TSTP Solution File: SWW613_2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWW613_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : n011.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 May 1 04:20:18 EDT 2024
% Result : Theorem 0.62s 0.80s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 69
% Syntax : Number of formulae : 97 ( 10 unt; 57 typ; 0 def)
% Number of atoms : 1176 ( 119 equ)
% Maximal formula atoms : 130 ( 29 avg)
% Number of connectives : 1649 ( 513 ~; 200 |; 810 &)
% ( 5 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 14 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 1180 ( 590 atm; 38 fun; 299 num; 253 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 56 ( 33 >; 23 *; 0 +; 0 <<)
% Number of predicates : 11 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 48 ( 45 usr; 21 con; 0-5 aty)
% Number of variables : 300 ( 167 !; 132 ?; 300 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 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 ).
tff(func_def_39,type,
sK1: $int ).
tff(func_def_40,type,
sK2: list_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: ( $int * $int ) > $int ).
tff(func_def_50,type,
sK12: ( $int * $int * $int ) > $int ).
tff(func_def_51,type,
sK13: $int > $int ).
tff(func_def_52,type,
sK14: $int > $int ).
tff(func_def_53,type,
sK15: $int > $int ).
tff(func_def_54,type,
sK16: $int > $int ).
tff(func_def_55,type,
sK17: $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(pred_def_9,type,
sQ18_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f983,plain,
$false,
inference(subsumption_resolution,[],[f982,f374]) ).
tff(f374,plain,
prime(sK10),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
( ~ coprime(sK6,sK10)
& $less(sK6,sK10)
& ~ $less(sK6,1)
& divides(sK10,sK3)
& $less(sK4,sK10)
& $less(sK6,sK10)
& divides(sK10,sK0)
& prime(sK10)
& divides(sK9,sK3)
& ( sK3 = $product(sK9,sK6) )
& ( div(sK3,sK6) = sK9 )
& ( tb2t(cons(int,t2tb1(sK6),t2tb(sK5))) = sK8 )
& ( sK6 = sK7 )
& prime(sK6)
& ! [X11: $int] :
( ~ divides(X11,sK3)
| ~ $less(X11,sK6)
| $less(X11,2) )
& divides(sK6,sK3)
& ~ $less(sK3,sK6)
& ~ $less(sK6,sK4)
& ! [X12: $int] :
( ~ divides(X12,sK3)
| ~ $less(X12,sK4)
| $less(X12,2) )
& ~ $less(sK3,sK4)
& ~ $less(sK4,2)
& ~ $less(sK3,2)
& ~ $less(sK3,sK4)
& ~ $less(sK3,2)
& divides(sK3,sK3)
& ~ $less(sK3,2)
& ! [X13: $int] :
( divides(X13,sK3)
| ~ $less(sK4,X13)
| ~ divides(X13,sK0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK0)
& ~ $less(X14,sK4) )
| $less(X14,2)
| ~ divides(X14,sK3) )
& prime(sK4)
& divides(sK4,sK0)
& ~ $less(sK0,sK4)
& ~ $less(sK4,2)
& ~ $less(sK0,sK3)
& ~ $less(sK3,1)
& ! [X15: $int] :
( ( divides(X15,div(sK0,sK1))
& coprime(sK1,X15) )
| ~ $less(sK1,X15)
| ~ divides(X15,sK0)
| ~ prime(X15) )
& divides(div(sK0,sK1),sK0)
& ( sK0 = $product(div(sK0,sK1),sK1) )
& ( tb2t(cons(int,t2tb1(sK1),nil(int))) = sK2 )
& ! [X16: $int] :
( ~ divides(X16,sK0)
| ~ $less(X16,sK1)
| $less(X16,2) )
& divides(sK1,sK0)
& ~ $less(sK0,sK1)
& ~ $less(sK1,2)
& ! [X17: $int] :
( ~ divides(X17,sK0)
| ~ $less(X17,2)
| $less(X17,2) )
& ~ $less(sK0,2)
& ~ $less(2,2)
& ~ $less(sK0,2)
& ~ $less(sK0,2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f293,f302,f301,f300,f299,f298,f297,f296,f295,f294]) ).
tff(f294,plain,
( ? [X0: $int] :
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X3: $int,X4: $int,X5: list_int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,X0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,X0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,X0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,X0)
& ~ $less(X0,X4)
& ~ $less(X4,2)
& ~ $less(X0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(X0,X1))
& coprime(X1,X15) )
| ~ $less(X1,X15)
| ~ divides(X15,X0)
| ~ prime(X15) )
& divides(div(X0,X1),X0)
& ( $product(div(X0,X1),X1) = X0 )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,X0)
| ~ $less(X16,X1)
| $less(X16,2) )
& divides(X1,X0)
& ~ $less(X0,X1)
& ~ $less(X1,2) )
& ! [X17: $int] :
( ~ divides(X17,X0)
| ~ $less(X17,2)
| $less(X17,2) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2) )
=> ( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK0)
& ~ $less(sK0,X4)
& ~ $less(X4,2)
& ~ $less(sK0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK0,X1))
& coprime(X1,X15) )
| ~ $less(X1,X15)
| ~ divides(X15,sK0)
| ~ prime(X15) )
& divides(div(sK0,X1),sK0)
& ( sK0 = $product(div(sK0,X1),X1) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,sK0)
| ~ $less(X16,X1)
| $less(X16,2) )
& divides(X1,sK0)
& ~ $less(sK0,X1)
& ~ $less(X1,2) )
& ! [X17: $int] :
( ~ divides(X17,sK0)
| ~ $less(X17,2)
| $less(X17,2) )
& ~ $less(sK0,2)
& ~ $less(2,2)
& ~ $less(sK0,2)
& ~ $less(sK0,2) ) ),
introduced(choice_axiom,[]) ).
tff(f295,plain,
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK0)
& ~ $less(sK0,X4)
& ~ $less(X4,2)
& ~ $less(sK0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK0,X1))
& coprime(X1,X15) )
| ~ $less(X1,X15)
| ~ divides(X15,sK0)
| ~ prime(X15) )
& divides(div(sK0,X1),sK0)
& ( sK0 = $product(div(sK0,X1),X1) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,sK0)
| ~ $less(X16,X1)
| $less(X16,2) )
& divides(X1,sK0)
& ~ $less(sK0,X1)
& ~ $less(X1,2) )
=> ( ? [X2: list_int] :
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK0)
& ~ $less(sK0,X4)
& ~ $less(X4,2)
& ~ $less(sK0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK0,sK1))
& coprime(sK1,X15) )
| ~ $less(sK1,X15)
| ~ divides(X15,sK0)
| ~ prime(X15) )
& divides(div(sK0,sK1),sK0)
& ( sK0 = $product(div(sK0,sK1),sK1) )
& ( tb2t(cons(int,t2tb1(sK1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,sK0)
| ~ $less(X16,sK1)
| $less(X16,2) )
& divides(sK1,sK0)
& ~ $less(sK0,sK1)
& ~ $less(sK1,2) ) ),
introduced(choice_axiom,[]) ).
tff(f296,plain,
( ? [X2: list_int] :
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK0)
& ~ $less(sK0,X4)
& ~ $less(X4,2)
& ~ $less(sK0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK0,sK1))
& coprime(sK1,X15) )
| ~ $less(sK1,X15)
| ~ divides(X15,sK0)
| ~ prime(X15) )
& divides(div(sK0,sK1),sK0)
& ( sK0 = $product(div(sK0,sK1),sK1) )
& ( tb2t(cons(int,t2tb1(sK1),nil(int))) = X2 ) )
=> ( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK0)
& ~ $less(sK0,X4)
& ~ $less(X4,2)
& ~ $less(sK0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK0,sK1))
& coprime(sK1,X15) )
| ~ $less(sK1,X15)
| ~ divides(X15,sK0)
| ~ prime(X15) )
& divides(div(sK0,sK1),sK0)
& ( sK0 = $product(div(sK0,sK1),sK1) )
& ( tb2t(cons(int,t2tb1(sK1),nil(int))) = sK2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f297,plain,
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK0)
& ~ $less(sK0,X4)
& ~ $less(X4,2)
& ~ $less(sK0,X3)
& ~ $less(X3,1) )
=> ( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(X6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,sK3)
& ( $product(X9,X6) = sK3 )
& ( div(sK3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(sK5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,sK3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,sK3)
& ~ $less(sK3,X6)
& ~ $less(X6,sK4) )
& ! [X12: $int] :
( ~ divides(X12,sK3)
| ~ $less(X12,sK4)
| $less(X12,2) )
& ~ $less(sK3,sK4)
& ~ $less(sK4,2)
& ~ $less(sK3,2)
& ~ $less(sK3,sK4)
& ~ $less(sK3,2)
& divides(sK3,sK3)
& ~ $less(sK3,2)
& ! [X13: $int] :
( divides(X13,sK3)
| ~ $less(sK4,X13)
| ~ divides(X13,sK0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK0)
& ~ $less(X14,sK4) )
| $less(X14,2)
| ~ divides(X14,sK3) )
& prime(sK4)
& divides(sK4,sK0)
& ~ $less(sK0,sK4)
& ~ $less(sK4,2)
& ~ $less(sK0,sK3)
& ~ $less(sK3,1) ) ),
introduced(choice_axiom,[]) ).
tff(f298,plain,
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(X6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,sK3)
& ( $product(X9,X6) = sK3 )
& ( div(sK3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(sK5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,sK3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,sK3)
& ~ $less(sK3,X6)
& ~ $less(X6,sK4) )
=> ( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK6,X10)
& $less(sK6,X10)
& ~ $less(sK6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(sK6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,sK3)
& ( sK3 = $product(X9,sK6) )
& ( div(sK3,sK6) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK6),t2tb(sK5))) = X8 ) )
& ( sK6 = X7 ) )
& prime(sK6)
& ! [X11: $int] :
( ~ divides(X11,sK3)
| ~ $less(X11,sK6)
| $less(X11,2) )
& divides(sK6,sK3)
& ~ $less(sK3,sK6)
& ~ $less(sK6,sK4) ) ),
introduced(choice_axiom,[]) ).
tff(f299,plain,
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK6,X10)
& $less(sK6,X10)
& ~ $less(sK6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(sK6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,sK3)
& ( sK3 = $product(X9,sK6) )
& ( div(sK3,sK6) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK6),t2tb(sK5))) = X8 ) )
& ( sK6 = X7 ) )
=> ( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK6,X10)
& $less(sK6,X10)
& ~ $less(sK6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(sK6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,sK3)
& ( sK3 = $product(X9,sK6) )
& ( div(sK3,sK6) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK6),t2tb(sK5))) = X8 ) )
& ( sK6 = sK7 ) ) ),
introduced(choice_axiom,[]) ).
tff(f300,plain,
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK6,X10)
& $less(sK6,X10)
& ~ $less(sK6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(sK6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,sK3)
& ( sK3 = $product(X9,sK6) )
& ( div(sK3,sK6) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK6),t2tb(sK5))) = X8 ) )
=> ( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK6,X10)
& $less(sK6,X10)
& ~ $less(sK6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(sK6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,sK3)
& ( sK3 = $product(X9,sK6) )
& ( div(sK3,sK6) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK6),t2tb(sK5))) = sK8 ) ) ),
introduced(choice_axiom,[]) ).
tff(f301,plain,
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK6,X10)
& $less(sK6,X10)
& ~ $less(sK6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(sK6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(X9,sK3)
& ( sK3 = $product(X9,sK6) )
& ( div(sK3,sK6) = X9 ) )
=> ( ? [X10: $int] :
( ~ coprime(sK6,X10)
& $less(sK6,X10)
& ~ $less(sK6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(sK6,X10)
& divides(X10,sK0)
& prime(X10) )
& divides(sK9,sK3)
& ( sK3 = $product(sK9,sK6) )
& ( div(sK3,sK6) = sK9 ) ) ),
introduced(choice_axiom,[]) ).
tff(f302,plain,
( ? [X10: $int] :
( ~ coprime(sK6,X10)
& $less(sK6,X10)
& ~ $less(sK6,1)
& divides(X10,sK3)
& $less(sK4,X10)
& $less(sK6,X10)
& divides(X10,sK0)
& prime(X10) )
=> ( ~ coprime(sK6,sK10)
& $less(sK6,sK10)
& ~ $less(sK6,1)
& divides(sK10,sK3)
& $less(sK4,sK10)
& $less(sK6,sK10)
& divides(sK10,sK0)
& prime(sK10) ) ),
introduced(choice_axiom,[]) ).
tff(f293,plain,
? [X0: $int] :
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X3: $int,X4: $int,X5: list_int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,X0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,X0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,X0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,X0)
& ~ $less(X0,X4)
& ~ $less(X4,2)
& ~ $less(X0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(X0,X1))
& coprime(X1,X15) )
| ~ $less(X1,X15)
| ~ divides(X15,X0)
| ~ prime(X15) )
& divides(div(X0,X1),X0)
& ( $product(div(X0,X1),X1) = X0 )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,X0)
| ~ $less(X16,X1)
| $less(X16,2) )
& divides(X1,X0)
& ~ $less(X0,X1)
& ~ $less(X1,2) )
& ! [X17: $int] :
( ~ divides(X17,X0)
| ~ $less(X17,2)
| $less(X17,2) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(rectify,[],[f231]) ).
tff(f231,plain,
? [X0: $int] :
( ? [X2: $int] :
( ? [X4: list_int] :
( ? [X6: $int,X7: $int,X8: 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(X7,X17)
& $less(X12,X17)
& divides(X17,X0)
& prime(X17) )
& divides(X16,X6)
& ( $product(X16,X12) = X6 )
& ( div(X6,X12) = X16 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 ) )
& ( X12 = X14 ) )
& prime(X12)
& ! [X13: $int] :
( ~ divides(X13,X6)
| ~ $less(X13,X12)
| $less(X13,2) )
& divides(X12,X6)
& ~ $less(X6,X12)
& ~ $less(X12,X7) )
& ! [X11: $int] :
( ~ divides(X11,X6)
| ~ $less(X11,X7)
| $less(X11,2) )
& ~ $less(X6,X7)
& ~ $less(X7,2)
& ~ $less(X6,2)
& ~ $less(X6,X7)
& ~ $less(X6,2)
& divides(X6,X6)
& ~ $less(X6,2)
& ! [X9: $int] :
( divides(X9,X6)
| ~ $less(X7,X9)
| ~ divides(X9,X0)
| ~ prime(X9) )
& ! [X10: $int] :
( ( divides(X10,X0)
& ~ $less(X10,X7) )
| $less(X10,2)
| ~ divides(X10,X6) )
& prime(X7)
& divides(X7,X0)
& ~ $less(X0,X7)
& ~ $less(X7,2)
& ~ $less(X0,X6)
& ~ $less(X6,1) )
& ! [X5: $int] :
( ( divides(X5,div(X0,X2))
& coprime(X2,X5) )
| ~ $less(X2,X5)
| ~ divides(X5,X0)
| ~ prime(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) )
& divides(X2,X0)
& ~ $less(X0,X2)
& ~ $less(X2,2) )
& ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,2)
| $less(X1,2) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(flattening,[],[f230]) ).
tff(f230,plain,
? [X0: $int] :
( ? [X2: $int] :
( ? [X4: list_int] :
( ? [X6: $int,X7: $int,X8: 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(X7,X17)
& $less(X12,X17)
& divides(X17,X0)
& prime(X17) )
& divides(X16,X6)
& ( $product(X16,X12) = X6 )
& ( div(X6,X12) = X16 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 ) )
& ( X12 = X14 ) )
& prime(X12)
& ! [X13: $int] :
( ~ divides(X13,X6)
| ~ $less(X13,X12)
| $less(X13,2) )
& divides(X12,X6)
& ~ $less(X6,X12)
& ~ $less(X12,X7) )
& ! [X11: $int] :
( ~ divides(X11,X6)
| ~ $less(X11,X7)
| $less(X11,2) )
& ~ $less(X6,X7)
& ~ $less(X7,2)
& ~ $less(X6,2)
& ~ $less(X6,X7)
& ~ $less(X6,2)
& divides(X6,X6)
& ~ $less(X6,2)
& ! [X9: $int] :
( divides(X9,X6)
| ~ $less(X7,X9)
| ~ divides(X9,X0)
| ~ prime(X9) )
& ! [X10: $int] :
( ( divides(X10,X0)
& ~ $less(X10,X7) )
| $less(X10,2)
| ~ divides(X10,X6) )
& prime(X7)
& divides(X7,X0)
& ~ $less(X0,X7)
& ~ $less(X7,2)
& ~ $less(X0,X6)
& ~ $less(X6,1) )
& ! [X5: $int] :
( ( divides(X5,div(X0,X2))
& coprime(X2,X5) )
| ~ $less(X2,X5)
| ~ divides(X5,X0)
| ~ prime(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) )
& divides(X2,X0)
& ~ $less(X0,X2)
& ~ $less(X2,2) )
& ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,2)
| $less(X1,2) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
~ ! [X0: $int] :
( ~ $less(X0,2)
=> ( ( ! [X1: $int] :
( ( $less(X1,2)
& ~ $less(X1,2) )
=> ~ divides(X1,X0) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2) )
=> ! [X2: $int] :
( ( ! [X3: $int] :
( ( $less(X3,X2)
& ~ $less(X3,2) )
=> ~ divides(X3,X0) )
& divides(X2,X0)
& ~ $less(X0,X2)
& ~ $less(X2,2) )
=> ! [X4: list_int] :
( ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 )
=> ( ( divides(div(X0,X2),X0)
& ( $product(div(X0,X2),X2) = X0 ) )
=> ( ! [X5: $int] :
( ( $less(X2,X5)
& divides(X5,X0)
& prime(X5) )
=> ( divides(X5,div(X0,X2))
& coprime(X2,X5) ) )
=> ! [X6: $int,X7: $int,X8: list_int] :
( ( ! [X9: $int] :
( ( $less(X7,X9)
& divides(X9,X0)
& prime(X9) )
=> divides(X9,X6) )
& ! [X10: $int] :
( ( ~ $less(X10,2)
& divides(X10,X6) )
=> ( divides(X10,X0)
& ~ $less(X10,X7) ) )
& prime(X7)
& divides(X7,X0)
& ~ $less(X0,X7)
& ~ $less(X7,2)
& ~ $less(X0,X6)
& ~ $less(X6,1) )
=> ( ~ $less(X6,2)
=> ( ( ~ $less(X6,X7)
& ~ $less(X6,2)
& divides(X6,X6) )
=> ( ( ! [X11: $int] :
( ( $less(X11,X7)
& ~ $less(X11,2) )
=> ~ divides(X11,X6) )
& ~ $less(X6,X7)
& ~ $less(X7,2)
& ~ $less(X6,2) )
=> ! [X12: $int] :
( ( ! [X13: $int] :
( ( $less(X13,X12)
& ~ $less(X13,2) )
=> ~ divides(X13,X6) )
& divides(X12,X6)
& ~ $less(X6,X12)
& ~ $less(X12,X7) )
=> ( prime(X12)
=> ! [X14: $int] :
( ( X12 = X14 )
=> ! [X15: list_int] :
( ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 )
=> ! [X16: $int] :
( ( div(X6,X12) = X16 )
=> ( ( divides(X16,X6)
& ( $product(X16,X12) = X6 ) )
=> ! [X17: $int] :
( ( $less(X12,X17)
& divides(X17,X0)
& prime(X17) )
=> ( $less(X7,X17)
=> ( divides(X17,X6)
=> ( ( $less(X12,X17)
& ~ $less(X12,1) )
=> coprime(X12,X17) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f140]) ).
tff(f140,plain,
~ ! [X9: $int] :
( ~ $less(X9,2)
=> ( ( ! [X19: $int] :
( ( $less(X19,2)
& ~ $less(X19,2) )
=> ~ divides(X19,X9) )
& ~ $less(X9,2)
& ~ $less(2,2)
& ~ $less(X9,2) )
=> ! [X8: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X8)
& ~ $less(X19,2) )
=> ~ divides(X19,X9) )
& divides(X8,X9)
& ~ $less(X9,X8)
& ~ $less(X8,2) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( divides(div(X9,X8),X9)
& ( $product(div(X9,X8),X8) = X9 ) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& divides(X19,X9)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X23: $int,X24: list_int] :
( ( ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& ! [X19: $int] :
( ( ~ $less(X19,2)
& divides(X19,X22) )
=> ( divides(X19,X9)
& ~ $less(X19,X23) ) )
& prime(X23)
& divides(X23,X9)
& ~ $less(X9,X23)
& ~ $less(X23,2)
& ~ $less(X9,X22)
& ~ $less(X22,1) )
=> ( ~ $less(X22,2)
=> ( ( ~ $less(X22,X23)
& ~ $less(X22,2)
& divides(X22,X22) )
=> ( ( ! [X19: $int] :
( ( $less(X19,X23)
& ~ $less(X19,2) )
=> ~ divides(X19,X22) )
& ~ $less(X22,X23)
& ~ $less(X23,2)
& ~ $less(X22,2) )
=> ! [X25: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X25)
& ~ $less(X19,2) )
=> ~ divides(X19,X22) )
& divides(X25,X22)
& ~ $less(X22,X25)
& ~ $less(X25,X23) )
=> ( 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] :
( ( $less(X25,X19)
& divides(X19,X9)
& 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)
=> ( ( ! [X19: $int] :
( ( $less(X19,2)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& $lesseq(2,X9)
& $lesseq(2,2)
& $lesseq(2,X9) )
=> ! [X8: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X8)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& divides(X8,X9)
& $lesseq(X8,X9)
& $lesseq(2,X8) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( divides(div(X9,X8),X9)
& ( $product(div(X9,X8),X8) = X9 ) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& divides(X19,X9)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X23: $int,X24: list_int] :
( ( ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& ! [X19: $int] :
( ( $lesseq(2,X19)
& divides(X19,X22) )
=> ( divides(X19,X9)
& $lesseq(X23,X19) ) )
& prime(X23)
& divides(X23,X9)
& $lesseq(X23,X9)
& $lesseq(2,X23)
& $lesseq(X22,X9)
& $lesseq(1,X22) )
=> ( $lesseq(2,X22)
=> ( ( $lesseq(X23,X22)
& $lesseq(2,X22)
& divides(X22,X22) )
=> ( ( ! [X19: $int] :
( ( $less(X19,X23)
& $lesseq(2,X19) )
=> ~ divides(X19,X22) )
& $lesseq(X23,X22)
& $lesseq(2,X23)
& $lesseq(2,X22) )
=> ! [X25: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X25)
& $lesseq(2,X19) )
=> ~ divides(X19,X22) )
& divides(X25,X22)
& $lesseq(X25,X22)
& $lesseq(X23,X25) )
=> ( 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] :
( ( $less(X25,X19)
& divides(X19,X9)
& 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)
=> ( ( ! [X19: $int] :
( ( $less(X19,2)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& $lesseq(2,X9)
& $lesseq(2,2)
& $lesseq(2,X9) )
=> ! [X8: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X8)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& divides(X8,X9)
& $lesseq(X8,X9)
& $lesseq(2,X8) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( divides(div(X9,X8),X9)
& ( $product(div(X9,X8),X8) = X9 ) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& divides(X19,X9)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X23: $int,X24: list_int] :
( ( ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& ! [X19: $int] :
( ( $lesseq(2,X19)
& divides(X19,X22) )
=> ( divides(X19,X9)
& $lesseq(X23,X19) ) )
& prime(X23)
& divides(X23,X9)
& $lesseq(X23,X9)
& $lesseq(2,X23)
& $lesseq(X22,X9)
& $lesseq(1,X22) )
=> ( $lesseq(2,X22)
=> ( ( $lesseq(X23,X22)
& $lesseq(2,X22)
& divides(X22,X22) )
=> ( ( ! [X19: $int] :
( ( $less(X19,X23)
& $lesseq(2,X19) )
=> ~ divides(X19,X22) )
& $lesseq(X23,X22)
& $lesseq(2,X23)
& $lesseq(2,X22) )
=> ! [X25: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X25)
& $lesseq(2,X19) )
=> ~ divides(X19,X22) )
& divides(X25,X22)
& $lesseq(X25,X22)
& $lesseq(X23,X25) )
=> ( 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] :
( ( $less(X25,X19)
& divides(X19,X9)
& prime(X19) )
=> ( $less(X23,X19)
=> ( divides(X19,X22)
=> ( ( $less(X25,X19)
& $lesseq(1,X25) )
=> coprime(X25,X19) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwn0Ci3Exn/Vampire---4.8_3542',wP_parameter_largest_prime_factor) ).
tff(f982,plain,
~ prime(sK10),
inference(subsumption_resolution,[],[f981,f478]) ).
tff(f478,plain,
~ $less(sK7,1),
inference(definition_unfolding,[],[f379,f369]) ).
tff(f369,plain,
sK6 = sK7,
inference(cnf_transformation,[],[f303]) ).
tff(f379,plain,
~ $less(sK6,1),
inference(cnf_transformation,[],[f303]) ).
tff(f981,plain,
( $less(sK7,1)
| ~ prime(sK10) ),
inference(subsumption_resolution,[],[f979,f477]) ).
tff(f477,plain,
$less(sK7,sK10),
inference(definition_unfolding,[],[f380,f369]) ).
tff(f380,plain,
$less(sK6,sK10),
inference(cnf_transformation,[],[f303]) ).
tff(f979,plain,
( ~ $less(sK7,sK10)
| $less(sK7,1)
| ~ prime(sK10) ),
inference(resolution,[],[f417,f476]) ).
tff(f476,plain,
~ coprime(sK7,sK10),
inference(definition_unfolding,[],[f381,f369]) ).
tff(f381,plain,
~ coprime(sK6,sK10),
inference(cnf_transformation,[],[f303]) ).
tff(f417,plain,
! [X2: $int,X0: $int] :
( coprime(X2,X0)
| ~ $less(X2,X0)
| $less(X2,1)
| ~ prime(X0) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $int] :
( ( prime(X0)
| ( ~ coprime(sK13(X0),X0)
& $less(sK13(X0),X0)
& ~ $less(sK13(X0),1) )
| $less(X0,2) )
& ( ( ! [X2: $int] :
( coprime(X2,X0)
| ~ $less(X2,X0)
| $less(X2,1) )
& ~ $less(X0,2) )
| ~ prime(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f312,f313]) ).
tff(f313,plain,
! [X0: $int] :
( ? [X1: $int] :
( ~ coprime(X1,X0)
& $less(X1,X0)
& ~ $less(X1,1) )
=> ( ~ coprime(sK13(X0),X0)
& $less(sK13(X0),X0)
& ~ $less(sK13(X0),1) ) ),
introduced(choice_axiom,[]) ).
tff(f312,plain,
! [X0: $int] :
( ( prime(X0)
| ? [X1: $int] :
( ~ coprime(X1,X0)
& $less(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X2: $int] :
( coprime(X2,X0)
| ~ $less(X2,X0)
| $less(X2,1) )
& ~ $less(X0,2) )
| ~ prime(X0) ) ),
inference(rectify,[],[f311]) ).
tff(f311,plain,
! [X0: $int] :
( ( prime(X0)
| ? [X1: $int] :
( ~ coprime(X1,X0)
& $less(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) )
| ~ prime(X0) ) ),
inference(flattening,[],[f310]) ).
tff(f310,plain,
! [X0: $int] :
( ( prime(X0)
| ? [X1: $int] :
( ~ coprime(X1,X0)
& $less(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) )
| ~ prime(X0) ) ),
inference(nnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) ) ),
inference(flattening,[],[f261]) ).
tff(f261,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) ) ),
inference(ennf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( ( $less(X1,X0)
& ~ $less(X1,1) )
=> coprime(X1,X0) )
& ~ $less(X0,2) ) ),
inference(rectify,[],[f139]) ).
tff(f139,plain,
! [X14: $int] :
( prime(X14)
<=> ( ! [X9: $int] :
( ( $less(X9,X14)
& ~ $less(X9,1) )
=> coprime(X9,X14) )
& ~ $less(X14,2) ) ),
inference(theory_normalization,[],[f88]) ).
tff(f88,axiom,
! [X14: $int] :
( prime(X14)
<=> ( ! [X9: $int] :
( ( $less(X9,X14)
& $lesseq(1,X9) )
=> coprime(X9,X14) )
& $lesseq(2,X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwn0Ci3Exn/Vampire---4.8_3542',prime_coprime) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWW613_2 : TPTP v8.1.2. Released v6.1.0.
% 0.13/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Apr 30 18:03:02 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 This is a TF0_THM_EQU_ARI problem
% 0.16/0.36 Running 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 300 /export/starexec/sandbox2/tmp/tmp.uwn0Ci3Exn/Vampire---4.8_3542
% 0.62/0.78 % (3738)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.62/0.78 % (3744)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.62/0.78 % (3740)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.78 % (3739)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.62/0.78 % (3741)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.62/0.78 % (3742)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.62/0.78 % (3743)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.62/0.78 % (3745)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.62/0.80 % (3738)First to succeed.
% 0.62/0.80 % (3743)Also succeeded, but the first one will report.
% 0.62/0.80 % (3738)Refutation found. Thanks to Tanya!
% 0.62/0.80 % SZS status Theorem for Vampire---4
% 0.62/0.80 % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.80 % (3738)------------------------------
% 0.62/0.80 % (3738)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.80 % (3738)Termination reason: Refutation
% 0.62/0.80
% 0.62/0.80 % (3738)Memory used [KB]: 1430
% 0.62/0.80 % (3738)Time elapsed: 0.020 s
% 0.62/0.80 % (3738)Instructions burned: 32 (million)
% 0.62/0.80 % (3738)------------------------------
% 0.62/0.80 % (3738)------------------------------
% 0.62/0.80 % (3710)Success in time 0.422 s
% 0.62/0.80 % Vampire---4.8 exiting
%------------------------------------------------------------------------------