,
( ! [X0: sK0 > $o] :
( ( $true
!= ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ X0 ) )
| ( ( 'const/sets/FINITE' @ sK0 @ X0 )
!= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/realax/real_add' @ sF4 @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ X0 @ sK1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/UNION' @ sK0 @ sK3 @ X0 ) @ sK1 ) ) )
| ~ spl11_11 ),
inference(forward_subsumption_resolution,[],[f126,f95]) ).
thf(f141,plain,
( ! [X0: sK0 > $o] :
( ( ( 'const/realax/real_add' @ sF4 @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ X0 @ sK1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/UNION' @ sK0 @ sK3 @ X0 ) @ sK1 ) )
| ( $true
!= ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ X0 ) )
| ( ( 'const/sets/FINITE' @ sK0 @ X0 )
!= $true ) )
| ~ spl11_11 ),
inference(forward_subsumption_resolution,[],[f135,f19]) ).
thf(f165,plain,
( ( ( 'const/sets/DISJOINT' @ sK0 @ sK3 @ sK2 )
!= $true )
| ( sF7
= ( 'const/realax/real_add' @ sF4 @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1 ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ~ spl11_11 ),
inference(constrained_superposition,[],[f141,f32]) ).
thf(f170,plain,
( ( sF7
= ( 'const/realax/real_add' @ sF4 @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1 ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ~ spl11_1
| ~ spl11_11 ),
inference(forward_subsumption_resolution,[],[f165,f50]) ).
thf(f174,plain,
( ( sF7
= ( 'const/realax/real_add' @ sF4 @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK1 ) ) )
| ~ spl11_1
| ~ spl11_5
| ~ spl11_11 ),
inference(forward_subsumption_resolution,[],[f170,f68]) ).
thf(f176,plain,
( ( ( 'const/realax/real_add' @ sF4 @ sF5 )
= sF7 )
| ~ spl11_1
| ~ spl11_5
| ~ spl11_11 ),
inference(forward_demodulation,[],[f174,f29]) ).
thf(f178,plain,
( ( sF7 = sF6 )
| ~ spl11_1
| ~ spl11_5
| ~ spl11_11 ),
inference(forward_demodulation,[],[f176,f31]) ).
thf(f181,plain,
( $false
| ~ spl11_1
| ~ spl11_5
| ~ spl11_11 ),
inference(forward_subsumption_resolution,[],[f178,f33]) ).
thf(f182,plain,
( ~ spl11_1
| ~ spl11_5
| ~ spl11_11 ),
inference(avatar_contradiction_clause,[],[f181]) ).
thf(f188,plain,
( ( $false = $true )
| ~ spl11_10
| ~ spl11_12 ),
inference(forward_demodulation,[],[f99,f90]) ).
thf(f189,plain,
( $false
| ~ spl11_10
| ~ spl11_12 ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f190,plain,
( ~ spl11_10
| ~ spl11_12 ),
inference(avatar_contradiction_clause,[],[f189]) ).
thf(f195,plain,
( ( $false = $true )
| ~ spl11_6
| ~ spl11_8 ),
inference(forward_demodulation,[],[f72,f81]) ).
thf(f196,plain,
( $false
| ~ spl11_6
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f197,plain,
( ~ spl11_6
| ~ spl11_8 ),
inference(avatar_contradiction_clause,[],[f196]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
( spl11_5
| spl11_6 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( spl11_11
| spl11_12 ),
inference(sat_conversion,[],[f100]) ).
cnf(s7,plain,
spl11_10,
inference(sat_conversion,[],[f101]) ).
cnf(s8,plain,
spl11_8,
inference(sat_conversion,[],[f102]) ).
cnf(s9,plain,
spl11_4,
inference(sat_conversion,[],[f103]) ).
cnf(s10,plain,
( ~ spl11_2
| ~ spl11_4 ),
inference(sat_conversion,[],[f106]) ).
cnf(s15,plain,
( ~ spl11_1
| ~ spl11_5
| ~ spl11_11 ),
inference(sat_conversion,[],[f182]) ).
cnf(s17,plain,
( ~ spl11_10
| ~ spl11_12 ),
inference(sat_conversion,[],[f190]) ).
cnf(s19,plain,
( ~ spl11_6
| ~ spl11_8 ),
inference(sat_conversion,[],[f197]) ).
cnf(s22,plain,
~ spl11_2,
inference(rat,[],[s10,s9]) ).
cnf(s23,plain,
~ spl11_6,
inference(rat,[],[s19,s8]) ).
cnf(s24,plain,
~ spl11_12,
inference(rat,[],[s17,s7]) ).
cnf(s25,plain,
spl11_11,
inference(rat,[],[s6,s24]) ).
cnf(s28,plain,
spl11_5,
inference(rat,[],[s3,s23]) ).
cnf(s31,plain,
~ spl11_1,
inference(rat,[],[s15,s25,s28]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s1,s22,s31]) ).
thf(f209,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA095^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n006.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:40:55 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.30 % (1073976)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (1073987)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (1073987)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.30 % (1073987)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1204779778:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (1073987) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1073976-1073987"...
% 0.22/0.30 % (1073983)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3862762729:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (1073981)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2470104564:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (1073982)lrs+10_16_si=on:nwc=1.5:random_seed=2050435846:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (1073985)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=401138511:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (1073984)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2123629706:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.30 % (1073986)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3552836472:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (1073987)...printing done.
% 0.22/0.30 % (1073987)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (1073987)------------------------------
% 0.22/0.30 % (1073987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1073987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1073987)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1073987)Termination reason: Refutation
% 0.22/0.30 % (1073987)Time elapsed: 0.007 s
% 0.22/0.30 % (1073987)Peak memory usage: 13 MB
% 0.22/0.30 % (1073987)Instructions burned: 19 (million)
% 0.22/0.30 % (1073976)Success in time 0.04 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------