TSTP Solution File: SWW613_2 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW613_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% 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 : Mon Jun 24 18:35:13 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 34 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 1167 ( 118 equ)
% Maximal formula atoms : 130 ( 34 avg)
% Number of connectives : 1641 ( 508 ~; 197 |; 810 &)
% ( 5 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 51 ( 19 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 1173 ( 586 atm; 38 fun; 296 num; 253 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 45 ( 42 usr; 21 con; 0-5 aty)
% Number of variables : 299 ( 167 !; 132 ?; 299 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
tuple0: $tType ).
tff(type_def_9,type,
list_int: $tType ).
tff(func_def_0,type,
witness: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool1: ty ).
tff(func_def_4,type,
true: bool ).
tff(func_def_5,type,
false: bool ).
tff(func_def_6,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(func_def_7,type,
tuple01: ty ).
tff(func_def_8,type,
tuple02: tuple0 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
abs: $int > $int ).
tff(func_def_14,type,
div: ( $int * $int ) > $int ).
tff(func_def_15,type,
mod: ( $int * $int ) > $int ).
tff(func_def_23,type,
gcd: ( $int * $int ) > $int ).
tff(func_def_24,type,
ref: ty > ty ).
tff(func_def_25,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_26,type,
contents: ( ty * uni ) > uni ).
tff(func_def_27,type,
list: ty > ty ).
tff(func_def_28,type,
nil: ty > uni ).
tff(func_def_29,type,
cons: ( ty * uni * uni ) > uni ).
tff(func_def_30,type,
match_list: ( ty * ty * uni * uni * uni ) > uni ).
tff(func_def_31,type,
cons_proj_1: ( ty * uni ) > uni ).
tff(func_def_32,type,
cons_proj_2: ( ty * uni ) > uni ).
tff(func_def_33,type,
t2tb: list_int > uni ).
tff(func_def_34,type,
tb2t: uni > list_int ).
tff(func_def_35,type,
t2tb1: $int > uni ).
tff(func_def_36,type,
tb2t1: uni > $int ).
tff(func_def_38,type,
sK0: ( $int * $int ) > $int ).
tff(func_def_39,type,
sK1: $int > $int ).
tff(func_def_40,type,
sK2: $int > $int ).
tff(func_def_41,type,
sK3: $int ).
tff(func_def_42,type,
sK4: $int ).
tff(func_def_43,type,
sK5: list_int ).
tff(func_def_44,type,
sK6: $int ).
tff(func_def_45,type,
sK7: list_int ).
tff(func_def_46,type,
sK8: $int ).
tff(func_def_47,type,
sK9: $int ).
tff(func_def_48,type,
sK10: $int ).
tff(func_def_49,type,
sK11: list_int ).
tff(func_def_50,type,
sK12: $int ).
tff(func_def_51,type,
sK13: $int ).
tff(func_def_52,type,
sK14: $int > $int ).
tff(pred_def_1,type,
sort: ( ty * uni ) > $o ).
tff(pred_def_4,type,
divides: ( $int * $int ) > $o ).
tff(pred_def_5,type,
even: $int > $o ).
tff(pred_def_6,type,
odd: $int > $o ).
tff(pred_def_7,type,
prime: $int > $o ).
tff(pred_def_8,type,
coprime: ( $int * $int ) > $o ).
tff(f453,plain,
$false,
inference(subsumption_resolution,[],[f449,f368]) ).
tff(f368,plain,
$less(sK9,sK13),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
( ~ $less(sK8,sK6)
& ! [X6: $int] :
( ~ $less(sK6,X6)
| ~ prime(X6)
| divides(X6,sK8)
| ~ divides(X6,sK3) )
& ~ $less(sK8,2)
& ! [X7: $int] :
( ~ divides(X7,sK8)
| ( ~ $less(X7,sK6)
& divides(X7,sK3) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,sK6)
| ~ divides(X8,sK8)
| $less(X8,2) )
& prime(sK6)
& ~ $less(sK8,sK6)
& ~ $less(sK8,1)
& divides(sK6,sK3)
& ~ $less(sK8,2)
& ~ $less(sK8,sK9)
& divides(sK9,sK8)
& ~ $less(sK9,sK6)
& ! [X10: $int] :
( ~ divides(X10,sK8)
| $less(X10,2)
| ~ $less(X10,sK9) )
& prime(sK9)
& ( sK9 = sK10 )
& divides(sK12,sK8)
& ( div(sK8,sK9) = sK12 )
& divides(sK13,sK3)
& $less(sK6,sK13)
& divides(sK13,sK8)
& $less(sK9,sK13)
& prime(sK13)
& $less(sK9,sK13)
& ~ $less(sK9,1)
& ~ coprime(sK9,sK13)
& ( sK8 = $product(sK12,sK9) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK7))) = sK11 )
& ~ $less(sK3,sK8)
& ~ $less(sK3,sK6)
& ~ $less(sK8,2)
& divides(sK8,sK8)
& ~ $less(sK6,2)
& ~ $less(sK6,2)
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ prime(X15) )
& ( sK3 = $product(div(sK3,sK4),sK4) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = sK5 )
& divides(div(sK3,sK4),sK3)
& ~ $less(sK3,sK4)
& ~ $less(sK4,2)
& ! [X16: $int] :
( ~ divides(X16,sK3)
| $less(X16,2)
| ~ $less(X16,sK4) )
& divides(sK4,sK3)
& ~ $less(2,2)
& ~ $less(sK3,2)
& ~ $less(sK3,2)
& ~ $less(sK3,2)
& ! [X17: $int] :
( ~ divides(X17,sK3)
| $less(X17,2)
| ~ $less(X17,2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13])],[f275,f284,f283,f282,f281,f280,f279,f278,f277,f276]) ).
tff(f276,plain,
( ? [X0: $int] :
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X3: $int,X4: list_int,X5: $int] :
( ~ $less(X5,X3)
& ! [X6: $int] :
( ~ $less(X3,X6)
| ~ prime(X6)
| divides(X6,X5)
| ~ divides(X6,X0) )
& ~ $less(X5,2)
& ! [X7: $int] :
( ~ divides(X7,X5)
| ( ~ $less(X7,X3)
& divides(X7,X0) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,X3)
| ~ divides(X8,X5)
| $less(X8,2) )
& prime(X3)
& ~ $less(X5,X3)
& ~ $less(X5,1)
& divides(X3,X0)
& ~ $less(X5,2)
& ? [X9: $int] :
( ~ $less(X5,X9)
& divides(X9,X5)
& ~ $less(X9,X3)
& ! [X10: $int] :
( ~ divides(X10,X5)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,X5)
& ( div(X5,X9) = X13 )
& ? [X14: $int] :
( divides(X14,X0)
& $less(X3,X14)
& divides(X14,X5)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = X5 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(X4))) = X12 ) ) ) )
& ~ $less(X0,X5)
& ~ $less(X0,X3)
& ~ $less(X5,2)
& divides(X5,X5)
& ~ $less(X3,2)
& ~ $less(X3,2) )
& ! [X15: $int] :
( ~ divides(X15,X0)
| ~ $less(X1,X15)
| ( divides(X15,div(X0,X1))
& coprime(X1,X15) )
| ~ prime(X15) )
& ( $product(div(X0,X1),X1) = X0 )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 )
& divides(div(X0,X1),X0) )
& ~ $less(X0,X1)
& ~ $less(X1,2)
& ! [X16: $int] :
( ~ divides(X16,X0)
| $less(X16,2)
| ~ $less(X16,X1) )
& divides(X1,X0) )
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2)
& ~ $less(X0,2)
& ! [X17: $int] :
( ~ divides(X17,X0)
| $less(X17,2)
| ~ $less(X17,2) ) )
=> ( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X5: $int,X4: list_int,X3: $int] :
( ~ $less(X5,X3)
& ! [X6: $int] :
( ~ $less(X3,X6)
| ~ prime(X6)
| divides(X6,X5)
| ~ divides(X6,sK3) )
& ~ $less(X5,2)
& ! [X7: $int] :
( ~ divides(X7,X5)
| ( ~ $less(X7,X3)
& divides(X7,sK3) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,X3)
| ~ divides(X8,X5)
| $less(X8,2) )
& prime(X3)
& ~ $less(X5,X3)
& ~ $less(X5,1)
& divides(X3,sK3)
& ~ $less(X5,2)
& ? [X9: $int] :
( ~ $less(X5,X9)
& divides(X9,X5)
& ~ $less(X9,X3)
& ! [X10: $int] :
( ~ divides(X10,X5)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,X5)
& ( div(X5,X9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(X3,X14)
& divides(X14,X5)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = X5 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(X4))) = X12 ) ) ) )
& ~ $less(sK3,X5)
& ~ $less(sK3,X3)
& ~ $less(X5,2)
& divides(X5,X5)
& ~ $less(X3,2)
& ~ $less(X3,2) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(X1,X15)
| ( divides(X15,div(sK3,X1))
& coprime(X1,X15) )
| ~ prime(X15) )
& ( sK3 = $product(div(sK3,X1),X1) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 )
& divides(div(sK3,X1),sK3) )
& ~ $less(sK3,X1)
& ~ $less(X1,2)
& ! [X16: $int] :
( ~ divides(X16,sK3)
| $less(X16,2)
| ~ $less(X16,X1) )
& divides(X1,sK3) )
& ~ $less(2,2)
& ~ $less(sK3,2)
& ~ $less(sK3,2)
& ~ $less(sK3,2)
& ! [X17: $int] :
( ~ divides(X17,sK3)
| $less(X17,2)
| ~ $less(X17,2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f277,plain,
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X5: $int,X4: list_int,X3: $int] :
( ~ $less(X5,X3)
& ! [X6: $int] :
( ~ $less(X3,X6)
| ~ prime(X6)
| divides(X6,X5)
| ~ divides(X6,sK3) )
& ~ $less(X5,2)
& ! [X7: $int] :
( ~ divides(X7,X5)
| ( ~ $less(X7,X3)
& divides(X7,sK3) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,X3)
| ~ divides(X8,X5)
| $less(X8,2) )
& prime(X3)
& ~ $less(X5,X3)
& ~ $less(X5,1)
& divides(X3,sK3)
& ~ $less(X5,2)
& ? [X9: $int] :
( ~ $less(X5,X9)
& divides(X9,X5)
& ~ $less(X9,X3)
& ! [X10: $int] :
( ~ divides(X10,X5)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,X5)
& ( div(X5,X9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(X3,X14)
& divides(X14,X5)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = X5 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(X4))) = X12 ) ) ) )
& ~ $less(sK3,X5)
& ~ $less(sK3,X3)
& ~ $less(X5,2)
& divides(X5,X5)
& ~ $less(X3,2)
& ~ $less(X3,2) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(X1,X15)
| ( divides(X15,div(sK3,X1))
& coprime(X1,X15) )
| ~ prime(X15) )
& ( sK3 = $product(div(sK3,X1),X1) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 )
& divides(div(sK3,X1),sK3) )
& ~ $less(sK3,X1)
& ~ $less(X1,2)
& ! [X16: $int] :
( ~ divides(X16,sK3)
| $less(X16,2)
| ~ $less(X16,X1) )
& divides(X1,sK3) )
=> ( ? [X2: list_int] :
( ? [X5: $int,X4: list_int,X3: $int] :
( ~ $less(X5,X3)
& ! [X6: $int] :
( ~ $less(X3,X6)
| ~ prime(X6)
| divides(X6,X5)
| ~ divides(X6,sK3) )
& ~ $less(X5,2)
& ! [X7: $int] :
( ~ divides(X7,X5)
| ( ~ $less(X7,X3)
& divides(X7,sK3) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,X3)
| ~ divides(X8,X5)
| $less(X8,2) )
& prime(X3)
& ~ $less(X5,X3)
& ~ $less(X5,1)
& divides(X3,sK3)
& ~ $less(X5,2)
& ? [X9: $int] :
( ~ $less(X5,X9)
& divides(X9,X5)
& ~ $less(X9,X3)
& ! [X10: $int] :
( ~ divides(X10,X5)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,X5)
& ( div(X5,X9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(X3,X14)
& divides(X14,X5)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = X5 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(X4))) = X12 ) ) ) )
& ~ $less(sK3,X5)
& ~ $less(sK3,X3)
& ~ $less(X5,2)
& divides(X5,X5)
& ~ $less(X3,2)
& ~ $less(X3,2) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ prime(X15) )
& ( sK3 = $product(div(sK3,sK4),sK4) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = X2 )
& divides(div(sK3,sK4),sK3) )
& ~ $less(sK3,sK4)
& ~ $less(sK4,2)
& ! [X16: $int] :
( ~ divides(X16,sK3)
| $less(X16,2)
| ~ $less(X16,sK4) )
& divides(sK4,sK3) ) ),
introduced(choice_axiom,[]) ).
tff(f278,plain,
( ? [X2: list_int] :
( ? [X5: $int,X4: list_int,X3: $int] :
( ~ $less(X5,X3)
& ! [X6: $int] :
( ~ $less(X3,X6)
| ~ prime(X6)
| divides(X6,X5)
| ~ divides(X6,sK3) )
& ~ $less(X5,2)
& ! [X7: $int] :
( ~ divides(X7,X5)
| ( ~ $less(X7,X3)
& divides(X7,sK3) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,X3)
| ~ divides(X8,X5)
| $less(X8,2) )
& prime(X3)
& ~ $less(X5,X3)
& ~ $less(X5,1)
& divides(X3,sK3)
& ~ $less(X5,2)
& ? [X9: $int] :
( ~ $less(X5,X9)
& divides(X9,X5)
& ~ $less(X9,X3)
& ! [X10: $int] :
( ~ divides(X10,X5)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,X5)
& ( div(X5,X9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(X3,X14)
& divides(X14,X5)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = X5 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(X4))) = X12 ) ) ) )
& ~ $less(sK3,X5)
& ~ $less(sK3,X3)
& ~ $less(X5,2)
& divides(X5,X5)
& ~ $less(X3,2)
& ~ $less(X3,2) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ prime(X15) )
& ( sK3 = $product(div(sK3,sK4),sK4) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = X2 )
& divides(div(sK3,sK4),sK3) )
=> ( ? [X5: $int,X4: list_int,X3: $int] :
( ~ $less(X5,X3)
& ! [X6: $int] :
( ~ $less(X3,X6)
| ~ prime(X6)
| divides(X6,X5)
| ~ divides(X6,sK3) )
& ~ $less(X5,2)
& ! [X7: $int] :
( ~ divides(X7,X5)
| ( ~ $less(X7,X3)
& divides(X7,sK3) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,X3)
| ~ divides(X8,X5)
| $less(X8,2) )
& prime(X3)
& ~ $less(X5,X3)
& ~ $less(X5,1)
& divides(X3,sK3)
& ~ $less(X5,2)
& ? [X9: $int] :
( ~ $less(X5,X9)
& divides(X9,X5)
& ~ $less(X9,X3)
& ! [X10: $int] :
( ~ divides(X10,X5)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,X5)
& ( div(X5,X9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(X3,X14)
& divides(X14,X5)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = X5 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(X4))) = X12 ) ) ) )
& ~ $less(sK3,X5)
& ~ $less(sK3,X3)
& ~ $less(X5,2)
& divides(X5,X5)
& ~ $less(X3,2)
& ~ $less(X3,2) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ prime(X15) )
& ( sK3 = $product(div(sK3,sK4),sK4) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = sK5 )
& divides(div(sK3,sK4),sK3) ) ),
introduced(choice_axiom,[]) ).
tff(f279,plain,
( ? [X5: $int,X4: list_int,X3: $int] :
( ~ $less(X5,X3)
& ! [X6: $int] :
( ~ $less(X3,X6)
| ~ prime(X6)
| divides(X6,X5)
| ~ divides(X6,sK3) )
& ~ $less(X5,2)
& ! [X7: $int] :
( ~ divides(X7,X5)
| ( ~ $less(X7,X3)
& divides(X7,sK3) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,X3)
| ~ divides(X8,X5)
| $less(X8,2) )
& prime(X3)
& ~ $less(X5,X3)
& ~ $less(X5,1)
& divides(X3,sK3)
& ~ $less(X5,2)
& ? [X9: $int] :
( ~ $less(X5,X9)
& divides(X9,X5)
& ~ $less(X9,X3)
& ! [X10: $int] :
( ~ divides(X10,X5)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,X5)
& ( div(X5,X9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(X3,X14)
& divides(X14,X5)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = X5 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(X4))) = X12 ) ) ) )
& ~ $less(sK3,X5)
& ~ $less(sK3,X3)
& ~ $less(X5,2)
& divides(X5,X5)
& ~ $less(X3,2)
& ~ $less(X3,2) )
=> ( ~ $less(sK8,sK6)
& ! [X6: $int] :
( ~ $less(sK6,X6)
| ~ prime(X6)
| divides(X6,sK8)
| ~ divides(X6,sK3) )
& ~ $less(sK8,2)
& ! [X7: $int] :
( ~ divides(X7,sK8)
| ( ~ $less(X7,sK6)
& divides(X7,sK3) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,sK6)
| ~ divides(X8,sK8)
| $less(X8,2) )
& prime(sK6)
& ~ $less(sK8,sK6)
& ~ $less(sK8,1)
& divides(sK6,sK3)
& ~ $less(sK8,2)
& ? [X9: $int] :
( ~ $less(sK8,X9)
& divides(X9,sK8)
& ~ $less(X9,sK6)
& ! [X10: $int] :
( ~ divides(X10,sK8)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,sK8)
& ( div(sK8,X9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = sK8 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(sK7))) = X12 ) ) ) )
& ~ $less(sK3,sK8)
& ~ $less(sK3,sK6)
& ~ $less(sK8,2)
& divides(sK8,sK8)
& ~ $less(sK6,2)
& ~ $less(sK6,2) ) ),
introduced(choice_axiom,[]) ).
tff(f280,plain,
( ? [X9: $int] :
( ~ $less(sK8,X9)
& divides(X9,sK8)
& ~ $less(X9,sK6)
& ! [X10: $int] :
( ~ divides(X10,sK8)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,sK8)
& ( div(sK8,X9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = sK8 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(sK7))) = X12 ) ) ) )
=> ( ~ $less(sK8,sK9)
& divides(sK9,sK8)
& ~ $less(sK9,sK6)
& ! [X10: $int] :
( ~ divides(X10,sK8)
| $less(X10,2)
| ~ $less(X10,sK9) )
& prime(sK9)
& ? [X11: $int] :
( ( sK9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,sK8)
& ( div(sK8,sK9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(sK9,X14)
& prime(X14)
& $less(sK9,X14)
& ~ $less(sK9,1)
& ~ coprime(sK9,X14) )
& ( sK8 = $product(X13,sK9) ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK7))) = X12 ) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f281,plain,
( ? [X11: $int] :
( ( sK9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,sK8)
& ( div(sK8,sK9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(sK9,X14)
& prime(X14)
& $less(sK9,X14)
& ~ $less(sK9,1)
& ~ coprime(sK9,X14) )
& ( sK8 = $product(X13,sK9) ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK7))) = X12 ) ) )
=> ( ( sK9 = sK10 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,sK8)
& ( div(sK8,sK9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(sK9,X14)
& prime(X14)
& $less(sK9,X14)
& ~ $less(sK9,1)
& ~ coprime(sK9,X14) )
& ( sK8 = $product(X13,sK9) ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK7))) = X12 ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f282,plain,
( ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,sK8)
& ( div(sK8,sK9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(sK9,X14)
& prime(X14)
& $less(sK9,X14)
& ~ $less(sK9,1)
& ~ coprime(sK9,X14) )
& ( sK8 = $product(X13,sK9) ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK7))) = X12 ) )
=> ( ? [X13: $int] :
( divides(X13,sK8)
& ( div(sK8,sK9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(sK9,X14)
& prime(X14)
& $less(sK9,X14)
& ~ $less(sK9,1)
& ~ coprime(sK9,X14) )
& ( sK8 = $product(X13,sK9) ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK7))) = sK11 ) ) ),
introduced(choice_axiom,[]) ).
tff(f283,plain,
( ? [X13: $int] :
( divides(X13,sK8)
& ( div(sK8,sK9) = X13 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(sK9,X14)
& prime(X14)
& $less(sK9,X14)
& ~ $less(sK9,1)
& ~ coprime(sK9,X14) )
& ( sK8 = $product(X13,sK9) ) )
=> ( divides(sK12,sK8)
& ( div(sK8,sK9) = sK12 )
& ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(sK9,X14)
& prime(X14)
& $less(sK9,X14)
& ~ $less(sK9,1)
& ~ coprime(sK9,X14) )
& ( sK8 = $product(sK12,sK9) ) ) ),
introduced(choice_axiom,[]) ).
tff(f284,plain,
( ? [X14: $int] :
( divides(X14,sK3)
& $less(sK6,X14)
& divides(X14,sK8)
& $less(sK9,X14)
& prime(X14)
& $less(sK9,X14)
& ~ $less(sK9,1)
& ~ coprime(sK9,X14) )
=> ( divides(sK13,sK3)
& $less(sK6,sK13)
& divides(sK13,sK8)
& $less(sK9,sK13)
& prime(sK13)
& $less(sK9,sK13)
& ~ $less(sK9,1)
& ~ coprime(sK9,sK13) ) ),
introduced(choice_axiom,[]) ).
tff(f275,plain,
? [X0: $int] :
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X3: $int,X4: list_int,X5: $int] :
( ~ $less(X5,X3)
& ! [X6: $int] :
( ~ $less(X3,X6)
| ~ prime(X6)
| divides(X6,X5)
| ~ divides(X6,X0) )
& ~ $less(X5,2)
& ! [X7: $int] :
( ~ divides(X7,X5)
| ( ~ $less(X7,X3)
& divides(X7,X0) )
| $less(X7,2) )
& ! [X8: $int] :
( ~ $less(X8,X3)
| ~ divides(X8,X5)
| $less(X8,2) )
& prime(X3)
& ~ $less(X5,X3)
& ~ $less(X5,1)
& divides(X3,X0)
& ~ $less(X5,2)
& ? [X9: $int] :
( ~ $less(X5,X9)
& divides(X9,X5)
& ~ $less(X9,X3)
& ! [X10: $int] :
( ~ divides(X10,X5)
| $less(X10,2)
| ~ $less(X10,X9) )
& prime(X9)
& ? [X11: $int] :
( ( X9 = X11 )
& ? [X12: list_int] :
( ? [X13: $int] :
( divides(X13,X5)
& ( div(X5,X9) = X13 )
& ? [X14: $int] :
( divides(X14,X0)
& $less(X3,X14)
& divides(X14,X5)
& $less(X9,X14)
& prime(X14)
& $less(X9,X14)
& ~ $less(X9,1)
& ~ coprime(X9,X14) )
& ( $product(X13,X9) = X5 ) )
& ( tb2t(cons(int,t2tb1(X9),t2tb(X4))) = X12 ) ) ) )
& ~ $less(X0,X5)
& ~ $less(X0,X3)
& ~ $less(X5,2)
& divides(X5,X5)
& ~ $less(X3,2)
& ~ $less(X3,2) )
& ! [X15: $int] :
( ~ divides(X15,X0)
| ~ $less(X1,X15)
| ( divides(X15,div(X0,X1))
& coprime(X1,X15) )
| ~ prime(X15) )
& ( $product(div(X0,X1),X1) = X0 )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 )
& divides(div(X0,X1),X0) )
& ~ $less(X0,X1)
& ~ $less(X1,2)
& ! [X16: $int] :
( ~ divides(X16,X0)
| $less(X16,2)
| ~ $less(X16,X1) )
& divides(X1,X0) )
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2)
& ~ $less(X0,2)
& ! [X17: $int] :
( ~ divides(X17,X0)
| $less(X17,2)
| ~ $less(X17,2) ) ),
inference(rectify,[],[f218]) ).
tff(f218,plain,
? [X0: $int] :
( ? [X2: $int] :
( ? [X4: list_int] :
( ? [X8: $int,X7: list_int,X6: $int] :
( ~ $less(X6,X8)
& ! [X9: $int] :
( ~ $less(X8,X9)
| ~ prime(X9)
| divides(X9,X6)
| ~ divides(X9,X0) )
& ~ $less(X6,2)
& ! [X10: $int] :
( ~ divides(X10,X6)
| ( ~ $less(X10,X8)
& divides(X10,X0) )
| $less(X10,2) )
& ! [X11: $int] :
( ~ $less(X11,X8)
| ~ divides(X11,X6)
| $less(X11,2) )
& prime(X8)
& ~ $less(X6,X8)
& ~ $less(X6,1)
& divides(X8,X0)
& ~ $less(X6,2)
& ? [X12: $int] :
( ~ $less(X6,X12)
& divides(X12,X6)
& ~ $less(X12,X8)
& ! [X13: $int] :
( ~ divides(X13,X6)
| $less(X13,2)
| ~ $less(X13,X12) )
& prime(X12)
& ? [X14: $int] :
( ( X12 = X14 )
& ? [X15: list_int] :
( ? [X16: $int] :
( divides(X16,X6)
& ( div(X6,X12) = X16 )
& ? [X17: $int] :
( divides(X17,X0)
& $less(X8,X17)
& divides(X17,X6)
& $less(X12,X17)
& prime(X17)
& $less(X12,X17)
& ~ $less(X12,1)
& ~ coprime(X12,X17) )
& ( $product(X16,X12) = X6 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X7))) = X15 ) ) ) )
& ~ $less(X0,X6)
& ~ $less(X0,X8)
& ~ $less(X6,2)
& divides(X6,X6)
& ~ $less(X8,2)
& ~ $less(X8,2) )
& ! [X5: $int] :
( ~ divides(X5,X0)
| ~ $less(X2,X5)
| ( divides(X5,div(X0,X2))
& coprime(X2,X5) )
| ~ prime(X5) )
& ( $product(div(X0,X2),X2) = X0 )
& ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 )
& divides(div(X0,X2),X0) )
& ~ $less(X0,X2)
& ~ $less(X2,2)
& ! [X3: $int] :
( ~ divides(X3,X0)
| $less(X3,2)
| ~ $less(X3,X2) )
& divides(X2,X0) )
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2)
& ~ $less(X0,2)
& ! [X1: $int] :
( ~ divides(X1,X0)
| $less(X1,2)
| ~ $less(X1,2) ) ),
inference(flattening,[],[f217]) ).
tff(f217,plain,
? [X0: $int] :
( ? [X2: $int] :
( ? [X4: list_int] :
( ? [X8: $int,X6: $int,X7: list_int] :
( ? [X12: $int] :
( ? [X14: $int] :
( ? [X15: list_int] :
( ? [X16: $int] :
( ? [X17: $int] :
( ~ coprime(X12,X17)
& $less(X12,X17)
& ~ $less(X12,1)
& divides(X17,X6)
& $less(X8,X17)
& divides(X17,X0)
& $less(X12,X17)
& prime(X17) )
& ( $product(X16,X12) = X6 )
& divides(X16,X6)
& ( div(X6,X12) = X16 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X7))) = X15 ) )
& ( X12 = X14 ) )
& prime(X12)
& ! [X13: $int] :
( ~ divides(X13,X6)
| ~ $less(X13,X12)
| $less(X13,2) )
& divides(X12,X6)
& ~ $less(X6,X12)
& ~ $less(X12,X8) )
& ! [X11: $int] :
( ~ divides(X11,X6)
| $less(X11,2)
| ~ $less(X11,X8) )
& ~ $less(X6,2)
& ~ $less(X6,X8)
& ~ $less(X8,2)
& ~ $less(X6,X8)
& divides(X6,X6)
& ~ $less(X6,2)
& ~ $less(X6,2)
& ! [X10: $int] :
( ( ~ $less(X10,X8)
& divides(X10,X0) )
| $less(X10,2)
| ~ divides(X10,X6) )
& ~ $less(X0,X6)
& prime(X8)
& ~ $less(X8,2)
& ! [X9: $int] :
( divides(X9,X6)
| ~ $less(X8,X9)
| ~ divides(X9,X0)
| ~ prime(X9) )
& ~ $less(X6,1)
& ~ $less(X0,X8)
& divides(X8,X0) )
& ! [X5: $int] :
( ( divides(X5,div(X0,X2))
& coprime(X2,X5) )
| ~ $less(X2,X5)
| ~ prime(X5)
| ~ divides(X5,X0) )
& ( $product(div(X0,X2),X2) = X0 )
& divides(div(X0,X2),X0)
& ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 ) )
& ~ $less(X0,X2)
& ! [X3: $int] :
( ~ divides(X3,X0)
| ~ $less(X3,X2)
| $less(X3,2) )
& ~ $less(X2,2)
& divides(X2,X0) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,2)
| $less(X1,2) )
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
~ ! [X0: $int] :
( ~ $less(X0,2)
=> ( ( ~ $less(X0,2)
& ~ $less(2,2)
& ! [X1: $int] :
( ( $less(X1,2)
& ~ $less(X1,2) )
=> ~ divides(X1,X0) )
& ~ $less(X0,2) )
=> ! [X2: $int] :
( ( ~ $less(X0,X2)
& ! [X3: $int] :
( ( $less(X3,X2)
& ~ $less(X3,2) )
=> ~ divides(X3,X0) )
& ~ $less(X2,2)
& divides(X2,X0) )
=> ! [X4: list_int] :
( ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 )
=> ( ( ( $product(div(X0,X2),X2) = X0 )
& divides(div(X0,X2),X0) )
=> ( ! [X5: $int] :
( ( $less(X2,X5)
& prime(X5)
& divides(X5,X0) )
=> ( divides(X5,div(X0,X2))
& coprime(X2,X5) ) )
=> ! [X8: $int,X6: $int,X7: list_int] :
( ( ! [X10: $int] :
( ( ~ $less(X10,2)
& divides(X10,X6) )
=> ( ~ $less(X10,X8)
& divides(X10,X0) ) )
& ~ $less(X0,X6)
& prime(X8)
& ~ $less(X8,2)
& ! [X9: $int] :
( ( $less(X8,X9)
& divides(X9,X0)
& prime(X9) )
=> divides(X9,X6) )
& ~ $less(X6,1)
& ~ $less(X0,X8)
& divides(X8,X0) )
=> ( ~ $less(X6,2)
=> ( ( ~ $less(X6,X8)
& divides(X6,X6)
& ~ $less(X6,2) )
=> ( ( ! [X11: $int] :
( ( ~ $less(X11,2)
& $less(X11,X8) )
=> ~ divides(X11,X6) )
& ~ $less(X6,2)
& ~ $less(X6,X8)
& ~ $less(X8,2) )
=> ! [X12: $int] :
( ( ! [X13: $int] :
( ( $less(X13,X12)
& ~ $less(X13,2) )
=> ~ divides(X13,X6) )
& divides(X12,X6)
& ~ $less(X6,X12)
& ~ $less(X12,X8) )
=> ( prime(X12)
=> ! [X14: $int] :
( ( X12 = X14 )
=> ! [X15: list_int] :
( ( tb2t(cons(int,t2tb1(X12),t2tb(X7))) = X15 )
=> ! [X16: $int] :
( ( div(X6,X12) = X16 )
=> ( ( ( $product(X16,X12) = X6 )
& divides(X16,X6) )
=> ! [X17: $int] :
( ( divides(X17,X0)
& $less(X12,X17)
& prime(X17) )
=> ( $less(X8,X17)
=> ( divides(X17,X6)
=> ( ( $less(X12,X17)
& ~ $less(X12,1) )
=> coprime(X12,X17) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f139]) ).
tff(f139,plain,
~ ! [X9: $int] :
( ~ $less(X9,2)
=> ( ( ! [X19: $int] :
( ( ~ $less(X19,2)
& $less(X19,2) )
=> ~ divides(X19,X9) )
& ~ $less(2,2)
& ~ $less(X9,2)
& ~ $less(X9,2) )
=> ! [X8: $int] :
( ( divides(X8,X9)
& ! [X19: $int] :
( ( $less(X19,X8)
& ~ $less(X19,2) )
=> ~ divides(X19,X9) )
& ~ $less(X9,X8)
& ~ $less(X8,2) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( ( $product(div(X9,X8),X8) = X9 )
& divides(div(X9,X8),X9) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& prime(X19)
& divides(X19,X9) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X24: list_int,X23: $int] :
( ( ~ $less(X9,X23)
& ! [X19: $int] :
( ( divides(X19,X9)
& $less(X23,X19)
& prime(X19) )
=> divides(X19,X22) )
& ~ $less(X22,1)
& ~ $less(X23,2)
& ! [X19: $int] :
( ( divides(X19,X22)
& ~ $less(X19,2) )
=> ( ~ $less(X19,X23)
& divides(X19,X9) ) )
& ~ $less(X9,X22)
& prime(X23)
& divides(X23,X9) )
=> ( ~ $less(X22,2)
=> ( ( ~ $less(X22,X23)
& divides(X22,X22)
& ~ $less(X22,2) )
=> ( ( ~ $less(X23,2)
& ! [X19: $int] :
( ( ~ $less(X19,2)
& $less(X19,X23) )
=> ~ divides(X19,X22) )
& ~ $less(X22,2)
& ~ $less(X22,X23) )
=> ! [X25: $int] :
( ( ~ $less(X25,X23)
& divides(X25,X22)
& ~ $less(X22,X25)
& ! [X19: $int] :
( ( ~ $less(X19,2)
& $less(X19,X25) )
=> ~ divides(X19,X22) ) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( ( $product(X28,X25) = X22 )
& divides(X28,X22) )
=> ! [X19: $int] :
( ( prime(X19)
& divides(X19,X9)
& $less(X25,X19) )
=> ( $less(X23,X19)
=> ( divides(X19,X22)
=> ( ( $less(X25,X19)
& ~ $less(X25,1) )
=> coprime(X25,X19) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(theory_normalization,[],[f114]) ).
tff(f114,negated_conjecture,
~ ! [X9: $int] :
( $lesseq(2,X9)
=> ( ( ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,2) )
=> ~ divides(X19,X9) )
& $lesseq(2,2)
& $lesseq(2,X9)
& $lesseq(2,X9) )
=> ! [X8: $int] :
( ( divides(X8,X9)
& ! [X19: $int] :
( ( $less(X19,X8)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& $lesseq(X8,X9)
& $lesseq(2,X8) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( ( $product(div(X9,X8),X8) = X9 )
& divides(div(X9,X8),X9) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& prime(X19)
& divides(X19,X9) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X24: list_int,X23: $int] :
( ( $lesseq(X23,X9)
& ! [X19: $int] :
( ( divides(X19,X9)
& $less(X23,X19)
& prime(X19) )
=> divides(X19,X22) )
& $lesseq(1,X22)
& $lesseq(2,X23)
& ! [X19: $int] :
( ( divides(X19,X22)
& $lesseq(2,X19) )
=> ( $lesseq(X23,X19)
& divides(X19,X9) ) )
& $lesseq(X22,X9)
& prime(X23)
& divides(X23,X9) )
=> ( $lesseq(2,X22)
=> ( ( $lesseq(X23,X22)
& divides(X22,X22)
& $lesseq(2,X22) )
=> ( ( $lesseq(2,X23)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,X23) )
=> ~ divides(X19,X22) )
& $lesseq(2,X22)
& $lesseq(X23,X22) )
=> ! [X25: $int] :
( ( $lesseq(X23,X25)
& divides(X25,X22)
& $lesseq(X25,X22)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,X25) )
=> ~ divides(X19,X22) ) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( ( $product(X28,X25) = X22 )
& divides(X28,X22) )
=> ! [X19: $int] :
( ( prime(X19)
& divides(X19,X9)
& $less(X25,X19) )
=> ( $less(X23,X19)
=> ( divides(X19,X22)
=> ( ( $less(X25,X19)
& $lesseq(1,X25) )
=> coprime(X25,X19) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f113]) ).
tff(f113,conjecture,
! [X9: $int] :
( $lesseq(2,X9)
=> ( ( ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,2) )
=> ~ divides(X19,X9) )
& $lesseq(2,2)
& $lesseq(2,X9)
& $lesseq(2,X9) )
=> ! [X8: $int] :
( ( divides(X8,X9)
& ! [X19: $int] :
( ( $less(X19,X8)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& $lesseq(X8,X9)
& $lesseq(2,X8) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( ( $product(div(X9,X8),X8) = X9 )
& divides(div(X9,X8),X9) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& prime(X19)
& divides(X19,X9) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X24: list_int,X23: $int] :
( ( $lesseq(X23,X9)
& ! [X19: $int] :
( ( divides(X19,X9)
& $less(X23,X19)
& prime(X19) )
=> divides(X19,X22) )
& $lesseq(1,X22)
& $lesseq(2,X23)
& ! [X19: $int] :
( ( divides(X19,X22)
& $lesseq(2,X19) )
=> ( $lesseq(X23,X19)
& divides(X19,X9) ) )
& $lesseq(X22,X9)
& prime(X23)
& divides(X23,X9) )
=> ( $lesseq(2,X22)
=> ( ( $lesseq(X23,X22)
& divides(X22,X22)
& $lesseq(2,X22) )
=> ( ( $lesseq(2,X23)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,X23) )
=> ~ divides(X19,X22) )
& $lesseq(2,X22)
& $lesseq(X23,X22) )
=> ! [X25: $int] :
( ( $lesseq(X23,X25)
& divides(X25,X22)
& $lesseq(X25,X22)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,X25) )
=> ~ divides(X19,X22) ) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( ( $product(X28,X25) = X22 )
& divides(X28,X22) )
=> ! [X19: $int] :
( ( prime(X19)
& divides(X19,X9)
& $less(X25,X19) )
=> ( $less(X23,X19)
=> ( divides(X19,X22)
=> ( ( $less(X25,X19)
& $lesseq(1,X25) )
=> coprime(X25,X19) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f449,plain,
~ $less(sK9,sK13),
inference(unit_resulting_resolution,[],[f369,f366,f367,f395]) ).
tff(f395,plain,
! [X2: $int,X0: $int] :
( ~ $less(X2,X0)
| coprime(X2,X0)
| ~ prime(X0)
| $less(X2,1) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: $int] :
( ( prime(X0)
| ( $less(sK14(X0),X0)
& ~ coprime(sK14(X0),X0)
& ~ $less(sK14(X0),1) )
| $less(X0,2) )
& ( ( ! [X2: $int] :
( ~ $less(X2,X0)
| coprime(X2,X0)
| $less(X2,1) )
& ~ $less(X0,2) )
| ~ prime(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f288,f289]) ).
tff(f289,plain,
! [X0: $int] :
( ? [X1: $int] :
( $less(X1,X0)
& ~ coprime(X1,X0)
& ~ $less(X1,1) )
=> ( $less(sK14(X0),X0)
& ~ coprime(sK14(X0),X0)
& ~ $less(sK14(X0),1) ) ),
introduced(choice_axiom,[]) ).
tff(f288,plain,
! [X0: $int] :
( ( prime(X0)
| ? [X1: $int] :
( $less(X1,X0)
& ~ coprime(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X2: $int] :
( ~ $less(X2,X0)
| coprime(X2,X0)
| $less(X2,1) )
& ~ $less(X0,2) )
| ~ prime(X0) ) ),
inference(rectify,[],[f287]) ).
tff(f287,plain,
! [X0: $int] :
( ( prime(X0)
| ? [X1: $int] :
( $less(X1,X0)
& ~ coprime(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X1: $int] :
( ~ $less(X1,X0)
| coprime(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) )
| ~ prime(X0) ) ),
inference(flattening,[],[f286]) ).
tff(f286,plain,
! [X0: $int] :
( ( prime(X0)
| ? [X1: $int] :
( $less(X1,X0)
& ~ coprime(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X1: $int] :
( ~ $less(X1,X0)
| coprime(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) )
| ~ prime(X0) ) ),
inference(nnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( ~ $less(X1,X0)
| coprime(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) ) ),
inference(flattening,[],[f226]) ).
tff(f226,plain,
! [X0: $int] :
( ( ~ $less(X0,2)
& ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) ) )
<=> prime(X0) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $int] :
( ( ~ $less(X0,2)
& ! [X1: $int] :
( ( ~ $less(X1,1)
& $less(X1,X0) )
=> coprime(X1,X0) ) )
<=> prime(X0) ),
inference(rectify,[],[f131]) ).
tff(f131,plain,
! [X14: $int] :
( ( ~ $less(X14,2)
& ! [X9: $int] :
( ( ~ $less(X9,1)
& $less(X9,X14) )
=> coprime(X9,X14) ) )
<=> prime(X14) ),
inference(theory_normalization,[],[f88]) ).
tff(f88,axiom,
! [X14: $int] :
( ( $lesseq(2,X14)
& ! [X9: $int] :
( ( $lesseq(1,X9)
& $less(X9,X14) )
=> coprime(X9,X14) ) )
<=> prime(X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f367,plain,
~ $less(sK9,1),
inference(cnf_transformation,[],[f285]) ).
tff(f366,plain,
~ coprime(sK9,sK13),
inference(cnf_transformation,[],[f285]) ).
tff(f369,plain,
prime(sK13),
inference(cnf_transformation,[],[f285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW613_2 : TPTP v8.2.0. Released v6.1.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 08:31:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TF0_THM_EQU_ARI problem
% 0.12/0.35 Running first-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.41 % (13921)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (13924)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/8Mi)
% 0.20/0.41 % (13921)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (13926)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.20/0.41 % (13921)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (13927)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/15Mi)
% 0.20/0.41 % (13921)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (13928)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/32Mi)
% 0.20/0.41 % (13921)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (13922)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59848Mi)
% 0.20/0.41 % (13921)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (13923)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/34Mi)
% 0.20/0.41 % (13921)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (13925)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.20/0.42 % (13925)Instruction limit reached!
% 0.20/0.42 % (13925)------------------------------
% 0.20/0.42 % (13925)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.42 % (13925)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.42 % (13925)Termination reason: Time limit
% 0.20/0.42 % (13925)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (13925)Memory used [KB]: 852
% 0.20/0.42 % (13925)Time elapsed: 0.004 s
% 0.20/0.42 % (13925)Instructions burned: 3 (million)
% 0.20/0.42 % (13924)Instruction limit reached!
% 0.20/0.42 % (13924)------------------------------
% 0.20/0.42 % (13924)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.42 % (13924)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.42 % (13924)Termination reason: Time limit
% 0.20/0.42 % (13924)Termination phase: Preprocessing 3
% 0.20/0.42
% 0.20/0.42 % (13924)Memory used [KB]: 1104
% 0.20/0.42 % (13924)Time elapsed: 0.006 s
% 0.20/0.42 % (13924)Instructions burned: 8 (million)
% 0.20/0.42 % (13927)Instruction limit reached!
% 0.20/0.42 % (13927)------------------------------
% 0.20/0.42 % (13927)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.42 % (13927)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.42 % (13927)Termination reason: Time limit
% 0.20/0.42 % (13927)Termination phase: Saturation
% 0.20/0.42
% 0.20/0.42 % (13927)Memory used [KB]: 1169
% 0.20/0.42 % (13927)Time elapsed: 0.012 s
% 0.20/0.42 % (13927)Instructions burned: 15 (million)
% 0.20/0.42 % (13928)First to succeed.
% 0.20/0.43 % (13928)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13921"
% 0.20/0.43 % (13923)Also succeeded, but the first one will report.
% 0.20/0.43 % (13921)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43 % (13928)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.43 % (13928)------------------------------
% 0.20/0.43 % (13928)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.43 % (13928)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.43 % (13928)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (13928)Memory used [KB]: 1141
% 0.20/0.43 % (13928)Time elapsed: 0.014 s
% 0.20/0.43 % (13928)Instructions burned: 21 (million)
% 0.20/0.43 % (13928)------------------------------
% 0.20/0.43 % (13928)------------------------------
% 0.20/0.43 % (13921)Success in time 0.06 s
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