%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA097^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.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 08:38:52 AM UTC 2026
% Result : Theorem 0.31s 1.24s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 219 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 636 ( 29 ~; 15 |; 17 &; 564 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 2 con; 0-5 aty)
% Number of variables : 66 ( 0 ^; 54 !; 12 ?; 66 :)
% 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/INTER':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_5,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_6,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_7,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_11,type,
sK1: sK0 > $o ).
thf(func_def_12,type,
sK2: sK0 > $o ).
thf(func_def_13,type,
sK3: sK0 > 'type/realax/real' ).
thf(func_def_15,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f30,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f29,f20]) ).
thf(f20,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2THF_17478.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f29,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f28,f22]) ).
thf(f22,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK2 ) @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/INTER' @ sK0 @ sK1 @ sK2 ) @ sK3 ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true )
& ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f17]) ).
thf(f17,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 ) @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INTER' @ X0 @ X1 @ X2 ) @ X3 ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
=> ( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK2 ) @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/INTER' @ sK0 @ sK1 @ sK2 ) @ sK3 ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true )
& ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 ) @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INTER' @ X0 @ X1 @ X2 ) @ X3 ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 ) @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INTER' @ X0 @ X1 @ X2 ) @ X3 ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 ) @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INTER' @ X0 @ X1 @ X2 ) @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 ) @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INTER' @ X0 @ X1 @ X2 ) @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 ) @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INTER' @ X0 @ X1 @ X2 ) @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) @ X3 ) @ ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INTER' @ X0 @ X1 @ X2 ) @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2THF_17478.p','thm/iterate/SUM_INCL_EXCL_') ).
thf(f28,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
!= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f27,f21]) ).
thf(f21,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f27,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
!= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
!= $true )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK3 ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK3 ) ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(superposition,[status(thm)],[f25,f24]) ).
thf(f24,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > $o,X4: X0 > $o,X5: X0 > X1] :
( ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INTER' @ X0 @ X3 @ X4 ) @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > $o,X4: X0 > $o,X5: X0 > X1] :
( ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INTER' @ X0 @ X3 @ X4 ) @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > $o,X4: X0 > $o,X5: X0 > X1] :
( ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INTER' @ X0 @ X3 @ X4 ) @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ! [X3: X0 > $o,X4: X0 > $o,X5: X0 > X1] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true ) )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INTER' @ X0 @ X3 @ X4 ) @ X5 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > $o,X4: X0 > $o,X5: X0 > X1] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INTER' @ X0 @ X3 @ X4 ) @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > $o,X4: X0 > $o,X5: X0 > X1] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INTER' @ X0 @ X3 @ X4 ) @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2THF_17478.p','thm/iterate/ITERATE_INCL_EXCL_') ).
thf(f25,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK3 ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK2 ) @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/INTER' @ sK0 @ sK1 @ sK2 ) @ sK3 ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f19,f19,f19,f19]) ).
thf(f19,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2THF_17478.p','thm/iterate/sum_') ).
thf(f23,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK2 ) @ sK3 ) @ ( 'const/iterate/sum' @ sK0 @ ( 'const/sets/INTER' @ sK0 @ sK1 @ sK2 ) @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA097^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 03:50:42 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : ANA097^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Analysis
% 0.19/0.45 % Problem : SUM_INCL_EXCL
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Kal16]
% 0.19/0.45 % Names : SUM_INCL_EXCL_.p [Kal16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 12 ( 2 unt; 8 typ; 1 def)
% 0.19/0.45 % Number of atoms : 13 ( 3 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 4 ( 3 avg)
% 0.19/0.45 % Number of connectives : 73 ( 0 ~; 0 |; 2 &; 68 @)
% 0.19/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 12 ( 7 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 8 ( 7 usr; 0 con; 2-5 aty)
% 0.19/0.45 % Number of variables : 18 ( 0 ^; 11 !; 0 ?; 18 :)
% 0.19/0.45 % ( 7 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : Exported from core HOL Light.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf('thf_type_type/realax/real',type,
% 0.19/0.45 'type/realax/real': $tType ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/UNION',type,
% 0.19/0.45 'const/sets/UNION':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/INTER',type,
% 0.19/0.45 'const/sets/INTER':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/FINITE',type,
% 0.19/0.45 'const/sets/FINITE':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/realax/real_add',type,
% 0.19/0.45 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/sum',type,
% 0.19/0.45 'const/iterate/sum':
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/monoidal',type,
% 0.19/0.45 'const/iterate/monoidal':
% 0.19/0.45 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/iterate/iterate',type,
% 0.19/0.45 'const/iterate/iterate':
% 0.19/0.45 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/ITERATE_INCL_EXCL_',axiom,
% 0.19/0.45 ! [A: $tType,A0: $tType,A1: A0 > A0 > A0] :
% 0.19/0.45 ( ( 'const/iterate/monoidal' @ A0 @ A1 )
% 0.19/0.45 => ! [A2: A > $o,A3: A > $o,A4: A > A0] :
% 0.19/0.45 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.19/0.45 & ( 'const/sets/FINITE' @ A @ A3 ) )
% 0.19/0.45 => ( ( A1 @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A2 @ A4 ) @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A3 @ A4 ) )
% 0.19/0.45 = ( A1 @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ ( 'const/sets/UNION' @ A @ A2 @ A3 ) @ A4 ) @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ ( 'const/sets/INTER' @ A @ A2 @ A3 ) @ A4 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 0.19/0.45 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/sum_',definition,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( 'const/iterate/sum' @ A )
% 0.19/0.45 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/iterate/SUM_INCL_EXCL_',conjecture,
% 0.19/0.45 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A > 'type/realax/real'] :
% 0.19/0.45 ( ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.19/0.45 & ( 'const/sets/FINITE' @ A @ A1 ) )
% 0.19/0.45 => ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A0 @ A2 ) @ ( 'const/iterate/sum' @ A @ A1 @ A2 ) )
% 0.19/0.45 = ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) @ A2 ) @ ( 'const/iterate/sum' @ A @ ( 'const/sets/INTER' @ A @ A0 @ A1 ) @ A2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 0.31/1.20 ---- Embedded in THF ---
% 0.31/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.20 %%% Generated on Tue Feb 24 03:50:42 EST 2026
% 0.31/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.20 %%% Logic specification used:
% 0.31/1.20 %%% thf(spec, logic, $$dhol).
% 0.31/1.20
% 0.31/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2DTF17478.p
% See solution above
% 0.31/1.20 ------------------------
% 0.31/1.21 ---- Cleaned THF ---
% 0.31/1.21 thf('thf_type_type/realax/real',type,
% 0.31/1.21 'type/realax/real': $tType ).
% 0.31/1.21
% 0.31/1.21 thf('thf_const_const/sets/UNION',type,
% 0.31/1.21 'const/sets/UNION':
% 0.31/1.21 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.31/1.21
% 0.31/1.21 thf('thf_const_const/sets/INTER',type,
% 0.31/1.21 'const/sets/INTER':
% 0.31/1.21 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.31/1.21
% 0.31/1.21 thf('thf_const_const/sets/FINITE',type,
% 0.31/1.21 'const/sets/FINITE':
% 0.31/1.21 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.31/1.21
% 0.31/1.21 thf('thf_const_const/realax/real_add',type,
% 0.31/1.21 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
% 0.31/1.21
% 0.31/1.21 thf('thf_const_const/iterate/sum',type,
% 0.31/1.21 'const/iterate/sum':
% 0.31/1.21 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.31/1.21
% 0.31/1.21 thf('thf_const_const/iterate/monoidal',type,
% 0.31/1.21 'const/iterate/monoidal':
% 0.31/1.21 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.31/1.21
% 0.31/1.21 thf('thf_const_const/iterate/iterate',type,
% 0.31/1.21 'const/iterate/iterate':
% 0.31/1.21 !>[A: $tType,A0: $tType] : ( ( A0 > A0 > A0 ) > ( A > $o ) > ( A > A0 ) > A0 ) ).
% 0.31/1.21
% 0.31/1.21 thf('thm/iterate/ITERATE_INCL_EXCL_',axiom,
% 0.31/1.21 ! [A: $tType,A0: $tType,A1: A0 > A0 > A0] :
% 0.31/1.21 ( ( 'const/iterate/monoidal' @ A0 @ A1 )
% 0.31/1.21 => ! [A2: A > $o,A3: A > $o,A4: A > A0] :
% 0.31/1.21 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.31/1.21 & ( 'const/sets/FINITE' @ A @ A3 ) )
% 0.31/1.21 => ( ( A1 @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A2 @ A4 ) @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ A3 @ A4 ) )
% 0.31/1.21 = ( A1 @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ ( 'const/sets/UNION' @ A @ A2 @ A3 ) @ A4 ) @ ( 'const/iterate/iterate' @ A @ A0 @ A1 @ ( 'const/sets/INTER' @ A @ A2 @ A3 ) @ A4 ) ) ) ) ) ).
% 0.31/1.21
% 0.31/1.21 thf('thm/iterate/MONOIDAL_REAL_ADD_',axiom,
% 0.31/1.21 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' ).
% 0.31/1.21
% 0.31/1.21 thf('thm/iterate/sum_',definition,
% 0.31/1.21 ! [A: $tType] :
% 0.31/1.21 ( ( 'const/iterate/sum' @ A )
% 0.31/1.21 = ( 'const/iterate/iterate' @ A @ 'type/realax/real' @ 'const/realax/real_add' ) ) ).
% 0.31/1.21
% 0.31/1.21 thf('thm/iterate/SUM_INCL_EXCL_',conjecture,
% 0.31/1.21 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A > 'type/realax/real'] :
% 0.31/1.21 ( ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.31/1.21 & ( 'const/sets/FINITE' @ A @ A1 ) )
% 0.31/1.21 => ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ A0 @ A2 ) @ ( 'const/iterate/sum' @ A @ A1 @ A2 ) )
% 0.31/1.21 = ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ A @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) @ A2 ) @ ( 'const/iterate/sum' @ A @ ( 'const/sets/INTER' @ A @ A0 @ A1 ) @ A2 ) ) ) ) ).
% 0.31/1.21 ------------------------
% 0.31/1.23 % (17770)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17478 for (2999ds/2Mi)
% 0.31/1.23 % (17768)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_17478 for (2999ds/4Mi)
% 0.31/1.23 % (17770)Instruction limit reached!
% 0.31/1.23 % (17770)------------------------------
% 0.31/1.23 % (17770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.23 % (17770)Termination reason: Unknown
% 0.31/1.23 % (17770)Termination phase: Preprocessing 3
% 0.31/1.23
% 0.31/1.23 % (17770)Memory used [KB]: 895
% 0.31/1.23 % (17770)Time elapsed: 0.002 s
% 0.31/1.23 % (17770)Instructions burned: 2 (million)
% 0.31/1.23 % (17770)------------------------------
% 0.31/1.23 % (17770)------------------------------
% 0.31/1.23 % (17768)Instruction limit reached!
% 0.31/1.23 % (17768)------------------------------
% 0.31/1.23 % (17768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.23 % (17768)Termination reason: Unknown
% 0.31/1.23 % (17768)Termination phase: Saturation
% 0.31/1.23
% 0.31/1.23 % (17768)Memory used [KB]: 5500
% 0.31/1.23 % (17768)Time elapsed: 0.003 s
% 0.31/1.23 % (17768)Instructions burned: 5 (million)
% 0.31/1.23 % (17768)------------------------------
% 0.31/1.23 % (17768)------------------------------
% 0.31/1.24 % (17767)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17478 for (2999ds/183Mi)
% 0.31/1.24 % (17771)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_17478 for (2999ds/2Mi)
% 0.31/1.24 % (17769)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_17478 for (2999ds/27Mi)
% 0.31/1.24 % (17772)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_17478 for (2999ds/275Mi)
% 0.31/1.24 % (17771)Instruction limit reached!
% 0.31/1.24 % (17771)------------------------------
% 0.31/1.24 % (17771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.24 % (17771)Termination reason: Unknown
% 0.31/1.24 % (17771)Termination phase: shuffling
% 0.31/1.24
% 0.31/1.24 % (17771)Memory used [KB]: 895
% 0.31/1.24 % (17771)Time elapsed: 0.003 s
% 0.31/1.24 % (17771)Instructions burned: 2 (million)
% 0.31/1.24 % (17771)------------------------------
% 0.31/1.24 % (17771)------------------------------
% 0.31/1.24 % (17773)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17478 for (2999ds/18Mi)
% 0.31/1.24 % (17774)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17478 for (2999ds/3Mi)
% 0.31/1.24 % (17774)Instruction limit reached!
% 0.31/1.24 % (17774)------------------------------
% 0.31/1.24 % (17774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.24 % (17774)Termination reason: Unknown
% 0.31/1.24 % (17774)Termination phase: Saturation
% 0.31/1.24
% 0.31/1.24 % (17774)Memory used [KB]: 5500
% 0.31/1.24 % (17774)Time elapsed: 0.002 s
% 0.31/1.24 % (17774)Instructions burned: 3 (million)
% 0.31/1.24 % (17774)------------------------------
% 0.31/1.24 % (17774)------------------------------
% 0.31/1.24 % (17772)First to succeed.
% 0.31/1.24 % (17775)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_17478 for (2999ds/37Mi)
% 0.31/1.24 % Exception at run slice level
% 0.31/1.24 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.31/1.24 % (17772)Refutation found. Thanks to Tanya!
% 0.31/1.24 % SZS status Theorem for DTF2THF_17478
% 0.31/1.24 % SZS output start Proof for DTF2THF_17478
% 0.31/1.24 thf(type_def_6, type, 'type/realax/real': $tType).
% 0.31/1.24 thf(type_def_7, type, sK0: $tType).
% 0.31/1.24 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.31/1.24 thf(func_def_1, type, 'const/sets/UNION': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 0.31/1.24 thf(func_def_2, type, 'const/sets/INTER': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 0.31/1.24 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 0.31/1.24 thf(func_def_4, type, 'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real').
% 0.31/1.24 thf(func_def_5, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 0.31/1.24 thf(func_def_6, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 0.31/1.24 thf(func_def_7, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1)).
% 0.31/1.24 thf(func_def_11, type, sK1: sK0 > $o).
% 0.31/1.24 thf(func_def_12, type, sK2: sK0 > $o).
% 0.31/1.24 thf(func_def_13, type, sK3: sK0 > 'type/realax/real').
% 0.31/1.24 thf(func_def_15, type, ph5: !>[X0: $tType]:(X0)).
% 0.31/1.24 thf(f30,plain,(
% 0.31/1.24 $false),
% 0.31/1.24 inference(subsumption_resolution,[status(thm)],[f29,f20])).
% 0.31/1.24 thf(f20,plain,(
% 0.31/1.24 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 0.31/1.24 inference(cnf_transformation,[status(thm)],[f10])).
% 0.31/1.24 thf(f10,plain,(
% 0.31/1.24 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') = $true)),
% 0.31/1.24 inference(fool_elimination,[status(thm)],[f9])).
% 0.31/1.24 thf(f9,plain,(
% 0.31/1.24 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.31/1.24 inference(rectify,[status(thm)],[f2])).
% 0.31/1.24 thf(f2,axiom,(
% 0.31/1.24 ('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add')),
% 0.31/1.24 file('/export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2THF_17478.p','thm/iterate/MONOIDAL_REAL_ADD_')).
% 0.31/1.24 thf(f29,plain,(
% 0.31/1.24 (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 0.31/1.24 inference(subsumption_resolution,[status(thm)],[f28,f22])).
% 0.31/1.24 thf(f22,plain,(
% 0.31/1.24 (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 0.31/1.24 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.24 thf(f18,plain,(
% 0.31/1.24 (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK1 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3)) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK1 @ sK2) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/INTER' @ sK0 @ sK1 @ sK2) @ sK3))) & (('const/sets/FINITE' @ sK0 @ sK1) = $true) & (('const/sets/FINITE' @ sK0 @ sK2) = $true)),
% 0.31/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f17])).
% 0.31/1.24 thf(f17,plain,(
% 0.31/1.24 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real'] : ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X3)) != ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/INTER' @ X0 @ X1 @ X2) @ X3))) & (('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/sets/FINITE' @ X0 @ X2) = $true)) => ((('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK1 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3)) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK1 @ sK2) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/INTER' @ sK0 @ sK1 @ sK2) @ sK3))) & (('const/sets/FINITE' @ sK0 @ sK1) = $true) & (('const/sets/FINITE' @ sK0 @ sK2) = $true))),
% 0.31/1.24 introduced(definition,[],[choice_axiom])).
% 0.31/1.24 thf(f14,plain,(
% 0.31/1.24 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real'] : ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X3)) != ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/INTER' @ X0 @ X1 @ X2) @ X3))) & (('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/sets/FINITE' @ X0 @ X2) = $true))),
% 0.31/1.24 inference(flattening,[status(thm)],[f13])).
% 0.31/1.24 thf(f13,plain,(
% 0.31/1.24 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real'] : ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X3)) != ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/INTER' @ X0 @ X1 @ X2) @ X3))) & ((('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/FINITE' @ X0 @ X1) = $true)))),
% 0.31/1.24 inference(ennf_transformation,[status(thm)],[f12])).
% 0.31/1.24 thf(f12,plain,(
% 0.31/1.24 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real'] : (((('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/FINITE' @ X0 @ X1) = $true)) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X3)) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/INTER' @ X0 @ X1 @ X2) @ X3))))),
% 0.31/1.24 inference(fool_elimination,[status(thm)],[f11])).
% 0.31/1.24 thf(f11,plain,(
% 0.31/1.24 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X1)) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X3)) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/INTER' @ X0 @ X1 @ X2) @ X3))))),
% 0.31/1.24 inference(rectify,[status(thm)],[f5])).
% 0.31/1.24 thf(f5,negated_conjecture,(
% 0.31/1.24 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X1)) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X3)) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/INTER' @ X0 @ X1 @ X2) @ X3))))),
% 0.31/1.24 inference(negated_conjecture,[status(cth)],[f4])).
% 0.31/1.24 thf(f4,conjecture,(
% 0.31/1.24 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/realax/real'] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X1)) => (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X1 @ X3) @ ('const/iterate/sum' @ X0 @ X2 @ X3)) = ('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X1 @ X2) @ X3) @ ('const/iterate/sum' @ X0 @ ('const/sets/INTER' @ X0 @ X1 @ X2) @ X3))))),
% 0.31/1.24 file('/export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2THF_17478.p','thm/iterate/SUM_INCL_EXCL_')).
% 0.31/1.24 thf(f28,plain,(
% 0.31/1.24 (('const/sets/FINITE' @ sK0 @ sK1) != $true) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 0.31/1.24 inference(subsumption_resolution,[status(thm)],[f27,f21])).
% 0.31/1.24 thf(f21,plain,(
% 0.31/1.24 (('const/sets/FINITE' @ sK0 @ sK2) = $true)),
% 0.31/1.24 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.24 thf(f27,plain,(
% 0.31/1.24 (('const/sets/FINITE' @ sK0 @ sK2) != $true) | (('const/sets/FINITE' @ sK0 @ sK1) != $true) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 0.31/1.24 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 0.31/1.24 thf(f26,plain,(
% 0.31/1.24 (('const/sets/FINITE' @ sK0 @ sK2) != $true) | (('const/sets/FINITE' @ sK0 @ sK1) != $true) | (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK3)) != ('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK3))) | (('const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add') != $true)),
% 0.31/1.24 inference(superposition,[status(thm)],[f25,f24])).
% 0.31/1.24 thf(f24,plain,(
% 0.31/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > X1,X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1] : (((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/INTER' @ X0 @ X3 @ X4) @ X5))) | (('const/sets/FINITE' @ X0 @ X4) != $true) | (('const/iterate/monoidal' @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X3) != $true)) )),
% 0.31/1.24 inference(cnf_transformation,[status(thm)],[f16])).
% 0.31/1.24 thf(f16,plain,(
% 0.31/1.24 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1] : (((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/INTER' @ X0 @ X3 @ X4) @ X5))) | (('const/sets/FINITE' @ X0 @ X3) != $true) | (('const/sets/FINITE' @ X0 @ X4) != $true)) | (('const/iterate/monoidal' @ X1 @ X2) != $true))),
% 0.31/1.24 inference(flattening,[status(thm)],[f15])).
% 0.31/1.24 thf(f15,plain,(
% 0.31/1.24 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1] : (((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/INTER' @ X0 @ X3 @ X4) @ X5))) | ((('const/sets/FINITE' @ X0 @ X4) != $true) | (('const/sets/FINITE' @ X0 @ X3) != $true))) | (('const/iterate/monoidal' @ X1 @ X2) != $true))),
% 0.31/1.24 inference(ennf_transformation,[status(thm)],[f8])).
% 0.31/1.24 thf(f8,plain,(
% 0.31/1.24 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : ((('const/iterate/monoidal' @ X1 @ X2) = $true) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1] : (((('const/sets/FINITE' @ X0 @ X4) = $true) & (('const/sets/FINITE' @ X0 @ X3) = $true)) => ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/INTER' @ X0 @ X3 @ X4) @ X5)))))),
% 0.31/1.24 inference(fool_elimination,[status(thm)],[f7])).
% 0.31/1.24 thf(f7,plain,(
% 0.31/1.24 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (('const/iterate/monoidal' @ X1 @ X2) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1] : ((('const/sets/FINITE' @ X0 @ X4) & ('const/sets/FINITE' @ X0 @ X3)) => ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/INTER' @ X0 @ X3 @ X4) @ X5)))))),
% 0.31/1.24 inference(rectify,[status(thm)],[f1])).
% 0.31/1.24 thf(f1,axiom,(
% 0.31/1.24 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > X1] : (('const/iterate/monoidal' @ X1 @ X2) => ! [X3 : X0 > $o,X4 : X0 > $o,X5 : X0 > X1] : ((('const/sets/FINITE' @ X0 @ X4) & ('const/sets/FINITE' @ X0 @ X3)) => ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)) = (X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/INTER' @ X0 @ X3 @ X4) @ X5)))))),
% 0.31/1.24 file('/export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2THF_17478.p','thm/iterate/ITERATE_INCL_EXCL_')).
% 0.31/1.24 thf(f25,plain,(
% 0.31/1.24 (('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK2 @ sK3)) != ('const/realax/real_add' @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/UNION' @ sK0 @ sK1 @ sK2) @ sK3) @ ('const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ ('const/sets/INTER' @ sK0 @ sK1 @ sK2) @ sK3)))),
% 0.31/1.24 inference(definition_unfolding,[status(thm)],[f23,f19,f19,f19,f19])).
% 0.31/1.24 thf(f19,plain,(
% 0.31/1.24 ( ! [X0 : $tType] : (('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))) )),
% 0.31/1.24 inference(cnf_transformation,[status(thm)],[f3])).
% 0.31/1.24 thf(f3,axiom,(
% 0.31/1.24 ! [X0 : $tType] : ('const/iterate/sum' @ X0 = ('const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add'))),
% 0.31/1.24 file('/export/starexec/sandbox/tmp/tmp.qmrz1MY1BV/DTF2THF_17478.p','thm/iterate/sum_')).
% 0.31/1.24 thf(f23,plain,(
% 0.31/1.24 (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK1 @ sK3) @ ('const/iterate/sum' @ sK0 @ sK2 @ sK3)) != ('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK1 @ sK2) @ sK3) @ ('const/iterate/sum' @ sK0 @ ('const/sets/INTER' @ sK0 @ sK1 @ sK2) @ sK3)))),
% 0.31/1.24 inference(cnf_transformation,[status(thm)],[f18])).
% 0.31/1.24 % SZS output end Proof for DTF2THF_17478
% 0.31/1.24 % (17772)------------------------------
% 0.31/1.24 % (17772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.24 % (17772)Termination reason: Refutation
% 0.31/1.24
% 0.31/1.24 % (17772)Memory used [KB]: 5500
% 0.31/1.24 % (17772)Time elapsed: 0.007 s
% 0.31/1.24 % (17772)Instructions burned: 4 (million)
% 0.31/1.24 % (17772)------------------------------
% 0.31/1.24 % (17772)------------------------------
% 0.31/1.24 % (17766)Success in time 0.023 s
%------------------------------------------------------------------------------