%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV510^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 1.36s 1.17s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 341 ( 92 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 742 ( 38 ~; 34 |; 22 &; 629 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 141 ( 26 ^; 100 !; 15 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
'type/realax/real': $tType ).
thf(type_def_8,type,
sK0: $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/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_5,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_6,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_7,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_8,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_13,type,
sK1: sK0 > $o ).
thf(func_def_14,type,
sK2: sK0 > 'type/realax/real' ).
thf(func_def_15,type,
sK3: 'type/realax/real' ).
thf(func_def_16,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > ( X0 > 'type/realax/real' ) > X0 ) ).
thf(func_def_18,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f47,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f45,f29]) ).
thf(f29,plain,
( $true
!= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) ) ),
inference(backward_demodulation,[status(thm)],[f22,f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real'] :
( ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : X0 )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : X0 )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f21,f23]) ).
thf(f23,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X4: sK0] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ X4 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK2 @ X4 ) @ sK3 ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ sK3 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f17]) ).
thf(f17,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 )
= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) )
!= $true ) )
=> ( ! [X4: sK0] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ X4 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK2 @ X4 ) @ sK3 ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ sK3 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 )
= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
=> ( ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 )
= $true ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
=> ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
=> ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
=> ( 'const/realax/real_le' @ ( X2 @ X4 ) @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X1 ) ) @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.idqcZtZszN/DTF2THF_9468.p','thm/iterate/SUM_BOUND_') ).
thf(f21,plain,
! [X0: $tType,X2: X0 > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : X1 ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/iterate/sum' @ X0 @ X2
@ ^ [X3: X0] : X1 )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/iterate/sum' @ X0 @ X2
@ ^ [X3: X0] : X1 )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.idqcZtZszN/DTF2THF_9468.p','thm/iterate/SUM_CONST_') ).
thf(f22,plain,
( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ sK0 @ sK1 ) ) @ sK3 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f45,plain,
( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
= ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] :
( sK2
@ ( ^ [Y1: sK0] : Y1
@ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $true
= ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] :
( sK2
@ ( ^ [Y1: sK0] : Y1
@ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) ) )
| ( $true
= ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] :
( sK2
@ ( ^ [Y1: sK0] : Y1
@ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) ) ) ),
inference(equality_resolution,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: sK0 > 'type/realax/real',X0: sK0 > sK0,X1: sK0 > 'type/realax/real'] :
( ( ( X0
@ ( sK4 @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3
@ ^ [Y0: sK0] : ( sK2 @ ( X0 @ Y0 ) ) ) )
!= ( sK4 @ sK0 @ sK1 @ X1 @ X2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X2 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) )
| ( ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : ( sK2 @ ( X0 @ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: sK0 > 'type/realax/real',X0: sK0 > sK0,X1: sK0 > 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X2 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) )
| ( ( X0
@ ( sK4 @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3
@ ^ [Y0: sK0] : ( sK2 @ ( X0 @ Y0 ) ) ) )
!= ( sK4 @ sK0 @ sK1 @ X1 @ X2 ) )
| ( $true != $true )
| ( ( 'const/realax/real_le'
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : ( sK2 @ ( X0 @ Y0 ) ) )
@ ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : sK3 ) )
= $true ) ),
inference(constrained_superposition,[status(thm)],[f35,f33]) ).
thf(f33,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK2 @ ( sK4 @ sK0 @ sK1 @ X0 @ X1 ) ) @ sK3 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK2 @ ( sK4 @ sK0 @ sK1 @ X0 @ X1 ) ) @ sK3 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f24,f31]) ).
thf(f31,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f26,f23]) ).
thf(f26,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) )
!= $true ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f15,f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
=> ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
=> ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
=> ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.idqcZtZszN/DTF2THF_9468.p','thm/iterate/SUM_LE_') ).
thf(f24,plain,
! [X4: sK0] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ X4 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK2 @ X4 ) @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f35,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( X0 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) ) @ ( X1 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ X1 ) ) )
| ( ( 'const/realax/real_le' @ ( X0 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) ) @ ( X1 @ ( sK4 @ sK0 @ sK1 @ X1 @ X0 ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f25,f23]) ).
thf(f25,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/realax/real_le' @ ( X1 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV510^1 : TPTP v9.2.1. Released v7.0.0.
% 0.10/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Feb 24 12:48:24 EST 2026
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEV510^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.44 % Domain : Analysis
% 0.17/0.44 % Problem : SUM_BOUND
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Kal16]
% 0.17/0.44 % Names : SUM_BOUND_.p [Kal16]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.17/0.44 % Syntax : Number of formulae : 12 ( 0 unt; 9 typ; 0 def)
% 0.17/0.44 % Number of atoms : 10 ( 1 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 4 ( 3 avg)
% 0.17/0.44 % Number of connectives : 52 ( 0 ~; 0 |; 2 &; 45 @)
% 0.17/0.44 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 12 ( 10 avg)
% 0.17/0.44 % Number of types : 3 ( 2 usr)
% 0.17/0.44 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 8 ( 7 usr; 0 con; 1-3 aty)
% 0.17/0.44 % Number of variables : 18 ( 1 ^; 13 !; 0 ?; 18 :)
% 0.17/0.44 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.44 % SPC : TH1_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : Exported from core HOL Light.
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf('thf_type_type/realax/real',type,
% 0.17/0.44 'type/realax/real': $tType ).
% 0.17/0.44
% 0.17/0.44 thf('thf_type_type/nums/num',type,
% 0.17/0.44 'type/nums/num': $tType ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/sets/IN',type,
% 0.17/0.44 'const/sets/IN':
% 0.17/0.44 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/sets/FINITE',type,
% 0.17/0.44 'const/sets/FINITE':
% 0.17/0.44 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/sets/CARD',type,
% 0.17/0.44 'const/sets/CARD':
% 0.17/0.44 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/realax/real_of_num',type,
% 0.17/0.44 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/realax/real_mul',type,
% 0.17/0.44 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/realax/real_le',type,
% 0.17/0.44 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/iterate/sum',type,
% 0.17/0.44 'const/iterate/sum':
% 0.17/0.44 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/iterate/SUM_LE_',axiom,
% 0.17/0.44 ! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
% 0.17/0.44 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.17/0.44 & ! [A3: A] :
% 0.17/0.44 ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 0.17/0.44 => ( 'const/realax/real_le' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) ) )
% 0.17/0.44 => ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/iterate/SUM_CONST_',axiom,
% 0.17/0.44 ! [A: $tType,A0: 'type/realax/real',A1: A > $o] :
% 0.17/0.44 ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.17/0.44 => ( ( 'const/iterate/sum' @ A @ A1
% 0.17/0.44 @ ^ [A2: A] : A0 )
% 0.17/0.44 = ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ A @ A1 ) ) @ A0 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/iterate/SUM_BOUND_',conjecture,
% 0.17/0.44 ! [A: $tType,A0: A > $o,A1: A > 'type/realax/real',A2: 'type/realax/real'] :
% 0.17/0.44 ( ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.17/0.44 & ! [A3: A] :
% 0.17/0.44 ( ( 'const/sets/IN' @ A @ A3 @ A0 )
% 0.17/0.44 => ( 'const/realax/real_le' @ ( A1 @ A3 ) @ A2 ) ) )
% 0.17/0.44 => ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ A @ A0 @ A1 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ A @ A0 ) ) @ A2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.36/1.13 ---- Embedded in THF ---
% 1.36/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.13 %%% Generated on Tue Feb 24 12:48:25 EST 2026
% 1.36/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.13 %%% Logic specification used:
% 1.36/1.13 %%% thf(spec, logic, $$dhol).
% 1.36/1.13
% 1.36/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.idqcZtZszN/DTF2DTF9468.p
% See solution above
% 1.36/1.13 ------------------------
% 1.36/1.14 ---- Cleaned THF ---
% 1.36/1.14 thf('thf_type_type/realax/real',type,
% 1.36/1.14 'type/realax/real': $tType ).
% 1.36/1.14
% 1.36/1.14 thf('thf_type_type/nums/num',type,
% 1.36/1.14 'type/nums/num': $tType ).
% 1.36/1.14
% 1.36/1.14 thf('thf_const_const/sets/IN',type,
% 1.36/1.14 'const/sets/IN':
% 1.36/1.14 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.36/1.14
% 1.36/1.14 thf('thf_const_const/sets/FINITE',type,
% 1.36/1.14 'const/sets/FINITE':
% 1.36/1.14 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.36/1.14
% 1.36/1.14 thf('thf_const_const/sets/CARD',type,
% 1.36/1.14 'const/sets/CARD':
% 1.36/1.14 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 1.36/1.14
% 1.36/1.14 thf('thf_const_const/realax/real_of_num',type,
% 1.36/1.14 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
% 1.36/1.14
% 1.36/1.14 thf('thf_const_const/realax/real_mul',type,
% 1.36/1.14 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.36/1.14
% 1.36/1.14 thf('thf_const_const/realax/real_le',type,
% 1.36/1.14 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.36/1.14
% 1.36/1.14 thf('thf_const_const/iterate/sum',type,
% 1.36/1.14 'const/iterate/sum':
% 1.36/1.14 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.36/1.14
% 1.36/1.14 thf('thm/iterate/SUM_LE_',axiom,
% 1.36/1.14 ! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
% 1.36/1.14 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 1.36/1.14 & ! [A3: A] :
% 1.36/1.14 ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 1.36/1.14 => ( 'const/realax/real_le' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) ) )
% 1.36/1.14 => ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ).
% 1.36/1.14
% 1.36/1.14 thf('thm/iterate/SUM_CONST_',axiom,
% 1.36/1.14 ! [A: $tType,A0: 'type/realax/real',A1: A > $o] :
% 1.36/1.14 ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.36/1.14 => ( ( 'const/iterate/sum' @ A @ A1
% 1.36/1.14 @ ^ [A2: A] : A0 )
% 1.36/1.14 = ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ A @ A1 ) ) @ A0 ) ) ) ).
% 1.36/1.14
% 1.36/1.14 thf('thm/iterate/SUM_BOUND_',conjecture,
% 1.36/1.14 ! [A: $tType,A0: A > $o,A1: A > 'type/realax/real',A2: 'type/realax/real'] :
% 1.36/1.14 ( ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.36/1.14 & ! [A3: A] :
% 1.36/1.14 ( ( 'const/sets/IN' @ A @ A3 @ A0 )
% 1.36/1.14 => ( 'const/realax/real_le' @ ( A1 @ A3 ) @ A2 ) ) )
% 1.36/1.14 => ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ A @ A0 @ A1 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ A @ A0 ) ) @ A2 ) ) ) ).
% 1.36/1.14 ------------------------
% 1.36/1.15 % (9568)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_9468 for (2999ds/27Mi)
% 1.36/1.15 % (9568)Refutation not found, incomplete strategy
% 1.36/1.15 % (9568)------------------------------
% 1.36/1.15 % (9568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.15 % (9568)Termination reason: Refutation not found, incomplete strategy
% 1.36/1.15
% 1.36/1.15
% 1.36/1.15 % (9568)Memory used [KB]: 5628
% 1.36/1.15 % (9568)Time elapsed: 0.006 s
% 1.36/1.15 % (9568)Instructions burned: 13 (million)
% 1.36/1.15 % (9568)------------------------------
% 1.36/1.15 % (9568)------------------------------
% 1.36/1.16 % (9566)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9468 for (2999ds/183Mi)
% 1.36/1.16 % (9570)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_9468 for (2999ds/2Mi)
% 1.36/1.16 % (9572)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9468 for (2999ds/18Mi)
% 1.36/1.16 % (9569)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9468 for (2999ds/2Mi)
% 1.36/1.16 % (9571)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_9468 for (2999ds/275Mi)
% 1.36/1.16 % (9567)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_9468 for (2999ds/4Mi)
% 1.36/1.16 % (9570)Instruction limit reached!
% 1.36/1.16 % (9570)------------------------------
% 1.36/1.16 % (9570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (9570)Termination reason: Unknown
% 1.36/1.16 % (9570)Termination phase: shuffling
% 1.36/1.16
% 1.36/1.16 % (9570)Memory used [KB]: 895
% 1.36/1.16 % (9570)Time elapsed: 0.002 s
% 1.36/1.16 % (9570)Instructions burned: 2 (million)
% 1.36/1.16 % (9570)------------------------------
% 1.36/1.16 % (9570)------------------------------
% 1.36/1.16 % (9569)Instruction limit reached!
% 1.36/1.16 % (9569)------------------------------
% 1.36/1.16 % (9569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (9569)Termination reason: Unknown
% 1.36/1.16 % (9569)Termination phase: Saturation
% 1.36/1.16
% 1.36/1.16 % (9569)Memory used [KB]: 5500
% 1.36/1.16 % (9569)Time elapsed: 0.003 s
% 1.36/1.16 % (9569)Instructions burned: 3 (million)
% 1.36/1.16 % (9569)------------------------------
% 1.36/1.16 % (9569)------------------------------
% 1.36/1.16 % (9571)Refutation not found, incomplete strategy
% 1.36/1.16 % (9571)------------------------------
% 1.36/1.16 % (9571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (9571)Termination reason: Refutation not found, incomplete strategy
% 1.36/1.16
% 1.36/1.16
% 1.36/1.16 % (9571)Memory used [KB]: 5500
% 1.36/1.16 % (9571)Time elapsed: 0.004 s
% 1.36/1.16 % (9571)Instructions burned: 3 (million)
% 1.36/1.16 % (9571)------------------------------
% 1.36/1.16 % (9571)------------------------------
% 1.36/1.16 % (9567)Instruction limit reached!
% 1.36/1.16 % (9567)------------------------------
% 1.36/1.16 % (9567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (9567)Termination reason: Unknown
% 1.36/1.16 % (9567)Termination phase: Saturation
% 1.36/1.16
% 1.36/1.16 % (9567)Memory used [KB]: 5500
% 1.36/1.16 % (9567)Time elapsed: 0.004 s
% 1.36/1.16 % (9567)Instructions burned: 5 (million)
% 1.36/1.16 % (9567)------------------------------
% 1.36/1.16 % (9567)------------------------------
% 1.36/1.16 % (9573)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9468 for (2999ds/3Mi)
% 1.36/1.16 % (9572)First to succeed.
% 1.36/1.17 % (9573)Instruction limit reached!
% 1.36/1.17 % (9573)------------------------------
% 1.36/1.17 % (9573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.17 % (9573)Termination reason: Unknown
% 1.36/1.17 % (9573)Termination phase: Saturation
% 1.36/1.17
% 1.36/1.17 % (9573)Memory used [KB]: 5500
% 1.36/1.17 % (9573)Time elapsed: 0.002 s
% 1.36/1.17 % (9573)Instructions burned: 3 (million)
% 1.36/1.17 % (9573)------------------------------
% 1.36/1.17 % (9573)------------------------------
% 1.36/1.17 % (9572)Refutation found. Thanks to Tanya!
% 1.36/1.17 % SZS status Theorem for DTF2THF_9468
% 1.36/1.17 % SZS output start Proof for DTF2THF_9468
% 1.36/1.17 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.36/1.17 thf(type_def_7, type, 'type/realax/real': $tType).
% 1.36/1.17 thf(type_def_8, type, sK0: $tType).
% 1.36/1.17 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.36/1.17 thf(func_def_1, type, 'type/nums/num': $tType).
% 1.36/1.17 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.36/1.17 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.36/1.17 thf(func_def_4, type, 'const/sets/CARD': !>[X0: $tType]:((X0 > $o) > 'type/nums/num')).
% 1.36/1.17 thf(func_def_5, type, 'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real').
% 1.36/1.17 thf(func_def_6, type, 'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.36/1.17 thf(func_def_7, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.36/1.17 thf(func_def_8, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.36/1.17 thf(func_def_13, type, sK1: sK0 > $o).
% 1.36/1.17 thf(func_def_14, type, sK2: sK0 > 'type/realax/real').
% 1.36/1.17 thf(func_def_15, type, sK3: 'type/realax/real').
% 1.36/1.17 thf(func_def_16, type, sK4: !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > (X0 > 'type/realax/real') > X0)).
% 1.36/1.17 thf(func_def_18, type, ph6: !>[X0: $tType]:(X0)).
% 1.36/1.17 thf(f47,plain,(
% 1.36/1.17 $false),
% 1.36/1.17 inference(subsumption_resolution,[status(thm)],[f45,f29])).
% 1.36/1.17 thf(f29,plain,(
% 1.36/1.17 ($true != ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ sK2) @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3)))))),
% 1.36/1.17 inference(backward_demodulation,[status(thm)],[f22,f28])).
% 1.36/1.17 thf(f28,plain,(
% 1.36/1.17 ( ! [X0 : 'type/realax/real'] : ((('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (X0))) = ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK0 @ sK1)) @ X0))) )),
% 1.36/1.17 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.36/1.17 thf(f27,plain,(
% 1.36/1.17 ( ! [X0 : 'type/realax/real'] : ((('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (X0))) = ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK0 @ sK1)) @ X0)) | ($true != $true)) )),
% 1.36/1.17 inference(superposition,[status(thm)],[f21,f23])).
% 1.36/1.17 thf(f23,plain,(
% 1.36/1.17 (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 1.36/1.17 inference(cnf_transformation,[status(thm)],[f18])).
% 1.36/1.17 thf(f18,plain,(
% 1.36/1.17 ! [X4 : sK0] : (($true != ('const/sets/IN' @ sK0 @ X4 @ sK1)) | ($true = ('const/realax/real_le' @ (sK2 @ X4) @ sK3))) & (('const/sets/FINITE' @ sK0 @ sK1) = $true) & (('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ sK2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK0 @ sK1)) @ sK3)) != $true)),
% 1.36/1.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f17])).
% 1.36/1.17 thf(f17,plain,(
% 1.36/1.17 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > 'type/realax/real',X3 : 'type/realax/real'] : (! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) != $true) | (('const/realax/real_le' @ (X2 @ X4) @ X3) = $true)) & (('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)) != $true)) => (! [X4 : sK0] : (($true != ('const/sets/IN' @ sK0 @ X4 @ sK1)) | ($true = ('const/realax/real_le' @ (sK2 @ X4) @ sK3))) & (('const/sets/FINITE' @ sK0 @ sK1) = $true) & (('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ sK2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK0 @ sK1)) @ sK3)) != $true))),
% 1.36/1.17 introduced(definition,[],[choice_axiom])).
% 1.36/1.17 thf(f13,plain,(
% 1.36/1.17 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > 'type/realax/real',X3 : 'type/realax/real'] : (! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) != $true) | (('const/realax/real_le' @ (X2 @ X4) @ X3) = $true)) & (('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)) != $true))),
% 1.36/1.17 inference(flattening,[status(thm)],[f12])).
% 1.36/1.17 thf(f12,plain,(
% 1.36/1.17 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > 'type/realax/real',X3 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)) != $true) & ((('const/sets/FINITE' @ X0 @ X1) = $true) & ! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) != $true) | (('const/realax/real_le' @ (X2 @ X4) @ X3) = $true))))),
% 1.36/1.17 inference(ennf_transformation,[status(thm)],[f9])).
% 1.36/1.17 thf(f9,plain,(
% 1.36/1.17 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > 'type/realax/real',X3 : 'type/realax/real'] : (((('const/sets/FINITE' @ X0 @ X1) = $true) & ! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) = $true) => (('const/realax/real_le' @ (X2 @ X4) @ X3) = $true))) => (('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)) = $true))),
% 1.36/1.17 inference(fool_elimination,[status(thm)],[f8])).
% 1.36/1.17 thf(f8,plain,(
% 1.36/1.17 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > 'type/realax/real',X3 : 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/realax/real_le' @ (X2 @ X4) @ X3))) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)))),
% 1.36/1.17 inference(rectify,[status(thm)],[f4])).
% 1.36/1.17 thf(f4,negated_conjecture,(
% 1.36/1.17 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > 'type/realax/real',X3 : 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/realax/real_le' @ (X2 @ X4) @ X3))) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)))),
% 1.36/1.17 inference(negated_conjecture,[status(cth)],[f3])).
% 1.36/1.17 thf(f3,conjecture,(
% 1.36/1.17 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > 'type/realax/real',X3 : 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X1) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X1) => ('const/realax/real_le' @ (X2 @ X4) @ X3))) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X1 @ X2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X1)) @ X3)))),
% 1.36/1.17 file('/export/starexec/sandbox2/tmp/tmp.idqcZtZszN/DTF2THF_9468.p','thm/iterate/SUM_BOUND_')).
% 1.36/1.17 thf(f21,plain,(
% 1.36/1.17 ( ! [X0 : $tType,X2 : X0 > $o,X1 : 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1) = ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: (X1))))) )),
% 1.36/1.17 inference(cnf_transformation,[status(thm)],[f16])).
% 1.36/1.17 thf(f16,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : 'type/realax/real',X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1) = ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: (X1)))))),
% 1.36/1.17 inference(ennf_transformation,[status(thm)],[f7])).
% 1.36/1.17 thf(f7,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : 'type/realax/real',X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) = $true) => (('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1) = ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: (X1)))))),
% 1.36/1.17 inference(fool_elimination,[status(thm)],[f6])).
% 1.36/1.17 thf(f6,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : 'type/realax/real',X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => (('const/iterate/sum' @ X0 @ X2 @ (^[X3 : X0] : (X1))) = ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1)))),
% 1.36/1.17 inference(rectify,[status(thm)],[f2])).
% 1.36/1.17 thf(f2,axiom,(
% 1.36/1.17 ! [X0 : $tType,X1 : 'type/realax/real',X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => (('const/iterate/sum' @ X0 @ X2 @ (^[X3 : X0] : (X1))) = ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ X0 @ X2)) @ X1)))),
% 1.36/1.17 file('/export/starexec/sandbox2/tmp/tmp.idqcZtZszN/DTF2THF_9468.p','thm/iterate/SUM_CONST_')).
% 1.36/1.17 thf(f22,plain,(
% 1.36/1.17 (('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ sK2) @ ('const/realax/real_mul' @ ('const/realax/real_of_num' @ ('const/sets/CARD' @ sK0 @ sK1)) @ sK3)) != $true)),
% 1.36/1.17 inference(cnf_transformation,[status(thm)],[f18])).
% 1.36/1.17 thf(f45,plain,(
% 1.36/1.17 ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ sK2) @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3)))))),
% 1.36/1.17 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.36/1.17 thf(f44,plain,(
% 1.36/1.17 ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK2 @ ((^[Y1 : sK0]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3)))))),
% 1.36/1.17 inference(duplicate_literal_removal,[status(thm)],[f42])).
% 1.36/1.17 thf(f42,plain,(
% 1.36/1.17 ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK2 @ ((^[Y1 : sK0]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3))))) | ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK2 @ ((^[Y1 : sK0]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3)))))),
% 1.36/1.17 inference(equality_resolution,[status(thm)],[f39])).
% 1.36/1.17 thf(f39,plain,(
% 1.36/1.17 ( ! [X2 : sK0 > 'type/realax/real',X0 : sK0 > sK0,X1 : sK0 > 'type/realax/real'] : (((X0 @ (sK4 @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3)) @ (^[Y0 : sK0]: (sK2 @ (X0 @ Y0))))) != (sK4 @ sK0 @ sK1 @ X1 @ X2)) | ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ X2) @ ('const/iterate/sum' @ sK0 @ sK1 @ X1))) | (('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3)))) = $true)) )),
% 1.36/1.17 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.36/1.17 thf(f38,plain,(
% 1.36/1.17 ( ! [X2 : sK0 > 'type/realax/real',X0 : sK0 > sK0,X1 : sK0 > 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ X2) @ ('const/iterate/sum' @ sK0 @ sK1 @ X1))) | ((X0 @ (sK4 @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3)) @ (^[Y0 : sK0]: (sK2 @ (X0 @ Y0))))) != (sK4 @ sK0 @ sK1 @ X1 @ X2)) | ($true != $true) | (('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK0 @ sK1 @ (^[Y0 : sK0]: (sK3)))) = $true)) )),
% 1.36/1.17 inference(constrained_superposition,[status(thm)],[f35,f33])).
% 1.36/1.17 thf(f33,plain,(
% 1.36/1.17 ( ! [X0 : sK0 > 'type/realax/real',X1 : sK0 > 'type/realax/real'] : ((('const/realax/real_le' @ (sK2 @ (sK4 @ sK0 @ sK1 @ X0 @ X1)) @ sK3) = $true) | ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ X1) @ ('const/iterate/sum' @ sK0 @ sK1 @ X0)))) )),
% 1.36/1.17 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.36/1.17 thf(f32,plain,(
% 1.36/1.17 ( ! [X0 : sK0 > 'type/realax/real',X1 : sK0 > 'type/realax/real'] : ((('const/realax/real_le' @ (sK2 @ (sK4 @ sK0 @ sK1 @ X0 @ X1)) @ sK3) = $true) | ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ X1) @ ('const/iterate/sum' @ sK0 @ sK1 @ X0))) | ($true != $true)) )),
% 1.36/1.17 inference(superposition,[status(thm)],[f24,f31])).
% 1.36/1.17 thf(f31,plain,(
% 1.36/1.17 ( ! [X0 : sK0 > 'type/realax/real',X1 : sK0 > 'type/realax/real'] : (($true = ('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK1 @ X1 @ X0) @ sK1)) | ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ X0) @ ('const/iterate/sum' @ sK0 @ sK1 @ X1)))) )),
% 1.36/1.17 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.36/1.17 thf(f30,plain,(
% 1.36/1.17 ( ! [X0 : sK0 > 'type/realax/real',X1 : sK0 > 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ X0) @ ('const/iterate/sum' @ sK0 @ sK1 @ X1))) | ($true = ('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK1 @ X1 @ X0) @ sK1)) | ($true != $true)) )),
% 1.36/1.17 inference(superposition,[status(thm)],[f26,f23])).
% 1.36/1.17 thf(f26,plain,(
% 1.36/1.17 ( ! [X0 : $tType,X2 : X0 > 'type/realax/real',X3 : X0 > $o,X1 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ X3) = $true)) )),
% 1.36/1.17 inference(cnf_transformation,[status(thm)],[f20])).
% 1.36/1.17 thf(f20,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ X3) = $true) & (('const/realax/real_le' @ (X1 @ (sK4 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK4 @ X0 @ X3 @ X2 @ X1))) != $true)) | (('const/sets/FINITE' @ X0 @ X3) != $true))),
% 1.36/1.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f15,f19])).
% 1.36/1.17 thf(f19,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) = $true) & (('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4)) != $true)) => ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ X3) = $true) & (('const/realax/real_le' @ (X1 @ (sK4 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK4 @ X0 @ X3 @ X2 @ X1))) != $true)))),
% 1.36/1.17 introduced(definition,[],[choice_axiom])).
% 1.36/1.17 thf(f15,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | ? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) = $true) & (('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4)) != $true)) | (('const/sets/FINITE' @ X0 @ X3) != $true))),
% 1.36/1.17 inference(flattening,[status(thm)],[f14])).
% 1.36/1.17 thf(f14,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) = $true) & (('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4)) != $true)) | (('const/sets/FINITE' @ X0 @ X3) != $true)))),
% 1.36/1.17 inference(ennf_transformation,[status(thm)],[f11])).
% 1.36/1.17 thf(f11,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) = $true) => (('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4)) = $true)) & (('const/sets/FINITE' @ X0 @ X3) = $true)) => (('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true))),
% 1.36/1.17 inference(fool_elimination,[status(thm)],[f10])).
% 1.36/1.17 thf(f10,plain,(
% 1.36/1.17 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 1.36/1.17 inference(rectify,[status(thm)],[f1])).
% 1.36/1.17 thf(f1,axiom,(
% 1.36/1.17 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 1.36/1.17 file('/export/starexec/sandbox2/tmp/tmp.idqcZtZszN/DTF2THF_9468.p','thm/iterate/SUM_LE_')).
% 1.36/1.17 thf(f24,plain,(
% 1.36/1.17 ( ! [X4 : sK0] : (($true != ('const/sets/IN' @ sK0 @ X4 @ sK1)) | ($true = ('const/realax/real_le' @ (sK2 @ X4) @ sK3))) )),
% 1.36/1.17 inference(cnf_transformation,[status(thm)],[f18])).
% 1.36/1.17 thf(f35,plain,(
% 1.36/1.17 ( ! [X0 : sK0 > 'type/realax/real',X1 : sK0 > 'type/realax/real'] : ((('const/realax/real_le' @ (X0 @ (sK4 @ sK0 @ sK1 @ X1 @ X0)) @ (X1 @ (sK4 @ sK0 @ sK1 @ X1 @ X0))) != $true) | ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ X0) @ ('const/iterate/sum' @ sK0 @ sK1 @ X1)))) )),
% 1.36/1.17 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.36/1.17 thf(f34,plain,(
% 1.36/1.17 ( ! [X0 : sK0 > 'type/realax/real',X1 : sK0 > 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ ('const/iterate/sum' @ sK0 @ sK1 @ X0) @ ('const/iterate/sum' @ sK0 @ sK1 @ X1))) | (('const/realax/real_le' @ (X0 @ (sK4 @ sK0 @ sK1 @ X1 @ X0)) @ (X1 @ (sK4 @ sK0 @ sK1 @ X1 @ X0))) != $true)) )),
% 1.36/1.17 inference(superposition,[status(thm)],[f25,f23])).
% 1.36/1.17 thf(f25,plain,(
% 1.36/1.17 ( ! [X0 : $tType,X2 : X0 > 'type/realax/real',X3 : X0 > $o,X1 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/realax/real_le' @ (X1 @ (sK4 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK4 @ X0 @ X3 @ X2 @ X1))) != $true) | (('const/realax/real_le' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true)) )),
% 1.36/1.17 inference(cnf_transformation,[status(thm)],[f20])).
% 1.36/1.17 % SZS output end Proof for DTF2THF_9468
% 1.36/1.17 % (9572)------------------------------
% 1.36/1.17 % (9572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.17 % (9572)Termination reason: Refutation
% 1.36/1.17
% 1.36/1.17 % (9572)Memory used [KB]: 5628
% 1.36/1.17 % (9572)Time elapsed: 0.011 s
% 1.36/1.17 % (9572)Instructions burned: 15 (million)
% 1.36/1.17 % (9572)------------------------------
% 1.36/1.17 % (9572)------------------------------
% 1.36/1.17 % (9565)Success in time 0.013 s
%------------------------------------------------------------------------------