TSTP Solution File: SEV512^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV512^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n018.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 : Sun May 5 09:43:28 EDT 2024
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 31
% Syntax : Number of formulae : 84 ( 19 unt; 24 typ; 0 def)
% Number of atoms : 592 ( 224 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 1782 ( 121 ~; 107 |; 58 &;1477 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 142 ( 142 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 3 con; 0-7 aty)
% Number of variables : 185 ( 0 ^ 145 !; 21 ?; 185 :)
% ( 19 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
'type/realax/real': $tType ).
thf(type_def_8,type,
sK2: $tType ).
thf(type_def_9,type,
sK3: $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'type/nums/num': $tType ).
thf(func_def_2,type,
'const/trivia/o':
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X2 ) > ( X1 > X0 ) > X1 > X2 ) ).
thf(func_def_3,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/IMAGE':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > $o ) > X1 > $o ) ).
thf(func_def_5,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_7,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_8,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_9,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_10,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_11,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_12,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_13,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_17,type,
sK0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > $o ) > ( X1 > X2 ) > ( X2 > X0 ) > ( X0 > X0 > X0 ) > X1 ) ).
thf(func_def_18,type,
sK1:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > $o ) > ( X1 > X2 ) > ( X2 > X0 ) > ( X0 > X0 > X0 ) > X1 ) ).
thf(func_def_19,type,
sK4: sK3 > 'type/realax/real' ).
thf(func_def_20,type,
sK5: sK2 > sK3 ).
thf(func_def_21,type,
sK6: sK2 > $o ).
thf(func_def_23,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f74,plain,
$false,
inference(subsumption_resolution,[],[f73,f32]) ).
thf(f32,plain,
( ( 'const/sets/FINITE' @ sK2 @ sK6 )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
( ! [X5: sK2,X6: sK2] :
( ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ X5 ) ) )
| ( ( 'const/sets/IN' @ sK2 @ X5 @ sK6 )
!= $true )
| ( X5 = X6 )
| ( ( sK5 @ X6 )
!= ( sK5 @ X5 ) )
| ( ( 'const/sets/IN' @ sK2 @ X6 @ sK6 )
!= $true ) )
& ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
= $true )
& ( ( 'const/iterate/sum' @ sK3 @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/sum' @ sK2 @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f18,f21]) ).
thf(f21,plain,
! [X0: $tType] :
( ? [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ! [X5: X0,X6: X0] :
( ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( X5 = X6 )
| ( ( X3 @ X6 )
!= ( X3 @ X5 ) )
| ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
!= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ( ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) )
!= ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 ) ) )
=> ( ! [X6: sK2,X5: sK2] :
( ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ X5 ) ) )
| ( ( 'const/sets/IN' @ sK2 @ X5 @ sK6 )
!= $true )
| ( X5 = X6 )
| ( ( sK5 @ X6 )
!= ( sK5 @ X5 ) )
| ( ( 'const/sets/IN' @ sK2 @ X6 @ sK6 )
!= $true ) )
& ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
= $true )
& ( ( 'const/iterate/sum' @ sK3 @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/sum' @ sK2 @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f18,plain,
? [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ! [X5: X0,X6: X0] :
( ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( X5 = X6 )
| ( ( X3 @ X6 )
!= ( X3 @ X5 ) )
| ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
!= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ( ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) )
!= ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 ) ) ),
inference(flattening,[],[f17]) ).
thf(f17,plain,
? [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ( ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) )
!= ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 ) )
& ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ! [X5: X0,X6: X0] :
( ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) )
| ( ( X3 @ X6 )
!= ( X3 @ X5 ) )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( X5 = X6 )
| ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ! [X5: X0,X6: X0] :
( ( ( ( X3 @ X6 )
= ( X3 @ X5 ) )
& ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
= $true )
& ( X5 != X6 )
& ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
= $true ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) ) ) )
=> ( ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) )
= ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: $tType,X2: X1 > 'type/realax/real',X3: X0 > X1,X4: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ! [X5: X0,X6: X0] :
( ( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
& ( ( X3 @ X6 )
= ( X3 @ X5 ) )
& ( X5 != X6 )
& ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X2 @ ( X3 @ X5 ) ) ) ) )
=> ( ( 'const/iterate/sum' @ X0 @ X4 @ ( 'const/trivia/o' @ X1 @ X0 @ 'type/realax/real' @ X2 @ X3 ) )
= ( 'const/iterate/sum' @ X1 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4 ) @ X2 ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X1: $tType,X0: $tType,X3: X0 > 'type/realax/real',X4: X1 > X0,X5: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X5 )
& ! [X6: X1,X7: X1] :
( ( ( 'const/sets/IN' @ X1 @ X7 @ X5 )
& ( ( X4 @ X6 )
= ( X4 @ X7 ) )
& ( X6 != X7 )
& ( 'const/sets/IN' @ X1 @ X6 @ X5 ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X3 @ ( X4 @ X6 ) ) ) ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/iterate/sum' @ X1 @ X5 @ ( 'const/trivia/o' @ X0 @ X1 @ 'type/realax/real' @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
! [X1: $tType,X0: $tType,X3: X0 > 'type/realax/real',X4: X1 > X0,X5: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X5 )
& ! [X6: X1,X7: X1] :
( ( ( 'const/sets/IN' @ X1 @ X7 @ X5 )
& ( ( X4 @ X6 )
= ( X4 @ X7 ) )
& ( X6 != X7 )
& ( 'const/sets/IN' @ X1 @ X6 @ X5 ) )
=> ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( X3 @ ( X4 @ X6 ) ) ) ) )
=> ( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/iterate/sum' @ X1 @ X5 @ ( 'const/trivia/o' @ X0 @ X1 @ 'type/realax/real' @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YvAiD4ghhh/Vampire---4.8_26806','thm/iterate/SUM_IMAGE_NONZERO_') ).
thf(f73,plain,
( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true ),
inference(subsumption_resolution,[],[f72,f34]) ).
thf(f34,plain,
( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ),
inference(definition_unfolding,[],[f31,f24,f24]) ).
thf(f24,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X1: $tType] :
( 'const/iterate/sum'
@ ( X1
= ( 'const/iterate/iterate' @ X1 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YvAiD4ghhh/Vampire---4.8_26806','thm/iterate/sum_') ).
thf(f31,plain,
( ( 'const/iterate/sum' @ sK3 @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/sum' @ sK2 @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f72,plain,
( ( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true ) ),
inference(subsumption_resolution,[],[f71,f23]) ).
thf(f23,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[],[f2]) ).
thf(f2,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox2/tmp/tmp.YvAiD4ghhh/Vampire---4.8_26806','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f71,plain,
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f70,plain,
( ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
!= ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
| ( ( 'const/iterate/iterate' @ sK2 @ 'type/realax/real' @ 'const/realax/real_add' @ sK6 @ ( 'const/trivia/o' @ sK3 @ sK2 @ 'type/realax/real' @ sK4 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(superposition,[],[f26,f63]) ).
thf(f63,plain,
( ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ),
inference(subsumption_resolution,[],[f62,f45]) ).
thf(f45,plain,
( ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
= $true ),
inference(subsumption_resolution,[],[f44,f23]) ).
thf(f44,plain,
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
= $true ) ),
inference(subsumption_resolution,[],[f40,f32]) ).
thf(f40,plain,
( ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f36,plain,
( ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) ) ),
inference(superposition,[],[f34,f25]) ).
thf(f25,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 )
= $true )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) )
| ( ( ( 'const/sets/IN' @ X1 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 )
= $true )
& ( ( 'const/iterate/neutral' @ X0 @ X3 )
!= ( X4 @ ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) ) )
& ( ( X5 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
= ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) )
& ( ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 )
!= ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
& ( ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 )
= $true ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f19]) ).
thf(f19,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: X0 > X0 > X0,X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ? [X7: X1,X8: X1] :
( ( ( 'const/sets/IN' @ X1 @ X8 @ X6 )
= $true )
& ( ( 'const/iterate/neutral' @ X0 @ X3 )
!= ( X4 @ ( X5 @ X7 ) ) )
& ( ( X5 @ X8 )
= ( X5 @ X7 ) )
& ( X7 != X8 )
& ( ( 'const/sets/IN' @ X1 @ X7 @ X6 )
= $true ) )
=> ( ( ( 'const/sets/IN' @ X1 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 )
= $true )
& ( ( 'const/iterate/neutral' @ X0 @ X3 )
!= ( X4 @ ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) ) )
& ( ( X5 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
= ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) )
& ( ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 )
!= ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
& ( ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f16,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) )
| ? [X7: X1,X8: X1] :
( ( ( 'const/sets/IN' @ X1 @ X8 @ X6 )
= $true )
& ( ( 'const/iterate/neutral' @ X0 @ X3 )
!= ( X4 @ ( X5 @ X7 ) ) )
& ( ( X5 @ X8 )
= ( X5 @ X7 ) )
& ( X7 != X8 )
& ( ( 'const/sets/IN' @ X1 @ X7 @ X6 )
= $true ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) )
| ? [X7: X1,X8: X1] :
( ( ( 'const/iterate/neutral' @ X0 @ X3 )
!= ( X4 @ ( X5 @ X7 ) ) )
& ( ( 'const/sets/IN' @ X1 @ X8 @ X6 )
= $true )
& ( ( 'const/sets/IN' @ X1 @ X7 @ X6 )
= $true )
& ( ( X5 @ X8 )
= ( X5 @ X7 ) )
& ( X7 != X8 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X3 )
= $true )
=> ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ! [X7: X1,X8: X1] :
( ( ( ( 'const/sets/IN' @ X1 @ X8 @ X6 )
= $true )
& ( ( 'const/sets/IN' @ X1 @ X7 @ X6 )
= $true )
& ( ( X5 @ X8 )
= ( X5 @ X7 ) )
& ( X7 != X8 ) )
=> ( ( 'const/iterate/neutral' @ X0 @ X3 )
= ( X4 @ ( X5 @ X7 ) ) ) )
& ( ( 'const/sets/FINITE' @ X1 @ X6 )
= $true ) )
=> ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X3 )
=> ! [X4: X2 > X0,X5: X1 > X2,X6: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X6 )
& ! [X7: X1,X8: X1] :
( ( ( ( X5 @ X8 )
= ( X5 @ X7 ) )
& ( 'const/sets/IN' @ X1 @ X8 @ X6 )
& ( 'const/sets/IN' @ X1 @ X7 @ X6 )
& ( X7 != X8 ) )
=> ( ( 'const/iterate/neutral' @ X0 @ X3 )
= ( X4 @ ( X5 @ X7 ) ) ) ) )
=> ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ! [X4: X0 > X2,X5: X1 > X0,X6: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X6 )
& ! [X7: X1,X8: X1] :
( ( ( ( X5 @ X7 )
= ( X5 @ X8 ) )
& ( 'const/sets/IN' @ X1 @ X8 @ X6 )
& ( 'const/sets/IN' @ X1 @ X7 @ X6 )
& ( X7 != X8 ) )
=> ( ( X4 @ ( X5 @ X7 ) )
= ( 'const/iterate/neutral' @ X2 @ X3 ) ) ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X5 @ X6 ) @ X4 )
= ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ ( 'const/trivia/o' @ X0 @ X1 @ X2 @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YvAiD4ghhh/Vampire---4.8_26806','thm/iterate/ITERATE_IMAGE_NONZERO_') ).
thf(f62,plain,
( ( ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
| ( ( 'const/sets/IN' @ sK2 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
!= $true ) ),
inference(equality_resolution,[],[f60]) ).
thf(f60,plain,
! [X0: sK2] :
( ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( ( 'const/sets/IN' @ sK2 @ X0 @ sK6 )
!= $true )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 ) ),
inference(subsumption_resolution,[],[f59,f48]) ).
thf(f48,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) ),
inference(forward_demodulation,[],[f47,f30]) ).
thf(f30,plain,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f4,axiom,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YvAiD4ghhh/Vampire---4.8_26806','thm/iterate/NEUTRAL_REAL_ADD_') ).
thf(f47,plain,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) ),
inference(subsumption_resolution,[],[f46,f23]) ).
thf(f46,plain,
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) ) ),
inference(subsumption_resolution,[],[f39,f32]) ).
thf(f39,plain,
( ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f37,plain,
( ( ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) )
| ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true ) ),
inference(superposition,[],[f34,f28]) ).
thf(f28,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( ( 'const/iterate/neutral' @ X0 @ X3 )
!= ( X4 @ ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f59,plain,
! [X0: sK2] :
( ( ( 'const/sets/IN' @ sK2 @ X0 @ sK6 )
!= $true )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) ) ),
inference(subsumption_resolution,[],[f58,f32]) ).
thf(f58,plain,
! [X0: sK2] :
( ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( ( 'const/sets/IN' @ sK2 @ X0 @ sK6 )
!= $true )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 ) ),
inference(subsumption_resolution,[],[f57,f43]) ).
thf(f43,plain,
( ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
= $true ),
inference(subsumption_resolution,[],[f42,f32]) ).
thf(f42,plain,
( ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
= $true ) ),
inference(subsumption_resolution,[],[f41,f23]) ).
thf(f41,plain,
( ( ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f38,plain,
( ( ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
= $true )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true ) ),
inference(superposition,[],[f34,f29]) ).
thf(f29,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/IN' @ X1 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) @ X6 )
= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f57,plain,
! [X0: sK2] :
( ( ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( ( 'const/sets/IN' @ sK2 @ X0 @ sK6 )
!= $true )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) ) ),
inference(subsumption_resolution,[],[f56,f23]) ).
thf(f56,plain,
! [X0: sK2] :
( ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
!= $true )
| ( ( 'const/sets/IN' @ sK2 @ X0 @ sK6 )
!= $true )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 ) ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f55,plain,
! [X0: sK2] :
( ( ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/iterate/iterate' @ sK3 @ 'type/realax/real' @ 'const/realax/real_add' @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ sK6 ) @ sK4 ) )
| ( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
!= $true )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) ) ) )
| ( ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' )
= X0 )
| ( ( 'const/sets/IN' @ sK2 @ ( sK1 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) @ sK6 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK2 @ sK6 )
!= $true )
| ( ( sK5 @ ( sK0 @ 'type/realax/real' @ sK2 @ sK3 @ sK6 @ sK5 @ sK4 @ 'const/realax/real_add' ) )
!= ( sK5 @ X0 ) )
| ( ( 'const/sets/IN' @ sK2 @ X0 @ sK6 )
!= $true ) ),
inference(superposition,[],[f34,f35]) ).
thf(f35,plain,
! [X0: $tType,X2: sK3 > X0,X3: X0 > X0 > X0,X1: sK2 > $o,X4: sK2] :
( ( ( 'const/iterate/iterate' @ sK2 @ X0 @ X3 @ X1 @ ( 'const/trivia/o' @ sK3 @ sK2 @ X0 @ X2 @ sK5 ) )
= ( 'const/iterate/iterate' @ sK3 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ sK2 @ sK3 @ sK5 @ X1 ) @ X2 ) )
| ( ( sK5 @ ( sK0 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3 ) )
!= ( sK5 @ X4 ) )
| ( ( 'const/sets/IN' @ sK2 @ X4 @ sK6 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK2 @ X1 )
!= $true )
| ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ ( sK0 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3 ) ) ) )
| ( ( 'const/sets/IN' @ sK2 @ ( sK1 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3 ) @ sK6 )
!= $true )
| ( ( sK1 @ X0 @ sK2 @ sK3 @ X1 @ sK5 @ X2 @ X3 )
= X4 ) ),
inference(superposition,[],[f33,f27]) ).
thf(f27,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( X5 @ ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
= ( X5 @ ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true )
| ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f33,plain,
! [X6: sK2,X5: sK2] :
( ( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( sK4 @ ( sK5 @ X5 ) ) )
| ( X5 = X6 )
| ( ( 'const/sets/IN' @ sK2 @ X5 @ sK6 )
!= $true )
| ( ( 'const/sets/IN' @ sK2 @ X6 @ sK6 )
!= $true )
| ( ( sK5 @ X6 )
!= ( sK5 @ X5 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f26,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X0 > X0,X6: X1 > $o,X4: X2 > X0,X5: X1 > X2] :
( ( ( sK1 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 )
!= ( sK0 @ X0 @ X1 @ X2 @ X6 @ X5 @ X4 @ X3 ) )
| ( ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X6 @ ( 'const/trivia/o' @ X2 @ X1 @ X0 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ ( 'const/sets/IMAGE' @ X1 @ X2 @ X5 @ X6 ) @ X4 ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X3 )
!= $true )
| ( ( 'const/sets/FINITE' @ X1 @ X6 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV512^1 : TPTP v8.1.2. Released v7.0.0.
% 0.08/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 12:07:01 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH1_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.YvAiD4ghhh/Vampire---4.8_26806
% 0.14/0.38 % (27030)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 Vampire---4 for (2999ds/27Mi)
% 0.14/0.38 % (27029)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 Vampire---4 for (2999ds/4Mi)
% 0.14/0.38 % (27033)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.14/0.38 % (27032)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.38 % (27031)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 % (27032)Instruction limit reached!
% 0.14/0.38 % (27032)------------------------------
% 0.14/0.38 % (27032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (27032)Termination reason: Unknown
% 0.14/0.38 % (27032)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (27032)Memory used [KB]: 1023
% 0.14/0.38 % (27032)Time elapsed: 0.003 s
% 0.14/0.38 % (27032)Instructions burned: 2 (million)
% 0.14/0.38 % (27032)------------------------------
% 0.14/0.38 % (27032)------------------------------
% 0.14/0.38 % (27035)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.14/0.38 % (27028)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.14/0.38 % (27029)Instruction limit reached!
% 0.14/0.38 % (27029)------------------------------
% 0.14/0.38 % (27029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (27029)Termination reason: Unknown
% 0.14/0.38 % (27029)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (27029)Memory used [KB]: 5500
% 0.14/0.38 % (27029)Time elapsed: 0.004 s
% 0.14/0.38 % (27029)Instructions burned: 4 (million)
% 0.14/0.38 % (27029)------------------------------
% 0.14/0.38 % (27029)------------------------------
% 0.14/0.38 % (27031)Instruction limit reached!
% 0.14/0.38 % (27031)------------------------------
% 0.14/0.38 % (27031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (27031)Termination reason: Unknown
% 0.14/0.38 % (27031)Termination phase: Preprocessing 3
% 0.14/0.38
% 0.14/0.38 % (27031)Memory used [KB]: 1023
% 0.14/0.38 % (27031)Time elapsed: 0.003 s
% 0.14/0.38 % (27031)Instructions burned: 2 (million)
% 0.14/0.38 % (27031)------------------------------
% 0.14/0.38 % (27031)------------------------------
% 0.14/0.38 % (27034)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.14/0.38 % (27035)Instruction limit reached!
% 0.14/0.38 % (27035)------------------------------
% 0.14/0.38 % (27035)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (27035)Termination reason: Unknown
% 0.14/0.38 % (27035)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (27035)Memory used [KB]: 1023
% 0.14/0.38 % (27035)Time elapsed: 0.004 s
% 0.14/0.38 % (27035)Instructions burned: 4 (million)
% 0.14/0.38 % (27035)------------------------------
% 0.14/0.38 % (27035)------------------------------
% 0.14/0.40 % (27041)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 Vampire---4 for (2999ds/37Mi)
% 0.14/0.40 % (27042)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.14/0.40 % Exception at run slice level
% 0.14/0.40 User error: % (27030)Instruction limit reached!
% 0.14/0.40 % (27030)------------------------------
% 0.14/0.40 % (27030)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.14/0.40 % (27030)Termination reason: Unknown
% 0.14/0.40 % (27030)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (27044)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.14/0.40 % (27030)Memory used [KB]: 5756
% 0.14/0.40 % (27030)Time elapsed: 0.021 s
% 0.14/0.40 % (27030)Instructions burned: 28 (million)
% 0.14/0.40 % (27030)------------------------------
% 0.14/0.40 % (27030)------------------------------
% 0.14/0.40 % (27034)Instruction limit reached!
% 0.14/0.40 % (27034)------------------------------
% 0.14/0.40 % (27034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (27034)Termination reason: Unknown
% 0.14/0.40 % (27034)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (27034)Memory used [KB]: 5628
% 0.14/0.40 % (27034)Time elapsed: 0.019 s
% 0.14/0.40 % (27034)Instructions burned: 19 (million)
% 0.14/0.40 % (27034)------------------------------
% 0.14/0.40 % (27034)------------------------------
% 0.14/0.40 % Exception at run slice level
% 0.14/0.40 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
% 0.14/0.40 % (27043)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.14/0.40 % (27043)Instruction limit reached!
% 0.14/0.40 % (27043)------------------------------
% 0.14/0.40 % (27043)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (27043)Termination reason: Unknown
% 0.14/0.40 % (27043)Termination phase: Preprocessing 3
% 0.14/0.40
% 0.14/0.40 % (27043)Memory used [KB]: 1023
% 0.14/0.40 % (27043)Time elapsed: 0.003 s
% 0.14/0.40 % (27043)Instructions burned: 3 (million)
% 0.14/0.40 % (27043)------------------------------
% 0.14/0.40 % (27043)------------------------------
% 0.21/0.41 % (27042)Instruction limit reached!
% 0.21/0.41 % (27042)------------------------------
% 0.21/0.41 % (27042)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27042)Termination reason: Unknown
% 0.21/0.41 % (27042)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (27042)Memory used [KB]: 5756
% 0.21/0.41 % (27042)Time elapsed: 0.037 s
% 0.21/0.41 % (27042)Instructions burned: 15 (million)
% 0.21/0.41 % (27042)------------------------------
% 0.21/0.41 % (27042)------------------------------
% 0.21/0.41 % (27033)First to succeed.
% 0.21/0.41 % (27050)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.21/0.41 % (27052)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.41 % (27049)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.42 % (27052)Instruction limit reached!
% 0.21/0.42 % (27052)------------------------------
% 0.21/0.42 % (27052)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27052)Termination reason: Unknown
% 0.21/0.42 % (27052)Termination phase: Preprocessing 3
% 0.21/0.42
% 0.21/0.42 % (27052)Memory used [KB]: 1023
% 0.21/0.42 % (27052)Time elapsed: 0.004 s
% 0.21/0.42 % (27052)Instructions burned: 3 (million)
% 0.21/0.42 % (27052)------------------------------
% 0.21/0.42 % (27052)------------------------------
% 0.21/0.42 % (27051)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.42 % (27054)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.42 % (27033)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for Vampire---4
% 0.21/0.42 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.42 % (27033)------------------------------
% 0.21/0.42 % (27033)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27033)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (27033)Memory used [KB]: 5756
% 0.21/0.42 % (27033)Time elapsed: 0.039 s
% 0.21/0.42 % (27033)Instructions burned: 54 (million)
% 0.21/0.42 % (27033)------------------------------
% 0.21/0.42 % (27033)------------------------------
% 0.21/0.42 % (27022)Success in time 0.061 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------