%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM475+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n003.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 Aug 31 17:59:51 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   38 (  15 unt;   0 def)
%            Number of atoms       :   99 (  28 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  113 (  52   ~;  41   |;  14   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   33 (  33   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f634,plain,
    $false,
    inference(subsumption_resolution,[],[f633,f195]) ).

fof(f195,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ( aNaturalNumber0(xm)
    & aNaturalNumber0(xl)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).

fof(f633,plain,
    ~ aNaturalNumber0(xl),
    inference(subsumption_resolution,[],[f632,f152]) ).

fof(f152,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    ( aNaturalNumber0(xp)
    & xm = sdtasdt0(xl,xp)
    & xp = sdtsldt0(xm,xl) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).

fof(f632,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xl) ),
    inference(resolution,[],[f631,f159]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(flattening,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X0)
        & aNaturalNumber0(X1) )
     => aNaturalNumber0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

fof(f631,plain,
    ~ aNaturalNumber0(sdtasdt0(xl,xp)),
    inference(subsumption_resolution,[],[f630,f163]) ).

fof(f163,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    ( xr = sdtmndt0(xq,xp)
    & aNaturalNumber0(xr)
    & xq = sdtpldt0(xp,xr) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1422) ).

fof(f630,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
    inference(subsumption_resolution,[],[f629,f195]) ).

fof(f629,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xl,xp))
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xr) ),
    inference(resolution,[],[f621,f159]) ).

fof(f621,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xl,xr))
    | ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
    inference(subsumption_resolution,[],[f620,f258]) ).

fof(f258,plain,
    ~ sQ5_eqProxy(xn,sdtasdt0(xl,xr)),
    inference(equality_proxy_replacement,[],[f176,f238]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( sQ5_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ5_eqProxy])]) ).

fof(f176,plain,
    xn != sdtasdt0(xl,xr),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    xn != sdtasdt0(xl,xr),
    inference(flattening,[],[f43]) ).

fof(f43,negated_conjecture,
    xn != sdtasdt0(xl,xr),
    inference(negated_conjecture,[],[f42]) ).

fof(f42,conjecture,
    xn = sdtasdt0(xl,xr),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f620,plain,
    ( sQ5_eqProxy(xn,sdtasdt0(xl,xr))
    | ~ aNaturalNumber0(sdtasdt0(xl,xr))
    | ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
    inference(resolution,[],[f530,f291]) ).

fof(f291,plain,
    ! [X0,X1] :
      ( ~ sQ5_eqProxy(X0,X1)
      | sQ5_eqProxy(X1,X0) ),
    inference(equality_proxy_axiom,[],[f238]) ).

fof(f530,plain,
    ( sQ5_eqProxy(sdtasdt0(xl,xr),xn)
    | ~ aNaturalNumber0(sdtasdt0(xl,xr))
    | ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
    inference(subsumption_resolution,[],[f527,f194]) ).

fof(f194,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f34]) ).

fof(f527,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xl,xp))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtasdt0(xl,xr))
    | sQ5_eqProxy(sdtasdt0(xl,xr),xn) ),
    inference(resolution,[],[f269,f251]) ).

fof(f251,plain,
    ! [X2,X0,X1] :
      ( ~ sQ5_eqProxy(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
      | ~ aNaturalNumber0(X2)
      | sQ5_eqProxy(X0,X1)
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1) ),
    inference(equality_proxy_replacement,[],[f166,f238,f238]) ).

fof(f166,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | ~ aNaturalNumber0(X2)
      | sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | ~ aNaturalNumber0(X2)
      | ( sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
        & sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f68]) ).

fof(f68,plain,
    ! [X2,X1,X0] :
      ( X1 = X2
      | ~ aNaturalNumber0(X0)
      | ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
        & sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0,X2,X1] :
      ( X1 = X2
      | ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
        & sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X2,X1] :
      ( ( aNaturalNumber0(X0)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
          | sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
       => X1 = X2 ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X2,X1] :
      ( ( aNaturalNumber0(X0)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
          | sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).

fof(f269,plain,
    sQ5_eqProxy(sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),sdtpldt0(sdtasdt0(xl,xp),xn)),
    inference(equality_proxy_replacement,[],[f197,f238]) ).

fof(f197,plain,
    sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1459) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM475+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 06:38:52 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  % (6104)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.48  % (6095)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.49  % (6093)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.50  % (6095)First to succeed.
% 0.20/0.50  % (6095)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (6095)------------------------------
% 0.20/0.50  % (6095)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (6095)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (6095)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (6095)Memory used [KB]: 1791
% 0.20/0.50  % (6095)Time elapsed: 0.097 s
% 0.20/0.50  % (6095)Instructions burned: 15 (million)
% 0.20/0.50  % (6095)------------------------------
% 0.20/0.50  % (6095)------------------------------
% 0.20/0.50  % (6082)Success in time 0.156 s
%------------------------------------------------------------------------------