TSTP Solution File: NUM430+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM430+3 : 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 : n029.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 17:59:29 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   50 (   5 unt;   0 def)
%            Number of atoms       :  178 (  39 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  196 (  68   ~;  59   |;  57   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   58 (  44   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f580,plain,
    $false,
    inference(avatar_sat_refutation,[],[f546,f568,f579]) ).

fof(f579,plain,
    spl4_2,
    inference(avatar_contradiction_clause,[],[f578]) ).

fof(f578,plain,
    ( $false
    | spl4_2 ),
    inference(subsumption_resolution,[],[f576,f104]) ).

fof(f104,plain,
    aInteger0(xc),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    ( aInteger0(xq)
    & aInteger0(xb)
    & aInteger0(xc)
    & aInteger0(xa)
    & sz00 != xq ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).

fof(f576,plain,
    ( ~ aInteger0(xc)
    | spl4_2 ),
    inference(resolution,[],[f575,f87]) ).

fof(f87,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | aInteger0(smndt0(X0)) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => aInteger0(smndt0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).

fof(f575,plain,
    ( ~ aInteger0(smndt0(xc))
    | spl4_2 ),
    inference(subsumption_resolution,[],[f573,f105]) ).

fof(f105,plain,
    aInteger0(xb),
    inference(cnf_transformation,[],[f22]) ).

fof(f573,plain,
    ( ~ aInteger0(xb)
    | ~ aInteger0(smndt0(xc))
    | spl4_2 ),
    inference(resolution,[],[f545,f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | aInteger0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | aInteger0(sdtpldt0(X0,X1)) ),
    inference(rectify,[],[f44]) ).

fof(f44,plain,
    ! [X1,X0] :
      ( ~ aInteger0(X1)
      | ~ aInteger0(X0)
      | aInteger0(sdtpldt0(X1,X0)) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( aInteger0(sdtpldt0(X1,X0))
      | ~ aInteger0(X0)
      | ~ aInteger0(X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( aInteger0(X0)
        & aInteger0(X1) )
     => aInteger0(sdtpldt0(X1,X0)) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => aInteger0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).

fof(f545,plain,
    ( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
    | spl4_2 ),
    inference(avatar_component_clause,[],[f543]) ).

fof(f543,plain,
    ( spl4_2
  <=> aInteger0(sdtpldt0(xb,smndt0(xc))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f568,plain,
    ( ~ spl4_2
    | spl4_1 ),
    inference(avatar_split_clause,[],[f567,f539,f543]) ).

fof(f539,plain,
    ( spl4_1
  <=> aInteger0(sK0(sdtpldt0(xb,smndt0(xc)),xq)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f567,plain,
    ( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
    | spl4_1 ),
    inference(subsumption_resolution,[],[f565,f120]) ).

fof(f120,plain,
    aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc))),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ( sdteqdtlpzmzozddtrp0(xb,xc,xq)
    & aInteger0(sK1)
    & sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,sK1)
    & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    & sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK2)
    & aInteger0(sK2)
    & sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f30,f81,f80]) ).

fof(f80,plain,
    ( ? [X0] :
        ( aInteger0(X0)
        & sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc)) )
   => ( aInteger0(sK1)
      & sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ( ? [X1] :
        ( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X1)
        & aInteger0(X1) )
   => ( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK2)
      & aInteger0(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ( sdteqdtlpzmzozddtrp0(xb,xc,xq)
    & ? [X0] :
        ( aInteger0(X0)
        & sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc)) )
    & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    & ? [X1] :
        ( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X1)
        & aInteger0(X1) )
    & sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ( ? [X0] :
        ( aInteger0(X0)
        & sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc)) )
    & sdteqdtlpzmzozddtrp0(xa,xb,xq)
    & aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    & sdteqdtlpzmzozddtrp0(xb,xc,xq)
    & aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
    & ? [X0] :
        ( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
        & aInteger0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__853) ).

fof(f565,plain,
    ( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
    | ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    | spl4_1 ),
    inference(resolution,[],[f541,f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( aInteger0(sK0(X0,X1))
      | ~ aDivisorOf0(X1,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( sz00 != X1
              & sdtasdt0(X1,sK0(X0,X1)) = X0
              & aInteger0(sK0(X0,X1))
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) )
          & ( aDivisorOf0(X1,X0)
            | sz00 = X1
            | ! [X3] :
                ( sdtasdt0(X1,X3) != X0
                | ~ aInteger0(X3) )
            | ~ aInteger0(X1) ) )
      | ~ aInteger0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f72,f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtasdt0(X1,X2) = X0
          & aInteger0(X2) )
     => ( sdtasdt0(X1,sK0(X0,X1)) = X0
        & aInteger0(sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( sz00 != X1
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) )
          & ( aDivisorOf0(X1,X0)
            | sz00 = X1
            | ! [X3] :
                ( sdtasdt0(X1,X3) != X0
                | ~ aInteger0(X3) )
            | ~ aInteger0(X1) ) )
      | ~ aInteger0(X0) ),
    inference(rectify,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( sz00 != X1
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) )
          & ( aDivisorOf0(X1,X0)
            | sz00 = X1
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | ~ aInteger0(X1) ) )
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( sz00 != X1
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aInteger0(X2) )
              & aInteger0(X1) )
            | ~ aDivisorOf0(X1,X0) )
          & ( aDivisorOf0(X1,X0)
            | sz00 = X1
            | ! [X2] :
                ( sdtasdt0(X1,X2) != X0
                | ~ aInteger0(X2) )
            | ~ aInteger0(X1) ) )
      | ~ aInteger0(X0) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sz00 != X1
            & ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & aInteger0(X1) )
        <=> aDivisorOf0(X1,X0) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ! [X1] :
          ( ( sz00 != X1
            & ? [X2] :
                ( sdtasdt0(X1,X2) = X0
                & aInteger0(X2) )
            & aInteger0(X1) )
        <=> aDivisorOf0(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).

fof(f541,plain,
    ( ~ aInteger0(sK0(sdtpldt0(xb,smndt0(xc)),xq))
    | spl4_1 ),
    inference(avatar_component_clause,[],[f539]) ).

fof(f546,plain,
    ( ~ spl4_1
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f537,f543,f539]) ).

fof(f537,plain,
    ( ~ aInteger0(sdtpldt0(xb,smndt0(xc)))
    | ~ aInteger0(sK0(sdtpldt0(xb,smndt0(xc)),xq)) ),
    inference(subsumption_resolution,[],[f536,f120]) ).

fof(f536,plain,
    ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
    | ~ aInteger0(sK0(sdtpldt0(xb,smndt0(xc)),xq))
    | ~ aInteger0(sdtpldt0(xb,smndt0(xc))) ),
    inference(resolution,[],[f158,f138]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ~ aDivisorOf0(X1,X0)
      | sQ3_eqProxy(sdtasdt0(X1,sK0(X0,X1)),X0)
      | ~ aInteger0(X0) ),
    inference(equality_proxy_replacement,[],[f95,f132]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( sQ3_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ3_eqProxy])]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( sdtasdt0(X1,sK0(X0,X1)) = X0
      | ~ aDivisorOf0(X1,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f158,plain,
    ! [X0] :
      ( ~ sQ3_eqProxy(sdtasdt0(xq,X0),sdtpldt0(xb,smndt0(xc)))
      | ~ aInteger0(X0) ),
    inference(equality_proxy_replacement,[],[f126,f132]) ).

fof(f126,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtasdt0(xq,X0) != sdtpldt0(xb,smndt0(xc)) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtasdt0(xq,X0) != sdtpldt0(xb,smndt0(xc)) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,negated_conjecture,
    ~ ? [X0] :
        ( sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc))
        & aInteger0(X0) ),
    inference(negated_conjecture,[],[f25]) ).

fof(f25,conjecture,
    ? [X0] :
      ( sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc))
      & aInteger0(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM430+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 06:41:27 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.48  % (4403)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)
% 0.19/0.50  % (4406)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (4410)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (4403)First to succeed.
% 0.19/0.50  % (4413)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.50  % (4418)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.51  % (4399)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (4394)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (4397)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (4395)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51  % (4395)Instruction limit reached!
% 0.19/0.51  % (4395)------------------------------
% 0.19/0.51  % (4395)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (4395)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (4395)Termination reason: Unknown
% 0.19/0.51  % (4395)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (4395)Memory used [KB]: 1407
% 0.19/0.51  % (4395)Time elapsed: 0.002 s
% 0.19/0.51  % (4395)Instructions burned: 3 (million)
% 0.19/0.51  % (4395)------------------------------
% 0.19/0.51  % (4395)------------------------------
% 0.19/0.51  % (4403)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (4403)------------------------------
% 0.19/0.51  % (4403)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (4403)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (4403)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (4403)Memory used [KB]: 6140
% 0.19/0.51  % (4403)Time elapsed: 0.107 s
% 0.19/0.51  % (4403)Instructions burned: 8 (million)
% 0.19/0.51  % (4403)------------------------------
% 0.19/0.51  % (4403)------------------------------
% 0.19/0.51  % (4392)Success in time 0.169 s
%------------------------------------------------------------------------------