TSTP Solution File: SEU151+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU151+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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 Aug 31 18:32:10 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   50 (  10 unt;   0 def)
%            Number of atoms       :  179 ( 112 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  219 (  90   ~;  79   |;  40   &)
%                                         (   8 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   84 (  68   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f113,plain,
    $false,
    inference(avatar_sat_refutation,[],[f61,f80,f93,f104,f107]) ).

fof(f107,plain,
    ~ spl5_4,
    inference(avatar_split_clause,[],[f26,f77]) ).

fof(f77,plain,
    ( spl5_4
  <=> sK0 = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f26,plain,
    sK0 != sK3,
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( sK0 != sK3
    & sK1 != sK0
    & unordered_pair(sK0,sK2) = unordered_pair(sK1,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f15]) ).

fof(f15,plain,
    ( ? [X0,X1,X2,X3] :
        ( X0 != X3
        & X0 != X1
        & unordered_pair(X1,X3) = unordered_pair(X0,X2) )
   => ( sK0 != sK3
      & sK1 != sK0
      & unordered_pair(sK0,sK2) = unordered_pair(sK1,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1,X2,X3] :
      ( X0 != X3
      & X0 != X1
      & unordered_pair(X1,X3) = unordered_pair(X0,X2) ),
    inference(rectify,[],[f12]) ).

fof(f12,plain,
    ? [X1,X2,X3,X0] :
      ( X0 != X1
      & X1 != X2
      & unordered_pair(X2,X0) = unordered_pair(X1,X3) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ~ ! [X3,X1,X2,X0] :
        ~ ( X0 != X1
          & X1 != X2
          & unordered_pair(X2,X0) = unordered_pair(X1,X3) ),
    inference(rectify,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ ! [X3,X0,X2,X1] :
        ~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
          & X0 != X2
          & X0 != X3 ),
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    ! [X3,X0,X2,X1] :
      ~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
        & X0 != X2
        & X0 != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).

fof(f104,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f103]) ).

fof(f103,plain,
    ( $false
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f102]) ).

fof(f102,plain,
    ( sK0 != sK0
    | ~ spl5_1 ),
    inference(backward_demodulation,[],[f25,f56]) ).

fof(f56,plain,
    ( sK1 = sK0
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f54]) ).

fof(f54,plain,
    ( spl5_1
  <=> sK1 = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f25,plain,
    sK1 != sK0,
    inference(cnf_transformation,[],[f16]) ).

fof(f93,plain,
    ( spl5_1
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(avatar_split_clause,[],[f91,f73,f58,f54]) ).

fof(f58,plain,
    ( spl5_2
  <=> sK1 = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f73,plain,
    ( spl5_3
  <=> sK1 = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f91,plain,
    ( sK1 = sK0
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(resolution,[],[f86,f34]) ).

fof(f34,plain,
    ! [X1,X4] : in(X4,unordered_pair(X4,X1)),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X4] :
      ( in(X4,X0)
      | unordered_pair(X4,X1) != X0 ),
    inference(equality_resolution,[],[f29]) ).

fof(f29,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | X2 != X4
      | unordered_pair(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X2,X1) = X0
        | ( ( ( sK4(X0,X1,X2) != X2
              & sK4(X0,X1,X2) != X1 )
            | ~ in(sK4(X0,X1,X2),X0) )
          & ( sK4(X0,X1,X2) = X2
            | sK4(X0,X1,X2) = X1
            | in(sK4(X0,X1,X2),X0) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X0)
              | ( X2 != X4
                & X1 != X4 ) )
            & ( X2 = X4
              | X1 = X4
              | ~ in(X4,X0) ) )
        | unordered_pair(X2,X1) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X2 != X3
              & X1 != X3 )
            | ~ in(X3,X0) )
          & ( X2 = X3
            | X1 = X3
            | in(X3,X0) ) )
     => ( ( ( sK4(X0,X1,X2) != X2
            & sK4(X0,X1,X2) != X1 )
          | ~ in(sK4(X0,X1,X2),X0) )
        & ( sK4(X0,X1,X2) = X2
          | sK4(X0,X1,X2) = X1
          | in(sK4(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X2,X1) = X0
        | ? [X3] :
            ( ( ( X2 != X3
                & X1 != X3 )
              | ~ in(X3,X0) )
            & ( X2 = X3
              | X1 = X3
              | in(X3,X0) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X0)
              | ( X2 != X4
                & X1 != X4 ) )
            & ( X2 = X4
              | X1 = X4
              | ~ in(X4,X0) ) )
        | unordered_pair(X2,X1) != X0 ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X1,X2,X0] :
      ( ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ( X0 != X3
                & X2 != X3 )
              | ~ in(X3,X1) )
            & ( X0 = X3
              | X2 = X3
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ( X0 != X3
                & X2 != X3 ) )
            & ( X0 = X3
              | X2 = X3
              | ~ in(X3,X1) ) )
        | unordered_pair(X0,X2) != X1 ) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X1,X2,X0] :
      ( ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ( X0 != X3
                & X2 != X3 )
              | ~ in(X3,X1) )
            & ( X0 = X3
              | X2 = X3
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ( X0 != X3
                & X2 != X3 ) )
            & ( X0 = X3
              | X2 = X3
              | ~ in(X3,X1) ) )
        | unordered_pair(X0,X2) != X1 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X1,X2,X0] :
      ( unordered_pair(X0,X2) = X1
    <=> ! [X3] :
          ( in(X3,X1)
        <=> ( X0 = X3
            | X2 = X3 ) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) )
    <=> unordered_pair(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f86,plain,
    ( ! [X0] :
        ( ~ in(X0,unordered_pair(sK0,sK1))
        | sK1 = X0 )
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(duplicate_literal_removal,[],[f82]) ).

fof(f82,plain,
    ( ! [X0] :
        ( sK1 = X0
        | sK1 = X0
        | ~ in(X0,unordered_pair(sK0,sK1)) )
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(backward_demodulation,[],[f62,f75]) ).

fof(f75,plain,
    ( sK1 = sK3
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f73]) ).

fof(f62,plain,
    ( ! [X0] :
        ( sK1 = X0
        | sK3 = X0
        | ~ in(X0,unordered_pair(sK0,sK1)) )
    | ~ spl5_2 ),
    inference(backward_demodulation,[],[f50,f60]) ).

fof(f60,plain,
    ( sK1 = sK2
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f50,plain,
    ! [X0] :
      ( sK1 = X0
      | sK3 = X0
      | ~ in(X0,unordered_pair(sK0,sK2)) ),
    inference(superposition,[],[f37,f24]) ).

fof(f24,plain,
    unordered_pair(sK0,sK2) = unordered_pair(sK1,sK3),
    inference(cnf_transformation,[],[f16]) ).

fof(f37,plain,
    ! [X2,X1,X4] :
      ( ~ in(X4,unordered_pair(X2,X1))
      | X2 = X4
      | X1 = X4 ),
    inference(equality_resolution,[],[f27]) ).

fof(f27,plain,
    ! [X2,X0,X1,X4] :
      ( X2 = X4
      | X1 = X4
      | ~ in(X4,X0)
      | unordered_pair(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f21]) ).

fof(f80,plain,
    ( spl5_3
    | spl5_4
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f70,f58,f77,f73]) ).

fof(f70,plain,
    ( sK0 = sK3
    | sK1 = sK3
    | ~ spl5_2 ),
    inference(resolution,[],[f64,f37]) ).

fof(f64,plain,
    ( in(sK3,unordered_pair(sK0,sK1))
    | ~ spl5_2 ),
    inference(backward_demodulation,[],[f39,f60]) ).

fof(f39,plain,
    in(sK3,unordered_pair(sK0,sK2)),
    inference(superposition,[],[f36,f24]) ).

fof(f36,plain,
    ! [X2,X4] : in(X4,unordered_pair(X2,X4)),
    inference(equality_resolution,[],[f35]) ).

fof(f35,plain,
    ! [X2,X0,X4] :
      ( in(X4,X0)
      | unordered_pair(X2,X4) != X0 ),
    inference(equality_resolution,[],[f28]) ).

fof(f28,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | X1 != X4
      | unordered_pair(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f21]) ).

fof(f61,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f49,f58,f54]) ).

fof(f49,plain,
    ( sK1 = sK2
    | sK1 = sK0 ),
    inference(resolution,[],[f37,f38]) ).

fof(f38,plain,
    in(sK1,unordered_pair(sK0,sK2)),
    inference(superposition,[],[f34,f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU151+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 16:27:35 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.51  % (10269)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/99Mi)
% 0.20/0.51  % (10285)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/355Mi)
% 0.20/0.52  % (10285)First to succeed.
% 0.20/0.52  % (10285)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (10285)------------------------------
% 0.20/0.52  % (10285)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (10285)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (10285)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (10285)Memory used [KB]: 5500
% 0.20/0.52  % (10285)Time elapsed: 0.103 s
% 0.20/0.52  % (10285)Instructions burned: 3 (million)
% 0.20/0.52  % (10285)------------------------------
% 0.20/0.52  % (10285)------------------------------
% 0.20/0.52  % (10255)Success in time 0.174 s
%------------------------------------------------------------------------------