%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW613_2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:40:31 PM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 434 ( 37 equ)
% Maximal formula atoms : 65 ( 17 avg)
% Number of connectives : 566 ( 157 ~; 45 |; 250 &)
% ( 4 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 13 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 468 ( 227 atm; 12 fun; 127 num; 102 var)
% Number of types : 7 ( 5 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 48 ( 45 usr; 21 con; 0-5 aty)
% Number of variables : 120 ( 98 !; 22 ?; 120 :)
% 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 > $int ).
tff(func_def_42,type,
sK4: $int > $int ).
tff(func_def_43,type,
sK5: ( $int * $int * $int ) > $int ).
tff(func_def_44,type,
sK6: $int > $int ).
tff(func_def_45,type,
sK7: $int ).
tff(func_def_46,type,
sK8: $int ).
tff(func_def_47,type,
sK9: list_int ).
tff(func_def_48,type,
sK10: $int ).
tff(func_def_49,type,
sK11: $int ).
tff(func_def_50,type,
sK12: list_int ).
tff(func_def_51,type,
sK13: $int ).
tff(func_def_52,type,
sK14: $int ).
tff(func_def_53,type,
sK15: list_int ).
tff(func_def_54,type,
sK16: $int ).
tff(func_def_55,type,
sK17: $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(f88,axiom,
! [X0: $int] :
( prime(X0)
<=> ( $lesseq(2,X0)
& ! [X1: $int] :
( ( $lesseq(1,X1)
& $less(X1,X0) )
=> coprime(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_coprime) ).
tff(f113,conjecture,
! [X0: $int] :
( $lesseq(2,X0)
=> ( ( $lesseq(2,X0)
& $lesseq(2,2)
& $lesseq(2,X0)
& ! [X1: $int] :
( ( $lesseq(2,X1)
& $less(X1,2) )
=> ~ divides(X1,X0) ) )
=> ! [X2: $int] :
( ( $lesseq(2,X2)
& $lesseq(X2,X0)
& divides(X2,X0)
& ! [X1: $int] :
( ( $lesseq(2,X1)
& $less(X1,X2) )
=> ~ divides(X1,X0) ) )
=> ! [X3: list_int] :
( ( X3 = tb2t(cons(int,t2tb1(X2),nil(int))) )
=> ( ( ( $product(div(X0,X2),X2) = X0 )
& divides(div(X0,X2),X0) )
=> ( ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X2,X1) )
=> ( coprime(X2,X1)
& divides(X1,div(X0,X2)) ) )
=> ! [X4: $int,X5: $int,X6: list_int] :
( ( $lesseq(1,X4)
& $lesseq(X4,X0)
& $lesseq(2,X5)
& $lesseq(X5,X0)
& divides(X5,X0)
& prime(X5)
& ! [X1: $int] :
( ( divides(X1,X4)
& $lesseq(2,X1) )
=> ( $lesseq(X5,X1)
& divides(X1,X0) ) )
& ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X5,X1) )
=> divides(X1,X4) ) )
=> ( $lesseq(2,X4)
=> ( ( divides(X4,X4)
& $lesseq(2,X4)
& $lesseq(X5,X4) )
=> ( ( $lesseq(2,X4)
& $lesseq(2,X5)
& $lesseq(X5,X4)
& ! [X1: $int] :
( ( $lesseq(2,X1)
& $less(X1,X5) )
=> ~ divides(X1,X4) ) )
=> ! [X7: $int] :
( ( $lesseq(X5,X7)
& $lesseq(X7,X4)
& divides(X7,X4)
& ! [X1: $int] :
( ( $lesseq(2,X1)
& $less(X1,X7) )
=> ~ divides(X1,X4) ) )
=> ( prime(X7)
=> ! [X8: $int] :
( ( X8 = X7 )
=> ! [X9: list_int] :
( ( X9 = tb2t(cons(int,t2tb1(X7),t2tb(X6))) )
=> ! [X10: $int] :
( ( X10 = div(X4,X7) )
=> ( ( ( $product(X10,X7) = X4 )
& divides(X10,X4) )
=> ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X7,X1) )
=> ( $less(X5,X1)
=> ( divides(X1,X4)
=> ( ( $lesseq(1,X7)
& $less(X7,X1) )
=> coprime(X7,X1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_largest_prime_factor) ).
tff(f114,negated_conjecture,
~ ! [X0: $int] :
( $lesseq(2,X0)
=> ( ( $lesseq(2,X0)
& $lesseq(2,2)
& $lesseq(2,X0)
& ! [X1: $int] :
( ( $lesseq(2,X1)
& $less(X1,2) )
=> ~ divides(X1,X0) ) )
=> ! [X2: $int] :
( ( $lesseq(2,X2)
& $lesseq(X2,X0)
& divides(X2,X0)
& ! [X1: $int] :
( ( $lesseq(2,X1)
& $less(X1,X2) )
=> ~ divides(X1,X0) ) )
=> ! [X3: list_int] :
( ( X3 = tb2t(cons(int,t2tb1(X2),nil(int))) )
=> ( ( ( $product(div(X0,X2),X2) = X0 )
& divides(div(X0,X2),X0) )
=> ( ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X2,X1) )
=> ( coprime(X2,X1)
& divides(X1,div(X0,X2)) ) )
=> ! [X4: $int,X5: $int,X6: list_int] :
( ( $lesseq(1,X4)
& $lesseq(X4,X0)
& $lesseq(2,X5)
& $lesseq(X5,X0)
& divides(X5,X0)
& prime(X5)
& ! [X1: $int] :
( ( divides(X1,X4)
& $lesseq(2,X1) )
=> ( $lesseq(X5,X1)
& divides(X1,X0) ) )
& ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X5,X1) )
=> divides(X1,X4) ) )
=> ( $lesseq(2,X4)
=> ( ( divides(X4,X4)
& $lesseq(2,X4)
& $lesseq(X5,X4) )
=> ( ( $lesseq(2,X4)
& $lesseq(2,X5)
& $lesseq(X5,X4)
& ! [X1: $int] :
( ( $lesseq(2,X1)
& $less(X1,X5) )
=> ~ divides(X1,X4) ) )
=> ! [X7: $int] :
( ( $lesseq(X5,X7)
& $lesseq(X7,X4)
& divides(X7,X4)
& ! [X1: $int] :
( ( $lesseq(2,X1)
& $less(X1,X7) )
=> ~ divides(X1,X4) ) )
=> ( prime(X7)
=> ! [X8: $int] :
( ( X8 = X7 )
=> ! [X9: list_int] :
( ( X9 = tb2t(cons(int,t2tb1(X7),t2tb(X6))) )
=> ! [X10: $int] :
( ( X10 = div(X4,X7) )
=> ( ( ( $product(X10,X7) = X4 )
& divides(X10,X4) )
=> ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X7,X1) )
=> ( $less(X5,X1)
=> ( divides(X1,X4)
=> ( ( $lesseq(1,X7)
& $less(X7,X1) )
=> coprime(X7,X1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f139,plain,
! [X0: $int] :
( prime(X0)
<=> ( ~ $less(X0,2)
& ! [X1: $int] :
( ( ~ $less(X1,1)
& $less(X1,X0) )
=> coprime(X1,X0) ) ) ),
inference(theory_normalization,[],[f88]) ).
tff(f140,plain,
~ ! [X0: $int] :
( ~ $less(X0,2)
=> ( ( ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ! [X1: $int] :
( ( ~ $less(X1,2)
& $less(X1,2) )
=> ~ divides(X1,X0) ) )
=> ! [X2: $int] :
( ( ~ $less(X2,2)
& ~ $less(X0,X2)
& divides(X2,X0)
& ! [X1: $int] :
( ( ~ $less(X1,2)
& $less(X1,X2) )
=> ~ divides(X1,X0) ) )
=> ! [X3: list_int] :
( ( X3 = tb2t(cons(int,t2tb1(X2),nil(int))) )
=> ( ( ( $product(div(X0,X2),X2) = X0 )
& divides(div(X0,X2),X0) )
=> ( ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X2,X1) )
=> ( coprime(X2,X1)
& divides(X1,div(X0,X2)) ) )
=> ! [X4: $int,X5: $int,X6: list_int] :
( ( ~ $less(X4,1)
& ~ $less(X0,X4)
& ~ $less(X5,2)
& ~ $less(X0,X5)
& divides(X5,X0)
& prime(X5)
& ! [X1: $int] :
( ( divides(X1,X4)
& ~ $less(X1,2) )
=> ( ~ $less(X1,X5)
& divides(X1,X0) ) )
& ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X5,X1) )
=> divides(X1,X4) ) )
=> ( ~ $less(X4,2)
=> ( ( divides(X4,X4)
& ~ $less(X4,2)
& ~ $less(X4,X5) )
=> ( ( ~ $less(X4,2)
& ~ $less(X5,2)
& ~ $less(X4,X5)
& ! [X1: $int] :
( ( ~ $less(X1,2)
& $less(X1,X5) )
=> ~ divides(X1,X4) ) )
=> ! [X7: $int] :
( ( ~ $less(X7,X5)
& ~ $less(X4,X7)
& divides(X7,X4)
& ! [X1: $int] :
( ( ~ $less(X1,2)
& $less(X1,X7) )
=> ~ divides(X1,X4) ) )
=> ( prime(X7)
=> ! [X8: $int] :
( ( X8 = X7 )
=> ! [X9: list_int] :
( ( X9 = tb2t(cons(int,t2tb1(X7),t2tb(X6))) )
=> ! [X10: $int] :
( ( X10 = div(X4,X7) )
=> ( ( ( $product(X10,X7) = X4 )
& divides(X10,X4) )
=> ! [X1: $int] :
( ( prime(X1)
& divides(X1,X0)
& $less(X7,X1) )
=> ( $less(X5,X1)
=> ( divides(X1,X4)
=> ( ( ~ $less(X7,1)
& $less(X7,X1) )
=> coprime(X7,X1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(theory_normalization,[],[f114]) ).
tff(f164,plain,
~ ! [X0: $int] :
( ~ $less(X0,2)
=> ( ( ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ! [X1: $int] :
( ( ~ $less(X1,2)
& $less(X1,2) )
=> ~ divides(X1,X0) ) )
=> ! [X2: $int] :
( ( ~ $less(X2,2)
& ~ $less(X0,X2)
& divides(X2,X0)
& ! [X3: $int] :
( ( ~ $less(X3,2)
& $less(X3,X2) )
=> ~ divides(X3,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] :
( ( prime(X5)
& divides(X5,X0)
& $less(X2,X5) )
=> ( coprime(X2,X5)
& divides(X5,div(X0,X2)) ) )
=> ! [X6: $int,X7: $int,X8: list_int] :
( ( ~ $less(X6,1)
& ~ $less(X0,X6)
& ~ $less(X7,2)
& ~ $less(X0,X7)
& divides(X7,X0)
& prime(X7)
& ! [X9: $int] :
( ( divides(X9,X6)
& ~ $less(X9,2) )
=> ( ~ $less(X9,X7)
& divides(X9,X0) ) )
& ! [X10: $int] :
( ( prime(X10)
& divides(X10,X0)
& $less(X7,X10) )
=> divides(X10,X6) ) )
=> ( ~ $less(X6,2)
=> ( ( divides(X6,X6)
& ~ $less(X6,2)
& ~ $less(X6,X7) )
=> ( ( ~ $less(X6,2)
& ~ $less(X7,2)
& ~ $less(X6,X7)
& ! [X11: $int] :
( ( ~ $less(X11,2)
& $less(X11,X7) )
=> ~ divides(X11,X6) ) )
=> ! [X12: $int] :
( ( ~ $less(X12,X7)
& ~ $less(X6,X12)
& divides(X12,X6)
& ! [X13: $int] :
( ( ~ $less(X13,2)
& $less(X13,X12) )
=> ~ divides(X13,X6) ) )
=> ( prime(X12)
=> ! [X14: $int] :
( ( X12 = X14 )
=> ! [X15: list_int] :
( ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 )
=> ! [X16: $int] :
( ( div(X6,X12) = X16 )
=> ( ( ( $product(X16,X12) = X6 )
& divides(X16,X6) )
=> ! [X17: $int] :
( ( prime(X17)
& divides(X17,X0)
& $less(X12,X17) )
=> ( $less(X7,X17)
=> ( divides(X17,X6)
=> ( ( ~ $less(X12,1)
& $less(X12,X17) )
=> coprime(X12,X17) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f140]) ).
tff(f246,plain,
! [X0: $int] :
( prime(X0)
<=> ( ~ $less(X0,2)
& ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) ) ) ),
inference(ennf_transformation,[],[f139]) ).
tff(f247,plain,
! [X0: $int] :
( prime(X0)
<=> ( ~ $less(X0,2)
& ! [X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0) ) ) ),
inference(flattening,[],[f246]) ).
tff(f258,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(X12,1)
& $less(X12,X17)
& divides(X17,X6)
& $less(X7,X17)
& prime(X17)
& divides(X17,X0)
& $less(X12,X17) )
& ( $product(X16,X12) = X6 )
& divides(X16,X6)
& ( div(X6,X12) = X16 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 ) )
& ( X12 = X14 ) )
& prime(X12)
& ~ $less(X12,X7)
& ~ $less(X6,X12)
& divides(X12,X6)
& ! [X13: $int] :
( ~ divides(X13,X6)
| $less(X13,2)
| ~ $less(X13,X12) ) )
& ~ $less(X6,2)
& ~ $less(X7,2)
& ~ $less(X6,X7)
& ! [X11: $int] :
( ~ divides(X11,X6)
| $less(X11,2)
| ~ $less(X11,X7) )
& divides(X6,X6)
& ~ $less(X6,2)
& ~ $less(X6,X7)
& ~ $less(X6,2)
& ~ $less(X6,1)
& ~ $less(X0,X6)
& ~ $less(X7,2)
& ~ $less(X0,X7)
& divides(X7,X0)
& prime(X7)
& ! [X9: $int] :
( ( ~ $less(X9,X7)
& divides(X9,X0) )
| ~ divides(X9,X6)
| $less(X9,2) )
& ! [X10: $int] :
( divides(X10,X6)
| ~ prime(X10)
| ~ divides(X10,X0)
| ~ $less(X7,X10) ) )
& ! [X5: $int] :
( ( coprime(X2,X5)
& divides(X5,div(X0,X2)) )
| ~ prime(X5)
| ~ divides(X5,X0)
| ~ $less(X2,X5) )
& ( $product(div(X0,X2),X2) = X0 )
& divides(div(X0,X2),X0)
& ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 ) )
& ~ $less(X2,2)
& ~ $less(X0,X2)
& divides(X2,X0)
& ! [X3: $int] :
( ~ divides(X3,X0)
| $less(X3,2)
| ~ $less(X3,X2) ) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ! [X1: $int] :
( ~ divides(X1,X0)
| $less(X1,2)
| ~ $less(X1,2) )
& ~ $less(X0,2) ),
inference(ennf_transformation,[],[f164]) ).
tff(f259,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(X12,1)
& $less(X12,X17)
& divides(X17,X6)
& $less(X7,X17)
& prime(X17)
& divides(X17,X0)
& $less(X12,X17) )
& ( $product(X16,X12) = X6 )
& divides(X16,X6)
& ( div(X6,X12) = X16 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 ) )
& ( X12 = X14 ) )
& prime(X12)
& ~ $less(X12,X7)
& ~ $less(X6,X12)
& divides(X12,X6)
& ! [X13: $int] :
( ~ divides(X13,X6)
| $less(X13,2)
| ~ $less(X13,X12) ) )
& ~ $less(X6,2)
& ~ $less(X7,2)
& ~ $less(X6,X7)
& ! [X11: $int] :
( ~ divides(X11,X6)
| $less(X11,2)
| ~ $less(X11,X7) )
& divides(X6,X6)
& ~ $less(X6,2)
& ~ $less(X6,X7)
& ~ $less(X6,2)
& ~ $less(X6,1)
& ~ $less(X0,X6)
& ~ $less(X7,2)
& ~ $less(X0,X7)
& divides(X7,X0)
& prime(X7)
& ! [X9: $int] :
( ( ~ $less(X9,X7)
& divides(X9,X0) )
| ~ divides(X9,X6)
| $less(X9,2) )
& ! [X10: $int] :
( divides(X10,X6)
| ~ prime(X10)
| ~ divides(X10,X0)
| ~ $less(X7,X10) ) )
& ! [X5: $int] :
( ( coprime(X2,X5)
& divides(X5,div(X0,X2)) )
| ~ prime(X5)
| ~ divides(X5,X0)
| ~ $less(X2,X5) )
& ( $product(div(X0,X2),X2) = X0 )
& divides(div(X0,X2),X0)
& ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 ) )
& ~ $less(X2,2)
& ~ $less(X0,X2)
& divides(X2,X0)
& ! [X3: $int] :
( ~ divides(X3,X0)
| $less(X3,2)
| ~ $less(X3,X2) ) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ! [X1: $int] :
( ~ divides(X1,X0)
| $less(X1,2)
| ~ $less(X1,2) )
& ~ $less(X0,2) ),
inference(flattening,[],[f258]) ).
tff(f371,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,1)
| coprime(X1,X0)
| ~ prime(X0) ),
inference(cnf_transformation,[],[f247]) ).
tff(f399,plain,
prime(sK17),
inference(cnf_transformation,[],[f259]) ).
tff(f402,plain,
$less(sK13,sK17),
inference(cnf_transformation,[],[f259]) ).
tff(f403,plain,
~ $less(sK13,1),
inference(cnf_transformation,[],[f259]) ).
tff(f404,plain,
~ coprime(sK13,sK17),
inference(cnf_transformation,[],[f259]) ).
tff(f409,plain,
sK13 = sK14,
inference(cnf_transformation,[],[f259]) ).
tff(f453,plain,
~ coprime(sK14,sK17),
inference(definition_unfolding,[],[f404,f409]) ).
tff(f454,plain,
~ $less(sK14,1),
inference(definition_unfolding,[],[f403,f409]) ).
tff(f455,plain,
$less(sK14,sK17),
inference(definition_unfolding,[],[f402,f409]) ).
tff(f513,plain,
! [X0: $int,X1: $int] :
( coprime(X1,X0)
| $less(X1,1)
| ~ $less(X1,X0)
| prime(X0) ),
inference(consistent_polarity_flipping,[],[f371]) ).
tff(f536,plain,
~ prime(sK17),
inference(consistent_polarity_flipping,[],[f399]) ).
tff(f1915,plain,
( $less(sK14,1)
| ~ $less(sK14,sK17)
| prime(sK17) ),
inference(resolution,[],[f513,f453]) ).
tff(f1918,plain,
( ~ $less(sK14,sK17)
| prime(sK17) ),
inference(forward_subsumption_resolution,[],[f1915,f454]) ).
tff(f1919,plain,
prime(sK17),
inference(forward_subsumption_resolution,[],[f1918,f455]) ).
tff(f1920,plain,
$false,
inference(forward_subsumption_resolution,[],[f1919,f536]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW613_2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 14:25:30 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.29 % (3882084)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (3882090)% WARNING: option uhcvi not known.
% 0.19/0.29 % (3882090)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=405761226:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (3882089)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3645717845_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (3882094)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3537442722:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (3882091)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3374946273:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (3882092)dis+10_1_sil=32000:sp=arity:random_seed=472458120:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (3882093)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3516787642:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (3882095)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1259638887:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (3882089)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.29 % (3882089)Terminated due to inappropriate strategy.
% 0.19/0.29 % (3882089)------------------------------
% 0.19/0.29 % (3882089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (3882089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (3882089)CaDiCaL version: 2.1.3
% 0.19/0.29 % (3882089)Termination reason: Inappropriate
% 0.19/0.29 % (3882089)Time elapsed: 0.005 s
% 0.19/0.29 % (3882089)Peak memory usage: 11 MB
% 0.19/0.29 % (3882089)Instructions burned: 9 (million)
% 0.19/0.29 % (3882089)------------------------------
% 0.19/0.29 % (3882089)------------------------------
% 0.19/0.29 % (3882090) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3882084-3882090"...
% 0.19/0.29 % (3882090)...printing done.
% 0.19/0.29 % (3882090)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (3882090)------------------------------
% 0.19/0.29 % (3882090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (3882090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (3882090)CaDiCaL version: 2.1.3
% 0.19/0.29 % (3882090)Termination reason: Refutation
% 0.19/0.29 % (3882090)Time elapsed: 0.023 s
% 0.19/0.29 % (3882090)Peak memory usage: 13 MB
% 0.19/0.29 % (3882090)Instructions burned: 59 (million)
% 0.19/0.29 % (3882084)Success in time 0.053 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------