%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV512^1 : 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 : n023.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 09:41:25 AM UTC 2026
% Result : Theorem 1.71s 1.34s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 592 ( 224 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 1774 ( 122 ~; 107 |; 58 &;1468 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 85 ( 85 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 3 con; 0-7 aty)
% Number of variables : 166 ( 0 ^; 145 !; 21 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
'type/realax/real': $tType ).
thf(type_def_8,type,
sK2: $tType ).
thf(type_def_9,type,
sK3: $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'type/nums/num': $tType ).
thf(func_def_2,type,
'const/trivia/o':
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X2 ) > ( X1 > X0 ) > X1 > X2 ) ).
thf(func_def_3,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/IMAGE':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > $o ) > X1 > $o ) ).
thf(func_def_5,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_7,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_8,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_9,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_10,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_11,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_12,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_13,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_17,type,
sK0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > $o ) > ( X1 > X2 ) > ( X2 > X0 ) > ( X0 > X0 > X0 ) > X1 ) ).
thf(func_def_18,type,
sK1:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > $o ) > ( X1 > X2 ) > ( X2 > X0 ) > ( X0 > X0 > X0 ) > X1 ) ).
thf(func_def_19,type,
sK4: sK3 > 'type/realax/real' ).
thf(func_def_20,type,
sK5: sK2 > sK3 ).
thf(func_def_21,type,
sK6: sK2 > $o ).
thf(func_def_23,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f74,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f73,f34]) ).
thf(f34,plain,
( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ),
inference(definition_unfolding,[status(thm)],[f30,f29,f29]) ).
thf(f29,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $tType] :
( 'const/iterate/sum'
@ ( X1
= ( 'const/iterate/iterate' @ X1 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/sum_') ).
thf(f30,plain,
( ( 'const/iterate/sum' @ sK2 @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
!= ( 'const/iterate/sum' @ sK3 @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X5: sK2,X6: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X5 @ sK6 ) )
| ( ( sK5 @ X6 )
!= ( sK5 @ X5 ) )
| ( X5 = X6 )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X6 @ sK6 ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ X5 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
& ( ( 'const/iterate/sum' @ sK2 @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
!= ( 'const/iterate/sum' @ sK3 @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f18,f21]) ).
thf(f21,plain,
! [X0: $tType] :
( ? [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ! [X5: X0,X6: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
| ( ( X3 @ X6 )
!= ( X3 @ X5 ) )
| ( X5 = X6 )
| ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
!= $true )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X0 @ X4 ) )
& ( ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 )
!= ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) ) ) )
=> ( ! [X6: sK2,X5: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X5 @ sK6 ) )
| ( ( sK5 @ X6 )
!= ( sK5 @ X5 ) )
| ( X5 = X6 )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X6 @ sK6 ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ X5 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
& ( ( 'const/iterate/sum' @ sK2 @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
!= ( 'const/iterate/sum' @ sK3 @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
? [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ! [X5: X0,X6: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
| ( ( X3 @ X6 )
!= ( X3 @ X5 ) )
| ( X5 = X6 )
| ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
!= $true )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X0 @ X4 ) )
& ( ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 )
!= ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
? [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ( ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 )
!= ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) ) )
& ! [X5: X0,X6: X0] :
( ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
| ( X5 = X6 )
| ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
!= $true )
| ( ( X3 @ X6 )
!= ( X3 @ X5 ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X0 @ X4 ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ( ! [X5: X0,X6: X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
& ( X5 != X6 )
& ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
= $true )
& ( ( X3 @ X6 )
= ( X3 @ X5 ) ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X0 @ X4 ) ) )
=> ( ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ( ! [X5: X0,X6: X0] :
( ( ( X5 != X6 )
& ( 'const/sets/IN' @ X0 @ X5 @ X4 )
& ( ( X3 @ X6 )
= ( X3 @ X5 ) )
& ( 'const/sets/IN' @ X0 @ X6 @ X4 ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) ) )
& ( 'const/sets/FINITE' @ X0 @ X4 ) )
=> ( ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X1: $tType,X0: $tType,X3: X0 > 'type/realax/real',X4: X1 > X0,X5: X1 > $o] :
( ( ! [X6: X1,X7: X1] :
( ( ( X6 != X7 )
& ( 'const/sets/IN' @ X1 @ X6 @ X5 )
& ( ( X4 @ X6 )
= ( X4 @ X7 ) )
& ( 'const/sets/IN' @ X1 @ X7 @ X5 ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X3 @ ( X4 @ X6 ) ) ) )
& ( 'const/sets/FINITE' @ X1 @ X5 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/iterate/sum' @ X1 @ X5 @ ( 'const/trivia/o' @ X0 @ X1 @ 'type/realax/real' @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X1: $tType,X0: $tType,X3: X0 > 'type/realax/real',X4: X1 > X0,X5: X1 > $o] :
( ( ! [X6: X1,X7: X1] :
( ( ( X6 != X7 )
& ( 'const/sets/IN' @ X1 @ X6 @ X5 )
& ( ( X4 @ X6 )
= ( X4 @ X7 ) )
& ( 'const/sets/IN' @ X1 @ X7 @ X5 ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X3 @ ( X4 @ X6 ) ) ) )
& ( 'const/sets/FINITE' @ X1 @ X5 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/iterate/sum' @ X1 @ X5 @ ( 'const/trivia/o' @ X0 @ X1 @ 'type/realax/real' @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/SUM_IMAGE_NONZERO_') ).
thf(f73,plain,
( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ),
inference(subsumption_resolution,[status(thm)],[f72,f23]) ).
thf(f23,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f72,plain,
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(subsumption_resolution,[status(thm)],[f71,f31]) ).
thf(f31,plain,
( $true
= ( 'const/sets/FINITE' @ sK2 @ sK6 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f71,plain,
( ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
!= ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
| ( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(superposition,[status(thm)],[f27,f63]) ).
thf(f63,plain,
( ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ),
inference(subsumption_resolution,[status(thm)],[f62,f48]) ).
thf(f48,plain,
( $true
= ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) ),
inference(subsumption_resolution,[status(thm)],[f47,f31]) ).
thf(f47,plain,
( ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) ) ),
inference(subsumption_resolution,[status(thm)],[f39,f23]) ).
thf(f39,plain,
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) )
| ( ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(superposition,[status(thm)],[f34,f25]) ).
thf(f25,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
| ( $true
= ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
| ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( ( $true
= ( 'const/sets/IN' @ X1 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 ) )
& ( ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 )
!= ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
& ( ( X4 @ ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) )
!= ( 'const/iterate/neutral' @ X0 @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 ) )
& ( ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
= ( X5 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f19]) ).
thf(f19,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: X0 > X0 > X0,X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ? [X7: X1,X8: X1] :
( ( ( 'const/sets/IN' @ X1 @ X8 @ X6 )
= $true )
& ( X7 != X8 )
& ( ( X4 @ ( X5 @ X7 ) )
!= ( 'const/iterate/neutral' @ X0 @ X3 ) )
& ( ( 'const/sets/IN' @ X1 @ X7 @ X6 )
= $true )
& ( ( X5 @ X8 )
= ( X5 @ X7 ) ) )
=> ( ( $true
= ( 'const/sets/IN' @ X1 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 ) )
& ( ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 )
!= ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
& ( ( X4 @ ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) )
!= ( 'const/iterate/neutral' @ X0 @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 ) )
& ( ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
= ( X5 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
| ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ? [X7: X1,X8: X1] :
( ( ( 'const/sets/IN' @ X1 @ X8 @ X6 )
= $true )
& ( X7 != X8 )
& ( ( X4 @ ( X5 @ X7 ) )
!= ( 'const/iterate/neutral' @ X0 @ X3 ) )
& ( ( 'const/sets/IN' @ X1 @ X7 @ X6 )
= $true )
& ( ( X5 @ X8 )
= ( X5 @ X7 ) ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) )
| ? [X7: X1,X8: X1] :
( ( ( X4 @ ( X5 @ X7 ) )
!= ( 'const/iterate/neutral' @ X0 @ X3 ) )
& ( ( X5 @ X8 )
= ( X5 @ X7 ) )
& ( X7 != X8 )
& ( ( 'const/sets/IN' @ X1 @ X7 @ X6 )
= $true )
& ( ( 'const/sets/IN' @ X1 @ X8 @ X6 )
= $true ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ( $true
= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
=> ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ! [X7: X1,X8: X1] :
( ( ( ( X5 @ X8 )
= ( X5 @ X7 ) )
& ( X7 != X8 )
& ( ( 'const/sets/IN' @ X1 @ X7 @ X6 )
= $true )
& ( ( 'const/sets/IN' @ X1 @ X8 @ X6 )
= $true ) )
=> ( ( X4 @ ( X5 @ X7 ) )
= ( 'const/iterate/neutral' @ X0 @ X3 ) ) )
& ( ( 'const/sets/FINITE' @ X1 @ X6 )
= $true ) )
=> ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X3 )
=> ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ! [X7: X1,X8: X1] :
( ( ( ( X5 @ X8 )
= ( X5 @ X7 ) )
& ( X7 != X8 )
& ( 'const/sets/IN' @ X1 @ X7 @ X6 )
& ( 'const/sets/IN' @ X1 @ X8 @ X6 ) )
=> ( ( X4 @ ( X5 @ X7 ) )
= ( 'const/iterate/neutral' @ X0 @ X3 ) ) )
& ( 'const/sets/FINITE' @ X1 @ X6 ) )
=> ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ! [X4: X0 > X2,X5: X1 > X0,X6: X1 > $o] :
( ( ! [X7: X1,X8: X1] :
( ( ( ( X5 @ X7 )
= ( X5 @ X8 ) )
& ( X7 != X8 )
& ( 'const/sets/IN' @ X1 @ X7 @ X6 )
& ( 'const/sets/IN' @ X1 @ X8 @ X6 ) )
=> ( ( X4 @ ( X5 @ X7 ) )
= ( 'const/iterate/neutral' @ X2 @ X3 ) ) )
& ( 'const/sets/FINITE' @ X1 @ X6 ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ ( 'const/trivia/o' @ X0 @ X1 @ X2 @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/ITERATE_IMAGE_NONZERO_') ).
thf(f62,plain,
( ( $true
!= ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) )
| ( ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ),
inference(equality_resolution,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: sK2] :
( ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK6 ) )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 ) ),
inference(subsumption_resolution,[status(thm)],[f59,f23]) ).
thf(f59,plain,
! [X0: sK2] :
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK6 ) )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f58,f31]) ).
thf(f58,plain,
! [X0: sK2] :
( ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK6 ) ) ),
inference(subsumption_resolution,[status(thm)],[f57,f44]) ).
thf(f44,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) ),
inference(forward_demodulation,[status(thm)],[f43,f33]) ).
thf(f33,plain,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/NEUTRAL_REAL_ADD_') ).
thf(f43,plain,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f42,f31]) ).
thf(f42,plain,
( ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f41,f23]) ).
thf(f41,plain,
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(superposition,[status(thm)],[f34,f26]) ).
thf(f26,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( ( X4 @ ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) )
!= ( 'const/iterate/neutral' @ X0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f57,plain,
! [X0: sK2] :
( ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK6 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f56,f46]) ).
thf(f46,plain,
( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) ),
inference(subsumption_resolution,[status(thm)],[f45,f23]) ).
thf(f45,plain,
( ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f40,f31]) ).
thf(f40,plain,
( ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(superposition,[status(thm)],[f34,f28]) ).
thf(f28,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( $true
= ( 'const/sets/IN' @ X1 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f56,plain,
! [X0: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: sK2] :
( ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK6 ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 ) )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK6 ) ) ),
inference(superposition,[status(thm)],[f34,f35]) ).
thf(f35,plain,
! [X0: $tType,X2: sK3 > X0,X3: X0 > X0 > X0,X1: sK2 > $o,X4: sK2] :
( ( ( 'const/iterate/iterate' @ sK2 @ X0 @ X3 @ X1 @ ( 'const/trivia/o' @ sK3 @ sK2 @ X0 @ X2 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ X1 ) @ X2 ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3 ) ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ ( sK1 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3 ) @ sK6 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ X1 ) )
| ( ( sK5 @ ( sK0 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3 ) )
!= ( sK5 @ X4 ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X4 @ sK6 ) )
| ( ( sK1 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3 )
= X4 ) ),
inference(superposition,[status(thm)],[f32,f24]) ).
thf(f24,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
= ( X5 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
| ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f32,plain,
! [X6: sK2,X5: sK2] :
( ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ X5 ) ) )
| ( X5 = X6 )
| ( ( sK5 @ X6 )
!= ( sK5 @ X5 ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X5 @ sK6 ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X6 @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f27,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 )
!= ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
| ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV512^1 : 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
% 0.15/0.33 % Computer : n023.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:49:04 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEV512^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Analysis
% 0.19/0.45 % Problem : SUM_IMAGE_NONZERO
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Kal16]
% 0.19/0.45 % Names : SUM_IMAGE_NONZERO_.p [Kal16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 19 ( 3 unt; 14 typ; 1 def)
% 0.19/0.45 % Number of atoms : 20 ( 10 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 8 ( 4 avg)
% 0.19/0.45 % Number of connectives : 89 ( 2 ~; 0 |; 8 &; 74 @)
% 0.19/0.45 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 19 ( 8 avg)
% 0.19/0.45 % Number of types : 3 ( 2 usr)
% 0.19/0.45 % Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 13 ( 12 usr; 1 con; 0-6 aty)
% 0.19/0.45 % Number of variables : 29 ( 0 ^; 17 !; 0 ?; 29 :)
% 0.19/0.45 % ( 12 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : Exported from core HOL Light.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf('thf_type_type/realax/real',type,
% 0.19/0.45 'type/realax/real': $tType ).
% 0.19/0.45
% 0.19/0.45 thf('thf_type_type/nums/num',type,
% 0.19/0.45 'type/nums/num': $tType ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/trivia/o',type,
% 0.19/0.45 'const/trivia/o':
% 0.19/0.45 !>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/IN',type,
% 0.19/0.45 'const/sets/IN':
% 0.19/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/IMAGE',type,
% 0.19/0.45 'const/sets/IMAGE':
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > $o ) > B > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/FINITE',type,
% 0.19/0.45 'const/sets/FINITE':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/realax/real_of_num',type,
% 0.19/0.45 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/realax/real_add',type,
% 0.19/0.45 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/nums/NUMERAL',type,
% 0.19/0.45 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/nums/_0',type,
% 0.19/0.45 'const/nums/_0': 'type/nums/num' ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/sum',type,
% 0.19/0.45 'const/iterate/sum':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/neutral',type,
% 0.19/0.45 'const/iterate/neutral':
% 0.19/0.45 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/monoidal',type,
% 0.19/0.45 'const/iterate/monoidal':
% 0.19/0.45 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/iterate',type,
% 0.19/0.45 'const/iterate/iterate':
% 0.19/0.45 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/ITERATE_IMAGE_NONZERO_',axiom,
% 0.19/0.45 ! [C: $tType,A: $tType,B: $tType,A0: C > C > C] :
% 0.19/0.45 ( ( 'const/iterate/monoidal' @ C @ A0 )
% 0.19/0.45 => ! [A1: B > C,A2: A > B,A3: A > $o] :
% 0.19/0.45 ( ( ( 'const/sets/FINITE' @ A @ A3 )
% 0.19/0.45 & ! [A4: A,A5: A] :
% 0.19/0.45 ( ( ( 'const/sets/IN' @ A @ A4 @ A3 )
% 0.19/0.45 & ( 'const/sets/IN' @ A @ A5 @ A3 )
% 0.19/0.45 & ( A4 != A5 )
% 0.19/0.45 & ( ( A2 @ A4 )
% 0.19/0.45 = ( A2 @ A5 ) ) )
% 0.19/0.45 => ( ( A1 @ ( A2 @ A4 ) )
% 0.19/0.45 = ( 'const/iterate/neutral' @ C @ A0 ) ) ) )
% 0.19/0.45 => ( ( 'const/iterate/iterate' @ B @ C @ A0 @ ( 'const/sets/IMAGE' @ A @ B @ A2 @ A3 ) @ A1 )
% 0.19/0.45 = ( 'const/iterate/iterate' @ A @ C @ A0 @ A3 @ ( 'const/trivia/o' @ B @ A @ C @ A1 @ A2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 0.19/0.45 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/sum_',definition,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( 'const/iterate/sum' @ A )
% 0.19/0.45 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/NEUTRAL_REAL_ADD_',axiom,
% 0.19/0.45 ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
% 0.19/0.45 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/SUM_IMAGE_NONZERO_',conjecture,
% 0.19/0.45 ! [A: $tType,B: $tType,A0: B > 'type/realax/real',A1: A > B,A2: A > $o] :
% 0.19/0.45 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.19/0.45 & ! [A3: A,A4: A] :
% 0.19/0.45 ( ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 0.19/0.45 & ( 'const/sets/IN' @ A @ A4 @ A2 )
% 0.19/0.45 & ( A3 != A4 )
% 0.19/0.45 & ( ( A1 @ A3 )
% 0.19/0.45 = ( A1 @ A4 ) ) )
% 0.19/0.45 => ( ( A0 @ ( A1 @ A3 ) )
% 0.19/0.45 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) )
% 0.19/0.45 => ( ( 'const/iterate/sum' @ B @ ( 'const/sets/IMAGE' @ A @ B @ A1 @ A2 ) @ A0 )
% 0.19/0.45 = ( 'const/iterate/sum' @ A @ A2 @ ( 'const/trivia/o' @ B @ A @ 'type/realax/real' @ A0 @ A1 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.54/1.28 ---- Embedded in THF ---
% 1.54/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.28 %%% Generated on Tue Feb 24 12:49:05 EST 2026
% 1.54/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.28 %%% Logic specification used:
% 1.54/1.28 %%% thf(spec, logic, $$dhol).
% 1.54/1.28
% 1.54/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2DTF30363.p
% See solution above
% 1.54/1.28 ------------------------
% 1.54/1.29 ---- Cleaned THF ---
% 1.54/1.29 thf('thf_type_type/realax/real',type,
% 1.54/1.29 'type/realax/real': $tType ).
% 1.54/1.29
% 1.54/1.29 thf('thf_type_type/nums/num',type,
% 1.54/1.29 'type/nums/num': $tType ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/trivia/o',type,
% 1.54/1.29 'const/trivia/o':
% 1.54/1.29 !>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/sets/IN',type,
% 1.54/1.29 'const/sets/IN':
% 1.54/1.29 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/sets/IMAGE',type,
% 1.54/1.29 'const/sets/IMAGE':
% 1.54/1.29 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > $o ) > B > $o ) ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/sets/FINITE',type,
% 1.54/1.29 'const/sets/FINITE':
% 1.54/1.29 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/realax/real_of_num',type,
% 1.54/1.29 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/realax/real_add',type,
% 1.54/1.29 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/nums/NUMERAL',type,
% 1.54/1.29 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/nums/_0',type,
% 1.54/1.29 'const/nums/_0': 'type/nums/num' ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/iterate/sum',type,
% 1.54/1.29 'const/iterate/sum':
% 1.54/1.29 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/iterate/neutral',type,
% 1.54/1.29 'const/iterate/neutral':
% 1.54/1.29 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/iterate/monoidal',type,
% 1.54/1.29 'const/iterate/monoidal':
% 1.54/1.29 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 1.54/1.29
% 1.54/1.29 thf('thf_const_const/iterate/iterate',type,
% 1.54/1.29 'const/iterate/iterate':
% 1.54/1.29 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 1.54/1.29
% 1.54/1.29 thf('thm/iterate/ITERATE_IMAGE_NONZERO_',axiom,
% 1.54/1.29 ! [C: $tType,A: $tType,B: $tType,A0: C > C > C] :
% 1.54/1.29 ( ( 'const/iterate/monoidal' @ C @ A0 )
% 1.54/1.29 => ! [A1: B > C,A2: A > B,A3: A > $o] :
% 1.54/1.29 ( ( ( 'const/sets/FINITE' @ A @ A3 )
% 1.54/1.29 & ! [A4: A,A5: A] :
% 1.54/1.29 ( ( ( 'const/sets/IN' @ A @ A4 @ A3 )
% 1.54/1.29 & ( 'const/sets/IN' @ A @ A5 @ A3 )
% 1.54/1.29 & ( A4 != A5 )
% 1.54/1.29 & ( ( A2 @ A4 )
% 1.54/1.29 = ( A2 @ A5 ) ) )
% 1.54/1.29 => ( ( A1 @ ( A2 @ A4 ) )
% 1.54/1.29 = ( 'const/iterate/neutral' @ C @ A0 ) ) ) )
% 1.54/1.29 => ( ( 'const/iterate/iterate' @ B @ C @ A0 @ ( 'const/sets/IMAGE' @ A @ B @ A2 @ A3 ) @ A1 )
% 1.54/1.29 = ( 'const/iterate/iterate' @ A @ C @ A0 @ A3 @ ( 'const/trivia/o' @ B @ A @ C @ A1 @ A2 ) ) ) ) ) ).
% 1.54/1.29
% 1.54/1.29 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 1.54/1.29 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 1.54/1.29
% 1.54/1.29 thf('thm/iterate/sum_',definition,
% 1.54/1.29 ! [A: $tType] :
% 1.54/1.29 ( ( 'const/iterate/sum' @ A )
% 1.54/1.29 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 1.54/1.29
% 1.54/1.29 thf('thm/iterate/NEUTRAL_REAL_ADD_',axiom,
% 1.54/1.29 ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
% 1.54/1.29 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 1.54/1.29
% 1.54/1.29 thf('thm/iterate/SUM_IMAGE_NONZERO_',conjecture,
% 1.54/1.29 ! [A: $tType,B: $tType,A0: B > 'type/realax/real',A1: A > B,A2: A > $o] :
% 1.54/1.29 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 1.54/1.29 & ! [A3: A,A4: A] :
% 1.54/1.29 ( ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 1.54/1.29 & ( 'const/sets/IN' @ A @ A4 @ A2 )
% 1.54/1.29 & ( A3 != A4 )
% 1.54/1.29 & ( ( A1 @ A3 )
% 1.54/1.29 = ( A1 @ A4 ) ) )
% 1.54/1.29 => ( ( A0 @ ( A1 @ A3 ) )
% 1.54/1.29 = ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) )
% 1.54/1.29 => ( ( 'const/iterate/sum' @ B @ ( 'const/sets/IMAGE' @ A @ B @ A1 @ A2 ) @ A0 )
% 1.54/1.29 = ( 'const/iterate/sum' @ A @ A2 @ ( 'const/trivia/o' @ B @ A @ 'type/realax/real' @ A0 @ A1 ) ) ) ) ).
% 1.54/1.29 ------------------------
% 1.71/1.30 % (30460)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/183Mi)
% 1.71/1.30 % (30462)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_30363 for (2999ds/27Mi)
% 1.71/1.30 % (30463)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/2Mi)
% 1.71/1.30 % (30463)Instruction limit reached!
% 1.71/1.30 % (30463)------------------------------
% 1.71/1.30 % (30463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.30 % (30463)Termination reason: Unknown
% 1.71/1.30 % (30463)Termination phase: Property scanning
% 1.71/1.30
% 1.71/1.30 % (30463)Memory used [KB]: 1023
% 1.71/1.30 % (30463)Time elapsed: 0.002 s
% 1.71/1.30 % (30463)Instructions burned: 3 (million)
% 1.71/1.30 % (30463)------------------------------
% 1.71/1.30 % (30463)------------------------------
% 1.71/1.31 % (30465)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_30363 for (2999ds/275Mi)
% 1.71/1.31 % (30464)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_30363 for (2999ds/2Mi)
% 1.71/1.31 % (30461)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_30363 for (2999ds/4Mi)
% 1.71/1.31 % Exception at run slice level
% 1.71/1.31 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
% 1.71/1.31 % (30461)Instruction limit reached!
% 1.71/1.31 % (30461)------------------------------
% 1.71/1.31 % (30461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.31 % (30462)Instruction limit reached!
% 1.71/1.31 % (30462)------------------------------
% 1.71/1.31 % (30462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.31 % (30462)Termination reason: Unknown
% 1.71/1.31 % (30462)Termination phase: Saturation
% 1.71/1.31 % (30461)Termination reason: Unknown
% 1.71/1.31
% 1.71/1.31 % (30462)Memory used [KB]: 5756
% 1.71/1.31 % (30462)Time elapsed: 0.012 s
% 1.71/1.31 % (30461)Termination phase: Saturation
% 1.71/1.31 % (30462)Instructions burned: 28 (million)
% 1.71/1.31
% 1.71/1.31 % (30462)------------------------------
% 1.71/1.31 % (30462)------------------------------
% 1.71/1.31 % (30461)Memory used [KB]: 5500
% 1.71/1.31 % (30461)Time elapsed: 0.005 s
% 1.71/1.31 % (30461)Instructions burned: 5 (million)
% 1.71/1.31 % (30461)------------------------------
% 1.71/1.31 % (30461)------------------------------
% 1.71/1.31 % (30467)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/3Mi)
% 1.71/1.32 % (30466)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/18Mi)
% 1.71/1.32 % (30467)Instruction limit reached!
% 1.71/1.32 % (30467)------------------------------
% 1.71/1.32 % (30467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.32 % (30467)Termination reason: Unknown
% 1.71/1.32 % (30467)Termination phase: Property scanning
% 1.71/1.32
% 1.71/1.32 % (30467)Memory used [KB]: 1023
% 1.71/1.32 % (30467)Time elapsed: 0.003 s
% 1.71/1.32 % (30467)Instructions burned: 4 (million)
% 1.71/1.32 % (30467)------------------------------
% 1.71/1.32 % (30467)------------------------------
% 1.71/1.32 % (30469)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/15Mi)
% 1.71/1.32 % (30466)Instruction limit reached!
% 1.71/1.32 % (30466)------------------------------
% 1.71/1.32 % (30466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.32 % (30466)Termination reason: Unknown
% 1.71/1.32 % (30466)Termination phase: Saturation
% 1.71/1.32
% 1.71/1.32 % (30466)Memory used [KB]: 5628
% 1.71/1.32 % (30466)Time elapsed: 0.011 s
% 1.71/1.32 % (30466)Instructions burned: 18 (million)
% 1.71/1.32 % (30466)------------------------------
% 1.71/1.32 % (30466)------------------------------
% 1.71/1.33 % (30471)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/1041Mi)
% 1.71/1.33 % Exception at run slice level
% 1.71/1.33 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
% 1.71/1.33 % (30469)Instruction limit reached!
% 1.71/1.33 % (30469)------------------------------
% 1.71/1.33 % (30469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (30469)Termination reason: Unknown
% 1.71/1.33 % (30469)Termination phase: Saturation
% 1.71/1.33
% 1.71/1.33 % (30469)Memory used [KB]: 5756
% 1.71/1.33 % (30469)Time elapsed: 0.007 s
% 1.71/1.33 % (30469)Instructions burned: 15 (million)
% 1.71/1.33 % (30469)------------------------------
% 1.71/1.33 % (30469)------------------------------
% 1.71/1.33 % (30468)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/37Mi)
% 1.71/1.33 % Exception at run slice level
% 1.71/1.33 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
% 1.71/1.33 % (30470)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/3Mi)
% 1.71/1.33 % (30470)Instruction limit reached!
% 1.71/1.33 % (30470)------------------------------
% 1.71/1.33 % (30470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (30470)Termination reason: Unknown
% 1.71/1.33 % (30470)Termination phase: Function definition elimination
% 1.71/1.33
% 1.71/1.33 % (30470)Memory used [KB]: 1023
% 1.71/1.33 % (30470)Time elapsed: 0.004 s
% 1.71/1.33 % (30470)Instructions burned: 4 (million)
% 1.71/1.33 % (30470)------------------------------
% 1.71/1.33 % (30470)------------------------------
% 1.71/1.34 % (30473)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/16Mi)
% 1.71/1.34 % (30465)First to succeed.
% 1.71/1.34 % (30474)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/3Mi)
% 1.71/1.34 % (30474)Instruction limit reached!
% 1.71/1.34 % (30474)------------------------------
% 1.71/1.34 % (30474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (30474)Termination reason: Unknown
% 1.71/1.34 % (30474)Termination phase: Twee Goal Transformation
% 1.71/1.34
% 1.71/1.34 % (30474)Memory used [KB]: 1023
% 1.71/1.34 % (30474)Time elapsed: 0.003 s
% 1.71/1.34 % (30474)Instructions burned: 4 (million)
% 1.71/1.34 % (30474)------------------------------
% 1.71/1.34 % (30474)------------------------------
% 1.71/1.34 % (30472)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30363 for (2999ds/7Mi)
% 1.71/1.34 % (30465)Refutation found. Thanks to Tanya!
% 1.71/1.34 % SZS status Theorem for DTF2THF_30363
% 1.71/1.34 % SZS output start Proof for DTF2THF_30363
% 1.71/1.34 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.71/1.34 thf(type_def_7, type, 'type/realax/real': $tType).
% 1.71/1.34 thf(type_def_8, type, sK2: $tType).
% 1.71/1.34 thf(type_def_9, type, sK3: $tType).
% 1.71/1.34 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.71/1.34 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.71/1.34 thf(func_def_2, type, 'const/trivia/o': !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X2) > (X1 > X0) > X1 > X2)).
% 1.71/1.34 thf(func_def_3, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.71/1.34 thf(func_def_4, type, 'const/sets/IMAGE': !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > $o) > X1 > $o)).
% 1.71/1.34 thf(func_def_5, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.71/1.34 thf(func_def_6, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 1.71/1.34 thf(func_def_7, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.71/1.34 thf(func_def_8, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.71/1.34 thf(func_def_9, type, 'const/nums/_0': 'type/nums/num').
% 1.71/1.34 thf(func_def_10, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.71/1.34 thf(func_def_11, type, 'const/iterate/neutral': !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.71/1.34 thf(func_def_12, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 1.71/1.34 thf(func_def_13, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 1.71/1.34 thf(func_def_17, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > $o) > (X1 > X2) > (X2 > X0) > (X0 > X0 > X0) > X1)).
% 1.71/1.34 thf(func_def_18, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > $o) > (X1 > X2) > (X2 > X0) > (X0 > X0 > X0) > X1)).
% 1.71/1.34 thf(func_def_19, type, sK4: sK3 > 'type/realax/real').
% 1.71/1.34 thf(func_def_20, type, sK5: sK2 > sK3).
% 1.71/1.34 thf(func_def_21, type, sK6: sK2 > $o).
% 1.71/1.34 thf(func_def_23, type, ph8: !>[X0: $tType]:(X0)).
% 1.71/1.34 thf(f74,plain,(
% 1.71/1.34 $false),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f73,f34])).
% 1.71/1.34 thf(f34,plain,(
% 1.71/1.34 (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5)) != ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(definition_unfolding,[status(thm)],[f30,f29,f29])).
% 1.71/1.34 thf(f29,plain,(
% 1.71/1.34 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 1.71/1.34 thf(f14,plain,(
% 1.71/1.34 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 1.71/1.34 inference(rectify,[status(thm)],[f3])).
% 1.71/1.34 thf(f3,axiom,(
% 1.71/1.34 ! [X1 : $tType] : ('const/iterate/sum' @ X1 = ('const/iterate/iterate' @ X1 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 1.71/1.34 file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/sum_')).
% 1.71/1.34 thf(f30,plain,(
% 1.71/1.34 (('const/iterate/sum' @ sK2 @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5)) != ('const/iterate/sum' @ sK3 @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f22])).
% 1.71/1.34 thf(f22,plain,(
% 1.71/1.34 ! [X5 : sK2,X6 : sK2] : (($true != ('const/sets/IN' @ sK2 @ X5 @ sK6)) | ((sK5 @ X6) != (sK5 @ X5)) | (X5 = X6) | ($true != ('const/sets/IN' @ sK2 @ X6 @ sK6)) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (sK4 @ (sK5 @ X5)))) & ($true = ('const/sets/FINITE' @ sK2 @ sK6)) & (('const/iterate/sum' @ sK2 @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5)) != ('const/iterate/sum' @ sK3 @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f18,f21])).
% 1.71/1.34 thf(f21,plain,(
% 1.71/1.34 ( ! [X0 : $tType] : (? [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : (! [X5 : X0,X6 : X0] : (($true != ('const/sets/IN' @ X0 @ X5 @ X4)) | ((X3 @ X6) != (X3 @ X5)) | (X5 = X6) | (('const/sets/IN' @ X0 @ X6 @ X4) != $true) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (X2 @ (X3 @ X5)))) & ($true = ('const/sets/FINITE' @ X0 @ X4)) & (('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4) @ X2) != ('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3)))) => (! [X6 : sK2,X5 : sK2] : (($true != ('const/sets/IN' @ sK2 @ X5 @ sK6)) | ((sK5 @ X6) != (sK5 @ X5)) | (X5 = X6) | ($true != ('const/sets/IN' @ sK2 @ X6 @ sK6)) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (sK4 @ (sK5 @ X5)))) & ($true = ('const/sets/FINITE' @ sK2 @ sK6)) & (('const/iterate/sum' @ sK2 @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5)) != ('const/iterate/sum' @ sK3 @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4)))) )),
% 1.71/1.34 introduced(definition,[],[choice_axiom])).
% 1.71/1.34 thf(f18,plain,(
% 1.71/1.34 ? [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : (! [X5 : X0,X6 : X0] : (($true != ('const/sets/IN' @ X0 @ X5 @ X4)) | ((X3 @ X6) != (X3 @ X5)) | (X5 = X6) | (('const/sets/IN' @ X0 @ X6 @ X4) != $true) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (X2 @ (X3 @ X5)))) & ($true = ('const/sets/FINITE' @ X0 @ X4)) & (('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4) @ X2) != ('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3))))),
% 1.71/1.34 inference(flattening,[status(thm)],[f17])).
% 1.71/1.34 thf(f17,plain,(
% 1.71/1.34 ? [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : ((('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4) @ X2) != ('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3))) & (! [X5 : X0,X6 : X0] : ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (X2 @ (X3 @ X5))) | (($true != ('const/sets/IN' @ X0 @ X5 @ X4)) | (X5 = X6) | (('const/sets/IN' @ X0 @ X6 @ X4) != $true) | ((X3 @ X6) != (X3 @ X5)))) & ($true = ('const/sets/FINITE' @ X0 @ X4))))),
% 1.71/1.34 inference(ennf_transformation,[status(thm)],[f9])).
% 1.71/1.34 thf(f9,plain,(
% 1.71/1.34 ~! [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : ((! [X5 : X0,X6 : X0] : ((($true = ('const/sets/IN' @ X0 @ X5 @ X4)) & (X5 != X6) & (('const/sets/IN' @ X0 @ X6 @ X4) = $true) & ((X3 @ X6) = (X3 @ X5))) => (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (X2 @ (X3 @ X5)))) & ($true = ('const/sets/FINITE' @ X0 @ X4))) => (('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4) @ X2) = ('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3))))),
% 1.71/1.34 inference(fool_elimination,[status(thm)],[f8])).
% 1.71/1.34 thf(f8,plain,(
% 1.71/1.34 ~! [X0 : $tType,X1 : $tType,X2 : X1 > 'type/realax/real',X3 : X0 > X1,X4 : X0 > $o] : ((! [X5 : X0,X6 : X0] : (((X5 != X6) & ('const/sets/IN' @ X0 @ X5 @ X4) & ((X3 @ X6) = (X3 @ X5)) & ('const/sets/IN' @ X0 @ X6 @ X4)) => (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (X2 @ (X3 @ X5)))) & ('const/sets/FINITE' @ X0 @ X4)) => (('const/iterate/sum' @ X1 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4) @ X2) = ('const/iterate/sum' @ X0 @ X4 @ ('const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3))))),
% 1.71/1.34 inference(rectify,[status(thm)],[f6])).
% 1.71/1.34 thf(f6,negated_conjecture,(
% 1.71/1.34 ~! [X1 : $tType,X0 : $tType,X3 : X0 > 'type/realax/real',X4 : X1 > X0,X5 : X1 > $o] : ((! [X6 : X1,X7 : X1] : (((X6 != X7) & ('const/sets/IN' @ X1 @ X6 @ X5) & ((X4 @ X6) = (X4 @ X7)) & ('const/sets/IN' @ X1 @ X7 @ X5)) => (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (X3 @ (X4 @ X6)))) & ('const/sets/FINITE' @ X1 @ X5)) => (('const/iterate/sum' @ X0 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X5) @ X3) = ('const/iterate/sum' @ X1 @ X5 @ ('const/trivia/o' @ X0 @ X1 @ 'type/realax/real' @ X3 @ X4))))),
% 1.71/1.34 inference(negated_conjecture,[status(cth)],[f5])).
% 1.71/1.34 thf(f5,conjecture,(
% 1.71/1.34 ! [X1 : $tType,X0 : $tType,X3 : X0 > 'type/realax/real',X4 : X1 > X0,X5 : X1 > $o] : ((! [X6 : X1,X7 : X1] : (((X6 != X7) & ('const/sets/IN' @ X1 @ X6 @ X5) & ((X4 @ X6) = (X4 @ X7)) & ('const/sets/IN' @ X1 @ X7 @ X5)) => (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (X3 @ (X4 @ X6)))) & ('const/sets/FINITE' @ X1 @ X5)) => (('const/iterate/sum' @ X0 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X5) @ X3) = ('const/iterate/sum' @ X1 @ X5 @ ('const/trivia/o' @ X0 @ X1 @ 'type/realax/real' @ X3 @ X4))))),
% 1.71/1.34 file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/SUM_IMAGE_NONZERO_')).
% 1.71/1.34 thf(f73,plain,(
% 1.71/1.34 (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5)) = ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f72,f23])).
% 1.71/1.34 thf(f23,plain,(
% 1.71/1.34 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f11])).
% 1.71/1.34 thf(f11,plain,(
% 1.71/1.34 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 1.71/1.34 inference(fool_elimination,[status(thm)],[f10])).
% 1.71/1.34 thf(f10,plain,(
% 1.71/1.34 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 1.71/1.34 inference(rectify,[status(thm)],[f2])).
% 1.71/1.34 thf(f2,axiom,(
% 1.71/1.34 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 1.71/1.34 file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 1.71/1.34 thf(f72,plain,(
% 1.71/1.34 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5)) = ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f71,f31])).
% 1.71/1.34 thf(f31,plain,(
% 1.71/1.34 ($true = ('const/sets/FINITE' @ sK2 @ sK6))),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f22])).
% 1.71/1.34 thf(f71,plain,(
% 1.71/1.34 ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5)) = ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.71/1.34 thf(f70,plain,(
% 1.71/1.34 ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') != (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')) | (('const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ('const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5)) = ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(superposition,[status(thm)],[f27,f63])).
% 1.71/1.34 thf(f63,plain,(
% 1.71/1.34 ((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') = (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add'))),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f62,f48])).
% 1.71/1.34 thf(f48,plain,(
% 1.71/1.34 ($true = ('const/sets/IN' @ sK2 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6))),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f47,f31])).
% 1.71/1.34 thf(f47,plain,(
% 1.71/1.34 ($true = ('const/sets/IN' @ sK2 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6)) | ($true != ('const/sets/FINITE' @ sK2 @ sK6))),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f39,f23])).
% 1.71/1.34 thf(f39,plain,(
% 1.71/1.34 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | ($true = ('const/sets/IN' @ sK2 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6))),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.71/1.34 thf(f36,plain,(
% 1.71/1.34 ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ($true = ('const/sets/IN' @ sK2 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6)) | (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4) != ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(superposition,[status(thm)],[f34,f25])).
% 1.71/1.34 thf(f25,plain,(
% 1.71/1.34 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X0 > X0,X6 : X1 > $o,X4 : X2 > X0,X5 : X1 > X2] : ((('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) | ($true != ('const/iterate/monoidal' @ X0 @ X3)) | ($true = ('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) | (('const/sets/FINITE' @ X1 @ X6) != $true)) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 1.71/1.34 thf(f20,plain,(
% 1.71/1.34 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (($true != ('const/iterate/monoidal' @ X0 @ X3)) | ! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) | (('const/sets/FINITE' @ X1 @ X6) != $true) | (($true = ('const/sets/IN' @ X1 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) & ((sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) != (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)) & ((X4 @ (X5 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))) != ('const/iterate/neutral' @ X0 @ X3)) & ($true = ('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) & ((X5 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)) = (X5 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))))))),
% 1.71/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f19])).
% 1.71/1.34 thf(f19,plain,(
% 1.71/1.34 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : X0 > X0 > X0,X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : (? [X7 : X1,X8 : X1] : ((('const/sets/IN' @ X1 @ X8 @ X6) = $true) & (X7 != X8) & ((X4 @ (X5 @ X7)) != ('const/iterate/neutral' @ X0 @ X3)) & (('const/sets/IN' @ X1 @ X7 @ X6) = $true) & ((X5 @ X8) = (X5 @ X7))) => (($true = ('const/sets/IN' @ X1 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) & ((sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) != (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)) & ((X4 @ (X5 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))) != ('const/iterate/neutral' @ X0 @ X3)) & ($true = ('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) & ((X5 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)) = (X5 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)))))),
% 1.71/1.34 introduced(definition,[],[choice_axiom])).
% 1.71/1.34 thf(f16,plain,(
% 1.71/1.34 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (($true != ('const/iterate/monoidal' @ X0 @ X3)) | ! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) | (('const/sets/FINITE' @ X1 @ X6) != $true) | ? [X7 : X1,X8 : X1] : ((('const/sets/IN' @ X1 @ X8 @ X6) = $true) & (X7 != X8) & ((X4 @ (X5 @ X7)) != ('const/iterate/neutral' @ X0 @ X3)) & (('const/sets/IN' @ X1 @ X7 @ X6) = $true) & ((X5 @ X8) = (X5 @ X7)))))),
% 1.71/1.34 inference(flattening,[status(thm)],[f15])).
% 1.71/1.34 thf(f15,plain,(
% 1.71/1.34 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) | (? [X7 : X1,X8 : X1] : (((X4 @ (X5 @ X7)) != ('const/iterate/neutral' @ X0 @ X3)) & (((X5 @ X8) = (X5 @ X7)) & (X7 != X8) & (('const/sets/IN' @ X1 @ X7 @ X6) = $true) & (('const/sets/IN' @ X1 @ X8 @ X6) = $true))) | (('const/sets/FINITE' @ X1 @ X6) != $true))) | ($true != ('const/iterate/monoidal' @ X0 @ X3)))),
% 1.71/1.34 inference(ennf_transformation,[status(thm)],[f13])).
% 1.71/1.34 thf(f13,plain,(
% 1.71/1.34 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (($true = ('const/iterate/monoidal' @ X0 @ X3)) => ! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((! [X7 : X1,X8 : X1] : ((((X5 @ X8) = (X5 @ X7)) & (X7 != X8) & (('const/sets/IN' @ X1 @ X7 @ X6) = $true) & (('const/sets/IN' @ X1 @ X8 @ X6) = $true)) => ((X4 @ (X5 @ X7)) = ('const/iterate/neutral' @ X0 @ X3))) & (('const/sets/FINITE' @ X1 @ X6) = $true)) => (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5)))))),
% 1.71/1.34 inference(fool_elimination,[status(thm)],[f12])).
% 1.71/1.34 thf(f12,plain,(
% 1.71/1.34 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X0 > X0] : (('const/iterate/monoidal' @ X0 @ X3) => ! [X4 : X2 > X0,X5 : X1 > X2,X6 : X1 > $o] : ((! [X7 : X1,X8 : X1] : ((((X5 @ X8) = (X5 @ X7)) & (X7 != X8) & ('const/sets/IN' @ X1 @ X7 @ X6) & ('const/sets/IN' @ X1 @ X8 @ X6)) => ((X4 @ (X5 @ X7)) = ('const/iterate/neutral' @ X0 @ X3))) & ('const/sets/FINITE' @ X1 @ X6)) => (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5)))))),
% 1.71/1.34 inference(rectify,[status(thm)],[f1])).
% 1.71/1.34 thf(f1,axiom,(
% 1.71/1.34 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : X2 > X2 > X2] : (('const/iterate/monoidal' @ X2 @ X3) => ! [X4 : X0 > X2,X5 : X1 > X0,X6 : X1 > $o] : ((! [X7 : X1,X8 : X1] : ((((X5 @ X7) = (X5 @ X8)) & (X7 != X8) & ('const/sets/IN' @ X1 @ X7 @ X6) & ('const/sets/IN' @ X1 @ X8 @ X6)) => ((X4 @ (X5 @ X7)) = ('const/iterate/neutral' @ X2 @ X3))) & ('const/sets/FINITE' @ X1 @ X6)) => (('const/iterate/iterate' @ X0 @ X2 @ X3 @ ('const/sets/IMAGE' @ X1 @ X0 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ ('const/trivia/o' @ X0 @ X1 @ X2 @ X4 @ X5)))))),
% 1.71/1.34 file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/ITERATE_IMAGE_NONZERO_')).
% 1.71/1.34 thf(f62,plain,(
% 1.71/1.34 ($true != ('const/sets/IN' @ sK2 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6)) | ((sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') = (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add'))),
% 1.71/1.34 inference(equality_resolution,[status(thm)],[f60])).
% 1.71/1.34 thf(f60,plain,(
% 1.71/1.34 ( ! [X0 : sK2] : (((sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')) != (sK5 @ X0)) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK6)) | ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') = X0)) )),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f59,f23])).
% 1.71/1.34 thf(f59,plain,(
% 1.71/1.34 ( ! [X0 : sK2] : ((('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') = X0) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK6)) | ((sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')) != (sK5 @ X0))) )),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f58,f31])).
% 1.71/1.34 thf(f58,plain,(
% 1.71/1.34 ( ! [X0 : sK2] : (($true != ('const/sets/FINITE' @ sK2 @ sK6)) | ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') = X0) | ((sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')) != (sK5 @ X0)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK6))) )),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f57,f44])).
% 1.71/1.34 thf(f44,plain,(
% 1.71/1.34 (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) != (sK4 @ (sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add'))))),
% 1.71/1.34 inference(forward_demodulation,[status(thm)],[f43,f33])).
% 1.71/1.34 thf(f33,plain,(
% 1.71/1.34 (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') = ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f4])).
% 1.71/1.34 thf(f4,axiom,(
% 1.71/1.34 (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') = ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.71/1.34 file('/export/starexec/sandbox/tmp/tmp.WsXp4LV8Vx/DTF2THF_30363.p','thm/iterate/NEUTRAL_REAL_ADD_')).
% 1.71/1.34 thf(f43,plain,(
% 1.71/1.34 (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') != (sK4 @ (sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add'))))),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f42,f31])).
% 1.71/1.34 thf(f42,plain,(
% 1.71/1.34 ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') != (sK4 @ (sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add'))))),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f41,f23])).
% 1.71/1.34 thf(f41,plain,(
% 1.71/1.34 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') != (sK4 @ (sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')))) | ($true != ('const/sets/FINITE' @ sK2 @ sK6))),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.71/1.34 thf(f37,plain,(
% 1.71/1.34 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | (('const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add') != (sK4 @ (sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')))) | ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4) != ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4))),
% 1.71/1.34 inference(superposition,[status(thm)],[f34,f26])).
% 1.71/1.34 thf(f26,plain,(
% 1.71/1.34 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X0 > X0,X6 : X1 > $o,X4 : X2 > X0,X5 : X1 > X2] : ((('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) | ($true != ('const/iterate/monoidal' @ X0 @ X3)) | (('const/sets/FINITE' @ X1 @ X6) != $true) | ((X4 @ (X5 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))) != ('const/iterate/neutral' @ X0 @ X3))) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 1.71/1.34 thf(f57,plain,(
% 1.71/1.34 ( ! [X0 : sK2] : (((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') = X0) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (sK4 @ (sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')))) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK6)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | ((sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')) != (sK5 @ X0))) )),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f56,f46])).
% 1.71/1.34 thf(f46,plain,(
% 1.71/1.34 ($true = ('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6))),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f45,f23])).
% 1.71/1.34 thf(f45,plain,(
% 1.71/1.34 ($true = ('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 1.71/1.34 inference(subsumption_resolution,[status(thm)],[f40,f31])).
% 1.71/1.34 thf(f40,plain,(
% 1.71/1.34 ($true = ('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6)) | ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.71/1.34 thf(f38,plain,(
% 1.71/1.34 (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4) != ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4)) | ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | ($true = ('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 1.71/1.34 inference(superposition,[status(thm)],[f34,f28])).
% 1.71/1.34 thf(f28,plain,(
% 1.71/1.34 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X0 > X0,X6 : X1 > $o,X4 : X2 > X0,X5 : X1 > X2] : ((('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) | (('const/sets/FINITE' @ X1 @ X6) != $true) | ($true = ('const/sets/IN' @ X1 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) @ X6)) | ($true != ('const/iterate/monoidal' @ X0 @ X3))) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 1.71/1.34 thf(f56,plain,(
% 1.71/1.34 ( ! [X0 : sK2] : (($true != ('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6)) | ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') = X0) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (sK4 @ (sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')))) | ((sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')) != (sK5 @ X0)) | ($true != ('const/sets/FINITE' @ sK2 @ sK6)) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK6))) )),
% 1.71/1.34 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.71/1.34 thf(f55,plain,(
% 1.71/1.34 ( ! [X0 : sK2] : (((sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')) != (sK5 @ X0)) | (('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4) != ('const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6) @ sK4)) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (sK4 @ (sK5 @ (sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add')))) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK6)) | ($true != ('const/sets/IN' @ sK2 @ (sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') @ sK6)) | ((sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add') = X0) | ($true != ('const/sets/FINITE' @ sK2 @ sK6))) )),
% 1.71/1.34 inference(superposition,[status(thm)],[f34,f35])).
% 1.71/1.34 thf(f35,plain,(
% 1.71/1.34 ( ! [X0 : $tType,X2 : sK3 > X0,X3 : X0 > X0 > X0,X1 : sK2 > $o,X4 : sK2] : ((('const/iterate/iterate' @ sK2 @ X0 @ X3 @ X1 @ ('const/trivia/o' @ sK3 @ sK2 @ X0 @ X2 @ sK5)) = ('const/iterate/iterate' @ sK3 @ X0 @ X3 @ ('const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ X1) @ X2)) | (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (sK4 @ (sK5 @ (sK0 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3)))) | ($true != ('const/sets/IN' @ sK2 @ (sK1 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3) @ sK6)) | ($true != ('const/sets/FINITE' @ sK2 @ X1)) | ((sK5 @ (sK0 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3)) != (sK5 @ X4)) | ($true != ('const/iterate/monoidal' @ X0 @ X3)) | ($true != ('const/sets/IN' @ sK2 @ X4 @ sK6)) | ((sK1 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3) = X4)) )),
% 1.71/1.34 inference(superposition,[status(thm)],[f32,f24])).
% 1.71/1.34 thf(f24,plain,(
% 1.71/1.34 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X0 > X0,X6 : X1 > $o,X4 : X2 > X0,X5 : X1 > X2] : (((X5 @ (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)) = (X5 @ (sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3))) | ($true != ('const/iterate/monoidal' @ X0 @ X3)) | (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) | (('const/sets/FINITE' @ X1 @ X6) != $true)) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 1.71/1.34 thf(f32,plain,(
% 1.71/1.34 ( ! [X6 : sK2,X5 : sK2] : ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = (sK4 @ (sK5 @ X5))) | (X5 = X6) | ((sK5 @ X6) != (sK5 @ X5)) | ($true != ('const/sets/IN' @ sK2 @ X5 @ sK6)) | ($true != ('const/sets/IN' @ sK2 @ X6 @ sK6))) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f22])).
% 1.71/1.34 thf(f27,plain,(
% 1.71/1.34 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X0 > X0,X6 : X1 > $o,X4 : X2 > X0,X5 : X1 > X2] : (((sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3) != (sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3)) | (('const/iterate/iterate' @ X2 @ X0 @ X3 @ ('const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6) @ X4) = ('const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ('const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5))) | (('const/sets/FINITE' @ X1 @ X6) != $true) | ($true != ('const/iterate/monoidal' @ X0 @ X3))) )),
% 1.71/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 1.71/1.34 % SZS output end Proof for DTF2THF_30363
% 1.71/1.34 % (30465)------------------------------
% 1.71/1.34 % (30465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (30465)Termination reason: Refutation
% 1.71/1.34
% 1.71/1.34 % (30465)Memory used [KB]: 5884
% 1.71/1.34 % (30465)Time elapsed: 0.034 s
% 1.71/1.34 % (30465)Instructions burned: 58 (million)
% 1.71/1.34 % (30465)------------------------------
% 1.71/1.34 % (30465)------------------------------
% 1.71/1.34 % (30459)Success in time 0.044 s
%------------------------------------------------------------------------------