TSTP Solution File: SWW613_2 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWW613_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 19:08:52 EDT 2022
% Result : Theorem 0.20s 0.56s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 65
% Syntax : Number of formulae : 87 ( 6 unt; 53 typ; 0 def)
% Number of atoms : 1167 ( 118 equ)
% Maximal formula atoms : 130 ( 34 avg)
% Number of connectives : 1640 ( 507 ~; 197 |; 810 &)
% ( 5 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 50 ( 18 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 1174 ( 586 atm; 38 fun; 297 num; 253 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 49 ( 29 >; 20 *; 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 ).
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: $int ).
tff(func_def_46,type,
sK8: list_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 ) > $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(f509,plain,
$false,
inference(subsumption_resolution,[],[f507,f359]) ).
tff(f359,plain,
~ $less(sK9,1),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
( ~ $less(2,2)
& ( sK3 = $product(div(sK3,sK4),sK4) )
& divides(div(sK3,sK4),sK3)
& ~ $less(sK3,sK7)
& prime(sK7)
& ~ $less(sK3,sK6)
& divides(sK7,sK3)
& divides(sK9,sK6)
& prime(sK9)
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = sK11 )
& ( sK6 = $product(sK12,sK9) )
& ~ $less(sK9,1)
& prime(sK13)
& ~ coprime(sK9,sK13)
& $less(sK9,sK13)
& divides(sK13,sK6)
& divides(sK13,sK3)
& $less(sK7,sK13)
& $less(sK9,sK13)
& ( div(sK6,sK9) = sK12 )
& divides(sK12,sK6)
& ( sK10 = sK9 )
& ~ $less(sK6,sK9)
& ~ $less(sK9,sK7)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,sK9)
| ~ divides(X11,sK6) )
& divides(sK6,sK6)
& ~ $less(sK6,2)
& ~ $less(sK6,sK7)
& ~ $less(sK7,2)
& ! [X12: $int] :
( ~ divides(X12,sK6)
| $less(X12,2)
| ( divides(X12,sK3)
& ~ $less(X12,sK7) ) )
& ~ $less(sK6,2)
& ~ $less(sK6,sK7)
& ! [X13: $int] :
( ~ $less(X13,sK7)
| ~ divides(X13,sK6)
| $less(X13,2) )
& ~ $less(sK7,2)
& ! [X14: $int] :
( ~ divides(X14,sK3)
| ~ $less(sK7,X14)
| divides(X14,sK6)
| ~ prime(X14) )
& ~ $less(sK6,2)
& ~ $less(sK6,1)
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ prime(X15) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = sK5 )
& ~ $less(sK4,2)
& ! [X16: $int] :
( ~ $less(X16,sK4)
| $less(X16,2)
| ~ divides(X16,sK3) )
& divides(sK4,sK3)
& ~ $less(sK3,sK4)
& ~ $less(sK3,2)
& ! [X17: $int] :
( ~ $less(X17,2)
| ~ divides(X17,sK3)
| $less(X17,2) )
& ~ $less(sK3,2)
& ~ $less(sK3,2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13])],[f265,f274,f273,f272,f271,f270,f269,f268,f267,f266]) ).
tff(f266,plain,
( ? [X0: $int] :
( ~ $less(2,2)
& ? [X1: $int] :
( ? [X2: list_int] :
( ( $product(div(X0,X1),X1) = X0 )
& divides(div(X0,X1),X0)
& ? [X3: $int,X4: $int,X5: list_int] :
( ~ $less(X0,X4)
& prime(X4)
& ~ $less(X0,X3)
& divides(X4,X0)
& ? [X6: $int] :
( divides(X6,X3)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 )
& ? [X9: $int] :
( ( $product(X9,X6) = X3 )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,X3)
& divides(X10,X0)
& $less(X4,X10)
& $less(X6,X10) )
& ( div(X3,X6) = X9 )
& divides(X9,X3) ) )
& ( X6 = X7 ) )
& ~ $less(X3,X6)
& ~ $less(X6,X4)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,X3) ) )
& divides(X3,X3)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ! [X12: $int] :
( ~ divides(X12,X3)
| $less(X12,2)
| ( divides(X12,X0)
& ~ $less(X12,X4) ) )
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ! [X13: $int] :
( ~ $less(X13,X4)
| ~ divides(X13,X3)
| $less(X13,2) )
& ~ $less(X4,2)
& ! [X14: $int] :
( ~ divides(X14,X0)
| ~ $less(X4,X14)
| divides(X14,X3)
| ~ prime(X14) )
& ~ $less(X3,2)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ~ divides(X15,X0)
| ~ $less(X1,X15)
| ( divides(X15,div(X0,X1))
& coprime(X1,X15) )
| ~ prime(X15) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ~ $less(X1,2)
& ! [X16: $int] :
( ~ $less(X16,X1)
| $less(X16,2)
| ~ divides(X16,X0) )
& divides(X1,X0)
& ~ $less(X0,X1) )
& ~ $less(X0,2)
& ! [X17: $int] :
( ~ $less(X17,2)
| ~ divides(X17,X0)
| $less(X17,2) )
& ~ $less(X0,2)
& ~ $less(X0,2) )
=> ( ~ $less(2,2)
& ? [X1: $int] :
( ? [X2: list_int] :
( ( sK3 = $product(div(sK3,X1),X1) )
& divides(div(sK3,X1),sK3)
& ? [X5: list_int,X4: $int,X3: $int] :
( ~ $less(sK3,X4)
& prime(X4)
& ~ $less(sK3,X3)
& divides(X4,sK3)
& ? [X6: $int] :
( divides(X6,X3)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 )
& ? [X9: $int] :
( ( $product(X9,X6) = X3 )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,X3)
& divides(X10,sK3)
& $less(X4,X10)
& $less(X6,X10) )
& ( div(X3,X6) = X9 )
& divides(X9,X3) ) )
& ( X6 = X7 ) )
& ~ $less(X3,X6)
& ~ $less(X6,X4)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,X3) ) )
& divides(X3,X3)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ! [X12: $int] :
( ~ divides(X12,X3)
| $less(X12,2)
| ( divides(X12,sK3)
& ~ $less(X12,X4) ) )
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ! [X13: $int] :
( ~ $less(X13,X4)
| ~ divides(X13,X3)
| $less(X13,2) )
& ~ $less(X4,2)
& ! [X14: $int] :
( ~ divides(X14,sK3)
| ~ $less(X4,X14)
| divides(X14,X3)
| ~ prime(X14) )
& ~ $less(X3,2)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(X1,X15)
| ( divides(X15,div(sK3,X1))
& coprime(X1,X15) )
| ~ prime(X15) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ~ $less(X1,2)
& ! [X16: $int] :
( ~ $less(X16,X1)
| $less(X16,2)
| ~ divides(X16,sK3) )
& divides(X1,sK3)
& ~ $less(sK3,X1) )
& ~ $less(sK3,2)
& ! [X17: $int] :
( ~ $less(X17,2)
| ~ divides(X17,sK3)
| $less(X17,2) )
& ~ $less(sK3,2)
& ~ $less(sK3,2) ) ),
introduced(choice_axiom,[]) ).
tff(f267,plain,
( ? [X1: $int] :
( ? [X2: list_int] :
( ( sK3 = $product(div(sK3,X1),X1) )
& divides(div(sK3,X1),sK3)
& ? [X5: list_int,X4: $int,X3: $int] :
( ~ $less(sK3,X4)
& prime(X4)
& ~ $less(sK3,X3)
& divides(X4,sK3)
& ? [X6: $int] :
( divides(X6,X3)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 )
& ? [X9: $int] :
( ( $product(X9,X6) = X3 )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,X3)
& divides(X10,sK3)
& $less(X4,X10)
& $less(X6,X10) )
& ( div(X3,X6) = X9 )
& divides(X9,X3) ) )
& ( X6 = X7 ) )
& ~ $less(X3,X6)
& ~ $less(X6,X4)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,X3) ) )
& divides(X3,X3)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ! [X12: $int] :
( ~ divides(X12,X3)
| $less(X12,2)
| ( divides(X12,sK3)
& ~ $less(X12,X4) ) )
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ! [X13: $int] :
( ~ $less(X13,X4)
| ~ divides(X13,X3)
| $less(X13,2) )
& ~ $less(X4,2)
& ! [X14: $int] :
( ~ divides(X14,sK3)
| ~ $less(X4,X14)
| divides(X14,X3)
| ~ prime(X14) )
& ~ $less(X3,2)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(X1,X15)
| ( divides(X15,div(sK3,X1))
& coprime(X1,X15) )
| ~ prime(X15) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ~ $less(X1,2)
& ! [X16: $int] :
( ~ $less(X16,X1)
| $less(X16,2)
| ~ divides(X16,sK3) )
& divides(X1,sK3)
& ~ $less(sK3,X1) )
=> ( ? [X2: list_int] :
( ( sK3 = $product(div(sK3,sK4),sK4) )
& divides(div(sK3,sK4),sK3)
& ? [X5: list_int,X4: $int,X3: $int] :
( ~ $less(sK3,X4)
& prime(X4)
& ~ $less(sK3,X3)
& divides(X4,sK3)
& ? [X6: $int] :
( divides(X6,X3)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 )
& ? [X9: $int] :
( ( $product(X9,X6) = X3 )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,X3)
& divides(X10,sK3)
& $less(X4,X10)
& $less(X6,X10) )
& ( div(X3,X6) = X9 )
& divides(X9,X3) ) )
& ( X6 = X7 ) )
& ~ $less(X3,X6)
& ~ $less(X6,X4)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,X3) ) )
& divides(X3,X3)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ! [X12: $int] :
( ~ divides(X12,X3)
| $less(X12,2)
| ( divides(X12,sK3)
& ~ $less(X12,X4) ) )
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ! [X13: $int] :
( ~ $less(X13,X4)
| ~ divides(X13,X3)
| $less(X13,2) )
& ~ $less(X4,2)
& ! [X14: $int] :
( ~ divides(X14,sK3)
| ~ $less(X4,X14)
| divides(X14,X3)
| ~ prime(X14) )
& ~ $less(X3,2)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ prime(X15) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = X2 ) )
& ~ $less(sK4,2)
& ! [X16: $int] :
( ~ $less(X16,sK4)
| $less(X16,2)
| ~ divides(X16,sK3) )
& divides(sK4,sK3)
& ~ $less(sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
tff(f268,plain,
( ? [X2: list_int] :
( ( sK3 = $product(div(sK3,sK4),sK4) )
& divides(div(sK3,sK4),sK3)
& ? [X5: list_int,X4: $int,X3: $int] :
( ~ $less(sK3,X4)
& prime(X4)
& ~ $less(sK3,X3)
& divides(X4,sK3)
& ? [X6: $int] :
( divides(X6,X3)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 )
& ? [X9: $int] :
( ( $product(X9,X6) = X3 )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,X3)
& divides(X10,sK3)
& $less(X4,X10)
& $less(X6,X10) )
& ( div(X3,X6) = X9 )
& divides(X9,X3) ) )
& ( X6 = X7 ) )
& ~ $less(X3,X6)
& ~ $less(X6,X4)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,X3) ) )
& divides(X3,X3)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ! [X12: $int] :
( ~ divides(X12,X3)
| $less(X12,2)
| ( divides(X12,sK3)
& ~ $less(X12,X4) ) )
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ! [X13: $int] :
( ~ $less(X13,X4)
| ~ divides(X13,X3)
| $less(X13,2) )
& ~ $less(X4,2)
& ! [X14: $int] :
( ~ divides(X14,sK3)
| ~ $less(X4,X14)
| divides(X14,X3)
| ~ prime(X14) )
& ~ $less(X3,2)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ prime(X15) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = X2 ) )
=> ( ( sK3 = $product(div(sK3,sK4),sK4) )
& divides(div(sK3,sK4),sK3)
& ? [X5: list_int,X4: $int,X3: $int] :
( ~ $less(sK3,X4)
& prime(X4)
& ~ $less(sK3,X3)
& divides(X4,sK3)
& ? [X6: $int] :
( divides(X6,X3)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 )
& ? [X9: $int] :
( ( $product(X9,X6) = X3 )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,X3)
& divides(X10,sK3)
& $less(X4,X10)
& $less(X6,X10) )
& ( div(X3,X6) = X9 )
& divides(X9,X3) ) )
& ( X6 = X7 ) )
& ~ $less(X3,X6)
& ~ $less(X6,X4)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,X3) ) )
& divides(X3,X3)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ! [X12: $int] :
( ~ divides(X12,X3)
| $less(X12,2)
| ( divides(X12,sK3)
& ~ $less(X12,X4) ) )
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ! [X13: $int] :
( ~ $less(X13,X4)
| ~ divides(X13,X3)
| $less(X13,2) )
& ~ $less(X4,2)
& ! [X14: $int] :
( ~ divides(X14,sK3)
| ~ $less(X4,X14)
| divides(X14,X3)
| ~ prime(X14) )
& ~ $less(X3,2)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ prime(X15) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = sK5 ) ) ),
introduced(choice_axiom,[]) ).
tff(f269,plain,
( ? [X5: list_int,X4: $int,X3: $int] :
( ~ $less(sK3,X4)
& prime(X4)
& ~ $less(sK3,X3)
& divides(X4,sK3)
& ? [X6: $int] :
( divides(X6,X3)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 )
& ? [X9: $int] :
( ( $product(X9,X6) = X3 )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,X3)
& divides(X10,sK3)
& $less(X4,X10)
& $less(X6,X10) )
& ( div(X3,X6) = X9 )
& divides(X9,X3) ) )
& ( X6 = X7 ) )
& ~ $less(X3,X6)
& ~ $less(X6,X4)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,X3) ) )
& divides(X3,X3)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ! [X12: $int] :
( ~ divides(X12,X3)
| $less(X12,2)
| ( divides(X12,sK3)
& ~ $less(X12,X4) ) )
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ! [X13: $int] :
( ~ $less(X13,X4)
| ~ divides(X13,X3)
| $less(X13,2) )
& ~ $less(X4,2)
& ! [X14: $int] :
( ~ divides(X14,sK3)
| ~ $less(X4,X14)
| divides(X14,X3)
| ~ prime(X14) )
& ~ $less(X3,2)
& ~ $less(X3,1) )
=> ( ~ $less(sK3,sK7)
& prime(sK7)
& ~ $less(sK3,sK6)
& divides(sK7,sK3)
& ? [X6: $int] :
( divides(X6,sK6)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(sK8))) = X8 )
& ? [X9: $int] :
( ( sK6 = $product(X9,X6) )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(X6,X10) )
& ( div(sK6,X6) = X9 )
& divides(X9,sK6) ) )
& ( X6 = X7 ) )
& ~ $less(sK6,X6)
& ~ $less(X6,sK7)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,sK6) ) )
& divides(sK6,sK6)
& ~ $less(sK6,2)
& ~ $less(sK6,sK7)
& ~ $less(sK7,2)
& ! [X12: $int] :
( ~ divides(X12,sK6)
| $less(X12,2)
| ( divides(X12,sK3)
& ~ $less(X12,sK7) ) )
& ~ $less(sK6,2)
& ~ $less(sK6,sK7)
& ! [X13: $int] :
( ~ $less(X13,sK7)
| ~ divides(X13,sK6)
| $less(X13,2) )
& ~ $less(sK7,2)
& ! [X14: $int] :
( ~ divides(X14,sK3)
| ~ $less(sK7,X14)
| divides(X14,sK6)
| ~ prime(X14) )
& ~ $less(sK6,2)
& ~ $less(sK6,1) ) ),
introduced(choice_axiom,[]) ).
tff(f270,plain,
( ? [X6: $int] :
( divides(X6,sK6)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(sK8))) = X8 )
& ? [X9: $int] :
( ( sK6 = $product(X9,X6) )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(X6,X10) )
& ( div(sK6,X6) = X9 )
& divides(X9,sK6) ) )
& ( X6 = X7 ) )
& ~ $less(sK6,X6)
& ~ $less(X6,sK7)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,sK6) ) )
=> ( divides(sK9,sK6)
& prime(sK9)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = X8 )
& ? [X9: $int] :
( ( sK6 = $product(X9,sK9) )
& ? [X10: $int] :
( ~ $less(sK9,1)
& prime(X10)
& ~ coprime(sK9,X10)
& $less(sK9,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(sK9,X10) )
& ( div(sK6,sK9) = X9 )
& divides(X9,sK6) ) )
& ( sK9 = X7 ) )
& ~ $less(sK6,sK9)
& ~ $less(sK9,sK7)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,sK9)
| ~ divides(X11,sK6) ) ) ),
introduced(choice_axiom,[]) ).
tff(f271,plain,
( ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = X8 )
& ? [X9: $int] :
( ( sK6 = $product(X9,sK9) )
& ? [X10: $int] :
( ~ $less(sK9,1)
& prime(X10)
& ~ coprime(sK9,X10)
& $less(sK9,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(sK9,X10) )
& ( div(sK6,sK9) = X9 )
& divides(X9,sK6) ) )
& ( sK9 = X7 ) )
=> ( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = X8 )
& ? [X9: $int] :
( ( sK6 = $product(X9,sK9) )
& ? [X10: $int] :
( ~ $less(sK9,1)
& prime(X10)
& ~ coprime(sK9,X10)
& $less(sK9,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(sK9,X10) )
& ( div(sK6,sK9) = X9 )
& divides(X9,sK6) ) )
& ( sK10 = sK9 ) ) ),
introduced(choice_axiom,[]) ).
tff(f272,plain,
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = X8 )
& ? [X9: $int] :
( ( sK6 = $product(X9,sK9) )
& ? [X10: $int] :
( ~ $less(sK9,1)
& prime(X10)
& ~ coprime(sK9,X10)
& $less(sK9,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(sK9,X10) )
& ( div(sK6,sK9) = X9 )
& divides(X9,sK6) ) )
=> ( ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = sK11 )
& ? [X9: $int] :
( ( sK6 = $product(X9,sK9) )
& ? [X10: $int] :
( ~ $less(sK9,1)
& prime(X10)
& ~ coprime(sK9,X10)
& $less(sK9,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(sK9,X10) )
& ( div(sK6,sK9) = X9 )
& divides(X9,sK6) ) ) ),
introduced(choice_axiom,[]) ).
tff(f273,plain,
( ? [X9: $int] :
( ( sK6 = $product(X9,sK9) )
& ? [X10: $int] :
( ~ $less(sK9,1)
& prime(X10)
& ~ coprime(sK9,X10)
& $less(sK9,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(sK9,X10) )
& ( div(sK6,sK9) = X9 )
& divides(X9,sK6) )
=> ( ( sK6 = $product(sK12,sK9) )
& ? [X10: $int] :
( ~ $less(sK9,1)
& prime(X10)
& ~ coprime(sK9,X10)
& $less(sK9,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(sK9,X10) )
& ( div(sK6,sK9) = sK12 )
& divides(sK12,sK6) ) ),
introduced(choice_axiom,[]) ).
tff(f274,plain,
( ? [X10: $int] :
( ~ $less(sK9,1)
& prime(X10)
& ~ coprime(sK9,X10)
& $less(sK9,X10)
& divides(X10,sK6)
& divides(X10,sK3)
& $less(sK7,X10)
& $less(sK9,X10) )
=> ( ~ $less(sK9,1)
& prime(sK13)
& ~ coprime(sK9,sK13)
& $less(sK9,sK13)
& divides(sK13,sK6)
& divides(sK13,sK3)
& $less(sK7,sK13)
& $less(sK9,sK13) ) ),
introduced(choice_axiom,[]) ).
tff(f265,plain,
? [X0: $int] :
( ~ $less(2,2)
& ? [X1: $int] :
( ? [X2: list_int] :
( ( $product(div(X0,X1),X1) = X0 )
& divides(div(X0,X1),X0)
& ? [X3: $int,X4: $int,X5: list_int] :
( ~ $less(X0,X4)
& prime(X4)
& ~ $less(X0,X3)
& divides(X4,X0)
& ? [X6: $int] :
( divides(X6,X3)
& prime(X6)
& ? [X7: $int] :
( ? [X8: list_int] :
( ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 )
& ? [X9: $int] :
( ( $product(X9,X6) = X3 )
& ? [X10: $int] :
( ~ $less(X6,1)
& prime(X10)
& ~ coprime(X6,X10)
& $less(X6,X10)
& divides(X10,X3)
& divides(X10,X0)
& $less(X4,X10)
& $less(X6,X10) )
& ( div(X3,X6) = X9 )
& divides(X9,X3) ) )
& ( X6 = X7 ) )
& ~ $less(X3,X6)
& ~ $less(X6,X4)
& ! [X11: $int] :
( $less(X11,2)
| ~ $less(X11,X6)
| ~ divides(X11,X3) ) )
& divides(X3,X3)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ! [X12: $int] :
( ~ divides(X12,X3)
| $less(X12,2)
| ( divides(X12,X0)
& ~ $less(X12,X4) ) )
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ! [X13: $int] :
( ~ $less(X13,X4)
| ~ divides(X13,X3)
| $less(X13,2) )
& ~ $less(X4,2)
& ! [X14: $int] :
( ~ divides(X14,X0)
| ~ $less(X4,X14)
| divides(X14,X3)
| ~ prime(X14) )
& ~ $less(X3,2)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ~ divides(X15,X0)
| ~ $less(X1,X15)
| ( divides(X15,div(X0,X1))
& coprime(X1,X15) )
| ~ prime(X15) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ~ $less(X1,2)
& ! [X16: $int] :
( ~ $less(X16,X1)
| $less(X16,2)
| ~ divides(X16,X0) )
& divides(X1,X0)
& ~ $less(X0,X1) )
& ~ $less(X0,2)
& ! [X17: $int] :
( ~ $less(X17,2)
| ~ divides(X17,X0)
| $less(X17,2) )
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(rectify,[],[f240]) ).
tff(f240,plain,
? [X0: $int] :
( ~ $less(2,2)
& ? [X2: $int] :
( ? [X4: list_int] :
( ( $product(div(X0,X2),X2) = X0 )
& divides(div(X0,X2),X0)
& ? [X8: $int,X6: $int,X7: list_int] :
( ~ $less(X0,X6)
& prime(X6)
& ~ $less(X0,X8)
& divides(X6,X0)
& ? [X12: $int] :
( divides(X12,X8)
& prime(X12)
& ? [X14: $int] :
( ? [X15: list_int] :
( ( tb2t(cons(int,t2tb1(X12),t2tb(X7))) = X15 )
& ? [X16: $int] :
( ( $product(X16,X12) = X8 )
& ? [X17: $int] :
( ~ $less(X12,1)
& prime(X17)
& ~ coprime(X12,X17)
& $less(X12,X17)
& divides(X17,X8)
& divides(X17,X0)
& $less(X6,X17)
& $less(X12,X17) )
& ( div(X8,X12) = X16 )
& divides(X16,X8) ) )
& ( X12 = X14 ) )
& ~ $less(X8,X12)
& ~ $less(X12,X6)
& ! [X13: $int] :
( $less(X13,2)
| ~ $less(X13,X12)
| ~ divides(X13,X8) ) )
& divides(X8,X8)
& ~ $less(X8,2)
& ~ $less(X8,X6)
& ~ $less(X6,2)
& ! [X9: $int] :
( ~ divides(X9,X8)
| $less(X9,2)
| ( divides(X9,X0)
& ~ $less(X9,X6) ) )
& ~ $less(X8,2)
& ~ $less(X8,X6)
& ! [X11: $int] :
( ~ $less(X11,X6)
| ~ divides(X11,X8)
| $less(X11,2) )
& ~ $less(X6,2)
& ! [X10: $int] :
( ~ divides(X10,X0)
| ~ $less(X6,X10)
| divides(X10,X8)
| ~ prime(X10) )
& ~ $less(X8,2)
& ~ $less(X8,1) )
& ! [X5: $int] :
( ~ divides(X5,X0)
| ~ $less(X2,X5)
| ( divides(X5,div(X0,X2))
& coprime(X2,X5) )
| ~ prime(X5) )
& ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 ) )
& ~ $less(X2,2)
& ! [X3: $int] :
( ~ $less(X3,X2)
| $less(X3,2)
| ~ divides(X3,X0) )
& divides(X2,X0)
& ~ $less(X0,X2) )
& ~ $less(X0,2)
& ! [X1: $int] :
( ~ $less(X1,2)
| ~ divides(X1,X0)
| $less(X1,2) )
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(flattening,[],[f239]) ).
tff(f239,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(X12,1)
& $less(X12,X17)
& divides(X17,X8)
& $less(X6,X17)
& divides(X17,X0)
& $less(X12,X17)
& prime(X17) )
& divides(X16,X8)
& ( $product(X16,X12) = X8 )
& ( div(X8,X12) = X16 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X7))) = X15 ) )
& ( X12 = X14 ) )
& prime(X12)
& ! [X13: $int] :
( ~ divides(X13,X8)
| $less(X13,2)
| ~ $less(X13,X12) )
& ~ $less(X8,X12)
& divides(X12,X8)
& ~ $less(X12,X6) )
& ! [X11: $int] :
( ~ divides(X11,X8)
| ~ $less(X11,X6)
| $less(X11,2) )
& ~ $less(X8,X6)
& ~ $less(X8,2)
& ~ $less(X6,2)
& ~ $less(X8,X6)
& divides(X8,X8)
& ~ $less(X8,2)
& ~ $less(X8,2)
& ~ $less(X0,X8)
& ~ $less(X6,2)
& ! [X10: $int] :
( divides(X10,X8)
| ~ $less(X6,X10)
| ~ prime(X10)
| ~ divides(X10,X0) )
& prime(X6)
& ~ $less(X0,X6)
& divides(X6,X0)
& ~ $less(X8,1)
& ! [X9: $int] :
( ( divides(X9,X0)
& ~ $less(X9,X6) )
| ~ divides(X9,X8)
| $less(X9,2) ) )
& ! [X5: $int] :
( ( divides(X5,div(X0,X2))
& coprime(X2,X5) )
| ~ prime(X5)
| ~ divides(X5,X0)
| ~ $less(X2,X5) )
& divides(div(X0,X2),X0)
& ( $product(div(X0,X2),X2) = X0 )
& ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 ) )
& ! [X3: $int] :
( ~ divides(X3,X0)
| ~ $less(X3,X2)
| $less(X3,2) )
& ~ $less(X2,2)
& ~ $less(X0,X2)
& divides(X2,X0) )
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2)
& ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,2)
| $less(X1,2) )
& ~ $less(X0,2) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
~ ! [X0: $int] :
( ~ $less(X0,2)
=> ( ( ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2)
& ! [X1: $int] :
( ( $less(X1,2)
& ~ $less(X1,2) )
=> ~ divides(X1,X0) ) )
=> ! [X2: $int] :
( ( ! [X3: $int] :
( ( $less(X3,X2)
& ~ $less(X3,2) )
=> ~ divides(X3,X0) )
& ~ $less(X2,2)
& ~ $less(X0,X2)
& divides(X2,X0) )
=> ! [X4: list_int] :
( ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 )
=> ( ( divides(div(X0,X2),X0)
& ( $product(div(X0,X2),X2) = X0 ) )
=> ( ! [X5: $int] :
( ( prime(X5)
& divides(X5,X0)
& $less(X2,X5) )
=> ( divides(X5,div(X0,X2))
& coprime(X2,X5) ) )
=> ! [X8: $int,X6: $int,X7: list_int] :
( ( ~ $less(X0,X8)
& ~ $less(X6,2)
& ! [X10: $int] :
( ( $less(X6,X10)
& prime(X10)
& divides(X10,X0) )
=> divides(X10,X8) )
& prime(X6)
& ~ $less(X0,X6)
& divides(X6,X0)
& ~ $less(X8,1)
& ! [X9: $int] :
( ( divides(X9,X8)
& ~ $less(X9,2) )
=> ( divides(X9,X0)
& ~ $less(X9,X6) ) ) )
=> ( ~ $less(X8,2)
=> ( ( ~ $less(X8,X6)
& divides(X8,X8)
& ~ $less(X8,2) )
=> ( ( ! [X11: $int] :
( ( $less(X11,X6)
& ~ $less(X11,2) )
=> ~ divides(X11,X8) )
& ~ $less(X8,X6)
& ~ $less(X8,2)
& ~ $less(X6,2) )
=> ! [X12: $int] :
( ( ! [X13: $int] :
( ( ~ $less(X13,2)
& $less(X13,X12) )
=> ~ divides(X13,X8) )
& ~ $less(X8,X12)
& divides(X12,X8)
& ~ $less(X12,X6) )
=> ( prime(X12)
=> ! [X14: $int] :
( ( X12 = X14 )
=> ! [X15: list_int] :
( ( tb2t(cons(int,t2tb1(X12),t2tb(X7))) = X15 )
=> ! [X16: $int] :
( ( div(X8,X12) = X16 )
=> ( ( divides(X16,X8)
& ( $product(X16,X12) = X8 ) )
=> ! [X17: $int] :
( ( divides(X17,X0)
& $less(X12,X17)
& prime(X17) )
=> ( $less(X6,X17)
=> ( divides(X17,X8)
=> ( ( ~ $less(X12,1)
& $less(X12,X17) )
=> coprime(X12,X17) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f116]) ).
tff(f116,plain,
~ ! [X9: $int] :
( ~ $less(X9,2)
=> ( ( ~ $less(X9,2)
& ! [X19: $int] :
( ( ~ $less(X19,2)
& $less(X19,2) )
=> ~ divides(X19,X9) )
& ~ $less(X9,2)
& ~ $less(2,2) )
=> ! [X8: $int] :
( ( divides(X8,X9)
& ~ $less(X9,X8)
& ~ $less(X8,2)
& ! [X19: $int] :
( ( $less(X19,X8)
& ~ $less(X19,2) )
=> ~ divides(X19,X9) ) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( ( $product(div(X9,X8),X8) = X9 )
& divides(div(X9,X8),X9) )
=> ( ! [X19: $int] :
( ( divides(X19,X9)
& $less(X8,X19)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X23: $int,X24: list_int,X22: $int] :
( ( ~ $less(X9,X22)
& ~ $less(X23,2)
& ! [X19: $int] :
( ( ~ $less(X19,2)
& divides(X19,X22) )
=> ( divides(X19,X9)
& ~ $less(X19,X23) ) )
& ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& divides(X23,X9)
& ~ $less(X9,X23)
& prime(X23)
& ~ $less(X22,1) )
=> ( ~ $less(X22,2)
=> ( ( ~ $less(X22,2)
& divides(X22,X22)
& ~ $less(X22,X23) )
=> ( ( ! [X19: $int] :
( ( ~ $less(X19,2)
& $less(X19,X23) )
=> ~ divides(X19,X22) )
& ~ $less(X23,2)
& ~ $less(X22,X23)
& ~ $less(X22,2) )
=> ! [X25: $int] :
( ( ~ $less(X25,X23)
& ~ $less(X22,X25)
& ! [X19: $int] :
( ( ~ $less(X19,2)
& $less(X19,X25) )
=> ~ divides(X19,X22) )
& divides(X25,X22) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( divides(X28,X22)
& ( $product(X28,X25) = X22 ) )
=> ! [X19: $int] :
( ( divides(X19,X9)
& $less(X25,X19)
& prime(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)
=> ( ( $lesseq(2,X9)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,2) )
=> ~ divides(X19,X9) )
& $lesseq(2,X9)
& $lesseq(2,2) )
=> ! [X8: $int] :
( ( divides(X8,X9)
& $lesseq(X8,X9)
& $lesseq(2,X8)
& ! [X19: $int] :
( ( $less(X19,X8)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) ) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( ( $product(div(X9,X8),X8) = X9 )
& divides(div(X9,X8),X9) )
=> ( ! [X19: $int] :
( ( divides(X19,X9)
& $less(X8,X19)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X23: $int,X24: list_int,X22: $int] :
( ( $lesseq(X22,X9)
& $lesseq(2,X23)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& divides(X19,X22) )
=> ( divides(X19,X9)
& $lesseq(X23,X19) ) )
& ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& divides(X23,X9)
& $lesseq(X23,X9)
& prime(X23)
& $lesseq(1,X22) )
=> ( $lesseq(2,X22)
=> ( ( $lesseq(2,X22)
& divides(X22,X22)
& $lesseq(X23,X22) )
=> ( ( ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,X23) )
=> ~ divides(X19,X22) )
& $lesseq(2,X23)
& $lesseq(X23,X22)
& $lesseq(2,X22) )
=> ! [X25: $int] :
( ( $lesseq(X23,X25)
& $lesseq(X25,X22)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,X25) )
=> ~ divides(X19,X22) )
& divides(X25,X22) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( divides(X28,X22)
& ( $product(X28,X25) = X22 ) )
=> ! [X19: $int] :
( ( divides(X19,X9)
& $less(X25,X19)
& prime(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)
=> ( ( $lesseq(2,X9)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,2) )
=> ~ divides(X19,X9) )
& $lesseq(2,X9)
& $lesseq(2,2) )
=> ! [X8: $int] :
( ( divides(X8,X9)
& $lesseq(X8,X9)
& $lesseq(2,X8)
& ! [X19: $int] :
( ( $less(X19,X8)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) ) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( ( $product(div(X9,X8),X8) = X9 )
& divides(div(X9,X8),X9) )
=> ( ! [X19: $int] :
( ( divides(X19,X9)
& $less(X8,X19)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X23: $int,X24: list_int,X22: $int] :
( ( $lesseq(X22,X9)
& $lesseq(2,X23)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& divides(X19,X22) )
=> ( divides(X19,X9)
& $lesseq(X23,X19) ) )
& ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& divides(X23,X9)
& $lesseq(X23,X9)
& prime(X23)
& $lesseq(1,X22) )
=> ( $lesseq(2,X22)
=> ( ( $lesseq(2,X22)
& divides(X22,X22)
& $lesseq(X23,X22) )
=> ( ( ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,X23) )
=> ~ divides(X19,X22) )
& $lesseq(2,X23)
& $lesseq(X23,X22)
& $lesseq(2,X22) )
=> ! [X25: $int] :
( ( $lesseq(X23,X25)
& $lesseq(X25,X22)
& ! [X19: $int] :
( ( $lesseq(2,X19)
& $less(X19,X25) )
=> ~ divides(X19,X22) )
& divides(X25,X22) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( divides(X28,X22)
& ( $product(X28,X25) = X22 ) )
=> ! [X19: $int] :
( ( divides(X19,X9)
& $less(X25,X19)
& prime(X19) )
=> ( $less(X23,X19)
=> ( divides(X19,X22)
=> ( ( $less(X25,X19)
& $lesseq(1,X25) )
=> coprime(X25,X19) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_largest_prime_factor) ).
tff(f507,plain,
$less(sK9,1),
inference(unit_resulting_resolution,[],[f358,f356,f357,f317]) ).
tff(f317,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ prime(X0)
| $less(X1,1)
| coprime(X1,X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $int] :
( ( ( ~ $less(X0,2)
& ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) ) )
| ~ prime(X0) )
& ( prime(X0)
| $less(X0,2)
| ( ~ coprime(sK2(X0),X0)
& ~ $less(sK2(X0),1)
& $less(sK2(X0),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f260,f261]) ).
tff(f261,plain,
! [X0: $int] :
( ? [X2: $int] :
( ~ coprime(X2,X0)
& ~ $less(X2,1)
& $less(X2,X0) )
=> ( ~ coprime(sK2(X0),X0)
& ~ $less(sK2(X0),1)
& $less(sK2(X0),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f260,plain,
! [X0: $int] :
( ( ( ~ $less(X0,2)
& ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) ) )
| ~ prime(X0) )
& ( prime(X0)
| $less(X0,2)
| ? [X2: $int] :
( ~ coprime(X2,X0)
& ~ $less(X2,1)
& $less(X2,X0) ) ) ),
inference(rectify,[],[f259]) ).
tff(f259,plain,
! [X0: $int] :
( ( ( ~ $less(X0,2)
& ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) ) )
| ~ prime(X0) )
& ( prime(X0)
| $less(X0,2)
| ? [X1: $int] :
( ~ coprime(X1,X0)
& ~ $less(X1,1)
& $less(X1,X0) ) ) ),
inference(flattening,[],[f258]) ).
tff(f258,plain,
! [X0: $int] :
( ( ( ~ $less(X0,2)
& ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) ) )
| ~ prime(X0) )
& ( prime(X0)
| $less(X0,2)
| ? [X1: $int] :
( ~ coprime(X1,X0)
& ~ $less(X1,1)
& $less(X1,X0) ) ) ),
inference(nnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $int] :
( ( ~ $less(X0,2)
& ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) ) )
<=> prime(X0) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) )
& ~ $less(X0,2) ) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( ( ~ $less(X1,1)
& $less(X1,X0) )
=> coprime(X1,X0) )
& ~ $less(X0,2) ) ),
inference(rectify,[],[f140]) ).
tff(f140,plain,
! [X14: $int] :
( ( ~ $less(X14,2)
& ! [X9: $int] :
( ( $less(X9,X14)
& ~ $less(X9,1) )
=> coprime(X9,X14) ) )
<=> prime(X14) ),
inference(theory_normalization,[],[f88]) ).
tff(f88,axiom,
! [X14: $int] :
( ( $lesseq(2,X14)
& ! [X9: $int] :
( ( $less(X9,X14)
& $lesseq(1,X9) )
=> coprime(X9,X14) ) )
<=> prime(X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_coprime) ).
tff(f357,plain,
~ coprime(sK9,sK13),
inference(cnf_transformation,[],[f275]) ).
tff(f356,plain,
$less(sK9,sK13),
inference(cnf_transformation,[],[f275]) ).
tff(f358,plain,
prime(sK13),
inference(cnf_transformation,[],[f275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW613=2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 20:57:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (707)lrs+10_1:1_ss=axioms:st=5.0:tha=off:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.50 % (707)Instruction limit reached!
% 0.20/0.50 % (707)------------------------------
% 0.20/0.50 % (707)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (699)lrs+10_1:1_canc=force:tha=some:to=lpo:i=35:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/35Mi)
% 0.20/0.51 % (693)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 (2999ds/37Mi)
% 0.20/0.51 % (707)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (707)Termination reason: Unknown
% 0.20/0.51 % (707)Termination phase: Saturation
% 0.20/0.51
% 0.20/0.51 % (707)Memory used [KB]: 5884
% 0.20/0.51 % (707)Time elapsed: 0.099 s
% 0.20/0.51 % (707)Instructions burned: 16 (million)
% 0.20/0.51 % (707)------------------------------
% 0.20/0.51 % (707)------------------------------
% 0.20/0.52 % (703)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52 % (692)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 (2999ds/2Mi)
% 0.20/0.52 % (695)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 (2999ds/32Mi)
% 0.20/0.52 % (692)Instruction limit reached!
% 0.20/0.52 % (692)------------------------------
% 0.20/0.52 % (692)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (692)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (692)Termination reason: Unknown
% 0.20/0.52 % (692)Termination phase: Property scanning
% 0.20/0.52
% 0.20/0.52 % (692)Memory used [KB]: 1023
% 0.20/0.52 % (692)Time elapsed: 0.002 s
% 0.20/0.52 % (692)Instructions burned: 3 (million)
% 0.20/0.52 % (692)------------------------------
% 0.20/0.52 % (692)------------------------------
% 0.20/0.53 % (716)lrs+1_3:1_ep=RSTC:sos=on:urr=on:i=43:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/43Mi)
% 0.20/0.53 % (711)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 0.20/0.53 % (690)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 (2999ds/34Mi)
% 0.20/0.53 % (709)dis+1002_1:5_av=off:nwc=2.0:sos=all:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.54 % (691)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 (2999ds/8Mi)
% 0.20/0.54 % (706)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.54 % (712)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54 % (721)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=41:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/41Mi)
% 0.20/0.54 % (689)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 (2999ds/59848Mi)
% 0.20/0.54 % (694)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.54 % (715)lrs+1002_1:1_br=off:canc=force:drc=off:s2a=on:sos=on:sp=reverse_frequency:urr=on:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/42Mi)
% 0.20/0.54 % (699)Instruction limit reached!
% 0.20/0.54 % (699)------------------------------
% 0.20/0.54 % (699)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (699)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (699)Termination reason: Unknown
% 0.20/0.54 % (699)Termination phase: Saturation
% 0.20/0.54
% 0.20/0.54 % (699)Memory used [KB]: 6268
% 0.20/0.54 % (699)Time elapsed: 0.135 s
% 0.20/0.54 % (699)Instructions burned: 35 (million)
% 0.20/0.54 % (699)------------------------------
% 0.20/0.54 % (699)------------------------------
% 0.20/0.54 % (714)lrs+1_1:10_av=off:drc=off:nwc=2.0:sp=reverse_frequency:thsq=on:thsqc=64:thsql=off:i=47:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/47Mi)
% 0.20/0.54 % (704)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.54 % (704)Instruction limit reached!
% 0.20/0.54 % (704)------------------------------
% 0.20/0.54 % (704)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (704)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (704)Termination reason: Unknown
% 0.20/0.54 % (704)Termination phase: Property scanning
% 0.20/0.54
% 0.20/0.54 % (704)Memory used [KB]: 1023
% 0.20/0.54 % (704)Time elapsed: 0.002 s
% 0.20/0.54 % (704)Instructions burned: 2 (million)
% 0.20/0.54 % (704)------------------------------
% 0.20/0.54 % (704)------------------------------
% 0.20/0.55 % (705)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55 % (698)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55 % (705)Instruction limit reached!
% 0.20/0.55 % (705)------------------------------
% 0.20/0.55 % (705)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (705)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (705)Termination reason: Unknown
% 0.20/0.55 % (705)Termination phase: shuffling
% 0.20/0.55 % (700)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.55
% 0.20/0.55 % (705)Memory used [KB]: 1023
% 0.20/0.55 % (705)Time elapsed: 0.002 s
% 0.20/0.55 % (705)Instructions burned: 2 (million)
% 0.20/0.55 % (705)------------------------------
% 0.20/0.55 % (705)------------------------------
% 0.20/0.55 % (698)Instruction limit reached!
% 0.20/0.55 % (698)------------------------------
% 0.20/0.55 % (698)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (698)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (698)Termination reason: Unknown
% 0.20/0.55 % (698)Termination phase: Property scanning
% 0.20/0.55
% 0.20/0.55 % (698)Memory used [KB]: 1023
% 0.20/0.55 % (698)Time elapsed: 0.003 s
% 0.20/0.55 % (698)Instructions burned: 4 (million)
% 0.20/0.55 % (698)------------------------------
% 0.20/0.55 % (698)------------------------------
% 0.20/0.55 % (701)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55 % (701)Instruction limit reached!
% 0.20/0.55 % (701)------------------------------
% 0.20/0.55 % (701)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (701)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (701)Termination reason: Unknown
% 0.20/0.55 % (701)Termination phase: shuffling
% 0.20/0.55
% 0.20/0.55 % (701)Memory used [KB]: 1023
% 0.20/0.55 % (701)Time elapsed: 0.002 s
% 0.20/0.55 % (701)Instructions burned: 2 (million)
% 0.20/0.55 % (701)------------------------------
% 0.20/0.55 % (701)------------------------------
% 0.20/0.55 % (697)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 0.20/0.55 % (695)First to succeed.
% 0.20/0.55 % (708)lrs+10_1:1_sd=10:sos=all:ss=axioms:st=5.0:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.56 % (695)Refutation found. Thanks to Tanya!
% 0.20/0.56 % SZS status Theorem for theBenchmark
% 0.20/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56 % (695)------------------------------
% 0.20/0.56 % (695)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (695)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (695)Termination reason: Refutation
% 0.20/0.56
% 0.20/0.56 % (695)Memory used [KB]: 6140
% 0.20/0.56 % (695)Time elapsed: 0.109 s
% 0.20/0.56 % (695)Instructions burned: 15 (million)
% 0.20/0.56 % (695)------------------------------
% 0.20/0.56 % (695)------------------------------
% 0.20/0.56 % (688)Success in time 0.195 s
%------------------------------------------------------------------------------