TSTP Solution File: NUN069+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUN069+2 : TPTP v8.1.2. Released v7.3.0.
% 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 : n009.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 03:36:21 EDT 2024

% Result   : Theorem 0.61s 0.79s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   30 (   5 unt;   1 typ;   0 def)
%            Number of atoms       :  112 (  23 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   71 (  14   ~;   7   |;  42   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   26 (  26 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  12 usr;   4 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   83 (  33   !;  49   ?;  14   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_5,type,
    sQ19_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f123,plain,
    $false,
    inference(resolution,[],[f117,f81]) ).

tff(f81,plain,
    r1(sK14),
    inference(cnf_transformation,[],[f48]) ).

tff(f48,plain,
    ( ( sK12 = sK13 )
    & r1(sK13)
    & r1(sK14) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f44,f47,f46,f45]) ).

tff(f45,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ( X1 = X2 )
            & r1(X2) )
        & ? [X3] : r1(X3) )
   => ( ? [X2] :
          ( ( sK12 = X2 )
          & r1(X2) )
      & ? [X3] : r1(X3) ) ),
    introduced(choice_axiom,[]) ).

tff(f46,plain,
    ( ? [X2] :
        ( ( sK12 = X2 )
        & r1(X2) )
   => ( ( sK12 = sK13 )
      & r1(sK13) ) ),
    introduced(choice_axiom,[]) ).

tff(f47,plain,
    ( ? [X3] : r1(X3)
   => r1(sK14) ),
    introduced(choice_axiom,[]) ).

tff(f44,plain,
    ? [X1] :
      ( ? [X2] :
          ( ( X1 = X2 )
          & r1(X2) )
      & ? [X3] : r1(X3) ),
    inference(rectify,[],[f24]) ).

tff(f24,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( ( X1 = X2 )
          & r1(X2) )
      & ? [X3] : r1(X3) ),
    inference(pure_predicate_removal,[],[f22]) ).

tff(f22,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( ( X1 = X2 )
          & r1(X2) )
      & ? [X3] :
          ( r4(X0,X3,X1)
          & r1(X3) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X32] :
    ? [X33] :
      ( ? [X35] :
          ( ( X33 = X35 )
          & r1(X35) )
      & ? [X34] :
          ( r4(X32,X34,X33)
          & r1(X34) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.lYM2DT3WsU/Vampire---4.8_21878',axiom_5a) ).

tff(f117,plain,
    ! [X0: $i] : ~ r1(X0),
    inference(resolution,[],[f113,f84]) ).

tff(f84,plain,
    ! [X1: $i] : r2(X1,sK18(X1)),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,plain,
    ! [X0,X1] :
      ( r3(sK16(X0,X1),X0,sK15(X0,X1))
      & ( sK15(X0,X1) = sK17(X0,X1) )
      & r2(X1,sK18(X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18])],[f25,f52,f51,f50,f49]) ).

tff(f49,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] : r3(X3,X0,X2)
          & ? [X4] :
              ( ( X2 = X4 )
              & ? [X5] : r2(X1,X5) ) )
     => ( ? [X3] : r3(X3,X0,sK15(X0,X1))
        & ? [X4] :
            ( ( sK15(X0,X1) = X4 )
            & ? [X5] : r2(X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f50,plain,
    ! [X0,X1] :
      ( ? [X3] : r3(X3,X0,sK15(X0,X1))
     => r3(sK16(X0,X1),X0,sK15(X0,X1)) ),
    introduced(choice_axiom,[]) ).

tff(f51,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ( sK15(X0,X1) = X4 )
          & ? [X5] : r2(X1,X5) )
     => ( ( sK15(X0,X1) = sK17(X0,X1) )
        & ? [X5] : r2(X1,X5) ) ),
    introduced(choice_axiom,[]) ).

tff(f52,plain,
    ! [X1] :
      ( ? [X5] : r2(X1,X5)
     => r2(X1,sK18(X1)) ),
    introduced(choice_axiom,[]) ).

tff(f25,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] : r3(X3,X0,X2)
      & ? [X4] :
          ( ( X2 = X4 )
          & ? [X5] : r2(X1,X5) ) ),
    inference(pure_predicate_removal,[],[f23]) ).

tff(f23,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,X2) )
      & ? [X4] :
          ( ( X2 = X4 )
          & ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X19,X20] :
    ? [X21] :
      ( ? [X24] :
          ( r4(X19,X20,X24)
          & r3(X24,X19,X21) )
      & ? [X22] :
          ( ( X21 = X22 )
          & ? [X23] :
              ( r4(X19,X23,X22)
              & r2(X20,X23) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.lYM2DT3WsU/Vampire---4.8_21878',axiom_2a) ).

tff(f113,plain,
    ! [X0: $i,X1: $i] :
      ( ~ r2(X0,X1)
      | ~ r1(X0) ),
    inference(resolution,[],[f110,f98]) ).

tff(f98,plain,
    ! [X0: $i,X1: $i] :
      ( ~ sQ19_eqProxy($i,X0,X0)
      | ~ r1(X1)
      | ~ r2(X1,X0) ),
    inference(equality_proxy_replacement,[],[f54,f97]) ).

tff(f97,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ19_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ19_eqProxy])]) ).

tff(f54,plain,
    ! [X0: $i,X1: $i] :
      ( ~ r2(X1,X0)
      | ~ r1(X1)
      | ( X0 != X0 ) ),
    inference(cnf_transformation,[],[f26]) ).

tff(f26,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ r2(X1,X0)
          | ~ r1(X1) )
      | ( X0 != X0 ) ),
    inference(ennf_transformation,[],[f14]) ).

tff(f14,plain,
    ~ ? [X0] :
        ( ? [X1] :
            ( r2(X1,X0)
            & r1(X1) )
        & ( X0 = X0 ) ),
    inference(rectify,[],[f13]) ).

tff(f13,negated_conjecture,
    ~ ? [X38] :
        ( ? [X21] :
            ( r2(X21,X38)
            & r1(X21) )
        & ( X38 = X38 ) ),
    inference(negated_conjecture,[],[f12]) ).

tff(f12,conjecture,
    ? [X38] :
      ( ? [X21] :
          ( r2(X21,X38)
          & r1(X21) )
      & ( X38 = X38 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.lYM2DT3WsU/Vampire---4.8_21878',oneeqone) ).

tff(f110,plain,
    ! [X0: $tType,X1: X0] : sQ19_eqProxy(X0,X1,X1),
    inference(equality_proxy_axiom,[],[f97]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : NUN069+2 : TPTP v8.1.2. Released v7.3.0.
% 0.08/0.15  % 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
% 0.15/0.36  % Computer : n009.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 17:35:26 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  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.lYM2DT3WsU/Vampire---4.8_21878
% 0.61/0.78  % (22069)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)
% 0.61/0.79  % (22075)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)
% 0.61/0.79  % (22069)First to succeed.
% 0.61/0.79  % (22072)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)
% 0.61/0.79  % (22071)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.61/0.79  % (22073)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)
% 0.61/0.79  % (22070)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)
% 0.61/0.79  % (22074)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)
% 0.61/0.79  % (22075)Also succeeded, but the first one will report.
% 0.61/0.79  % (22076)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)
% 0.61/0.79  % (22069)Refutation found. Thanks to Tanya!
% 0.61/0.79  % SZS status Theorem for Vampire---4
% 0.61/0.79  % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.79  % (22069)------------------------------
% 0.61/0.79  % (22069)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.79  % (22069)Termination reason: Refutation
% 0.61/0.79  
% 0.61/0.79  % (22069)Memory used [KB]: 1061
% 0.61/0.79  % (22069)Time elapsed: 0.004 s
% 0.61/0.79  % (22069)Instructions burned: 4 (million)
% 0.61/0.79  % (22069)------------------------------
% 0.61/0.79  % (22069)------------------------------
% 0.61/0.79  % (22044)Success in time 0.419 s
% 0.61/0.79  % Vampire---4.8 exiting
%------------------------------------------------------------------------------