TSTP Solution File: SEV478^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV478^1 : 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 : n016.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 09:43:20 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 49 ( 10 unt; 20 typ; 0 def)
% Number of atoms : 189 ( 66 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 891 ( 32 ~; 13 |; 15 &; 816 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 4 con; 0-5 aty)
% Number of variables : 140 ( 23 ^ 86 !; 15 ?; 140 :)
% ( 16 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/ITSET':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > ( X0 > $o ) > X1 > X1 ) ).
thf(func_def_2,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( 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/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_7,type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
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/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_12,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK1: sK0 ).
thf(func_def_18,type,
sK2: sK0 > $o ).
thf(func_def_19,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X0 ) ).
thf(func_def_20,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X0 ) ).
thf(func_def_21,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X1 ) ).
thf(func_def_23,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f42,plain,
$false,
inference(trivial_inequality_removal,[],[f41]) ).
thf(f41,plain,
( ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) )
!= ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) ) ),
inference(superposition,[],[f19,f40]) ).
thf(f40,plain,
! [X0: sK0] :
( ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ X0 @ sK2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) ),
inference(forward_demodulation,[],[f39,f25]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
@ ^ [Y0: X0] : 'const/nums/SUC'
@ X1
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(beta_eta_normalization,[],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
@ ^ [Y0: X0,Y1: 'type/nums/num'] : ( 'const/nums/SUC' @ Y1 )
@ X1
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
@ ^ [Y0: X0,Y1: 'type/nums/num'] : ( 'const/nums/SUC' @ Y1 )
@ X1
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
@ ^ [X2: X0,X3: 'type/nums/num'] : ( 'const/nums/SUC' @ X3 )
@ X1
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/sets/CARD' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.w15wCglWaW/Vampire---4.8_18595','thm/sets/CARD_') ).
thf(f39,plain,
! [X0: sK0] :
( ( 'const/sets/ITSET' @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ sK0 @ X0 @ sK2 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f38,plain,
! [X0: sK0] :
( ( ( 'const/sets/ITSET' @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ sK0 @ X0 @ sK2 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) ) )
| ( ( 'const/nums/SUC'
@ ( 'const/nums/SUC'
@ ( sK5 @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC' ) ) )
!= ( 'const/nums/SUC'
@ ( 'const/nums/SUC'
@ ( sK5 @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC' ) ) ) ) ),
inference(beta_eta_normalization,[],[f37]) ).
thf(f37,plain,
! [X0: sK0] :
( ( ( ^ [Y0: sK0] : 'const/nums/SUC'
@ ( sK3 @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC' )
@ ( ^ [Y0: sK0] : 'const/nums/SUC'
@ ( sK4 @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC' )
@ ( sK5 @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC' ) ) )
!= ( ^ [Y0: sK0] : 'const/nums/SUC'
@ ( sK4 @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC' )
@ ( ^ [Y0: sK0] : 'const/nums/SUC'
@ ( sK3 @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC' )
@ ( sK5 @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC' ) ) ) )
| ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 )
@ ( ^ [Y0: sK0] : 'const/nums/SUC'
@ X0
@ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) )
= ( 'const/sets/ITSET' @ sK0 @ 'type/nums/num'
@ ^ [Y0: sK0] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ sK0 @ X0 @ sK2 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(superposition,[],[f34,f25]) ).
thf(f34,plain,
! [X0: $tType,X2: sK0,X3: X0,X1: sK0 > X0 > X0] :
( ( ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK0 @ X2 @ sK2 ) @ ( 'const/sets/ITSET' @ sK0 @ X0 @ X1 @ sK2 @ X3 ) @ ( X1 @ X2 @ ( 'const/sets/ITSET' @ sK0 @ X0 @ X1 @ sK2 @ X3 ) ) )
= ( 'const/sets/ITSET' @ sK0 @ X0 @ X1 @ ( 'const/sets/INSERT' @ sK0 @ X2 @ sK2 ) @ X3 ) )
| ( ( X1 @ ( sK3 @ sK0 @ X0 @ X1 ) @ ( X1 @ ( sK4 @ sK0 @ X0 @ X1 ) @ ( sK5 @ sK0 @ X0 @ X1 ) ) )
!= ( X1 @ ( sK4 @ sK0 @ X0 @ X1 ) @ ( X1 @ ( sK3 @ sK0 @ X0 @ X1 ) @ ( sK5 @ sK0 @ X0 @ X1 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f33,plain,
! [X0: $tType,X2: sK0,X3: X0,X1: sK0 > X0 > X0] :
( ( $true != $true )
| ( ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK0 @ X2 @ sK2 ) @ ( 'const/sets/ITSET' @ sK0 @ X0 @ X1 @ sK2 @ X3 ) @ ( X1 @ X2 @ ( 'const/sets/ITSET' @ sK0 @ X0 @ X1 @ sK2 @ X3 ) ) )
= ( 'const/sets/ITSET' @ sK0 @ X0 @ X1 @ ( 'const/sets/INSERT' @ sK0 @ X2 @ sK2 ) @ X3 ) )
| ( ( X1 @ ( sK3 @ sK0 @ X0 @ X1 ) @ ( X1 @ ( sK4 @ sK0 @ X0 @ X1 ) @ ( sK5 @ sK0 @ X0 @ X1 ) ) )
!= ( X1 @ ( sK4 @ sK0 @ X0 @ X1 ) @ ( X1 @ ( sK3 @ sK0 @ X0 @ X1 ) @ ( sK5 @ sK0 @ X0 @ X1 ) ) ) ) ),
inference(superposition,[],[f23,f18]) ).
thf(f18,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) )
!= ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $tType,X1: X0,X2: X0 > $o] :
( ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
!= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
=> ( ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) )
!= ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) ) )
& ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
? [X0: $tType,X1: X0,X2: X0 > $o] :
( ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
!= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
=> ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.w15wCglWaW/Vampire---4.8_18595','thm/sets/CARD_CLAUSES_1') ).
thf(f23,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > X1,X3: X1,X4: X0,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true )
| ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ X4 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) )
| ( ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) )
!= ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ( ! [X4: X0,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true )
| ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ X4 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 ) )
| ( ( ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) )
!= ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) ) )
& ( ( sK4 @ X0 @ X1 @ X2 )
!= ( sK3 @ X0 @ X1 @ X2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f15,f16]) ).
thf(f16,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > X1] :
( ? [X6: X0,X7: X0,X8: X1] :
( ( ( X2 @ X6 @ ( X2 @ X7 @ X8 ) )
!= ( X2 @ X7 @ ( X2 @ X6 @ X8 ) ) )
& ( X6 != X7 ) )
=> ( ( ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) )
!= ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK3 @ X0 @ X1 @ X2 ) @ ( sK5 @ X0 @ X1 @ X2 ) ) ) )
& ( ( sK4 @ X0 @ X1 @ X2 )
!= ( sK3 @ X0 @ X1 @ X2 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ( ! [X4: X0,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true )
| ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ X4 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 ) )
| ? [X6: X0,X7: X0,X8: X1] :
( ( ( X2 @ X6 @ ( X2 @ X7 @ X8 ) )
!= ( X2 @ X7 @ ( X2 @ X6 @ X8 ) ) )
& ( X6 != X7 ) ) ),
inference(rectify,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ( ! [X7: X0,X8: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X8 )
!= $true )
| ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 ) )
| ? [X4: X0,X5: X0,X6: X1] :
( ( ( X2 @ X5 @ ( X2 @ X4 @ X6 ) )
!= ( X2 @ X4 @ ( X2 @ X5 @ X6 ) ) )
& ( X4 != X5 ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ! [X4: X0,X5: X0,X6: X1] :
( ( X4 != X5 )
=> ( ( X2 @ X5 @ ( X2 @ X4 @ X6 ) )
= ( X2 @ X4 @ ( X2 @ X5 @ X6 ) ) ) )
=> ( ! [X7: X0,X8: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X8 )
= $true )
=> ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ! [X4: X0,X5: X0,X6: X1] :
( ( X4 != X5 )
=> ( ( X2 @ X5 @ ( X2 @ X4 @ X6 ) )
= ( X2 @ X4 @ ( X2 @ X5 @ X6 ) ) ) )
=> ( ! [X7: X0,X8: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X8 )
=> ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X4: $tType,X1: X0 > X4 > X4,X2: X4] :
( ! [X3: X0,X5: X0,X6: X4] :
( ( X3 != X5 )
=> ( ( X1 @ X3 @ ( X1 @ X5 @ X6 ) )
= ( X1 @ X5 @ ( X1 @ X3 @ X6 ) ) ) )
=> ( ! [X3: X0,X5: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X5 )
=> ( ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X3 @ X5 ) @ X2 )
= ( 'const/class/COND' @ X4 @ ( 'const/sets/IN' @ X0 @ X3 @ X5 ) @ ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ X5 @ X2 ) @ ( X1 @ X3 @ ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ X5 @ X2 ) ) ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ 'const/sets/EMPTY' @ X0 @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.w15wCglWaW/Vampire---4.8_18595','thm/sets/FINITE_RECURSION_') ).
thf(f19,plain,
( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) @ ( 'const/sets/CARD' @ sK0 @ sK2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK0 @ sK2 ) ) )
!= ( 'const/sets/CARD' @ sK0 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEV478^1 : TPTP v8.1.2. Released v7.0.0.
% 0.10/0.14 % 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
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 12:41:31 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH1_THM_EQU_NAR problem
% 0.15/0.36 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.w15wCglWaW/Vampire---4.8_18595
% 0.15/0.38 % (18783)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)
% 0.15/0.38 % (18782)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)
% 0.15/0.38 % (18784)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)
% 0.15/0.38 % (18786)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)
% 0.15/0.38 % (18785)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (18787)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)
% 0.15/0.38 % (18789)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)
% 0.15/0.38 % (18785)Instruction limit reached!
% 0.15/0.38 % (18785)------------------------------
% 0.15/0.38 % (18785)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (18785)Termination reason: Unknown
% 0.15/0.38 % (18785)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (18785)Memory used [KB]: 895
% 0.15/0.38 % (18785)Time elapsed: 0.003 s
% 0.15/0.38 % (18785)Instructions burned: 2 (million)
% 0.15/0.38 % (18785)------------------------------
% 0.15/0.38 % (18785)------------------------------
% 0.15/0.38 % (18788)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.38 % Exception at run slice level
% 0.15/0.38 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
% 0.15/0.38 % (18783)Instruction limit reached!
% 0.15/0.38 % (18783)------------------------------
% 0.15/0.38 % (18783)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (18783)Termination reason: Unknown
% 0.15/0.38 % (18783)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (18783)Memory used [KB]: 5500
% 0.15/0.38 % (18783)Time elapsed: 0.005 s
% 0.15/0.38 % (18783)Instructions burned: 5 (million)
% 0.15/0.38 % (18783)------------------------------
% 0.15/0.38 % (18783)------------------------------
% 0.15/0.38 % (18789)Instruction limit reached!
% 0.15/0.38 % (18789)------------------------------
% 0.15/0.38 % (18789)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (18789)Termination reason: Unknown
% 0.15/0.38 % (18789)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (18789)Memory used [KB]: 1023
% 0.15/0.38 % (18789)Time elapsed: 0.004 s
% 0.15/0.38 % (18787)Refutation not found, incomplete strategy
% 0.15/0.38 % (18787)------------------------------
% 0.15/0.38 % (18787)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (18789)Instructions burned: 3 (million)
% 0.15/0.38 % (18789)------------------------------
% 0.15/0.38 % (18789)------------------------------
% 0.15/0.38 % (18787)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (18787)Memory used [KB]: 5500
% 0.15/0.38 % (18787)Time elapsed: 0.004 s
% 0.15/0.38 % (18787)Instructions burned: 2 (million)
% 0.15/0.38 % (18787)------------------------------
% 0.15/0.38 % (18787)------------------------------
% 0.15/0.39 % (18784)First to succeed.
% 0.15/0.39 % (18788)Instruction limit reached!
% 0.15/0.39 % (18788)------------------------------
% 0.15/0.39 % (18788)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (18788)Termination reason: Unknown
% 0.15/0.39 % (18788)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (18788)Memory used [KB]: 5756
% 0.15/0.39 % (18788)Time elapsed: 0.014 s
% 0.15/0.39 % (18788)Instructions burned: 19 (million)
% 0.15/0.39 % (18788)------------------------------
% 0.15/0.39 % (18788)------------------------------
% 0.15/0.39 % (18784)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for Vampire---4
% 0.15/0.39 % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.39 % (18784)------------------------------
% 0.15/0.39 % (18784)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (18784)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (18784)Memory used [KB]: 5756
% 0.15/0.39 % (18784)Time elapsed: 0.016 s
% 0.15/0.39 % (18784)Instructions burned: 18 (million)
% 0.15/0.39 % (18784)------------------------------
% 0.15/0.39 % (18784)------------------------------
% 0.15/0.39 % (18779)Success in time 0.025 s
% 0.15/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------