TSTP Solution File: SEU406+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% 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 : n012.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 18:29:50 EDT 2022

% Result   : Theorem 0.19s 0.57s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   50 (  10 unt;   0 def)
%            Number of atoms       :  227 (  16 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  295 ( 118   ~;  91   |;  76   &)
%                                         (   8 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   72 (  56   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f152,plain,
    $false,
    inference(avatar_sat_refutation,[],[f90,f96,f102,f103,f133,f151]) ).

fof(f151,plain,
    ( spl5_2
    | spl5_3 ),
    inference(avatar_contradiction_clause,[],[f150]) ).

fof(f150,plain,
    ( $false
    | spl5_2
    | spl5_3 ),
    inference(subsumption_resolution,[],[f149,f97]) ).

fof(f97,plain,
    r2_hidden(sK0,k2_xboole_0(sK1,sK3)),
    inference(forward_demodulation,[],[f57,f72]) ).

fof(f72,plain,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f57,plain,
    r2_hidden(sK0,k2_xboole_0(sK3,sK1)),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ( ( ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1))
      | ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1)) )
    & r2_hidden(sK2,k2_xboole_0(sK3,sK1))
    & ( ~ r2_hidden(sK2,sK1)
      | ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1)) )
    & r2_hidden(sK0,k2_xboole_0(sK3,sK1))
    & ( ~ r2_hidden(sK2,sK1)
      | ~ r2_hidden(sK0,sK1) )
    & ( ~ r2_hidden(sK0,sK1)
      | ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f42,f43]) ).

fof(f43,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ r2_hidden(X0,k4_xboole_0(X3,X1))
          | ~ r2_hidden(X2,k4_xboole_0(X3,X1)) )
        & r2_hidden(X2,k2_xboole_0(X3,X1))
        & ( ~ r2_hidden(X2,X1)
          | ~ r2_hidden(X0,k4_xboole_0(X3,X1)) )
        & r2_hidden(X0,k2_xboole_0(X3,X1))
        & ( ~ r2_hidden(X2,X1)
          | ~ r2_hidden(X0,X1) )
        & ( ~ r2_hidden(X0,X1)
          | ~ r2_hidden(X2,k4_xboole_0(X3,X1)) ) )
   => ( ( ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1))
        | ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1)) )
      & r2_hidden(sK2,k2_xboole_0(sK3,sK1))
      & ( ~ r2_hidden(sK2,sK1)
        | ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1)) )
      & r2_hidden(sK0,k2_xboole_0(sK3,sK1))
      & ( ~ r2_hidden(sK2,sK1)
        | ~ r2_hidden(sK0,sK1) )
      & ( ~ r2_hidden(sK0,sK1)
        | ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ r2_hidden(X0,k4_xboole_0(X3,X1))
        | ~ r2_hidden(X2,k4_xboole_0(X3,X1)) )
      & r2_hidden(X2,k2_xboole_0(X3,X1))
      & ( ~ r2_hidden(X2,X1)
        | ~ r2_hidden(X0,k4_xboole_0(X3,X1)) )
      & r2_hidden(X0,k2_xboole_0(X3,X1))
      & ( ~ r2_hidden(X2,X1)
        | ~ r2_hidden(X0,X1) )
      & ( ~ r2_hidden(X0,X1)
        | ~ r2_hidden(X2,k4_xboole_0(X3,X1)) ) ),
    inference(rectify,[],[f41]) ).

fof(f41,plain,
    ? [X3,X2,X1,X0] :
      ( ( ~ r2_hidden(X3,k4_xboole_0(X0,X2))
        | ~ r2_hidden(X1,k4_xboole_0(X0,X2)) )
      & r2_hidden(X1,k2_xboole_0(X0,X2))
      & ( ~ r2_hidden(X1,X2)
        | ~ r2_hidden(X3,k4_xboole_0(X0,X2)) )
      & r2_hidden(X3,k2_xboole_0(X0,X2))
      & ( ~ r2_hidden(X1,X2)
        | ~ r2_hidden(X3,X2) )
      & ( ~ r2_hidden(X3,X2)
        | ~ r2_hidden(X1,k4_xboole_0(X0,X2)) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,plain,
    ~ ! [X3,X0,X2,X1] :
        ~ ( ~ ( r2_hidden(X3,k4_xboole_0(X0,X2))
              & r2_hidden(X1,X2) )
          & r2_hidden(X3,k2_xboole_0(X0,X2))
          & ~ ( r2_hidden(X3,X2)
              & r2_hidden(X1,k4_xboole_0(X0,X2)) )
          & ~ ( r2_hidden(X3,X2)
              & r2_hidden(X1,X2) )
          & r2_hidden(X1,k2_xboole_0(X0,X2))
          & ~ ( r2_hidden(X3,k4_xboole_0(X0,X2))
              & r2_hidden(X1,k4_xboole_0(X0,X2)) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X2,X0,X3,X1] :
        ~ ( ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
              & r2_hidden(X0,k4_xboole_0(X2,X3)) )
          & r2_hidden(X1,k2_xboole_0(X2,X3))
          & ~ ( r2_hidden(X0,X3)
              & r2_hidden(X1,k4_xboole_0(X2,X3)) )
          & ~ ( r2_hidden(X1,X3)
              & r2_hidden(X0,X3) )
          & ~ ( r2_hidden(X1,X3)
              & r2_hidden(X0,k4_xboole_0(X2,X3)) )
          & r2_hidden(X0,k2_xboole_0(X2,X3)) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X2,X0,X3,X1] :
      ~ ( ~ ( r2_hidden(X1,k4_xboole_0(X2,X3))
            & r2_hidden(X0,k4_xboole_0(X2,X3)) )
        & r2_hidden(X1,k2_xboole_0(X2,X3))
        & ~ ( r2_hidden(X0,X3)
            & r2_hidden(X1,k4_xboole_0(X2,X3)) )
        & ~ ( r2_hidden(X1,X3)
            & r2_hidden(X0,X3) )
        & ~ ( r2_hidden(X1,X3)
            & r2_hidden(X0,k4_xboole_0(X2,X3)) )
        & r2_hidden(X0,k2_xboole_0(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).

fof(f149,plain,
    ( ~ r2_hidden(sK0,k2_xboole_0(sK1,sK3))
    | spl5_2
    | spl5_3 ),
    inference(forward_demodulation,[],[f141,f70]) ).

fof(f70,plain,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).

fof(f141,plain,
    ( ~ r2_hidden(sK0,k2_xboole_0(sK1,k4_xboole_0(sK3,sK1)))
    | spl5_2
    | spl5_3 ),
    inference(unit_resulting_resolution,[],[f95,f89,f81]) ).

fof(f81,plain,
    ! [X2,X3,X0] :
      ( ~ r2_hidden(X3,k2_xboole_0(X2,X0))
      | r2_hidden(X3,X0)
      | r2_hidden(X3,X2) ),
    inference(equality_resolution,[],[f66]) ).

fof(f66,plain,
    ! [X2,X3,X0,X1] :
      ( r2_hidden(X3,X2)
      | r2_hidden(X3,X0)
      | ~ r2_hidden(X3,X1)
      | k2_xboole_0(X2,X0) != X1 ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( r2_hidden(X3,X1)
              | ( ~ r2_hidden(X3,X2)
                & ~ r2_hidden(X3,X0) ) )
            & ( r2_hidden(X3,X2)
              | r2_hidden(X3,X0)
              | ~ r2_hidden(X3,X1) ) )
        | k2_xboole_0(X2,X0) != X1 )
      & ( k2_xboole_0(X2,X0) = X1
        | ( ( ( ~ r2_hidden(sK4(X0,X1,X2),X2)
              & ~ r2_hidden(sK4(X0,X1,X2),X0) )
            | ~ r2_hidden(sK4(X0,X1,X2),X1) )
          & ( r2_hidden(sK4(X0,X1,X2),X2)
            | r2_hidden(sK4(X0,X1,X2),X0)
            | r2_hidden(sK4(X0,X1,X2),X1) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f47,f48]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ( ~ r2_hidden(X4,X2)
              & ~ r2_hidden(X4,X0) )
            | ~ r2_hidden(X4,X1) )
          & ( r2_hidden(X4,X2)
            | r2_hidden(X4,X0)
            | r2_hidden(X4,X1) ) )
     => ( ( ( ~ r2_hidden(sK4(X0,X1,X2),X2)
            & ~ r2_hidden(sK4(X0,X1,X2),X0) )
          | ~ r2_hidden(sK4(X0,X1,X2),X1) )
        & ( r2_hidden(sK4(X0,X1,X2),X2)
          | r2_hidden(sK4(X0,X1,X2),X0)
          | r2_hidden(sK4(X0,X1,X2),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( r2_hidden(X3,X1)
              | ( ~ r2_hidden(X3,X2)
                & ~ r2_hidden(X3,X0) ) )
            & ( r2_hidden(X3,X2)
              | r2_hidden(X3,X0)
              | ~ r2_hidden(X3,X1) ) )
        | k2_xboole_0(X2,X0) != X1 )
      & ( k2_xboole_0(X2,X0) = X1
        | ? [X4] :
            ( ( ( ~ r2_hidden(X4,X2)
                & ~ r2_hidden(X4,X0) )
              | ~ r2_hidden(X4,X1) )
            & ( r2_hidden(X4,X2)
              | r2_hidden(X4,X0)
              | r2_hidden(X4,X1) ) ) ) ),
    inference(rectify,[],[f46]) ).

fof(f46,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( r2_hidden(X3,X1)
              | ( ~ r2_hidden(X3,X0)
                & ~ r2_hidden(X3,X2) ) )
            & ( r2_hidden(X3,X0)
              | r2_hidden(X3,X2)
              | ~ r2_hidden(X3,X1) ) )
        | k2_xboole_0(X0,X2) != X1 )
      & ( k2_xboole_0(X0,X2) = X1
        | ? [X3] :
            ( ( ( ~ r2_hidden(X3,X0)
                & ~ r2_hidden(X3,X2) )
              | ~ r2_hidden(X3,X1) )
            & ( r2_hidden(X3,X0)
              | r2_hidden(X3,X2)
              | r2_hidden(X3,X1) ) ) ) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( r2_hidden(X3,X1)
              | ( ~ r2_hidden(X3,X0)
                & ~ r2_hidden(X3,X2) ) )
            & ( r2_hidden(X3,X0)
              | r2_hidden(X3,X2)
              | ~ r2_hidden(X3,X1) ) )
        | k2_xboole_0(X0,X2) != X1 )
      & ( k2_xboole_0(X0,X2) = X1
        | ? [X3] :
            ( ( ( ~ r2_hidden(X3,X0)
                & ~ r2_hidden(X3,X2) )
              | ~ r2_hidden(X3,X1) )
            & ( r2_hidden(X3,X0)
              | r2_hidden(X3,X2)
              | r2_hidden(X3,X1) ) ) ) ),
    inference(nnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X2,X1,X0] :
      ( ! [X3] :
          ( r2_hidden(X3,X1)
        <=> ( r2_hidden(X3,X0)
            | r2_hidden(X3,X2) ) )
    <=> k2_xboole_0(X0,X2) = X1 ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X2,X1] :
      ( k2_xboole_0(X0,X1) = X2
    <=> ! [X3] :
          ( r2_hidden(X3,X2)
        <=> ( r2_hidden(X3,X1)
            | r2_hidden(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f89,plain,
    ( ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1))
    | spl5_2 ),
    inference(avatar_component_clause,[],[f87]) ).

fof(f87,plain,
    ( spl5_2
  <=> r2_hidden(sK0,k4_xboole_0(sK3,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f95,plain,
    ( ~ r2_hidden(sK0,sK1)
    | spl5_3 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f93,plain,
    ( spl5_3
  <=> r2_hidden(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f133,plain,
    ( spl5_1
    | spl5_4 ),
    inference(avatar_contradiction_clause,[],[f132]) ).

fof(f132,plain,
    ( $false
    | spl5_1
    | spl5_4 ),
    inference(subsumption_resolution,[],[f131,f91]) ).

fof(f91,plain,
    r2_hidden(sK2,k2_xboole_0(sK1,sK3)),
    inference(forward_demodulation,[],[f59,f72]) ).

fof(f59,plain,
    r2_hidden(sK2,k2_xboole_0(sK3,sK1)),
    inference(cnf_transformation,[],[f44]) ).

fof(f131,plain,
    ( ~ r2_hidden(sK2,k2_xboole_0(sK1,sK3))
    | spl5_1
    | spl5_4 ),
    inference(forward_demodulation,[],[f123,f70]) ).

fof(f123,plain,
    ( ~ r2_hidden(sK2,k2_xboole_0(sK1,k4_xboole_0(sK3,sK1)))
    | spl5_1
    | spl5_4 ),
    inference(unit_resulting_resolution,[],[f85,f101,f81]) ).

fof(f101,plain,
    ( ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1))
    | spl5_4 ),
    inference(avatar_component_clause,[],[f99]) ).

fof(f99,plain,
    ( spl5_4
  <=> r2_hidden(sK2,k4_xboole_0(sK3,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f85,plain,
    ( ~ r2_hidden(sK2,sK1)
    | spl5_1 ),
    inference(avatar_component_clause,[],[f83]) ).

fof(f83,plain,
    ( spl5_1
  <=> r2_hidden(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f103,plain,
    ( ~ spl5_4
    | ~ spl5_3 ),
    inference(avatar_split_clause,[],[f55,f93,f99]) ).

fof(f55,plain,
    ( ~ r2_hidden(sK0,sK1)
    | ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1)) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f102,plain,
    ( ~ spl5_2
    | ~ spl5_4 ),
    inference(avatar_split_clause,[],[f60,f99,f87]) ).

fof(f60,plain,
    ( ~ r2_hidden(sK2,k4_xboole_0(sK3,sK1))
    | ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1)) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f96,plain,
    ( ~ spl5_1
    | ~ spl5_3 ),
    inference(avatar_split_clause,[],[f56,f93,f83]) ).

fof(f56,plain,
    ( ~ r2_hidden(sK0,sK1)
    | ~ r2_hidden(sK2,sK1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f90,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f58,f87,f83]) ).

fof(f58,plain,
    ( ~ r2_hidden(sK0,k4_xboole_0(sK3,sK1))
    | ~ r2_hidden(sK2,sK1) ),
    inference(cnf_transformation,[],[f44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% 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
% 0.13/0.34  % Computer : n012.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 15:25:35 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.55  % (17540)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.55  % (17548)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.56  % (17555)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.56  % (17543)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)
% 0.19/0.56  % (17540)First to succeed.
% 0.19/0.57  % (17555)Instruction limit reached!
% 0.19/0.57  % (17555)------------------------------
% 0.19/0.57  % (17555)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57  % (17555)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57  % (17555)Termination reason: Unknown
% 0.19/0.57  % (17555)Termination phase: Saturation
% 0.19/0.57  
% 0.19/0.57  % (17555)Memory used [KB]: 1407
% 0.19/0.57  % (17555)Time elapsed: 0.004 s
% 0.19/0.57  % (17555)Instructions burned: 2 (million)
% 0.19/0.57  % (17555)------------------------------
% 0.19/0.57  % (17555)------------------------------
% 0.19/0.57  % (17540)Refutation found. Thanks to Tanya!
% 0.19/0.57  % SZS status Theorem for theBenchmark
% 0.19/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.57  % (17540)------------------------------
% 0.19/0.57  % (17540)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57  % (17540)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57  % (17540)Termination reason: Refutation
% 0.19/0.57  
% 0.19/0.57  % (17540)Memory used [KB]: 6012
% 0.19/0.57  % (17540)Time elapsed: 0.135 s
% 0.19/0.57  % (17540)Instructions burned: 4 (million)
% 0.19/0.57  % (17540)------------------------------
% 0.19/0.57  % (17540)------------------------------
% 0.19/0.57  % (17536)Success in time 0.219 s
%------------------------------------------------------------------------------