%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV497^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Wed Feb 25 09:41:23 AM UTC 2026
% Result : Theorem 1.44s 1.20s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 3 unt; 0 typ; 3 def)
% Number of atoms : 334 ( 89 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1077 ( 52 ~; 41 |; 22 &; 939 @)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 6 con; 0-6 aty)
% Number of variables : 132 ( 0 ^; 108 !; 24 ?; 132 :)
% 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_12,type,
sK3: sK2 > sK2 > sK2 ).
thf(func_def_13,type,
sK4: sK0 > sK2 ).
thf(func_def_14,type,
sK5: sK1 > sK2 ).
thf(func_def_15,type,
sK6: sK1 ).
thf(func_def_16,type,
sK7: sK1 > $o ).
thf(func_def_18,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f71,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f35,f40,f47,f70]) ).
thf(f70,plain,
( ~ spl8_2
| spl8_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f69]) ).
thf(f69,plain,
( $false
| ~ spl8_2
| spl8_3 ),
inference(subsumption_resolution,[status(thm)],[f68,f34]) ).
thf(f34,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ sK7 )
= $true )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl8_2
<=> ( ( 'const/sets/FINITE' @ sK1 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f68,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ sK7 )
!= $true )
| spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ sK7 )
!= $true )
| ( $true != $true )
| spl8_3 ),
inference(superposition,[status(thm)],[f66,f25]) ).
thf(f25,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[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 )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X4 )
= $true )
=> ( ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,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,[status(thm)],[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/tmp/tmp.tmThA7dBK2/DTF2THF_2209.p','thm/iterate/FINITE_SUPPORT_') ).
thf(f66,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ ( 'const/iterate/support' @ sK2 @ sK1 @ sK3 @ sK5 @ sK7 ) )
!= $true )
| spl8_3 ),
inference(subsumption_resolution,[status(thm)],[f65,f20]) ).
thf(f20,plain,
( ( 'const/iterate/monoidal' @ sK2 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4 ) )
| ( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK6 @ sK7 ) @ sK5 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK6 @ sK7 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) @ ( sK3 @ ( sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) ) ) )
& ( ( 'const/sets/FINITE' @ sK1 @ sK7 )
= $true ) ) )
& ( ( 'const/iterate/monoidal' @ sK2 @ sK3 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f12,f18,f17,f16]) ).
thf(f16,plain,
( ? [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ? [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
!= ( 'const/iterate/neutral' @ X2 @ X3 ) )
| ? [X5: X1 > X2,X6: X1,X7: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X6 @ X7 ) @ X5 )
!= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X1 @ X7 ) ) ) )
& ( ( 'const/iterate/monoidal' @ X2 @ X3 )
= $true ) )
=> ( ( ? [X4: sK0 > sK2] :
( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ X4 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
| ? [X7: sK1 > $o,X6: sK1,X5: sK1 > sK2] :
( ( ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X7 @ X5 ) @ ( sK3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X7 @ X5 ) ) )
!= ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ X6 @ X7 ) @ X5 ) )
& ( $true
= ( 'const/sets/FINITE' @ sK1 @ X7 ) ) ) )
& ( ( 'const/iterate/monoidal' @ sK2 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X4: sK0 > sK2] :
( ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ X4 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
=> ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X7: sK1 > $o,X6: sK1,X5: sK1 > sK2] :
( ( ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X7 @ X5 ) @ ( sK3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X7 @ X5 ) ) )
!= ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ X6 @ X7 ) @ X5 ) )
& ( $true
= ( 'const/sets/FINITE' @ sK1 @ X7 ) ) )
=> ( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK6 @ sK7 ) @ sK5 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK6 @ sK7 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) @ ( sK3 @ ( sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) ) ) )
& ( ( 'const/sets/FINITE' @ sK1 @ sK7 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ? [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
!= ( 'const/iterate/neutral' @ X2 @ X3 ) )
| ? [X5: X1 > X2,X6: X1,X7: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X6 @ X7 ) @ X5 )
!= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X1 @ X7 ) ) ) )
& ( ( 'const/iterate/monoidal' @ X2 @ X3 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ( 'const/iterate/monoidal' @ X2 @ X3 )
= $true )
=> ( ! [X5: X1 > X2,X6: X1,X7: X1 > $o] :
( ( $true
= ( 'const/sets/FINITE' @ X1 @ X7 ) )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X6 @ X7 ) @ X5 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) ) ) ) )
& ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) )
& ! [X5: X1 > X2,X6: X1,X7: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X7 )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X6 @ X7 ) @ X5 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X6 @ X7 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X2: $tType,X3: $tType,X4: X3 > X3 > X3] :
( ( 'const/iterate/monoidal' @ X3 @ X4 )
=> ( ! [X5: X0 > X3] :
( ( 'const/iterate/iterate' @ X0 @ X3 @ X4 @ 'const/sets/EMPTY' @ X0 @ X5 )
= ( 'const/iterate/neutral' @ 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 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X2: $tType,X3: $tType,X4: X3 > X3 > X3] :
( ( 'const/iterate/monoidal' @ X3 @ X4 )
=> ( ! [X5: X0 > X3] :
( ( 'const/iterate/iterate' @ X0 @ X3 @ X4 @ 'const/sets/EMPTY' @ X0 @ X5 )
= ( 'const/iterate/neutral' @ 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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tmThA7dBK2/DTF2THF_2209.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(f65,plain,
( ( ( 'const/iterate/monoidal' @ sK2 @ sK3 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ ( 'const/iterate/support' @ sK2 @ sK1 @ sK3 @ sK5 @ sK7 ) )
!= $true )
| spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ ( 'const/iterate/support' @ sK2 @ sK1 @ sK3 @ sK5 @ sK7 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ sK2 @ sK3 )
!= $true )
| ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK6 @ sK7 ) @ sK5 )
!= ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK6 @ sK7 ) @ sK5 ) )
| spl8_3 ),
inference(superposition,[status(thm)],[f39,f26]) ).
thf(f26,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X6: X0 > $o,X4: X0 > X1,X5: X0] :
( ( ( '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 )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X6: X0 > $o,X4: X0 > X1,X5: X0] :
( ( ( '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 )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,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] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) ) )
| ( ( '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(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ! [X4: X0 > X1,X5: X0,X6: X0 > $o] :
( ( ( '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 ) )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) ) )
| ( ( '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 ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ( ! [X4: X0 > X1,X5: X0,X6: X0 > $o] :
( ( ( $true
= ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) ) )
& ( ( '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 ) ) )
& ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ( ! [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 )
& ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6 ) ) )
=> ( ( '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(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ( ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) )
& ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) ) )
=> ( ( '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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tmThA7dBK2/DTF2THF_2209.p','thm/iterate/ITERATE_CLAUSES_GEN_') ).
thf(f39,plain,
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK6 @ sK7 ) @ sK5 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK6 @ sK7 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) @ ( sK3 @ ( sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) ) ) )
| spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl8_3
<=> ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK6 @ sK7 ) @ sK5 )
= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK6 @ sK7 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) @ ( sK3 @ ( sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f47,plain,
spl8_1,
inference(avatar_contradiction_clause,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
| spl8_1 ),
inference(subsumption_resolution,[status(thm)],[f45,f20]) ).
thf(f45,plain,
( ( ( 'const/iterate/monoidal' @ sK2 @ sK3 )
!= $true )
| spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( 'const/iterate/monoidal' @ sK2 @ sK3 )
!= $true )
| ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
| spl8_1 ),
inference(superposition,[status(thm)],[f30,f24]) ).
thf(f24,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f30,plain,
( ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4 ) )
| spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl8_1
<=> ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f40,plain,
( ~ spl8_1
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f22,f37,f28]) ).
thf(f22,plain,
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK6 @ sK7 ) @ sK5 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK6 @ sK7 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) @ ( sK3 @ ( sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5 ) ) ) )
| ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f35,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f32,f28]) ).
thf(f21,plain,
( ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4 ) )
| ( ( 'const/sets/FINITE' @ sK1 @ sK7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV497^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:48:12 EST 2026
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : SEV497^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.44 % Domain : Analysis
% 0.16/0.44 % Problem : ITERATE_CLAUSES
% 0.16/0.44 % Version : Especial.
% 0.16/0.44 % English :
% 0.16/0.44
% 0.16/0.44 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.16/0.44 % Source : [Kal16]
% 0.16/0.44 % Names : ITERATE_CLAUSES_.p [Kal16]
% 0.16/0.44
% 0.16/0.44 % Status : ContradictoryAxioms
% 0.16/0.44 % Rating : 0.00 v7.1.0
% 0.16/0.44 % Syntax : Number of formulae : 12 ( 0 unt; 9 typ; 0 def)
% 0.16/0.44 % Number of atoms : 19 ( 4 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 6 ( 6 avg)
% 0.16/0.44 % Number of connectives : 104 ( 0 ~; 0 |; 3 &; 96 @)
% 0.16/0.44 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 17 ( 14 avg)
% 0.16/0.44 % Number of types : 1 ( 0 usr)
% 0.16/0.44 % Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 10 ( 9 usr; 0 con; 2-6 aty)
% 0.16/0.44 % Number of variables : 31 ( 0 ^; 20 !; 0 ?; 31 :)
% 0.16/0.44 % ( 11 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.44 % SPC : TH1_CAX_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : Exported from core HOL Light.
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 thf('thf_const_const/sets/INSERT',type,
% 0.16/0.44 'const/sets/INSERT':
% 0.16/0.44 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf('thf_const_const/sets/IN',type,
% 0.16/0.44 'const/sets/IN':
% 0.16/0.44 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf('thf_const_const/sets/FINITE',type,
% 0.16/0.44 'const/sets/FINITE':
% 0.16/0.44 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf('thf_const_const/sets/EMPTY',type,
% 0.16/0.44 'const/sets/EMPTY':
% 0.16/0.44 !>[A: $tType] : ( A > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf('thf_const_const/iterate/support',type,
% 0.16/0.44 'const/iterate/support':
% 0.16/0.44 !>[B: $tType,A: $tType] : ( ( B > B > B ) > ( A > B ) > ( A > $o ) > A > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf('thf_const_const/iterate/neutral',type,
% 0.16/0.44 'const/iterate/neutral':
% 0.16/0.44 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 0.16/0.44
% 0.16/0.44 thf('thf_const_const/iterate/monoidal',type,
% 0.16/0.44 'const/iterate/monoidal':
% 0.16/0.44 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf('thf_const_const/iterate/iterate',type,
% 0.16/0.44 'const/iterate/iterate':
% 0.16/0.44 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.16/0.44
% 0.16/0.44 thf('thf_const_const/class/COND',type,
% 0.16/0.44 'const/class/COND':
% 0.16/0.44 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.44
% 0.16/0.44 thf('thm/iterate/ITERATE_CLAUSES_GEN_',axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,A0: B > B > B] :
% 0.16/0.44 ( ( 'const/iterate/monoidal' @ B @ A0 )
% 0.16/0.44 => ( ! [A1: A > B] :
% 0.16/0.44 ( ( 'const/iterate/iterate' @ A @ B @ A0 @ ( 'const/sets/EMPTY' @ A ) @ A1 )
% 0.16/0.44 = ( 'const/iterate/neutral' @ B @ A0 ) )
% 0.16/0.44 & ! [A1: A > B,A2: A,A3: A > $o] :
% 0.16/0.44 ( ( ( 'const/iterate/monoidal' @ B @ A0 )
% 0.16/0.44 & ( 'const/sets/FINITE' @ A @ ( 'const/iterate/support' @ B @ A @ A0 @ A1 @ A3 ) ) )
% 0.16/0.44 => ( ( 'const/iterate/iterate' @ A @ B @ A0 @ ( 'const/sets/INSERT' @ A @ A2 @ A3 ) @ A1 )
% 0.16/0.44 = ( 'const/class/COND' @ B @ ( 'const/sets/IN' @ A @ A2 @ A3 ) @ ( 'const/iterate/iterate' @ A @ B @ A0 @ A3 @ A1 ) @ ( A0 @ ( A1 @ A2 ) @ ( 'const/iterate/iterate' @ A @ B @ A0 @ A3 @ A1 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf('thm/iterate/FINITE_SUPPORT_',axiom,
% 0.16/0.44 ! [A: $tType,A0: $tType,A1: A > A > A,A2: A0 > A,A3: A0 > $o] :
% 0.16/0.44 ( ( 'const/sets/FINITE' @ A0 @ A3 )
% 0.16/0.44 => ( 'const/sets/FINITE' @ A0 @ ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf('thm/iterate/ITERATE_CLAUSES_',conjecture,
% 0.16/0.44 ! [A: $tType,A0: $tType,A1: $tType,A2: A1 > A1 > A1] :
% 0.16/0.44 ( ( 'const/iterate/monoidal' @ A1 @ A2 )
% 0.16/0.44 => ( ! [A3: A > A1] :
% 0.16/0.44 ( ( 'const/iterate/iterate' @ A @ A1 @ A2 @ ( 'const/sets/EMPTY' @ A ) @ A3 )
% 0.16/0.44 = ( 'const/iterate/neutral' @ A1 @ A2 ) )
% 0.16/0.44 & ! [A3: A0 > A1,A4: A0,A5: A0 > $o] :
% 0.16/0.44 ( ( 'const/sets/FINITE' @ A0 @ A5 )
% 0.16/0.44 => ( ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ ( 'const/sets/INSERT' @ A0 @ A4 @ A5 ) @ A3 )
% 0.16/0.44 = ( 'const/class/COND' @ A1 @ ( 'const/sets/IN' @ A0 @ A4 @ A5 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) @ ( A2 @ ( A3 @ A4 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 1.36/1.16 ---- Embedded in THF ---
% 1.36/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.16 %%% Generated on Tue Feb 24 12:48:13 EST 2026
% 1.36/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.16 %%% Logic specification used:
% 1.36/1.16 %%% thf(spec, logic, $$dhol).
% 1.36/1.16
% 1.36/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tmThA7dBK2/DTF2DTF2209.p
% See solution above
% 1.36/1.16 ------------------------
% 1.36/1.17 ---- Cleaned THF ---
% 1.36/1.17 thf('thf_const_const/sets/INSERT',type,
% 1.36/1.17 'const/sets/INSERT':
% 1.36/1.17 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.36/1.17
% 1.36/1.17 thf('thf_const_const/sets/IN',type,
% 1.36/1.17 'const/sets/IN':
% 1.36/1.17 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.36/1.17
% 1.36/1.17 thf('thf_const_const/sets/FINITE',type,
% 1.36/1.17 'const/sets/FINITE':
% 1.36/1.17 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.36/1.17
% 1.36/1.17 thf('thf_const_const/sets/EMPTY',type,
% 1.36/1.17 'const/sets/EMPTY':
% 1.36/1.17 !>[A: $tType] : ( A > $o ) ).
% 1.36/1.17
% 1.36/1.17 thf('thf_const_const/iterate/support',type,
% 1.36/1.17 'const/iterate/support':
% 1.36/1.17 !>[B: $tType,A: $tType] : ( ( B > B > B ) > ( A > B ) > ( A > $o ) > A > $o ) ).
% 1.36/1.17
% 1.36/1.17 thf('thf_const_const/iterate/neutral',type,
% 1.36/1.17 'const/iterate/neutral':
% 1.36/1.17 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 1.36/1.17
% 1.36/1.17 thf('thf_const_const/iterate/monoidal',type,
% 1.36/1.17 'const/iterate/monoidal':
% 1.36/1.17 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 1.36/1.17
% 1.36/1.17 thf('thf_const_const/iterate/iterate',type,
% 1.36/1.17 'const/iterate/iterate':
% 1.36/1.17 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 1.36/1.17
% 1.36/1.17 thf('thf_const_const/class/COND',type,
% 1.36/1.17 'const/class/COND':
% 1.36/1.17 !>[A: $tType] : ( $o > A > A > A ) ).
% 1.36/1.17
% 1.36/1.17 thf('thm/iterate/ITERATE_CLAUSES_GEN_',axiom,
% 1.36/1.17 ! [A: $tType,B: $tType,A0: B > B > B] :
% 1.36/1.17 ( ( 'const/iterate/monoidal' @ B @ A0 )
% 1.36/1.17 => ( ! [A1: A > B] :
% 1.36/1.17 ( ( 'const/iterate/iterate' @ A @ B @ A0 @ ( 'const/sets/EMPTY' @ A ) @ A1 )
% 1.36/1.17 = ( 'const/iterate/neutral' @ B @ A0 ) )
% 1.36/1.17 & ! [A1: A > B,A2: A,A3: A > $o] :
% 1.36/1.17 ( ( ( 'const/iterate/monoidal' @ B @ A0 )
% 1.36/1.17 & ( 'const/sets/FINITE' @ A @ ( 'const/iterate/support' @ B @ A @ A0 @ A1 @ A3 ) ) )
% 1.36/1.17 => ( ( 'const/iterate/iterate' @ A @ B @ A0 @ ( 'const/sets/INSERT' @ A @ A2 @ A3 ) @ A1 )
% 1.36/1.17 = ( 'const/class/COND' @ B @ ( 'const/sets/IN' @ A @ A2 @ A3 ) @ ( 'const/iterate/iterate' @ A @ B @ A0 @ A3 @ A1 ) @ ( A0 @ ( A1 @ A2 ) @ ( 'const/iterate/iterate' @ A @ B @ A0 @ A3 @ A1 ) ) ) ) ) ) ) ).
% 1.36/1.17
% 1.36/1.17 thf('thm/iterate/FINITE_SUPPORT_',axiom,
% 1.36/1.17 ! [A: $tType,A0: $tType,A1: A > A > A,A2: A0 > A,A3: A0 > $o] :
% 1.36/1.17 ( ( 'const/sets/FINITE' @ A0 @ A3 )
% 1.36/1.17 => ( 'const/sets/FINITE' @ A0 @ ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A3 ) ) ) ).
% 1.36/1.17
% 1.36/1.17 thf('thm/iterate/ITERATE_CLAUSES_',conjecture,
% 1.36/1.17 ! [A: $tType,A0: $tType,A1: $tType,A2: A1 > A1 > A1] :
% 1.36/1.17 ( ( 'const/iterate/monoidal' @ A1 @ A2 )
% 1.36/1.17 => ( ! [A3: A > A1] :
% 1.36/1.17 ( ( 'const/iterate/iterate' @ A @ A1 @ A2 @ ( 'const/sets/EMPTY' @ A ) @ A3 )
% 1.36/1.17 = ( 'const/iterate/neutral' @ A1 @ A2 ) )
% 1.36/1.17 & ! [A3: A0 > A1,A4: A0,A5: A0 > $o] :
% 1.36/1.17 ( ( 'const/sets/FINITE' @ A0 @ A5 )
% 1.36/1.17 => ( ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ ( 'const/sets/INSERT' @ A0 @ A4 @ A5 ) @ A3 )
% 1.36/1.17 = ( 'const/class/COND' @ A1 @ ( 'const/sets/IN' @ A0 @ A4 @ A5 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) @ ( A2 @ ( A3 @ A4 ) @ ( 'const/iterate/iterate' @ A0 @ A1 @ A2 @ A5 @ A3 ) ) ) ) ) ) ) ).
% 1.36/1.17 ------------------------
% 1.36/1.18 % (2308)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2209 for (2999ds/183Mi)
% 1.36/1.19 % (2313)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_2209 for (2999ds/275Mi)
% 1.36/1.19 % (2309)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 DTF2THF_2209 for (2999ds/4Mi)
% 1.36/1.19 % (2311)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2209 for (2999ds/2Mi)
% 1.36/1.19 % (2310)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 DTF2THF_2209 for (2999ds/27Mi)
% 1.36/1.19 % (2312)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_2209 for (2999ds/2Mi)
% 1.36/1.19 % (2314)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2209 for (2999ds/18Mi)
% 1.36/1.19 % Exception at run slice level
% 1.36/1.19 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
% 1.36/1.19 % (2311)Instruction limit reached!
% 1.36/1.19 % (2311)------------------------------
% 1.36/1.19 % (2311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.19 % (2311)Termination reason: Unknown
% 1.36/1.19 % (2311)Termination phase: Property scanning
% 1.36/1.19
% 1.36/1.19 % (2311)Memory used [KB]: 1023
% 1.36/1.19 % (2311)Time elapsed: 0.003 s
% 1.36/1.19 % (2311)Instructions burned: 3 (million)
% 1.36/1.19 % (2311)------------------------------
% 1.36/1.19 % (2311)------------------------------
% 1.36/1.19 % (2309)Instruction limit reached!
% 1.36/1.19 % (2309)------------------------------
% 1.36/1.19 % (2309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.19 % (2309)Termination reason: Unknown
% 1.36/1.19 % (2309)Termination phase: Saturation
% 1.36/1.19
% 1.36/1.19 % (2309)Memory used [KB]: 5500
% 1.36/1.19 % (2309)Time elapsed: 0.004 s
% 1.36/1.19 % (2309)Instructions burned: 5 (million)
% 1.36/1.19 % (2309)------------------------------
% 1.36/1.19 % (2309)------------------------------
% 1.36/1.19 % (2313)First to succeed.
% 1.36/1.19 % (2314)Instruction limit reached!
% 1.36/1.19 % (2314)------------------------------
% 1.36/1.19 % (2314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.19 % (2314)Termination reason: Unknown
% 1.36/1.19 % (2314)Termination phase: Saturation
% 1.36/1.19
% 1.36/1.19 % (2314)Memory used [KB]: 5628
% 1.36/1.19 % (2314)Time elapsed: 0.011 s
% 1.36/1.19 % (2314)Instructions burned: 19 (million)
% 1.36/1.19 % (2314)------------------------------
% 1.36/1.19 % (2314)------------------------------
% 1.44/1.20 % (2313)Refutation found. Thanks to Tanya!
% 1.44/1.20 % SZS status Theorem for DTF2THF_2209
% 1.44/1.20 % SZS output start Proof for DTF2THF_2209
% 1.44/1.20 thf(type_def_6, type, sK0: $tType).
% 1.44/1.20 thf(type_def_7, type, sK1: $tType).
% 1.44/1.20 thf(type_def_8, type, sK2: $tType).
% 1.44/1.20 thf(func_def_0, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.44/1.20 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.44/1.20 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.44/1.20 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.44/1.20 thf(func_def_4, type, 'const/iterate/support': !>[X0: $tType, X1: $tType]:((X0 > X0 > X0) > (X1 > X0) > (X1 > $o) > X1 > $o)).
% 1.44/1.20 thf(func_def_5, type, 'const/iterate/neutral': !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.44/1.20 thf(func_def_6, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 1.44/1.20 thf(func_def_7, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 1.44/1.20 thf(func_def_8, type, 'const/class/COND': !>[X0: $tType]:($o > X0 > X0 > X0)).
% 1.44/1.20 thf(func_def_12, type, sK3: sK2 > sK2 > sK2).
% 1.44/1.20 thf(func_def_13, type, sK4: sK0 > sK2).
% 1.44/1.20 thf(func_def_14, type, sK5: sK1 > sK2).
% 1.44/1.20 thf(func_def_15, type, sK6: sK1).
% 1.44/1.20 thf(func_def_16, type, sK7: sK1 > $o).
% 1.44/1.20 thf(func_def_18, type, ph9: !>[X0: $tType]:(X0)).
% 1.44/1.20 thf(f71,plain,(
% 1.44/1.20 $false),
% 1.44/1.20 inference(avatar_sat_refutation,[status(thm)],[f35,f40,f47,f70])).
% 1.44/1.20 thf(f70,plain,(
% 1.44/1.20 ~spl8_2 | spl8_3),
% 1.44/1.20 inference(avatar_contradiction_clause,[status(thm)],[f69])).
% 1.44/1.20 thf(f69,plain,(
% 1.44/1.20 $false | (~spl8_2 | spl8_3)),
% 1.44/1.20 inference(subsumption_resolution,[status(thm)],[f68,f34])).
% 1.44/1.20 thf(f34,plain,(
% 1.44/1.20 (('const/sets/FINITE' @ sK1 @ sK7) = $true) | ~spl8_2),
% 1.44/1.20 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.44/1.20 thf(f32,definition,(
% 1.44/1.20 spl8_2 <=> (('const/sets/FINITE' @ sK1 @ sK7) = $true)),
% 1.44/1.20 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.44/1.20 thf(f68,plain,(
% 1.44/1.20 (('const/sets/FINITE' @ sK1 @ sK7) != $true) | spl8_3),
% 1.44/1.20 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.44/1.20 thf(f67,plain,(
% 1.44/1.20 (('const/sets/FINITE' @ sK1 @ sK7) != $true) | ($true != $true) | spl8_3),
% 1.44/1.20 inference(superposition,[status(thm)],[f66,f25])).
% 1.44/1.20 thf(f25,plain,(
% 1.44/1.20 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X0 > X0,X3 : X1 > X0,X4 : X1 > $o] : ((('const/sets/FINITE' @ X1 @ ('const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4)) = $true) | (('const/sets/FINITE' @ X1 @ X4) != $true)) )),
% 1.44/1.20 inference(cnf_transformation,[status(thm)],[f15])).
% 1.44/1.20 thf(f15,plain,(
% 1.44/1.20 ! [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) | (('const/sets/FINITE' @ X1 @ X4) != $true))),
% 1.44/1.20 inference(ennf_transformation,[status(thm)],[f9])).
% 1.44/1.20 thf(f9,plain,(
% 1.44/1.20 ! [X0 : $tType,X1 : $tType,X2 : X0 > X0 > X0,X3 : X1 > X0,X4 : X1 > $o] : ((('const/sets/FINITE' @ X1 @ X4) = $true) => (('const/sets/FINITE' @ X1 @ ('const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4)) = $true))),
% 1.44/1.20 inference(fool_elimination,[status(thm)],[f8])).
% 1.44/1.20 thf(f8,plain,(
% 1.44/1.20 ! [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)))),
% 1.44/1.20 inference(rectify,[status(thm)],[f2])).
% 1.44/1.20 thf(f2,axiom,(
% 1.44/1.20 ! [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)))),
% 1.44/1.20 file('/export/starexec/sandbox/tmp/tmp.tmThA7dBK2/DTF2THF_2209.p','thm/iterate/FINITE_SUPPORT_')).
% 1.44/1.20 thf(f66,plain,(
% 1.44/1.20 (('const/sets/FINITE' @ sK1 @ ('const/iterate/support' @ sK2 @ sK1 @ sK3 @ sK5 @ sK7)) != $true) | spl8_3),
% 1.44/1.20 inference(subsumption_resolution,[status(thm)],[f65,f20])).
% 1.44/1.20 thf(f20,plain,(
% 1.44/1.20 (('const/iterate/monoidal' @ sK2 @ sK3) = $true)),
% 1.44/1.20 inference(cnf_transformation,[status(thm)],[f19])).
% 1.44/1.20 thf(f19,plain,(
% 1.44/1.20 ((('const/iterate/neutral' @ sK2 @ sK3) != ('const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4)) | ((('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ sK6 @ sK7) @ sK5) != ('const/class/COND' @ sK2 @ ('const/sets/IN' @ sK1 @ sK6 @ sK7) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5) @ (sK3 @ (sK5 @ sK6) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5)))) & (('const/sets/FINITE' @ sK1 @ sK7) = $true))) & (('const/iterate/monoidal' @ sK2 @ sK3) = $true)),
% 1.44/1.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f12,f18,f17,f16])).
% 1.44/1.20 thf(f16,plain,(
% 1.44/1.20 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : ((? [X4 : X0 > X2] : (('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4) != ('const/iterate/neutral' @ X2 @ X3)) | ? [X5 : X1 > X2,X6 : X1,X7 : X1 > $o] : ((('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X6 @ X7) @ X5) != ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X6 @ X7) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5) @ (X3 @ (X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5)))) & ($true = ('const/sets/FINITE' @ X1 @ X7)))) & (('const/iterate/monoidal' @ X2 @ X3) = $true)) => ((? [X4 : sK0 > sK2] : (('const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ X4) != ('const/iterate/neutral' @ sK2 @ sK3)) | ? [X7 : sK1 > $o,X6 : sK1,X5 : sK1 > sK2] : ((('const/class/COND' @ sK2 @ ('const/sets/IN' @ sK1 @ X6 @ X7) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X7 @ X5) @ (sK3 @ (X5 @ X6) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X7 @ X5))) != ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ X6 @ X7) @ X5)) & ($true = ('const/sets/FINITE' @ sK1 @ X7)))) & (('const/iterate/monoidal' @ sK2 @ sK3) = $true))),
% 1.44/1.20 introduced(definition,[],[choice_axiom])).
% 1.44/1.20 thf(f17,plain,(
% 1.44/1.20 ? [X4 : sK0 > sK2] : (('const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ X4) != ('const/iterate/neutral' @ sK2 @ sK3)) => (('const/iterate/neutral' @ sK2 @ sK3) != ('const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4))),
% 1.44/1.20 introduced(definition,[],[choice_axiom])).
% 1.44/1.20 thf(f18,plain,(
% 1.44/1.20 ? [X7 : sK1 > $o,X6 : sK1,X5 : sK1 > sK2] : ((('const/class/COND' @ sK2 @ ('const/sets/IN' @ sK1 @ X6 @ X7) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X7 @ X5) @ (sK3 @ (X5 @ X6) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ X7 @ X5))) != ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ X6 @ X7) @ X5)) & ($true = ('const/sets/FINITE' @ sK1 @ X7))) => ((('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ sK6 @ sK7) @ sK5) != ('const/class/COND' @ sK2 @ ('const/sets/IN' @ sK1 @ sK6 @ sK7) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5) @ (sK3 @ (sK5 @ sK6) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5)))) & (('const/sets/FINITE' @ sK1 @ sK7) = $true))),
% 1.44/1.20 introduced(definition,[],[choice_axiom])).
% 1.44/1.20 thf(f12,plain,(
% 1.44/1.20 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : ((? [X4 : X0 > X2] : (('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4) != ('const/iterate/neutral' @ X2 @ X3)) | ? [X5 : X1 > X2,X6 : X1,X7 : X1 > $o] : ((('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X6 @ X7) @ X5) != ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X6 @ X7) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5) @ (X3 @ (X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5)))) & ($true = ('const/sets/FINITE' @ X1 @ X7)))) & (('const/iterate/monoidal' @ X2 @ X3) = $true))),
% 1.44/1.20 inference(ennf_transformation,[status(thm)],[f7])).
% 1.44/1.20 thf(f7,plain,(
% 1.44/1.20 ~! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : ((('const/iterate/monoidal' @ X2 @ X3) = $true) => (! [X5 : X1 > X2,X6 : X1,X7 : X1 > $o] : (($true = ('const/sets/FINITE' @ X1 @ X7)) => (('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X6 @ X7) @ X5) = ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X6 @ X7) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5) @ (X3 @ (X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5))))) & ! [X4 : X0 > X2] : (('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4) = ('const/iterate/neutral' @ X2 @ X3))))),
% 1.44/1.20 inference(fool_elimination,[status(thm)],[f6])).
% 1.44/1.20 thf(f6,plain,(
% 1.44/1.20 ~! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X2 > X2] : (('const/iterate/monoidal' @ X2 @ X3) => (! [X4 : X0 > X2] : (('const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4) = ('const/iterate/neutral' @ X2 @ X3)) & ! [X5 : X1 > X2,X6 : X1,X7 : X1 > $o] : (('const/sets/FINITE' @ X1 @ X7) => (('const/iterate/iterate' @ X1 @ X2 @ X3 @ ('const/sets/INSERT' @ X1 @ X6 @ X7) @ X5) = ('const/class/COND' @ X2 @ ('const/sets/IN' @ X1 @ X6 @ X7) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5) @ (X3 @ (X5 @ X6) @ ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X7 @ X5)))))))),
% 1.44/1.20 inference(rectify,[status(thm)],[f4])).
% 1.44/1.20 thf(f4,negated_conjecture,(
% 1.44/1.20 ~! [X0 : $tType,X2 : $tType,X3 : $tType,X4 : X3 > X3 > X3] : (('const/iterate/monoidal' @ X3 @ X4) => (! [X5 : X0 > X3] : (('const/iterate/iterate' @ X0 @ X3 @ X4 @ 'const/sets/EMPTY' @ X0 @ X5) = ('const/iterate/neutral' @ 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)))))))),
% 1.44/1.20 inference(negated_conjecture,[status(cth)],[f3])).
% 1.44/1.20 thf(f3,conjecture,(
% 1.44/1.20 ! [X0 : $tType,X2 : $tType,X3 : $tType,X4 : X3 > X3 > X3] : (('const/iterate/monoidal' @ X3 @ X4) => (! [X5 : X0 > X3] : (('const/iterate/iterate' @ X0 @ X3 @ X4 @ 'const/sets/EMPTY' @ X0 @ X5) = ('const/iterate/neutral' @ 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)))))))),
% 1.44/1.20 file('/export/starexec/sandbox/tmp/tmp.tmThA7dBK2/DTF2THF_2209.p','thm/iterate/ITERATE_CLAUSES_')).
% 1.44/1.20 thf(f65,plain,(
% 1.44/1.20 (('const/iterate/monoidal' @ sK2 @ sK3) != $true) | (('const/sets/FINITE' @ sK1 @ ('const/iterate/support' @ sK2 @ sK1 @ sK3 @ sK5 @ sK7)) != $true) | spl8_3),
% 1.44/1.20 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.44/1.20 thf(f64,plain,(
% 1.44/1.20 (('const/sets/FINITE' @ sK1 @ ('const/iterate/support' @ sK2 @ sK1 @ sK3 @ sK5 @ sK7)) != $true) | (('const/iterate/monoidal' @ sK2 @ sK3) != $true) | (('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ sK6 @ sK7) @ sK5) != ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ sK6 @ sK7) @ sK5)) | spl8_3),
% 1.44/1.20 inference(superposition,[status(thm)],[f39,f26])).
% 1.44/1.20 thf(f26,plain,(
% 1.44/1.20 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X6 : X0 > $o,X4 : X0 > X1,X5 : X0] : ((('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) != $true) | ($true != ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6)))) )),
% 1.44/1.20 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 1.44/1.20 thf(f23,plain,(
% 1.44/1.20 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X6 : X0 > $o,X4 : X0 > X1,X5 : X0] : ((('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) != $true) | ($true != ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6))) | (('const/iterate/monoidal' @ X1 @ X2) != $true)) )),
% 1.44/1.20 inference(cnf_transformation,[status(thm)],[f14])).
% 1.44/1.20 thf(f14,plain,(
% 1.44/1.20 ! [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 > $o] : (($true != ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6))) | (('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)))))),
% 1.44/1.20 inference(flattening,[status(thm)],[f13])).
% 1.44/1.20 thf(f13,plain,(
% 1.44/1.20 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : ((! [X4 : X0 > X1,X5 : X0,X6 : X0 > $o] : ((('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X5 @ X6) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X6 @ X4) @ (X2 @ (X4 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X6 @ X4))) = ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X5 @ X6) @ X4)) | (($true != ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6))) | (('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))) | (('const/iterate/monoidal' @ X1 @ X2) != $true))),
% 1.44/1.20 inference(ennf_transformation,[status(thm)],[f11])).
% 1.44/1.20 thf(f11,plain,(
% 1.44/1.20 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : ((('const/iterate/monoidal' @ X1 @ X2) = $true) => (! [X4 : X0 > X1,X5 : X0,X6 : X0 > $o] : ((($true = ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6))) & (('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))) & ! [X3 : X0 > X1] : (('const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3) = ('const/iterate/neutral' @ X1 @ X2))))),
% 1.44/1.20 inference(fool_elimination,[status(thm)],[f10])).
% 1.44/1.20 thf(f10,plain,(
% 1.44/1.20 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (('const/iterate/monoidal' @ X1 @ X2) => (! [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) & ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X6))) => (('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)))))),
% 1.44/1.20 inference(rectify,[status(thm)],[f1])).
% 1.44/1.20 thf(f1,axiom,(
% 1.44/1.20 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (('const/iterate/monoidal' @ X1 @ X2) => (! [X3 : X0 > X1] : (('const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3) = ('const/iterate/neutral' @ X1 @ X2)) & ! [X3 : X0 > X1,X4 : X0,X5 : X0 > $o] : ((('const/iterate/monoidal' @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ ('const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5))) => (('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)))))))),
% 1.44/1.20 file('/export/starexec/sandbox/tmp/tmp.tmThA7dBK2/DTF2THF_2209.p','thm/iterate/ITERATE_CLAUSES_GEN_')).
% 1.44/1.20 thf(f39,plain,(
% 1.44/1.20 (('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ sK6 @ sK7) @ sK5) != ('const/class/COND' @ sK2 @ ('const/sets/IN' @ sK1 @ sK6 @ sK7) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5) @ (sK3 @ (sK5 @ sK6) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5)))) | spl8_3),
% 1.44/1.20 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.44/1.20 thf(f37,definition,(
% 1.44/1.20 spl8_3 <=> (('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ sK6 @ sK7) @ sK5) = ('const/class/COND' @ sK2 @ ('const/sets/IN' @ sK1 @ sK6 @ sK7) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5) @ (sK3 @ (sK5 @ sK6) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5))))),
% 1.44/1.20 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.44/1.20 thf(f47,plain,(
% 1.44/1.20 spl8_1),
% 1.44/1.20 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.44/1.20 thf(f46,plain,(
% 1.44/1.20 $false | spl8_1),
% 1.44/1.20 inference(subsumption_resolution,[status(thm)],[f45,f20])).
% 1.44/1.20 thf(f45,plain,(
% 1.44/1.20 (('const/iterate/monoidal' @ sK2 @ sK3) != $true) | spl8_1),
% 1.44/1.20 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.44/1.20 thf(f44,plain,(
% 1.44/1.20 (('const/iterate/monoidal' @ sK2 @ sK3) != $true) | (('const/iterate/neutral' @ sK2 @ sK3) != ('const/iterate/neutral' @ sK2 @ sK3)) | spl8_1),
% 1.44/1.20 inference(superposition,[status(thm)],[f30,f24])).
% 1.44/1.20 thf(f24,plain,(
% 1.44/1.20 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X3 : X0 > X1] : ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3) = ('const/iterate/neutral' @ X1 @ X2)) | (('const/iterate/monoidal' @ X1 @ X2) != $true)) )),
% 1.44/1.20 inference(cnf_transformation,[status(thm)],[f14])).
% 1.44/1.20 thf(f30,plain,(
% 1.44/1.20 (('const/iterate/neutral' @ sK2 @ sK3) != ('const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4)) | spl8_1),
% 1.44/1.20 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.44/1.20 thf(f28,definition,(
% 1.44/1.20 spl8_1 <=> (('const/iterate/neutral' @ sK2 @ sK3) = ('const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4))),
% 1.44/1.20 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.44/1.20 thf(f40,plain,(
% 1.44/1.20 ~spl8_1 | ~spl8_3),
% 1.44/1.20 inference(avatar_split_clause,[status(thm)],[f22,f37,f28])).
% 1.44/1.20 thf(f22,plain,(
% 1.44/1.20 (('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ('const/sets/INSERT' @ sK1 @ sK6 @ sK7) @ sK5) != ('const/class/COND' @ sK2 @ ('const/sets/IN' @ sK1 @ sK6 @ sK7) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5) @ (sK3 @ (sK5 @ sK6) @ ('const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK7 @ sK5)))) | (('const/iterate/neutral' @ sK2 @ sK3) != ('const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4))),
% 1.44/1.20 inference(cnf_transformation,[status(thm)],[f19])).
% 1.44/1.20 thf(f35,plain,(
% 1.44/1.20 ~spl8_1 | spl8_2),
% 1.44/1.20 inference(avatar_split_clause,[status(thm)],[f21,f32,f28])).
% 1.44/1.20 thf(f21,plain,(
% 1.44/1.20 (('const/iterate/neutral' @ sK2 @ sK3) != ('const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK4)) | (('const/sets/FINITE' @ sK1 @ sK7) = $true)),
% 1.44/1.20 inference(cnf_transformation,[status(thm)],[f19])).
% 1.44/1.20 % SZS output end Proof for DTF2THF_2209
% 1.44/1.20 % (2313)------------------------------
% 1.44/1.20 % (2313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.20 % (2313)Termination reason: Refutation
% 1.44/1.20
% 1.44/1.20 % (2313)Memory used [KB]: 5756
% 1.44/1.20 % (2313)Time elapsed: 0.011 s
% 1.44/1.20 % (2313)Instructions burned: 15 (million)
% 1.44/1.20 % (2313)------------------------------
% 1.44/1.20 % (2313)------------------------------
% 1.44/1.20 % (2307)Success in time 0.026 s
%------------------------------------------------------------------------------