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
%------------------------------------------------------------------------------