TSTP Solution File: NUM945_5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM945_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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n005.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 08:16:53 EDT 2024

% Result   : Theorem 0.57s 0.75s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   70 (  16 unt;  32 typ;   0 def)
%            Number of atoms       :   61 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   43 (  20   ~;  14   |;   0   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   25 (  14   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  17 usr;   5 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-3 aty)
%            Number of variables   :   48 (  29   !;   5   ?;  48   :)
%                                         (  14  !>;   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(type_def_8,type,
    real: $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,
    power_power: 
      !>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).

tff(func_def_9,type,
    legendre: ( int * int ) > int ).

tff(func_def_10,type,
    fFalse: bool ).

tff(func_def_11,type,
    fTrue: bool ).

tff(func_def_12,type,
    m: int ).

tff(func_def_13,type,
    sK0: ( int * int * int ) > int ).

tff(func_def_14,type,
    sK1: ( int * int ) > 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,
    semiring_1: 
      !>[X0: $tType] : $o ).

tff(pred_def_6,type,
    monoid_mult: 
      !>[X0: $tType] : $o ).

tff(pred_def_7,type,
    number_semiring: 
      !>[X0: $tType] : $o ).

tff(pred_def_8,type,
    comm_semiring_1: 
      !>[X0: $tType] : $o ).

tff(pred_def_9,type,
    zcong: ( int * int * int ) > $o ).

tff(pred_def_10,type,
    zprime: int > $o ).

tff(pred_def_11,type,
    quadRes: ( int * int ) > $o ).

tff(pred_def_12,type,
    pp: bool > $o ).

tff(pred_def_14,type,
    sQ2_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f564,plain,
    $false,
    inference(avatar_sat_refutation,[],[f484,f485,f496,f563]) ).

tff(f563,plain,
    ( ~ spl3_1
    | ~ spl3_3 ),
    inference(avatar_contradiction_clause,[],[f562]) ).

tff(f562,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f559,f479]) ).

tff(f479,plain,
    ( ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,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)))),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)))
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f478]) ).

tff(f478,plain,
    ( spl3_1
  <=> ! [X0: int] : ~ zcong(power_power(int,X0,number_number_of(nat,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)))),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))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

tff(f559,plain,
    ( zcong(power_power(int,sK1(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))),number_number_of(nat,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)))),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)))
    | ~ spl3_3 ),
    inference(resolution,[],[f489,f380]) ).

tff(f380,plain,
    ! [X0: int,X1: int] :
      ( ~ quadRes(X1,X0)
      | zcong(power_power(int,sK1(X0,X1),number_number_of(nat,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,X1) ),
    inference(definition_unfolding,[],[f327,f274,f257]) ).

tff(f257,plain,
    ! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
    inference(cnf_transformation,[],[f132]) ).

tff(f132,plain,
    ! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
    inference(rectify,[],[f66]) ).

tff(f66,axiom,
    ! [X5: int] : ( bit1(X5) = plus_plus(int,plus_plus(int,one_one(int),X5),X5) ),
    file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',fact_65_Bit1__def) ).

tff(f274,plain,
    ! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
    inference(cnf_transformation,[],[f144]) ).

tff(f144,plain,
    ! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X5: int] : ( bit0(X5) = plus_plus(int,X5,X5) ),
    file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',fact_56_Bit0__def) ).

tff(f327,plain,
    ! [X0: int,X1: int] :
      ( zcong(power_power(int,sK1(X0,X1),number_number_of(nat,bit0(bit1(pls)))),X0,X1)
      | ~ quadRes(X1,X0) ),
    inference(cnf_transformation,[],[f242]) ).

tff(f242,plain,
    ! [X0: int,X1: int] :
      ( zcong(power_power(int,sK1(X0,X1),number_number_of(nat,bit0(bit1(pls)))),X0,X1)
      | ~ quadRes(X1,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f227,f241]) ).

tff(f241,plain,
    ! [X0: int,X1: int] :
      ( ? [X2: int] : zcong(power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),X0,X1)
     => zcong(power_power(int,sK1(X0,X1),number_number_of(nat,bit0(bit1(pls)))),X0,X1) ),
    introduced(choice_axiom,[]) ).

tff(f227,plain,
    ! [X0: int,X1: int] :
      ( ? [X2: int] : zcong(power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),X0,X1)
      | ~ quadRes(X1,X0) ),
    inference(ennf_transformation,[],[f193]) ).

tff(f193,plain,
    ! [X0: int,X1: int] :
      ( quadRes(X1,X0)
     => ? [X2: int] : zcong(power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f192]) ).

tff(f192,plain,
    ! [X0: int,X1: int] :
      ( quadRes(X1,X0)
    <=> ? [X2: int] : zcong(power_power(int,X2,number_number_of(nat,bit0(bit1(pls)))),X0,X1) ),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X11: int,X22: int] :
      ( quadRes(X22,X11)
    <=> ? [X23: int] : zcong(power_power(int,X23,number_number_of(nat,bit0(bit1(pls)))),X11,X22) ),
    file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',fact_85_QuadRes__def) ).

tff(f489,plain,
    ( quadRes(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)),number_number_of(int,min))
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f487]) ).

tff(f487,plain,
    ( spl3_3
  <=> quadRes(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)),number_number_of(int,min)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

tff(f496,plain,
    spl3_3,
    inference(avatar_split_clause,[],[f383,f487]) ).

tff(f383,plain,
    quadRes(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)),number_number_of(int,min)),
    inference(definition_unfolding,[],[f330,f274,f274,f257]) ).

tff(f330,plain,
    quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,min)),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    quadRes(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,min)),
    file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',fact_0__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).

tff(f485,plain,
    ~ spl3_2,
    inference(avatar_split_clause,[],[f244,f481]) ).

tff(f481,plain,
    ( spl3_2
  <=> thesis ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

tff(f244,plain,
    ~ thesis,
    inference(cnf_transformation,[],[f126]) ).

tff(f126,plain,
    ~ thesis,
    inference(flattening,[],[f124]) ).

tff(f124,negated_conjecture,
    ~ thesis,
    inference(negated_conjecture,[],[f123]) ).

tff(f123,conjecture,
    thesis,
    file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',conj_1) ).

tff(f484,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f331,f481,f478]) ).

tff(f331,plain,
    ! [X0: int] :
      ( thesis
      | ~ zcong(power_power(int,X0,number_number_of(nat,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)))),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,[],[f243,f274,f257,f274,f274,f257]) ).

tff(f243,plain,
    ! [X0: int] :
      ( thesis
      | ~ zcong(power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),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,[],[f203]) ).

tff(f203,plain,
    ! [X0: int] :
      ( thesis
      | ~ zcong(power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
    inference(ennf_transformation,[],[f125]) ).

tff(f125,plain,
    ! [X0: int] :
      ( zcong(power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
     => thesis ),
    inference(rectify,[],[f122]) ).

tff(f122,axiom,
    ! [X32: int] :
      ( zcong(power_power(int,X32,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
     => thesis ),
    file('/export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM945_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35  % Computer : n005.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 14:41:22 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TF1_THM_EQU_NAR problem
% 0.21/0.35  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.RlUrg03JyU/Vampire---4.8_25712
% 0.57/0.73  % (25827)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 (2996ds/83Mi)
% 0.57/0.73  % (25820)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)
% 0.57/0.73  % (25823)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.73  % (25821)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)
% 0.57/0.73  % (25824)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)
% 0.57/0.73  % (25827)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.57/0.73  % (25825)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)
% 0.57/0.73  % (25826)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)
% 0.57/0.73  % (25827)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.57/0.73  % (25825)Refutation not found, incomplete strategy% (25825)------------------------------
% 0.57/0.73  % (25825)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.73  % (25825)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.73  
% 0.57/0.73  % (25825)Memory used [KB]: 1241
% 0.57/0.73  % (25825)Time elapsed: 0.007 s
% 0.57/0.73  % (25825)Instructions burned: 11 (million)
% 0.57/0.73  % (25828)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)
% 0.57/0.73  % (25825)------------------------------
% 0.57/0.73  % (25825)------------------------------
% 0.57/0.74  % (25820)First to succeed.
% 0.57/0.74  % (25820)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25819"
% 0.57/0.74  % (25828)Refutation not found, incomplete strategy% (25828)------------------------------
% 0.57/0.74  % (25828)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.74  % (25828)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.74  
% 0.57/0.74  % (25828)Memory used [KB]: 1112
% 0.57/0.74  % (25828)Time elapsed: 0.006 s
% 0.57/0.74  % (25828)Instructions burned: 10 (million)
% 0.57/0.74  % (25828)------------------------------
% 0.57/0.74  % (25828)------------------------------
% 0.57/0.75  % (25820)Refutation found. Thanks to Tanya!
% 0.57/0.75  % SZS status Theorem for Vampire---4
% 0.57/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.75  % (25820)------------------------------
% 0.57/0.75  % (25820)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.75  % (25820)Termination reason: Refutation
% 0.57/0.75  
% 0.57/0.75  % (25820)Memory used [KB]: 1218
% 0.57/0.75  % (25820)Time elapsed: 0.011 s
% 0.57/0.75  % (25820)Instructions burned: 18 (million)
% 0.57/0.75  % (25819)Success in time 0.376 s
% 0.57/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------