TSTP Solution File: NUM942_5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM942_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : 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 : Sun May 5 08:16:52 EDT 2024
% Result : Theorem 0.56s 0.74s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of formulae : 49 ( 17 unt; 25 typ; 0 def)
% Number of atoms : 31 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 4 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 13 ( 9 >; 4 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 27 ( 15 !; 0 ?; 27 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
min: int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
legendre: ( int * int ) > int ).
tff(func_def_9,type,
fFalse: bool ).
tff(func_def_10,type,
fTrue: bool ).
tff(func_def_11,type,
m: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zprime: int > $o ).
tff(pred_def_9,type,
pp: bool > $o ).
tff(pred_def_10,type,
sQ0_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f295,plain,
$false,
inference(subsumption_resolution,[],[f294,f234]) ).
tff(f234,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))),
inference(definition_unfolding,[],[f204,f159,f159,f158]) ).
tff(f158,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f115]) ).
tff(f115,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X5: int] : ( bit1(X5) = plus_plus(int,plus_plus(int,one_one(int),X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.6UCqjcxLg1/Vampire---4.8_31014',fact_48_Bit1__def) ).
tff(f159,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X5: int] : ( bit0(X5) = plus_plus(int,X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.6UCqjcxLg1/Vampire---4.8_31014',fact_39_Bit0__def) ).
tff(f204,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox2/tmp/tmp.6UCqjcxLg1/Vampire---4.8_31014',fact_0_p) ).
tff(f294,plain,
~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))),
inference(resolution,[],[f247,f292]) ).
tff(f292,plain,
! [X0: int] :
( sQ0_eqProxy(int,one_one(int),legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))))
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(equality_proxy_replacement,[],[f233,f246]) ).
tff(f246,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ0_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ0_eqProxy])]) ).
tff(f233,plain,
! [X0: int] :
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(definition_unfolding,[],[f203,f159,f159,f158,f159,f159,f158]) ).
tff(f203,plain,
! [X0: int] :
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) ),
inference(cnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: int] :
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: int] :
( zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int)))
=> ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X3: int] :
( zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X3),one_one(int)))
=> ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X3),one_one(int))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6UCqjcxLg1/Vampire---4.8_31014',fact_4_Legendre__1mod4) ).
tff(f247,plain,
~ sQ0_eqProxy(int,one_one(int),legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)))),
inference(equality_proxy_replacement,[],[f206,f246]) ).
tff(f206,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))),
inference(definition_unfolding,[],[f156,f159,f159,f158]) ).
tff(f156,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f114]) ).
tff(f114,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(flattening,[],[f113]) ).
tff(f113,negated_conjecture,
( ~ one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
inference(negated_conjecture,[],[f112]) ).
tff(f112,conjecture,
one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox2/tmp/tmp.6UCqjcxLg1/Vampire---4.8_31014',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM942_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 15:19:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TF1_THM_EQU_NAR problem
% 0.14/0.35 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.6UCqjcxLg1/Vampire---4.8_31014
% 0.56/0.74 % (31129)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 (2996ds/56Mi)
% 0.56/0.74 % (31122)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 (2996ds/34Mi)
% 0.56/0.74 % (31124)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.56/0.74 % (31126)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 (2996ds/34Mi)
% 0.56/0.74 % (31125)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.56/0.74 % (31127)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.56/0.74 % (31123)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 (2996ds/51Mi)
% 0.56/0.74 % (31129)First to succeed.
% 0.56/0.74 % (31129)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31121"
% 0.56/0.74 % (31129)Refutation found. Thanks to Tanya!
% 0.56/0.74 % SZS status Theorem for Vampire---4
% 0.56/0.74 % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.74 % (31129)------------------------------
% 0.56/0.74 % (31129)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (31129)Termination reason: Refutation
% 0.56/0.74
% 0.56/0.74 % (31129)Memory used [KB]: 1095
% 0.56/0.74 % (31129)Time elapsed: 0.003 s
% 0.56/0.74 % (31129)Instructions burned: 7 (million)
% 0.56/0.74 % (31121)Success in time 0.376 s
% 0.56/0.74 % Vampire---4.8 exiting
%------------------------------------------------------------------------------