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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SEU407+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 12:53:09 PM UTC 2026

% Result   : Theorem 0.35s 0.48s
% Output   : Refutation 0.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   91 (  25 unt;   4 def)
%            Number of atoms       :  247 (  26 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  272 ( 116   ~; 103   |;  30   &)
%                                         (   9 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   5 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-6 aty)
%            Number of variables   :   88 (   0 sgn  82   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [X0] :
      ( ( ~ v3_struct_0(X0)
        & l1_orders_2(X0) )
     => ! [X1] :
          ( ( ~ v3_struct_0(X1)
            & l1_orders_2(X1) )
         => ! [X2] :
              ( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
             => ( r2_hidden(X2,u1_struct_0(X0))
                | r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_latsum_1) ).

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

fof(f6,axiom,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f7,axiom,
    ! [X0] :
      ( l1_orders_2(X0)
     => ! [X1] :
          ( l1_orders_2(X1)
         => ! [X2] :
              ( ( v1_orders_2(X2)
                & l1_orders_2(X2) )
             => ( X2 = k1_latsum_1(X0,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))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_latsum_1) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( X2 = k2_xboole_0(X0,X1)
    <=> ! [X3] :
          ( r2_hidden(X3,X2)
        <=> ( r2_hidden(X3,X0)
            | r2_hidden(X3,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ( l1_orders_2(X0)
        & l1_orders_2(X1) )
     => ( v1_orders_2(k1_latsum_1(X0,X1))
        & l1_orders_2(k1_latsum_1(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).

fof(f18,axiom,
    ! [X0] :
      ( l1_orders_2(X0)
     => l1_struct_0(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).

fof(f31,axiom,
    ! [X0] :
      ( ( ~ v3_struct_0(X0)
        & l1_struct_0(X0) )
     => ~ v1_xboole_0(u1_struct_0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( ( ~ v3_struct_0(X0)
        & l1_orders_2(X0)
        & l1_orders_2(X1) )
     => ( ~ v3_struct_0(k1_latsum_1(X0,X1))
        & v1_orders_2(k1_latsum_1(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_latsum_1) ).

fof(f47,axiom,
    ! [X0,X1] :
      ( m1_subset_1(X0,X1)
     => ( v1_xboole_0(X1)
        | r2_hidden(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f48,axiom,
    ! [X0,X1] : k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).

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

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

fof(f66,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( X2 = k1_latsum_1(X0,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))) ) )
              | ~ v1_orders_2(X2)
              | ~ l1_orders_2(X2) )
          | ~ l1_orders_2(X1) )
      | ~ l1_orders_2(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( X2 = k1_latsum_1(X0,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))) ) )
              | ~ v1_orders_2(X2)
              | ~ l1_orders_2(X2) )
          | ~ l1_orders_2(X1) )
      | ~ l1_orders_2(X0) ),
    inference(flattening,[],[f66]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ( v1_orders_2(k1_latsum_1(X0,X1))
        & l1_orders_2(k1_latsum_1(X0,X1)) )
      | ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ( v1_orders_2(k1_latsum_1(X0,X1))
        & l1_orders_2(k1_latsum_1(X0,X1)) )
      | ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1) ),
    inference(flattening,[],[f69]) ).

fof(f75,plain,
    ! [X0] :
      ( l1_struct_0(X0)
      | ~ l1_orders_2(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f80,plain,
    ! [X0] :
      ( ~ v1_xboole_0(u1_struct_0(X0))
      | v3_struct_0(X0)
      | ~ l1_struct_0(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ v1_xboole_0(u1_struct_0(X0))
      | v3_struct_0(X0)
      | ~ l1_struct_0(X0) ),
    inference(flattening,[],[f80]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( ~ v3_struct_0(k1_latsum_1(X0,X1))
        & v1_orders_2(k1_latsum_1(X0,X1)) )
      | v3_struct_0(X0)
      | ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( ~ v3_struct_0(k1_latsum_1(X0,X1))
        & v1_orders_2(k1_latsum_1(X0,X1)) )
      | v3_struct_0(X0)
      | ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1) ),
    inference(flattening,[],[f82]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( v1_xboole_0(X1)
      | r2_hidden(X0,X1)
      | ~ m1_subset_1(X0,X1) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( v1_xboole_0(X1)
      | r2_hidden(X0,X1)
      | ~ m1_subset_1(X0,X1) ),
    inference(flattening,[],[f92]) ).

fof(f101,plain,
    m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
    inference(cnf_transformation,[],[f61]) ).

fof(f102,plain,
    ~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0))),
    inference(cnf_transformation,[],[f61]) ).

fof(f103,plain,
    ~ r2_hidden(sK2,u1_struct_0(sK0)),
    inference(cnf_transformation,[],[f61]) ).

fof(f104,plain,
    l1_orders_2(sK1),
    inference(cnf_transformation,[],[f61]) ).

fof(f105,plain,
    ~ v3_struct_0(sK1),
    inference(cnf_transformation,[],[f61]) ).

fof(f106,plain,
    l1_orders_2(sK0),
    inference(cnf_transformation,[],[f61]) ).

fof(f111,plain,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f113,plain,
    ! [X2,X0,X1] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(X2)
      | ~ v1_orders_2(X2)
      | u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
      | k1_latsum_1(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f67]) ).

fof(f118,plain,
    ! [X2,X3,X0,X1] :
      ( r2_hidden(X3,X1)
      | r2_hidden(X3,X0)
      | ~ r2_hidden(X3,X2)
      | k2_xboole_0(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f8]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( l1_orders_2(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( v1_orders_2(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f127,plain,
    ! [X0] :
      ( l1_struct_0(X0)
      | ~ l1_orders_2(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f137,plain,
    ! [X0] :
      ( ~ l1_struct_0(X0)
      | v3_struct_0(X0)
      | ~ v1_xboole_0(u1_struct_0(X0)) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ~ v3_struct_0(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(X0)
      | v3_struct_0(X0)
      | ~ l1_orders_2(X1) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ~ m1_subset_1(X0,X1)
      | r2_hidden(X0,X1)
      | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f159,plain,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
    inference(cnf_transformation,[],[f48]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(k1_latsum_1(X0,X1))
      | ~ v1_orders_2(k1_latsum_1(X0,X1))
      | u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
    inference(equality_resolution,[],[f113]) ).

fof(f172,plain,
    ! [X3,X0,X1] :
      ( ~ r2_hidden(X3,k2_xboole_0(X0,X1))
      | r2_hidden(X3,X0)
      | r2_hidden(X3,X1) ),
    inference(equality_resolution,[],[f118]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | ~ v1_orders_2(k1_latsum_1(X0,X1))
      | u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
    inference(forward_subsumption_resolution,[],[f168,f123]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
    inference(forward_subsumption_resolution,[],[f174,f124]) ).

fof(f203,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v1_xboole_0(u1_struct_0(X0))
      | ~ l1_orders_2(X0) ),
    inference(resolution,[],[f137,f127]) ).

fof(f239,plain,
    ( r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
    | v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1))) ),
    inference(resolution,[],[f158,f101]) ).

fof(f244,definition,
    ( spl13_4
  <=> v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1))) ),
    introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).

fof(f246,plain,
    ( v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1)))
    | ~ spl13_4 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f248,definition,
    ( spl13_5
  <=> r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))) ),
    introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).

fof(f250,plain,
    ( r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
    | ~ spl13_5 ),
    inference(avatar_component_clause,[],[f248]) ).

fof(f251,plain,
    ( spl13_4
    | spl13_5 ),
    inference(avatar_split_clause,[],[f239,f248,f244]) ).

fof(f359,plain,
    ! [X2,X0,X1] :
      ( r2_hidden(X2,k4_xboole_0(X1,X0))
      | r2_hidden(X2,X0)
      | ~ r2_hidden(X2,k2_xboole_0(X0,X1)) ),
    inference(superposition,[],[f172,f159]) ).

fof(f384,plain,
    ! [X0] :
      ( ~ l1_orders_2(X0)
      | u1_struct_0(k1_latsum_1(sK0,X0)) = k2_xboole_0(u1_struct_0(sK0),u1_struct_0(X0)) ),
    inference(resolution,[],[f176,f106]) ).

fof(f385,plain,
    ! [X0] :
      ( ~ l1_orders_2(X0)
      | u1_struct_0(k1_latsum_1(sK1,X0)) = k2_xboole_0(u1_struct_0(sK1),u1_struct_0(X0)) ),
    inference(resolution,[],[f176,f104]) ).

fof(f397,plain,
    u1_struct_0(k1_latsum_1(sK0,sK1)) = k2_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),
    inference(resolution,[],[f384,f104]) ).

fof(f517,plain,
    u1_struct_0(k1_latsum_1(sK1,sK0)) = k2_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)),
    inference(resolution,[],[f385,f106]) ).

fof(f521,plain,
    k2_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)) = u1_struct_0(k1_latsum_1(sK1,sK0)),
    inference(forward_demodulation,[],[f517,f111]) ).

fof(f524,plain,
    u1_struct_0(k1_latsum_1(sK0,sK1)) = u1_struct_0(k1_latsum_1(sK1,sK0)),
    inference(forward_demodulation,[],[f521,f397]) ).

fof(f628,definition,
    ( spl13_17
  <=> l1_orders_2(k1_latsum_1(sK1,sK0)) ),
    introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition]) ).

fof(f629,plain,
    ( l1_orders_2(k1_latsum_1(sK1,sK0))
    | ~ spl13_17 ),
    inference(avatar_component_clause,[],[f628]) ).

fof(f630,plain,
    ( ~ l1_orders_2(k1_latsum_1(sK1,sK0))
    | spl13_17 ),
    inference(avatar_component_clause,[],[f628]) ).

fof(f650,plain,
    ( ~ l1_orders_2(sK1)
    | ~ l1_orders_2(sK0)
    | spl13_17 ),
    inference(resolution,[],[f630,f123]) ).

fof(f651,plain,
    ( ~ l1_orders_2(sK0)
    | spl13_17 ),
    inference(forward_subsumption_resolution,[],[f650,f104]) ).

fof(f652,plain,
    ( $false
    | spl13_17 ),
    inference(forward_subsumption_resolution,[],[f651,f106]) ).

fof(f653,plain,
    spl13_17,
    inference(avatar_contradiction_clause,[],[f652]) ).

fof(f969,definition,
    ( spl13_29
  <=> v3_struct_0(k1_latsum_1(sK1,sK0)) ),
    introduced(definition,[new_symbols(definition,[spl13_29])],[avatar_definition]) ).

fof(f970,plain,
    ( ~ v3_struct_0(k1_latsum_1(sK1,sK0))
    | spl13_29 ),
    inference(avatar_component_clause,[],[f969]) ).

fof(f971,plain,
    ( v3_struct_0(k1_latsum_1(sK1,sK0))
    | ~ spl13_29 ),
    inference(avatar_component_clause,[],[f969]) ).

fof(f1060,plain,
    ( ~ l1_orders_2(sK1)
    | v3_struct_0(sK1)
    | ~ l1_orders_2(sK0)
    | ~ spl13_29 ),
    inference(resolution,[],[f971,f140]) ).

fof(f1063,plain,
    ( v3_struct_0(sK1)
    | ~ l1_orders_2(sK0)
    | ~ spl13_29 ),
    inference(forward_subsumption_resolution,[],[f1060,f104]) ).

fof(f1065,plain,
    ( ~ l1_orders_2(sK0)
    | ~ spl13_29 ),
    inference(forward_subsumption_resolution,[],[f1063,f105]) ).

fof(f1068,plain,
    ( $false
    | ~ spl13_29 ),
    inference(forward_subsumption_resolution,[],[f1065,f106]) ).

fof(f1069,plain,
    ~ spl13_29,
    inference(avatar_contradiction_clause,[],[f1068]) ).

fof(f1102,plain,
    ( ~ v1_xboole_0(u1_struct_0(k1_latsum_1(sK1,sK0)))
    | ~ l1_orders_2(k1_latsum_1(sK1,sK0))
    | spl13_29 ),
    inference(resolution,[],[f970,f203]) ).

fof(f1103,plain,
    ( ~ v1_xboole_0(u1_struct_0(k1_latsum_1(sK1,sK0)))
    | ~ spl13_17
    | spl13_29 ),
    inference(forward_subsumption_resolution,[],[f1102,f629]) ).

fof(f1105,plain,
    ( ~ v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1)))
    | ~ spl13_17
    | spl13_29 ),
    inference(forward_demodulation,[],[f1103,f524]) ).

fof(f1174,plain,
    ( r2_hidden(sK2,u1_struct_0(sK0))
    | ~ r2_hidden(sK2,k2_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) ),
    inference(resolution,[],[f359,f102]) ).

fof(f1181,plain,
    ~ r2_hidden(sK2,k2_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),
    inference(forward_subsumption_resolution,[],[f1174,f103]) ).

fof(f1182,plain,
    ~ r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
    inference(forward_demodulation,[],[f1181,f397]) ).

fof(f1183,plain,
    ( $false
    | ~ spl13_5 ),
    inference(forward_subsumption_resolution,[],[f1182,f250]) ).

fof(f1184,plain,
    ~ spl13_5,
    inference(avatar_contradiction_clause,[],[f1183]) ).

fof(f1185,plain,
    ( $false
    | ~ spl13_4
    | ~ spl13_17
    | spl13_29 ),
    inference(forward_subsumption_resolution,[],[f1105,f246]) ).

fof(f1186,plain,
    ( ~ spl13_4
    | ~ spl13_17
    | spl13_29 ),
    inference(avatar_contradiction_clause,[],[f1185]) ).

cnf(s3,plain,
    ( spl13_4
    | spl13_5 ),
    inference(sat_conversion,[],[f251]) ).

cnf(s15,plain,
    spl13_17,
    inference(sat_conversion,[],[f653]) ).

cnf(s31,plain,
    ~ spl13_29,
    inference(sat_conversion,[],[f1069]) ).

cnf(s34,plain,
    ~ spl13_5,
    inference(sat_conversion,[],[f1184]) ).

cnf(s35,plain,
    ( ~ spl13_4
    | ~ spl13_17
    | spl13_29 ),
    inference(sat_conversion,[],[f1186]) ).

cnf(s44,plain,
    ~ spl13_4,
    inference(rat,[],[s35,s31,s15]) ).

cnf(s52,plain,
    $false,
    inference(rat,[],[s3,s34,s44]) ).

fof(f1187,plain,
    $false,
    inference(avatar_sat_refutation,[],[s52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU407+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37  % Computer : n010.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Mon Sep 28 05:10:47 UTC 2026
% 0.09/0.38  % CPUTime  : 
% 0.09/0.38  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41  Running first-order model finding
% 0.09/0.41  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.48  % (1569267)Will run a generic schedule for satisfiability detection.
% 0.35/0.48  % (1569274)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4066158868:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.35/0.48  % (1569272)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1569976120_2999 on theBenchmark for (2999ds/0Mi)
% 0.35/0.48  % (1569275)dis+10_1_sil=32000:sp=arity:random_seed=444826988:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.35/0.48  % (1569276)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=363785862:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.35/0.48  % (1569277)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1891757466:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.35/0.48  % (1569278)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1442365543:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.35/0.48  % (1569273)% WARNING: option uhcvi not known.
% 0.35/0.48  % TRYING [1]
% 0.35/0.48  % (1569273)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1005677530:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.35/0.48  % TRYING [2]
% 0.35/0.48  % TRYING [3]
% 0.35/0.48  % (1569276) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1569267-1569276"...
% 0.35/0.48  % (1569276)...printing done.
% 0.35/0.48  % (1569273) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1569267-1569273"...
% 0.35/0.48  % (1569276)Refutation found. Thanks to Tanya!
% 0.35/0.48  % SZS status Theorem for theBenchmark
% 0.35/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.48  % (1569276)------------------------------
% 0.35/0.48  % (1569276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.48  % (1569276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.48  % (1569276)CaDiCaL version: 2.1.3
% 0.35/0.48  % (1569276)Termination reason: Refutation
% 0.35/0.48  % (1569276)Time elapsed: 0.031 s
% 0.35/0.48  % (1569276)Peak memory usage: 13 MB
% 0.35/0.48  % (1569276)Instructions burned: 43 (million)
% 0.35/0.48  % (1569267)Success in time 0.066 s
% 0.35/0.48  % Vampire exiting
%------------------------------------------------------------------------------