TSTP Solution File: SEV505^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV505^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n017.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 09:43:27 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 26
% Syntax : Number of formulae : 63 ( 17 unt; 19 typ; 0 def)
% Number of atoms : 421 ( 124 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 988 ( 64 ~; 47 |; 34 &; 824 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 3 con; 0-6 aty)
% Number of variables : 112 ( 0 ^ 85 !; 15 ?; 112 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(func_def_0,type,
'type/nums/num': $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/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_7,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_8,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_9,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_10,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_11,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_15,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > X1 ) > ( X1 > X1 > X1 ) > X0 ) ).
thf(func_def_16,type,
sK2: sK1 > 'type/nums/num' ).
thf(func_def_17,type,
sK3: sK1 > $o ).
thf(func_def_18,type,
sK4: sK1 > $o ).
thf(func_def_20,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f45,plain,
$false,
inference(subsumption_resolution,[],[f44,f42]) ).
thf(f42,plain,
( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
!= ( sK2 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) ) ),
inference(forward_demodulation,[],[f41,f24]) ).
thf(f24,plain,
( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f4,axiom,
( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ),
file('/export/starexec/sandbox/tmp/tmp.1waw5NPHlu/Vampire---4.8_2583','thm/iterate/NEUTRAL_ADD_') ).
thf(f41,plain,
( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
!= ( sK2 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) ) ),
inference(subsumption_resolution,[],[f40,f29]) ).
thf(f29,plain,
( ( 'const/sets/FINITE' @ sK1 @ sK3 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f21,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ sK4 )
= $true )
& ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
= $true )
& ! [X4: sK1] :
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK2 @ X4 ) )
| ( ( 'const/sets/IN' @ sK1 @ X4 @ ( 'const/sets/INTER' @ sK1 @ sK3 @ sK4 ) )
!= $true ) )
& ( ( 'const/iterate/nsum' @ sK1 @ ( 'const/sets/UNION' @ sK1 @ sK3 @ sK4 ) @ sK2 )
!= ( 'const/arith/+' @ ( 'const/iterate/nsum' @ sK1 @ sK3 @ sK2 ) @ ( 'const/iterate/nsum' @ sK1 @ sK4 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f15,f20]) ).
thf(f20,plain,
( ? [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ! [X4: X0] :
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X4 ) )
| ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) )
!= $true ) )
& ( ( 'const/arith/+' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) )
!= ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 ) ) )
=> ( ( ( 'const/sets/FINITE' @ sK1 @ sK4 )
= $true )
& ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
= $true )
& ! [X4: sK1] :
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK2 @ X4 ) )
| ( ( 'const/sets/IN' @ sK1 @ X4 @ ( 'const/sets/INTER' @ sK1 @ sK3 @ sK4 ) )
!= $true ) )
& ( ( 'const/iterate/nsum' @ sK1 @ ( 'const/sets/UNION' @ sK1 @ sK3 @ sK4 ) @ sK2 )
!= ( 'const/arith/+' @ ( 'const/iterate/nsum' @ sK1 @ sK3 @ sK2 ) @ ( 'const/iterate/nsum' @ sK1 @ sK4 @ sK2 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
? [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ! [X4: X0] :
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X4 ) )
| ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) )
!= $true ) )
& ( ( 'const/arith/+' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) )
!= ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 ) ) ),
inference(flattening,[],[f14]) ).
thf(f14,plain,
? [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0 > $o] :
( ( ( 'const/arith/+' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) )
!= ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 ) )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ! [X4: X0] :
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X4 ) )
| ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) )
!= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) )
= $true )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X4 ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true ) )
=> ( ( 'const/arith/+' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0 > $o] :
( ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/INTER' @ X0 @ X2 @ X3 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X4 ) ) )
& ( 'const/sets/FINITE' @ X0 @ X3 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( ( 'const/arith/+' @ ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X3: X0 > $o,X4: X0 > $o] :
( ( ! [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/INTER' @ X0 @ X3 @ X4 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X5 ) ) )
& ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X1 )
= ( 'const/arith/+' @ ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/nsum' @ X0 @ X4 @ X1 ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > 'type/nums/num',X3: X0 > $o,X4: X0 > $o] :
( ( ! [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/INTER' @ X0 @ X3 @ X4 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X5 ) ) )
& ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X3 ) )
=> ( ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X1 )
= ( 'const/arith/+' @ ( 'const/iterate/nsum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/nsum' @ X0 @ X4 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1waw5NPHlu/Vampire---4.8_2583','thm/iterate/NSUM_UNION_NONZERO_') ).
thf(f40,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
!= ( sK2 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) ) ) ),
inference(subsumption_resolution,[],[f39,f30]) ).
thf(f30,plain,
( ( 'const/sets/FINITE' @ sK1 @ sK4 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f39,plain,
( ( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
!= ( sK2 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) ) )
| ( ( 'const/sets/FINITE' @ sK1 @ sK4 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
!= $true ) ),
inference(subsumption_resolution,[],[f34,f22]) ).
thf(f22,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
inference(rectify,[],[f2]) ).
thf(f2,axiom,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
file('/export/starexec/sandbox/tmp/tmp.1waw5NPHlu/Vampire---4.8_2583','thm/iterate/MONOIDAL_ADD_') ).
thf(f34,plain,
( ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ sK4 )
!= $true )
| ( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
!= ( sK2 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) ) )
| ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f33,plain,
( ( ( 'const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+' )
!= ( sK2 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) ) )
| ( ( 'const/iterate/iterate' @ sK1 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/UNION' @ sK1 @ sK3 @ sK4 ) @ sK2 )
!= ( 'const/iterate/iterate' @ sK1 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/UNION' @ sK1 @ sK3 @ sK4 ) @ sK2 ) )
| ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ sK4 )
!= $true ) ),
inference(superposition,[],[f31,f25]) ).
thf(f25,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) )
| ( ( 'const/iterate/neutral' @ X1 @ X2 )
!= ( X3 @ ( sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
= $true )
& ( ( 'const/iterate/neutral' @ X1 @ X2 )
!= ( X3 @ ( sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f18]) ).
thf(f18,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ? [X6: X0] :
( ( ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
= $true )
& ( ( X3 @ X6 )
!= ( 'const/iterate/neutral' @ X1 @ X2 ) ) )
=> ( ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
= $true )
& ( ( 'const/iterate/neutral' @ X1 @ X2 )
!= ( X3 @ ( sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ? [X6: X0] :
( ( ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
= $true )
& ( ( X3 @ X6 )
!= ( 'const/iterate/neutral' @ X1 @ X2 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true ) ) ),
inference(flattening,[],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ? [X6: X0] :
( ( ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
= $true )
& ( ( X3 @ X6 )
!= ( 'const/iterate/neutral' @ X1 @ X2 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ! [X6: X0] :
( ( ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
= $true )
=> ( ( X3 @ X6 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X5 )
= $true ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X5 )
& ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
=> ( ( X3 @ X6 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) ) ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X2: $tType,X1: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X1 )
=> ! [X3: X0 > X2,X4: X0 > $o,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X5 )
& ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
=> ( ( X3 @ X6 )
= ( 'const/iterate/neutral' @ X2 @ X1 ) ) ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X2 @ X1 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X1 @ ( 'const/iterate/iterate' @ X0 @ X2 @ X1 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X2 @ X1 @ X5 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1waw5NPHlu/Vampire---4.8_2583','thm/iterate/ITERATE_UNION_NONZERO_') ).
thf(f31,plain,
( ( 'const/arith/+' @ ( 'const/iterate/iterate' @ sK1 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ sK2 ) @ ( 'const/iterate/iterate' @ sK1 @ 'type/nums/num' @ 'const/arith/+' @ sK4 @ sK2 ) )
!= ( 'const/iterate/iterate' @ sK1 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/UNION' @ sK1 @ sK3 @ sK4 ) @ sK2 ) ),
inference(definition_unfolding,[],[f27,f23,f23,f23]) ).
thf(f23,plain,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f3,axiom,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1waw5NPHlu/Vampire---4.8_2583','thm/iterate/nsum_') ).
thf(f27,plain,
( ( 'const/iterate/nsum' @ sK1 @ ( 'const/sets/UNION' @ sK1 @ sK3 @ sK4 ) @ sK2 )
!= ( 'const/arith/+' @ ( 'const/iterate/nsum' @ sK1 @ sK3 @ sK2 ) @ ( 'const/iterate/nsum' @ sK1 @ sK4 @ sK2 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f44,plain,
( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK2 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) ) ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f43,plain,
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK2 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) ) )
| ( $true != $true ) ),
inference(superposition,[],[f28,f38]) ).
thf(f38,plain,
( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) @ ( 'const/sets/INTER' @ sK1 @ sK3 @ sK4 ) )
= $true ),
inference(subsumption_resolution,[],[f37,f29]) ).
thf(f37,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) @ ( 'const/sets/INTER' @ sK1 @ sK3 @ sK4 ) )
= $true ) ),
inference(subsumption_resolution,[],[f36,f30]) ).
thf(f36,plain,
( ( ( 'const/sets/FINITE' @ sK1 @ sK4 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) @ ( 'const/sets/INTER' @ sK1 @ sK3 @ sK4 ) )
= $true ) ),
inference(subsumption_resolution,[],[f35,f22]) ).
thf(f35,plain,
( ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) @ ( 'const/sets/INTER' @ sK1 @ sK3 @ sK4 ) )
= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ sK4 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f32,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ 'type/nums/num' @ sK4 @ sK3 @ sK2 @ 'const/arith/+' ) @ ( 'const/sets/INTER' @ sK1 @ sK3 @ sK4 ) )
= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( ( 'const/sets/FINITE' @ sK1 @ sK4 )
!= $true )
| ( ( 'const/iterate/iterate' @ sK1 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/UNION' @ sK1 @ sK3 @ sK4 ) @ sK2 )
!= ( 'const/iterate/iterate' @ sK1 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/UNION' @ sK1 @ sK3 @ sK4 ) @ sK2 ) ) ),
inference(superposition,[],[f31,f26]) ).
thf(f26,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o,X5: X0 > $o] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/UNION' @ X0 @ X4 @ X5 ) @ X3 )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ ( 'const/sets/INTER' @ X0 @ X4 @ X5 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
! [X4: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X4 @ ( 'const/sets/INTER' @ sK1 @ sK3 @ sK4 ) )
!= $true )
| ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK2 @ X4 ) ) ),
inference(cnf_transformation,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEV505^1 : TPTP v8.1.2. Released v7.0.0.
% 0.05/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.30 % Computer : n017.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 11:26:51 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 This is a TH1_THM_EQU_NAR problem
% 0.10/0.30 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/sandbox/tmp/tmp.1waw5NPHlu/Vampire---4.8_2583
% 0.15/0.32 % (2691)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)
% 0.15/0.32 % (2692)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)
% 0.15/0.32 % (2693)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)
% 0.15/0.32 % (2695)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)
% 0.15/0.32 % (2694)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.32 % (2696)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)
% 0.15/0.32 % (2697)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.32 % (2698)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)
% 0.15/0.32 % Exception at run slice level
% 0.15/0.32 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
% 0.15/0.32 % (2692)Instruction limit reached!
% 0.15/0.32 % (2692)------------------------------
% 0.15/0.32 % (2692)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (2692)Termination reason: Unknown
% 0.15/0.32 % (2692)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (2692)Memory used [KB]: 5500
% 0.15/0.32 % (2692)Time elapsed: 0.004 s
% 0.15/0.32 % (2692)Instructions burned: 5 (million)
% 0.15/0.32 % (2692)------------------------------
% 0.15/0.32 % (2692)------------------------------
% 0.15/0.32 % (2694)Instruction limit reached!
% 0.15/0.32 % (2694)------------------------------
% 0.15/0.32 % (2694)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (2694)Termination reason: Unknown
% 0.15/0.32 % (2694)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (2694)Memory used [KB]: 1023
% 0.15/0.32 % (2694)Time elapsed: 0.003 s
% 0.15/0.32 % (2694)Instructions burned: 3 (million)
% 0.15/0.32 % (2694)------------------------------
% 0.15/0.32 % (2694)------------------------------
% 0.15/0.32 % (2698)Instruction limit reached!
% 0.15/0.32 % (2698)------------------------------
% 0.15/0.32 % (2698)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (2698)Termination reason: Unknown
% 0.15/0.32 % (2698)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (2698)Memory used [KB]: 1023
% 0.15/0.32 % (2698)Time elapsed: 0.003 s
% 0.15/0.32 % (2698)Instructions burned: 3 (million)
% 0.15/0.32 % (2698)------------------------------
% 0.15/0.32 % (2698)------------------------------
% 0.15/0.33 % (2696)First to succeed.
% 0.15/0.33 % (2696)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for Vampire---4
% 0.15/0.33 % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.33 % (2696)------------------------------
% 0.15/0.33 % (2696)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (2696)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (2696)Memory used [KB]: 5500
% 0.15/0.33 % (2696)Time elapsed: 0.008 s
% 0.15/0.33 % (2696)Instructions burned: 9 (million)
% 0.15/0.33 % (2696)------------------------------
% 0.15/0.33 % (2696)------------------------------
% 0.15/0.33 % (2690)Success in time 0.011 s
% 0.15/0.33 % Vampire---4.8 exiting
%------------------------------------------------------------------------------