%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA102^1 : 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 : 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 08:38:53 AM UTC 2026
% Result : Theorem 1.67s 1.31s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 418 ( 119 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 745 ( 45 ~; 35 |; 32 &; 622 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 2 con; 0-4 aty)
% Number of variables : 134 ( 0 ^; 119 !; 15 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_2,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/INTER':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
'const/sets/DISJOINT':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_8,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_10,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_15,type,
sK2: sK0 > $o ).
thf(func_def_16,type,
sK3: sK0 > $o ).
thf(func_def_17,type,
sK4: sK0 > $o ).
thf(func_def_19,type,
ph6:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK7:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(f101,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK1 )
!= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK1 ) ),
inference(superposition,[status(thm)],[f38,f74]) ).
thf(f74,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f72,f58]) ).
thf(f58,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true != $true )
| ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f53,f37]) ).
thf(f37,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) ),
inference(definition_unfolding,[status(thm)],[f30,f29]) ).
thf(f29,plain,
( ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 )
= sK4 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( 'const/sets/EMPTY'
@ ( sK0
= ( 'const/sets/INTER' @ sK0 @ sK2 @ sK3 ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK4 ) )
& ( ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 )
= sK4 )
& ( ( 'const/iterate/sum' @ sK0 @ sK4 @ sK1 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f26]) ).
thf(f26,plain,
( ? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( 'const/sets/EMPTY'
@ ( X0
= ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 )
& ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
!= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) ) )
=> ( ( 'const/sets/EMPTY'
@ ( sK0
= ( 'const/sets/INTER' @ sK0 @ sK2 @ sK3 ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK4 ) )
& ( ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 )
= sK4 )
& ( ( 'const/iterate/sum' @ sK0 @ sK4 @ sK1 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( 'const/sets/EMPTY'
@ ( X0
= ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 )
& ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
!= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
!= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) )
& ( 'const/sets/EMPTY'
@ ( X0
= ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) ) )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 )
& ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( 'const/sets/EMPTY'
@ ( X0
= ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) ) )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 )
& ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 )
& ( 'const/sets/EMPTY'
@ ( X0
= ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) ) ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 )
& ( 'const/sets/EMPTY'
@ ( X0
= ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) ) ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o,X4: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 )
= X4 )
& ( 'const/sets/EMPTY'
@ ( X0
= ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) ) ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X4 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/iterate/SUM_UNION_EQ_') ).
thf(f30,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f53,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f32,f35]) ).
thf(f35,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/sets/SUBSET_UNION_0') ).
thf(f32,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
=> ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/sets/FINITE_SUBSET_') ).
thf(f72,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ X0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
inference(forward_demodulation,[status(thm)],[f70,f56]) ).
thf(f56,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true != $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f47,f37]) ).
thf(f47,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f32,f34]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/sets/SUBSET_UNION_1') ).
thf(f70,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
!= $true )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ X0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: sK0 > 'type/realax/real'] :
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ( $true != $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK3 )
!= $true )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ X0 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ X0 ) )
= ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f33,f68]) ).
thf(f68,plain,
( ( 'const/sets/DISJOINT' @ sK0 @ sK2 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( 'const/sets/EMPTY' @ ( sK0 != 'const/sets/EMPTY' ) @ sK0 )
| ( ( 'const/sets/DISJOINT' @ sK0 @ sK2 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f42,f31]) ).
thf(f31,plain,
( 'const/sets/EMPTY'
@ ( sK0
= ( 'const/sets/INTER' @ sK0 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f42,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
!= 'const/sets/EMPTY' )
@ X0 )
| ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= $true )
| ( ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/DISJOINT' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/INTER' @ X0 @ X1 @ X2 )
= 'const/sets/EMPTY' )
@ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/sets/DISJOINT_') ).
thf(f33,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
!= $true )
| ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
!= $true )
| ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
= $true ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
& ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/sets/DISJOINT' @ X0 @ X2 @ X3 )
& ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/iterate/SUM_UNION_') ).
thf(f38,plain,
( ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK1 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f29]) ).
thf(f28,plain,
( ( 'const/iterate/sum' @ sK0 @ sK4 @ sK1 )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA102^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n023.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 03:51:04 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : ANA102^1 : TPTP v9.2.1. Released v7.0.0.
% 0.27/0.47 % Domain : Analysis
% 0.27/0.47 % Problem : SUM_UNION_EQ
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Kal16]
% 0.27/0.47 % Names : SUM_UNION_EQ_.p [Kal16]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v7.1.0
% 0.27/0.47 % Syntax : Number of formulae : 15 ( 1 unt; 9 typ; 0 def)
% 0.27/0.47 % Number of atoms : 24 ( 6 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.27/0.47 % Number of connectives : 75 ( 0 ~; 0 |; 5 &; 67 @)
% 0.27/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 11 ( 8 avg)
% 0.27/0.47 % Number of types : 2 ( 1 usr)
% 0.27/0.47 % Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 9 ( 8 usr; 0 con; 2-4 aty)
% 0.27/0.47 % Number of variables : 28 ( 0 ^; 21 !; 0 ?; 28 :)
% 0.27/0.47 % ( 7 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.47 % SPC : TH1_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : Exported from core HOL Light.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf('thf_type_type/realax/real',type,
% 0.27/0.47 'type/realax/real': $tType ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/UNION',type,
% 0.27/0.47 'const/sets/UNION':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/SUBSET',type,
% 0.27/0.47 'const/sets/SUBSET':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/INTER',type,
% 0.27/0.47 'const/sets/INTER':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/FINITE',type,
% 0.27/0.47 'const/sets/FINITE':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/EMPTY',type,
% 0.27/0.47 'const/sets/EMPTY':
% 0.27/0.47 !>[A: $tType] : ( A > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/DISJOINT',type,
% 0.27/0.47 'const/sets/DISJOINT':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/realax/real_add',type,
% 0.27/0.47 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/iterate/sum',type,
% 0.27/0.47 'const/iterate/sum':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.27/0.47
% 0.27/0.47 thf('thm/sets/SUBSET_UNION_1',axiom,
% 0.27/0.47 ! [A: $tType,A0: A > $o,A1: A > $o] : ( 'const/sets/SUBSET' @ A @ A0 @ ( 'const/sets/UNION' @ A @ A1 @ A0 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf('thm/sets/SUBSET_UNION_0',axiom,
% 0.27/0.47 ! [A: $tType,A0: A > $o,A1: A > $o] : ( 'const/sets/SUBSET' @ A @ A0 @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf('thm/sets/FINITE_SUBSET_',axiom,
% 0.27/0.47 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.27/0.47 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.27/0.47 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 0.27/0.47 => ( 'const/sets/FINITE' @ A @ A0 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf('thm/sets/DISJOINT_',axiom,
% 0.27/0.47 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.27/0.47 ( ( 'const/sets/DISJOINT' @ A @ A0 @ A1 )
% 0.27/0.47 = ( ( 'const/sets/INTER' @ A @ A0 @ A1 )
% 0.27/0.47 = ( 'const/sets/EMPTY' @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf('thm/iterate/SUM_UNION_',axiom,
% 0.27/0.47 ! [A: $tType,A0: A > 'type/realax/real',A1: A > $o,A2: A > $o] :
% 0.27/0.47 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.27/0.47 & ( 'const/sets/FINITE' @ A @ A2 )
% 0.27/0.47 & ( 'const/sets/DISJOINT' @ A @ A1 @ A2 ) )
% 0.27/0.47 => ( ( 'const/iterate/sum' @ A @ ( 'const/sets/UNION' @ A @ A1 @ A2 ) @ A0 )
% 0.27/0.47 = ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A1 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf('thm/iterate/SUM_UNION_EQ_',conjecture,
% 0.27/0.47 ! [A: $tType,A0: A > 'type/realax/real',A1: A > $o,A2: A > $o,A3: A > $o] :
% 0.27/0.47 ( ( ( 'const/sets/FINITE' @ A @ A3 )
% 0.27/0.47 & ( ( 'const/sets/INTER' @ A @ A1 @ A2 )
% 0.27/0.47 = ( 'const/sets/EMPTY' @ A ) )
% 0.27/0.47 & ( ( 'const/sets/UNION' @ A @ A1 @ A2 )
% 0.27/0.47 = A3 ) )
% 0.27/0.47 => ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A1 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) )
% 0.27/0.47 = ( 'const/iterate/sum' @ A @ A3 @ A0 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.50/1.27 ---- Embedded in THF ---
% 1.50/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.27 %%% Generated on Tue Feb 24 03:51:05 EST 2026
% 1.50/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.27 %%% Logic specification used:
% 1.50/1.27 %%% thf(spec, logic, $$dhol).
% 1.50/1.27
% 1.50/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2DTF20501.p
% See solution above
% 1.50/1.27 ------------------------
% 1.50/1.28 ---- Cleaned THF ---
% 1.50/1.28 thf('thf_type_type/realax/real',type,
% 1.50/1.28 'type/realax/real': $tType ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/UNION',type,
% 1.50/1.28 'const/sets/UNION':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/SUBSET',type,
% 1.50/1.28 'const/sets/SUBSET':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/INTER',type,
% 1.50/1.28 'const/sets/INTER':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/FINITE',type,
% 1.50/1.28 'const/sets/FINITE':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/EMPTY',type,
% 1.50/1.28 'const/sets/EMPTY':
% 1.50/1.28 !>[A: $tType] : ( A > $o ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/sets/DISJOINT',type,
% 1.50/1.28 'const/sets/DISJOINT':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/realax/real_add',type,
% 1.50/1.28 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 1.50/1.28
% 1.50/1.28 thf('thf_const_const/iterate/sum',type,
% 1.50/1.28 'const/iterate/sum':
% 1.50/1.28 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 1.50/1.28
% 1.50/1.28 thf('thm/sets/SUBSET_UNION_1',axiom,
% 1.50/1.28 ! [A: $tType,A0: A > $o,A1: A > $o] : ( 'const/sets/SUBSET' @ A @ A0 @ ( 'const/sets/UNION' @ A @ A1 @ A0 ) ) ).
% 1.50/1.28
% 1.50/1.28 thf('thm/sets/SUBSET_UNION_0',axiom,
% 1.50/1.28 ! [A: $tType,A0: A > $o,A1: A > $o] : ( 'const/sets/SUBSET' @ A @ A0 @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) ) ).
% 1.50/1.28
% 1.50/1.28 thf('thm/sets/FINITE_SUBSET_',axiom,
% 1.50/1.28 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.50/1.28 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.50/1.28 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 1.50/1.28 => ( 'const/sets/FINITE' @ A @ A0 ) ) ).
% 1.50/1.28
% 1.50/1.28 thf('thm/sets/DISJOINT_',axiom,
% 1.50/1.28 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.50/1.28 ( ( 'const/sets/DISJOINT' @ A @ A0 @ A1 )
% 1.50/1.28 = ( ( 'const/sets/INTER' @ A @ A0 @ A1 )
% 1.50/1.28 = ( 'const/sets/EMPTY' @ A ) ) ) ).
% 1.50/1.28
% 1.50/1.28 thf('thm/iterate/SUM_UNION_',axiom,
% 1.50/1.28 ! [A: $tType,A0: A > 'type/realax/real',A1: A > $o,A2: A > $o] :
% 1.50/1.28 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.50/1.28 & ( 'const/sets/FINITE' @ A @ A2 )
% 1.50/1.28 & ( 'const/sets/DISJOINT' @ A @ A1 @ A2 ) )
% 1.50/1.28 => ( ( 'const/iterate/sum' @ A @ ( 'const/sets/UNION' @ A @ A1 @ A2 ) @ A0 )
% 1.50/1.28 = ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A1 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) ) ) ) ).
% 1.50/1.28
% 1.50/1.28 thf('thm/iterate/SUM_UNION_EQ_',conjecture,
% 1.50/1.28 ! [A: $tType,A0: A > 'type/realax/real',A1: A > $o,A2: A > $o,A3: A > $o] :
% 1.50/1.28 ( ( ( 'const/sets/FINITE' @ A @ A3 )
% 1.50/1.28 & ( ( 'const/sets/INTER' @ A @ A1 @ A2 )
% 1.50/1.28 = ( 'const/sets/EMPTY' @ A ) )
% 1.50/1.28 & ( ( 'const/sets/UNION' @ A @ A1 @ A2 )
% 1.50/1.28 = A3 ) )
% 1.50/1.28 => ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A1 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) )
% 1.50/1.28 = ( 'const/iterate/sum' @ A @ A3 @ A0 ) ) ) ).
% 1.50/1.28 ------------------------
% 1.67/1.30 % (20721)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20501 for (2999ds/2Mi)
% 1.67/1.30 % (20721)Instruction limit reached!
% 1.67/1.30 % (20721)------------------------------
% 1.67/1.30 % (20721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.30 % (20721)Termination reason: Unknown
% 1.67/1.30 % (20721)Termination phase: Preprocessing 3
% 1.67/1.30
% 1.67/1.30 % (20721)Memory used [KB]: 895
% 1.67/1.30 % (20721)Time elapsed: 0.002 s
% 1.67/1.30 % (20721)Instructions burned: 2 (million)
% 1.67/1.30 % (20721)------------------------------
% 1.67/1.30 % (20721)------------------------------
% 1.67/1.30 % (20720)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_20501 for (2999ds/27Mi)
% 1.67/1.30 % (20718)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20501 for (2999ds/183Mi)
% 1.67/1.30 % (20719)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_20501 for (2999ds/4Mi)
% 1.67/1.31 % (20722)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_20501 for (2999ds/2Mi)
% 1.67/1.31 % (20720)First to succeed.
% 1.67/1.31 % (20724)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20501 for (2999ds/18Mi)
% 1.67/1.31 % (20723)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_20501 for (2999ds/275Mi)
% 1.67/1.31 % (20722)Instruction limit reached!
% 1.67/1.31 % (20722)------------------------------
% 1.67/1.31 % (20722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (20722)Termination reason: Unknown
% 1.67/1.31 % (20722)Termination phase: shuffling
% 1.67/1.31
% 1.67/1.31 % (20722)Memory used [KB]: 895
% 1.67/1.31 % (20722)Time elapsed: 0.003 s
% 1.67/1.31 % (20722)Instructions burned: 2 (million)
% 1.67/1.31 % (20722)------------------------------
% 1.67/1.31 % (20722)------------------------------
% 1.67/1.31 % (20720)Refutation found. Thanks to Tanya!
% 1.67/1.31 % SZS status Theorem for DTF2THF_20501
% 1.67/1.31 % SZS output start Proof for DTF2THF_20501
% 1.67/1.31 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.67/1.31 thf(type_def_7, type, sK0: $tType).
% 1.67/1.31 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.67/1.31 thf(func_def_1, type, 'const/sets/UNION': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 1.67/1.31 thf(func_def_2, type, 'const/sets/SUBSET': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.67/1.31 thf(func_def_3, type, 'const/sets/INTER': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 1.67/1.31 thf(func_def_4, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.67/1.31 thf(func_def_5, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.67/1.31 thf(func_def_6, type, 'const/sets/DISJOINT': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.67/1.31 thf(func_def_7, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 1.67/1.31 thf(func_def_8, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.67/1.31 thf(func_def_10, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/1.31 thf(func_def_14, type, sK1: sK0 > 'type/realax/real').
% 1.67/1.31 thf(func_def_15, type, sK2: sK0 > $o).
% 1.67/1.31 thf(func_def_16, type, sK3: sK0 > $o).
% 1.67/1.31 thf(func_def_17, type, sK4: sK0 > $o).
% 1.67/1.31 thf(func_def_19, type, ph6: !>[X0: $tType]:(X0)).
% 1.67/1.31 thf(func_def_20, type, sK7: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.67/1.31 thf(f101,plain,(
% 1.67/1.31 $false),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.67/1.31 thf(f100,plain,(
% 1.67/1.31 (('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ sK1) != ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ sK1))),
% 1.67/1.31 inference(superposition,[status(thm)],[f38,f74])).
% 1.67/1.31 thf(f74,plain,(
% 1.67/1.31 ( ! [X0 : sK0 > 'type/realax/real'] : ((('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)) = ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0))) )),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.67/1.31 thf(f73,plain,(
% 1.67/1.31 ( ! [X0 : sK0 > 'type/realax/real'] : (($true != $true) | (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)) = ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0))) )),
% 1.67/1.31 inference(forward_demodulation,[status(thm)],[f72,f58])).
% 1.67/1.31 thf(f58,plain,(
% 1.67/1.31 ($true = ('const/sets/FINITE' @ sK0 @ sK2))),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.67/1.31 thf(f57,plain,(
% 1.67/1.31 ($true != $true) | ($true = ('const/sets/FINITE' @ sK0 @ sK2))),
% 1.67/1.31 inference(superposition,[status(thm)],[f53,f37])).
% 1.67/1.31 thf(f37,plain,(
% 1.67/1.31 ($true = ('const/sets/FINITE' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3)))),
% 1.67/1.31 inference(definition_unfolding,[status(thm)],[f30,f29])).
% 1.67/1.31 thf(f29,plain,(
% 1.67/1.31 (('const/sets/UNION' @ sK0 @ sK2 @ sK3) = sK4)),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.67/1.31 thf(f27,plain,(
% 1.67/1.31 ('const/sets/EMPTY' @ sK0 = ('const/sets/INTER' @ sK0 @ sK2 @ sK3)) & ($true = ('const/sets/FINITE' @ sK0 @ sK4)) & (('const/sets/UNION' @ sK0 @ sK2 @ sK3) = sK4) & (('const/iterate/sum' @ sK0 @ sK4 @ sK1) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1)))),
% 1.67/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f26])).
% 1.67/1.31 thf(f26,plain,(
% 1.67/1.31 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o,X4 : X0 > $o] : (('const/sets/EMPTY' @ X0 = ('const/sets/INTER' @ X0 @ X2 @ X3)) & (('const/sets/FINITE' @ X0 @ X4) = $true) & (('const/sets/UNION' @ X0 @ X2 @ X3) = X4) & (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)) != ('const/iterate/sum' @ X0 @ X4 @ X1))) => (('const/sets/EMPTY' @ sK0 = ('const/sets/INTER' @ sK0 @ sK2 @ sK3)) & ($true = ('const/sets/FINITE' @ sK0 @ sK4)) & (('const/sets/UNION' @ sK0 @ sK2 @ sK3) = sK4) & (('const/iterate/sum' @ sK0 @ sK4 @ sK1) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1))))),
% 1.67/1.31 introduced(definition,[],[choice_axiom])).
% 1.67/1.31 thf(f21,plain,(
% 1.67/1.31 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o,X4 : X0 > $o] : (('const/sets/EMPTY' @ X0 = ('const/sets/INTER' @ X0 @ X2 @ X3)) & (('const/sets/FINITE' @ X0 @ X4) = $true) & (('const/sets/UNION' @ X0 @ X2 @ X3) = X4) & (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)) != ('const/iterate/sum' @ X0 @ X4 @ X1)))),
% 1.67/1.31 inference(flattening,[status(thm)],[f20])).
% 1.67/1.31 thf(f20,plain,(
% 1.67/1.31 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o,X4 : X0 > $o] : ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)) != ('const/iterate/sum' @ X0 @ X4 @ X1)) & (('const/sets/EMPTY' @ X0 = ('const/sets/INTER' @ X0 @ X2 @ X3)) & (('const/sets/UNION' @ X0 @ X2 @ X3) = X4) & (('const/sets/FINITE' @ X0 @ X4) = $true)))),
% 1.67/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.67/1.31 thf(f11,plain,(
% 1.67/1.31 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o,X4 : X0 > $o] : ((('const/sets/EMPTY' @ X0 = ('const/sets/INTER' @ X0 @ X2 @ X3)) & (('const/sets/UNION' @ X0 @ X2 @ X3) = X4) & (('const/sets/FINITE' @ X0 @ X4) = $true)) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)) = ('const/iterate/sum' @ X0 @ X4 @ X1)))),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.31 thf(f10,plain,(
% 1.67/1.31 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o,X4 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X4) & (('const/sets/UNION' @ X0 @ X2 @ X3) = X4) & ('const/sets/EMPTY' @ X0 = ('const/sets/INTER' @ X0 @ X2 @ X3))) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)) = ('const/iterate/sum' @ X0 @ X4 @ X1)))),
% 1.67/1.31 inference(rectify,[status(thm)],[f7])).
% 1.67/1.31 thf(f7,negated_conjecture,(
% 1.67/1.31 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o,X4 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X4) & (('const/sets/UNION' @ X0 @ X2 @ X3) = X4) & ('const/sets/EMPTY' @ X0 = ('const/sets/INTER' @ X0 @ X2 @ X3))) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)) = ('const/iterate/sum' @ X0 @ X4 @ X1)))),
% 1.67/1.31 inference(negated_conjecture,[status(cth)],[f6])).
% 1.67/1.31 thf(f6,conjecture,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o,X4 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X4) & (('const/sets/UNION' @ X0 @ X2 @ X3) = X4) & ('const/sets/EMPTY' @ X0 = ('const/sets/INTER' @ X0 @ X2 @ X3))) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)) = ('const/iterate/sum' @ X0 @ X4 @ X1)))),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/iterate/SUM_UNION_EQ_')).
% 1.67/1.31 thf(f30,plain,(
% 1.67/1.31 ($true = ('const/sets/FINITE' @ sK0 @ sK4))),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.67/1.31 thf(f53,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != ('const/sets/FINITE' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2))) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.67/1.31 thf(f52,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) | ($true != $true) | ($true != ('const/sets/FINITE' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2)))) )),
% 1.67/1.31 inference(superposition,[status(thm)],[f32,f35])).
% 1.67/1.31 thf(f35,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = $true)) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.67/1.31 thf(f15,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = $true)),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f14])).
% 1.67/1.31 thf(f14,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X1 @ X2))),
% 1.67/1.31 inference(rectify,[status(thm)],[f2])).
% 1.67/1.31 thf(f2,axiom,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X1 @ X2))),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/sets/SUBSET_UNION_0')).
% 1.67/1.31 thf(f32,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.31 thf(f23,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X1) = $true))),
% 1.67/1.31 inference(flattening,[status(thm)],[f22])).
% 1.67/1.31 thf(f22,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X2) != $true)))),
% 1.67/1.31 inference(ennf_transformation,[status(thm)],[f13])).
% 1.67/1.31 thf(f13,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) & (('const/sets/FINITE' @ X0 @ X2) = $true)) => (('const/sets/FINITE' @ X0 @ X1) = $true))),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f12])).
% 1.67/1.31 thf(f12,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 1.67/1.31 inference(rectify,[status(thm)],[f3])).
% 1.67/1.31 thf(f3,axiom,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/sets/FINITE_SUBSET_')).
% 1.67/1.31 thf(f72,plain,(
% 1.67/1.31 ( ! [X0 : sK0 > 'type/realax/real'] : (($true != ('const/sets/FINITE' @ sK0 @ sK2)) | (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)) = ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0))) )),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.67/1.31 thf(f71,plain,(
% 1.67/1.31 ( ! [X0 : sK0 > 'type/realax/real'] : (($true != $true) | (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)) = ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0)) | ($true != ('const/sets/FINITE' @ sK0 @ sK2))) )),
% 1.67/1.31 inference(forward_demodulation,[status(thm)],[f70,f56])).
% 1.67/1.31 thf(f56,plain,(
% 1.67/1.31 (('const/sets/FINITE' @ sK0 @ sK3) = $true)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.67/1.31 thf(f55,plain,(
% 1.67/1.31 ($true != $true) | (('const/sets/FINITE' @ sK0 @ sK3) = $true)),
% 1.67/1.31 inference(superposition,[status(thm)],[f47,f37])).
% 1.67/1.31 thf(f47,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != ('const/sets/FINITE' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X1))) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.67/1.31 thf(f46,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) | ($true != $true) | ($true != ('const/sets/FINITE' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X1)))) )),
% 1.67/1.31 inference(superposition,[status(thm)],[f32,f34])).
% 1.67/1.31 thf(f34,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X2 @ X1)) = $true)) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.31 thf(f17,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X2 @ X1)) = $true)),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f16])).
% 1.67/1.31 thf(f16,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X2 @ X1))),
% 1.67/1.31 inference(rectify,[status(thm)],[f1])).
% 1.67/1.31 thf(f1,axiom,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X2 @ X1))),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/sets/SUBSET_UNION_1')).
% 1.67/1.31 thf(f70,plain,(
% 1.67/1.31 ( ! [X0 : sK0 > 'type/realax/real'] : ((('const/sets/FINITE' @ sK0 @ sK3) != $true) | (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)) = ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0)) | ($true != ('const/sets/FINITE' @ sK0 @ sK2))) )),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.67/1.31 thf(f69,plain,(
% 1.67/1.31 ( ! [X0 : sK0 > 'type/realax/real'] : (($true != ('const/sets/FINITE' @ sK0 @ sK2)) | ($true != $true) | (('const/sets/FINITE' @ sK0 @ sK3) != $true) | (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)) = ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0))) )),
% 1.67/1.31 inference(superposition,[status(thm)],[f33,f68])).
% 1.67/1.31 thf(f68,plain,(
% 1.67/1.31 (('const/sets/DISJOINT' @ sK0 @ sK2 @ sK3) = $true)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.67/1.31 thf(f63,plain,(
% 1.67/1.31 ('const/sets/EMPTY' @ sK0 != 'const/sets/EMPTY' @ sK0) | (('const/sets/DISJOINT' @ sK0 @ sK2 @ sK3) = $true)),
% 1.67/1.31 inference(superposition,[status(thm)],[f42,f31])).
% 1.67/1.31 thf(f31,plain,(
% 1.67/1.31 ('const/sets/EMPTY' @ sK0 = ('const/sets/INTER' @ sK0 @ sK2 @ sK3))),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.67/1.31 thf(f42,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/INTER' @ X0 @ X1 @ X2) != 'const/sets/EMPTY' @ X0) | (('const/sets/DISJOINT' @ X0 @ X1 @ X2) = $true)) )),
% 1.67/1.31 inference(equality_proxy_clausification,[status(thm)],[f39])).
% 1.67/1.31 thf(f39,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/DISJOINT' @ X0 @ X1 @ X2) = $true) | ((('const/sets/INTER' @ X0 @ X1 @ X2) = 'const/sets/EMPTY' @ X0) = $false)) )),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.67/1.31 thf(f36,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/DISJOINT' @ X0 @ X1 @ X2) = (('const/sets/INTER' @ X0 @ X1 @ X2) = 'const/sets/EMPTY' @ X0))) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.67/1.31 thf(f9,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/DISJOINT' @ X0 @ X1 @ X2) = (('const/sets/INTER' @ X0 @ X1 @ X2) = 'const/sets/EMPTY' @ X0))),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.31 thf(f4,axiom,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/DISJOINT' @ X0 @ X1 @ X2) = (('const/sets/INTER' @ X0 @ X1 @ X2) = 'const/sets/EMPTY' @ X0))),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/sets/DISJOINT_')).
% 1.67/1.31 thf(f33,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0 > 'type/realax/real'] : ((('const/sets/DISJOINT' @ X0 @ X2 @ X3) != $true) | (('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))) | (('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X3) != $true)) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f25])).
% 1.67/1.31 thf(f25,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/sets/DISJOINT' @ X0 @ X2 @ X3) != $true) | (('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))))),
% 1.67/1.31 inference(flattening,[status(thm)],[f24])).
% 1.67/1.31 thf(f24,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o] : ((('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))) | ((('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/DISJOINT' @ X0 @ X2 @ X3) != $true)))),
% 1.67/1.31 inference(ennf_transformation,[status(thm)],[f19])).
% 1.67/1.31 thf(f19,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o] : (((('const/sets/FINITE' @ X0 @ X3) = $true) & (('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/DISJOINT' @ X0 @ X2 @ X3) = $true)) => (('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))))),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f18])).
% 1.67/1.31 thf(f18,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o] : ((('const/sets/DISJOINT' @ X0 @ X2 @ X3) & ('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X3)) => (('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))))),
% 1.67/1.31 inference(rectify,[status(thm)],[f5])).
% 1.67/1.31 thf(f5,axiom,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > $o,X3 : X0 > $o] : ((('const/sets/DISJOINT' @ X0 @ X2 @ X3) & ('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X3)) => (('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))))),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.Ui91kaG1QY/DTF2THF_20501.p','thm/iterate/SUM_UNION_')).
% 1.67/1.31 thf(f38,plain,(
% 1.67/1.31 (('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ sK1) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1)))),
% 1.67/1.31 inference(definition_unfolding,[status(thm)],[f28,f29])).
% 1.67/1.31 thf(f28,plain,(
% 1.67/1.31 (('const/iterate/sum' @ sK0 @ sK4 @ sK1) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1)))),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.67/1.31 % SZS output end Proof for DTF2THF_20501
% 1.67/1.31 % (20720)------------------------------
% 1.67/1.31 % (20720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (20720)Termination reason: Refutation
% 1.67/1.31
% 1.67/1.31 % (20720)Memory used [KB]: 5628
% 1.67/1.31 % (20720)Time elapsed: 0.009 s
% 1.67/1.31 % (20720)Instructions burned: 17 (million)
% 1.67/1.31 % (20720)------------------------------
% 1.67/1.31 % (20720)------------------------------
% 1.67/1.31 % (20717)Success in time 0.02 s
%------------------------------------------------------------------------------