TSTP Solution File: SEU407+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU407+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n008.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 : Thu Aug 31 17:58:48 EDT 2023

% Result   : Theorem 0.22s 0.45s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   99 (  31 unt;   0 def)
%            Number of atoms       :  354 (  54 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  428 ( 173   ~; 141   |;  88   &)
%                                         (   8 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   4 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   8 con; 0-6 aty)
%            Number of variables   :  124 (; 105   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f858,plain,
    $false,
    inference(avatar_sat_refutation,[],[f274,f293,f848,f857]) ).

fof(f857,plain,
    ~ spl18_5,
    inference(avatar_split_clause,[],[f851,f263]) ).

fof(f263,plain,
    ( spl18_5
  <=> v3_struct_0(sF16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).

fof(f851,plain,
    ~ v3_struct_0(sF16),
    inference(subsumption_resolution,[],[f850,f132]) ).

fof(f132,plain,
    l1_orders_2(sK0),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ( ~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)))
    & ~ r2_hidden(sK2,u1_struct_0(sK0))
    & m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
    & l1_orders_2(sK1)
    & ~ v3_struct_0(sK1)
    & l1_orders_2(sK0)
    & ~ v3_struct_0(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f61,f103,f102,f101]) ).

fof(f101,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
                & ~ r2_hidden(X2,u1_struct_0(X0))
                & m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
            & l1_orders_2(X1)
            & ~ v3_struct_0(X1) )
        & l1_orders_2(X0)
        & ~ v3_struct_0(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(sK0)))
              & ~ r2_hidden(X2,u1_struct_0(sK0))
              & m1_subset_1(X2,u1_struct_0(k1_latsum_1(sK0,X1))) )
          & l1_orders_2(X1)
          & ~ v3_struct_0(X1) )
      & l1_orders_2(sK0)
      & ~ v3_struct_0(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(sK0)))
            & ~ r2_hidden(X2,u1_struct_0(sK0))
            & m1_subset_1(X2,u1_struct_0(k1_latsum_1(sK0,X1))) )
        & l1_orders_2(X1)
        & ~ v3_struct_0(X1) )
   => ( ? [X2] :
          ( ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)))
          & ~ r2_hidden(X2,u1_struct_0(sK0))
          & m1_subset_1(X2,u1_struct_0(k1_latsum_1(sK0,sK1))) )
      & l1_orders_2(sK1)
      & ~ v3_struct_0(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ( ? [X2] :
        ( ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)))
        & ~ r2_hidden(X2,u1_struct_0(sK0))
        & m1_subset_1(X2,u1_struct_0(k1_latsum_1(sK0,sK1))) )
   => ( ~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)))
      & ~ r2_hidden(sK2,u1_struct_0(sK0))
      & m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
              & ~ r2_hidden(X2,u1_struct_0(X0))
              & m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
          & l1_orders_2(X1)
          & ~ v3_struct_0(X1) )
      & l1_orders_2(X0)
      & ~ v3_struct_0(X0) ),
    inference(flattening,[],[f60]) ).

fof(f60,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
              & ~ r2_hidden(X2,u1_struct_0(X0))
              & m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
          & l1_orders_2(X1)
          & ~ v3_struct_0(X1) )
      & l1_orders_2(X0)
      & ~ v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( ( l1_orders_2(X0)
          & ~ v3_struct_0(X0) )
       => ! [X1] :
            ( ( l1_orders_2(X1)
              & ~ v3_struct_0(X1) )
           => ! [X2] :
                ( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
               => ( r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
                  | r2_hidden(X2,u1_struct_0(X0)) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X0] :
      ( ( l1_orders_2(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( ( l1_orders_2(X1)
            & ~ v3_struct_0(X1) )
         => ! [X2] :
              ( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
             => ( r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
                | r2_hidden(X2,u1_struct_0(X0)) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',t7_latsum_1) ).

fof(f850,plain,
    ( ~ v3_struct_0(sF16)
    | ~ l1_orders_2(sK0) ),
    inference(subsumption_resolution,[],[f849,f133]) ).

fof(f133,plain,
    ~ v3_struct_0(sK1),
    inference(cnf_transformation,[],[f104]) ).

fof(f849,plain,
    ( ~ v3_struct_0(sF16)
    | v3_struct_0(sK1)
    | ~ l1_orders_2(sK0) ),
    inference(subsumption_resolution,[],[f399,f134]) ).

fof(f134,plain,
    l1_orders_2(sK1),
    inference(cnf_transformation,[],[f104]) ).

fof(f399,plain,
    ( ~ v3_struct_0(sF16)
    | ~ l1_orders_2(sK1)
    | v3_struct_0(sK1)
    | ~ l1_orders_2(sK0) ),
    inference(superposition,[],[f169,f208]) ).

fof(f208,plain,
    k1_latsum_1(sK0,sK1) = sF16,
    introduced(function_definition,[]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( ~ v3_struct_0(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(X1)
      | v3_struct_0(X1)
      | ~ l1_orders_2(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( v1_orders_2(k1_latsum_1(X0,X1))
        & ~ v3_struct_0(k1_latsum_1(X0,X1)) )
      | ~ l1_orders_2(X1)
      | v3_struct_0(X1)
      | ~ l1_orders_2(X0) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ( v1_orders_2(k1_latsum_1(X0,X1))
        & ~ v3_struct_0(k1_latsum_1(X0,X1)) )
      | ~ l1_orders_2(X1)
      | v3_struct_0(X1)
      | ~ l1_orders_2(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ( l1_orders_2(X1)
        & ~ v3_struct_0(X1)
        & l1_orders_2(X0) )
     => ( v1_orders_2(k1_latsum_1(X0,X1))
        & ~ v3_struct_0(k1_latsum_1(X0,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',fc1_latsum_1) ).

fof(f848,plain,
    spl18_7,
    inference(avatar_contradiction_clause,[],[f847]) ).

fof(f847,plain,
    ( $false
    | spl18_7 ),
    inference(subsumption_resolution,[],[f842,f279]) ).

fof(f279,plain,
    ( r2_hidden(sK2,sF17)
    | spl18_7 ),
    inference(subsumption_resolution,[],[f276,f273]) ).

fof(f273,plain,
    ( ~ v1_xboole_0(sF17)
    | spl18_7 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f271,plain,
    ( spl18_7
  <=> v1_xboole_0(sF17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).

fof(f276,plain,
    ( v1_xboole_0(sF17)
    | r2_hidden(sK2,sF17) ),
    inference(resolution,[],[f161,f210]) ).

fof(f210,plain,
    m1_subset_1(sK2,sF17),
    inference(definition_folding,[],[f135,f209,f208]) ).

fof(f209,plain,
    u1_struct_0(sF16) = sF17,
    introduced(function_definition,[]) ).

fof(f135,plain,
    m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
    inference(cnf_transformation,[],[f104]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ~ m1_subset_1(X0,X1)
      | v1_xboole_0(X1)
      | r2_hidden(X0,X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( r2_hidden(X0,X1)
      | v1_xboole_0(X1)
      | ~ m1_subset_1(X0,X1) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( r2_hidden(X0,X1)
      | v1_xboole_0(X1)
      | ~ m1_subset_1(X0,X1) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,axiom,
    ! [X0,X1] :
      ( m1_subset_1(X0,X1)
     => ( r2_hidden(X0,X1)
        | v1_xboole_0(X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',t2_subset) ).

fof(f842,plain,
    ~ r2_hidden(sK2,sF17),
    inference(backward_demodulation,[],[f682,f838]) ).

fof(f838,plain,
    sF17 = k2_xboole_0(sF14,sF13),
    inference(forward_demodulation,[],[f837,f209]) ).

fof(f837,plain,
    u1_struct_0(sF16) = k2_xboole_0(sF14,sF13),
    inference(forward_demodulation,[],[f836,f208]) ).

fof(f836,plain,
    u1_struct_0(k1_latsum_1(sK0,sK1)) = k2_xboole_0(sF14,sF13),
    inference(forward_demodulation,[],[f835,f155]) ).

fof(f155,plain,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',commutativity_k2_xboole_0) ).

fof(f835,plain,
    u1_struct_0(k1_latsum_1(sK0,sK1)) = k2_xboole_0(sF13,sF14),
    inference(forward_demodulation,[],[f831,f204]) ).

fof(f204,plain,
    u1_struct_0(sK0) = sF14,
    introduced(function_definition,[]) ).

fof(f831,plain,
    u1_struct_0(k1_latsum_1(sK0,sK1)) = k2_xboole_0(sF13,u1_struct_0(sK0)),
    inference(resolution,[],[f635,f132]) ).

fof(f635,plain,
    ! [X7] :
      ( ~ l1_orders_2(X7)
      | u1_struct_0(k1_latsum_1(X7,sK1)) = k2_xboole_0(sF13,u1_struct_0(X7)) ),
    inference(forward_demodulation,[],[f634,f155]) ).

fof(f634,plain,
    ! [X7] :
      ( u1_struct_0(k1_latsum_1(X7,sK1)) = k2_xboole_0(u1_struct_0(X7),sF13)
      | ~ l1_orders_2(X7) ),
    inference(forward_demodulation,[],[f629,f203]) ).

fof(f203,plain,
    u1_struct_0(sK1) = sF13,
    introduced(function_definition,[]) ).

fof(f629,plain,
    ! [X7] :
      ( u1_struct_0(k1_latsum_1(X7,sK1)) = k2_xboole_0(u1_struct_0(X7),u1_struct_0(sK1))
      | ~ l1_orders_2(X7) ),
    inference(resolution,[],[f613,f134]) ).

fof(f613,plain,
    ! [X0,X1] :
      ( ~ l1_orders_2(X1)
      | u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
      | ~ l1_orders_2(X0) ),
    inference(subsumption_resolution,[],[f612,f171]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( v1_orders_2(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ( l1_orders_2(k1_latsum_1(X0,X1))
        & v1_orders_2(k1_latsum_1(X0,X1)) )
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(X0) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ( l1_orders_2(k1_latsum_1(X0,X1))
        & v1_orders_2(k1_latsum_1(X0,X1)) )
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ( l1_orders_2(X1)
        & l1_orders_2(X0) )
     => ( l1_orders_2(k1_latsum_1(X0,X1))
        & v1_orders_2(k1_latsum_1(X0,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',dt_k1_latsum_1) ).

fof(f612,plain,
    ! [X0,X1] :
      ( u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
      | ~ v1_orders_2(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(X0) ),
    inference(subsumption_resolution,[],[f199,f172]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( l1_orders_2(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
      | ~ l1_orders_2(k1_latsum_1(X0,X1))
      | ~ v1_orders_2(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(X0) ),
    inference(equality_resolution,[],[f146]) ).

fof(f146,plain,
    ! [X2,X0,X1] :
      ( u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
      | k1_latsum_1(X0,X1) != X2
      | ~ l1_orders_2(X2)
      | ~ v1_orders_2(X2)
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( k1_latsum_1(X0,X1) = X2
                  | u1_orders_2(X2) != k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
                  | u1_struct_0(X2) != k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) )
                & ( ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
                    & u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) )
                  | k1_latsum_1(X0,X1) != X2 ) )
              | ~ l1_orders_2(X2)
              | ~ v1_orders_2(X2) )
          | ~ l1_orders_2(X1) )
      | ~ l1_orders_2(X0) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( k1_latsum_1(X0,X1) = X2
                  | u1_orders_2(X2) != k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
                  | u1_struct_0(X2) != k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) )
                & ( ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
                    & u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) )
                  | k1_latsum_1(X0,X1) != X2 ) )
              | ~ l1_orders_2(X2)
              | ~ v1_orders_2(X2) )
          | ~ l1_orders_2(X1) )
      | ~ l1_orders_2(X0) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( k1_latsum_1(X0,X1) = X2
              <=> ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
                  & u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ) )
              | ~ l1_orders_2(X2)
              | ~ v1_orders_2(X2) )
          | ~ l1_orders_2(X1) )
      | ~ l1_orders_2(X0) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( k1_latsum_1(X0,X1) = X2
              <=> ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
                  & u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ) )
              | ~ l1_orders_2(X2)
              | ~ v1_orders_2(X2) )
          | ~ l1_orders_2(X1) )
      | ~ l1_orders_2(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( l1_orders_2(X0)
     => ! [X1] :
          ( l1_orders_2(X1)
         => ! [X2] :
              ( ( l1_orders_2(X2)
                & v1_orders_2(X2) )
             => ( k1_latsum_1(X0,X1) = X2
              <=> ( u1_orders_2(X2) = k2_xboole_0(k2_xboole_0(u1_orders_2(X0),u1_orders_2(X1)),k7_relset_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X0),u1_orders_2(X1)))
                  & u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',d2_latsum_1) ).

fof(f682,plain,
    ~ r2_hidden(sK2,k2_xboole_0(sF14,sF13)),
    inference(subsumption_resolution,[],[f681,f207]) ).

fof(f207,plain,
    ~ r2_hidden(sK2,sF14),
    inference(definition_folding,[],[f136,f204]) ).

fof(f136,plain,
    ~ r2_hidden(sK2,u1_struct_0(sK0)),
    inference(cnf_transformation,[],[f104]) ).

fof(f681,plain,
    ( ~ r2_hidden(sK2,k2_xboole_0(sF14,sF13))
    | r2_hidden(sK2,sF14) ),
    inference(superposition,[],[f535,f341]) ).

fof(f341,plain,
    k2_xboole_0(sF14,sF13) = k2_xboole_0(sF14,sF15),
    inference(superposition,[],[f156,f205]) ).

fof(f205,plain,
    k4_xboole_0(sF13,sF14) = sF15,
    introduced(function_definition,[]) ).

fof(f156,plain,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,axiom,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',t39_xboole_1) ).

fof(f535,plain,
    ! [X28] :
      ( ~ r2_hidden(sK2,k2_xboole_0(X28,sF15))
      | r2_hidden(sK2,X28) ),
    inference(resolution,[],[f202,f206]) ).

fof(f206,plain,
    ~ r2_hidden(sK2,sF15),
    inference(definition_folding,[],[f137,f205,f204,f203]) ).

fof(f137,plain,
    ~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0))),
    inference(cnf_transformation,[],[f104]) ).

fof(f202,plain,
    ! [X0,X1,X4] :
      ( r2_hidden(X4,X1)
      | r2_hidden(X4,X0)
      | ~ r2_hidden(X4,k2_xboole_0(X0,X1)) ),
    inference(equality_resolution,[],[f183]) ).

fof(f183,plain,
    ! [X2,X0,X1,X4] :
      ( r2_hidden(X4,X1)
      | r2_hidden(X4,X0)
      | ~ r2_hidden(X4,X2)
      | k2_xboole_0(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0,X1,X2] :
      ( ( k2_xboole_0(X0,X1) = X2
        | ( ( ( ~ r2_hidden(sK7(X0,X1,X2),X1)
              & ~ r2_hidden(sK7(X0,X1,X2),X0) )
            | ~ r2_hidden(sK7(X0,X1,X2),X2) )
          & ( r2_hidden(sK7(X0,X1,X2),X1)
            | r2_hidden(sK7(X0,X1,X2),X0)
            | r2_hidden(sK7(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( r2_hidden(X4,X2)
              | ( ~ r2_hidden(X4,X1)
                & ~ r2_hidden(X4,X0) ) )
            & ( r2_hidden(X4,X1)
              | r2_hidden(X4,X0)
              | ~ r2_hidden(X4,X2) ) )
        | k2_xboole_0(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f118,f119]) ).

fof(f119,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ r2_hidden(X3,X1)
              & ~ r2_hidden(X3,X0) )
            | ~ r2_hidden(X3,X2) )
          & ( r2_hidden(X3,X1)
            | r2_hidden(X3,X0)
            | r2_hidden(X3,X2) ) )
     => ( ( ( ~ r2_hidden(sK7(X0,X1,X2),X1)
            & ~ r2_hidden(sK7(X0,X1,X2),X0) )
          | ~ r2_hidden(sK7(X0,X1,X2),X2) )
        & ( r2_hidden(sK7(X0,X1,X2),X1)
          | r2_hidden(sK7(X0,X1,X2),X0)
          | r2_hidden(sK7(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f118,plain,
    ! [X0,X1,X2] :
      ( ( k2_xboole_0(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ r2_hidden(X3,X1)
                & ~ r2_hidden(X3,X0) )
              | ~ r2_hidden(X3,X2) )
            & ( r2_hidden(X3,X1)
              | r2_hidden(X3,X0)
              | r2_hidden(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( r2_hidden(X4,X2)
              | ( ~ r2_hidden(X4,X1)
                & ~ r2_hidden(X4,X0) ) )
            & ( r2_hidden(X4,X1)
              | r2_hidden(X4,X0)
              | ~ r2_hidden(X4,X2) ) )
        | k2_xboole_0(X0,X1) != X2 ) ),
    inference(rectify,[],[f117]) ).

fof(f117,plain,
    ! [X0,X1,X2] :
      ( ( k2_xboole_0(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ r2_hidden(X3,X1)
                & ~ r2_hidden(X3,X0) )
              | ~ r2_hidden(X3,X2) )
            & ( r2_hidden(X3,X1)
              | r2_hidden(X3,X0)
              | r2_hidden(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( r2_hidden(X3,X2)
              | ( ~ r2_hidden(X3,X1)
                & ~ r2_hidden(X3,X0) ) )
            & ( r2_hidden(X3,X1)
              | r2_hidden(X3,X0)
              | ~ r2_hidden(X3,X2) ) )
        | k2_xboole_0(X0,X1) != X2 ) ),
    inference(flattening,[],[f116]) ).

fof(f116,plain,
    ! [X0,X1,X2] :
      ( ( k2_xboole_0(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ r2_hidden(X3,X1)
                & ~ r2_hidden(X3,X0) )
              | ~ r2_hidden(X3,X2) )
            & ( r2_hidden(X3,X1)
              | r2_hidden(X3,X0)
              | r2_hidden(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( r2_hidden(X3,X2)
              | ( ~ r2_hidden(X3,X1)
                & ~ r2_hidden(X3,X0) ) )
            & ( r2_hidden(X3,X1)
              | r2_hidden(X3,X0)
              | ~ r2_hidden(X3,X2) ) )
        | k2_xboole_0(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( k2_xboole_0(X0,X1) = X2
    <=> ! [X3] :
          ( r2_hidden(X3,X2)
        <=> ( r2_hidden(X3,X1)
            | r2_hidden(X3,X0) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',d2_xboole_0) ).

fof(f293,plain,
    spl18_6,
    inference(avatar_contradiction_clause,[],[f292]) ).

fof(f292,plain,
    ( $false
    | spl18_6 ),
    inference(subsumption_resolution,[],[f291,f132]) ).

fof(f291,plain,
    ( ~ l1_orders_2(sK0)
    | spl18_6 ),
    inference(subsumption_resolution,[],[f290,f134]) ).

fof(f290,plain,
    ( ~ l1_orders_2(sK1)
    | ~ l1_orders_2(sK0)
    | spl18_6 ),
    inference(subsumption_resolution,[],[f289,f275]) ).

fof(f275,plain,
    ( ~ l1_orders_2(sF16)
    | spl18_6 ),
    inference(resolution,[],[f269,f143]) ).

fof(f143,plain,
    ! [X0] :
      ( l1_struct_0(X0)
      | ~ l1_orders_2(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( l1_struct_0(X0)
      | ~ l1_orders_2(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( l1_orders_2(X0)
     => l1_struct_0(X0) ),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',dt_l1_orders_2) ).

fof(f269,plain,
    ( ~ l1_struct_0(sF16)
    | spl18_6 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f267,plain,
    ( spl18_6
  <=> l1_struct_0(sF16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).

fof(f289,plain,
    ( l1_orders_2(sF16)
    | ~ l1_orders_2(sK1)
    | ~ l1_orders_2(sK0) ),
    inference(superposition,[],[f172,f208]) ).

fof(f274,plain,
    ( spl18_5
    | ~ spl18_6
    | ~ spl18_7 ),
    inference(avatar_split_clause,[],[f220,f271,f267,f263]) ).

fof(f220,plain,
    ( ~ v1_xboole_0(sF17)
    | ~ l1_struct_0(sF16)
    | v3_struct_0(sF16) ),
    inference(superposition,[],[f149,f209]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ v1_xboole_0(u1_struct_0(X0))
      | ~ l1_struct_0(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ v1_xboole_0(u1_struct_0(X0))
      | ~ l1_struct_0(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ v1_xboole_0(u1_struct_0(X0))
      | ~ l1_struct_0(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0] :
      ( ( l1_struct_0(X0)
        & ~ v3_struct_0(X0) )
     => ~ v1_xboole_0(u1_struct_0(X0)) ),
    file('/export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608',fc1_struct_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU407+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36  % Computer : n008.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Wed Aug 23 15:29:02 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.PXN9lGHj3x/Vampire---4.8_10608
% 0.14/0.37  % (10783)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (10785)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.43  % (10784)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.43  % (10787)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.22/0.43  % (10786)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.43  % (10789)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.43  % (10788)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.43  % (10790)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.43  % (10787)Refutation not found, incomplete strategy% (10787)------------------------------
% 0.22/0.43  % (10787)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43  % (10787)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43  % (10787)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43  
% 0.22/0.43  % (10787)Memory used [KB]: 10106
% 0.22/0.43  % (10787)Time elapsed: 0.007 s
% 0.22/0.43  % (10787)------------------------------
% 0.22/0.43  % (10787)------------------------------
% 0.22/0.45  % (10789)First to succeed.
% 0.22/0.45  % (10789)Refutation found. Thanks to Tanya!
% 0.22/0.45  % SZS status Theorem for Vampire---4
% 0.22/0.45  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.45  % (10789)------------------------------
% 0.22/0.45  % (10789)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45  % (10789)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45  % (10789)Termination reason: Refutation
% 0.22/0.45  
% 0.22/0.45  % (10789)Memory used [KB]: 5884
% 0.22/0.45  % (10789)Time elapsed: 0.024 s
% 0.22/0.45  % (10789)------------------------------
% 0.22/0.45  % (10789)------------------------------
% 0.22/0.45  % (10783)Success in time 0.082 s
% 0.22/0.45  % Vampire---4.8 exiting
%------------------------------------------------------------------------------