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

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SYN417+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n007.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 02:07:48 PM UTC 2026

% Result   : Theorem 0.08s 0.24s
% Output   : Refutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  107 (   9 unt;   8 def)
%            Number of atoms       :  383 ( 162 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  517 ( 241   ~; 235   |;  23   &)
%                                         (  11 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   10 (   8 usr;   9 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-1 aty)
%            Number of variables   :   60 (   0 sgn  44   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ( ? [X0] :
        ( X0 = f(g(X0))
        & ! [X1] :
            ( X1 = f(g(X1))
           => X0 = X1 ) )
  <=> ? [X0] :
        ( X0 = g(f(X0))
        & ! [X1] :
            ( X1 = g(f(X1))
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cute) ).

fof(f2,negated_conjecture,
    ~ ( ? [X0] :
          ( X0 = f(g(X0))
          & ! [X1] :
              ( X1 = f(g(X1))
             => X0 = X1 ) )
    <=> ? [X0] :
          ( X0 = g(f(X0))
          & ! [X1] :
              ( X1 = g(f(X1))
             => X0 = X1 ) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,plain,
    ~ ( ? [X0] :
          ( X0 = f(g(X0))
          & ! [X1] :
              ( X1 = f(g(X1))
             => X0 = X1 ) )
    <=> ? [X2] :
          ( g(f(X2)) = X2
          & ! [X3] :
              ( g(f(X3)) = X3
             => X2 = X3 ) ) ),
    inference(rectify,[],[f2]) ).

fof(f4,plain,
    ( ? [X0] :
        ( X0 = f(g(X0))
        & ! [X1] :
            ( X0 = X1
            | f(g(X1)) != X1 ) )
  <~> ? [X2] :
        ( g(f(X2)) = X2
        & ! [X3] :
            ( X2 = X3
            | g(f(X3)) != X3 ) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f5,plain,
    ( ( ! [X2] :
          ( g(f(X2)) != X2
          | ? [X3] :
              ( X2 != X3
              & g(f(X3)) = X3 ) )
      | ! [X0] :
          ( f(g(X0)) != X0
          | ? [X1] :
              ( X0 != X1
              & f(g(X1)) = X1 ) ) )
    & ( ? [X2] :
          ( g(f(X2)) = X2
          & ! [X3] :
              ( X2 = X3
              | g(f(X3)) != X3 ) )
      | ? [X0] :
          ( X0 = f(g(X0))
          & ! [X1] :
              ( X0 = X1
              | f(g(X1)) != X1 ) ) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f6,plain,
    ( ( ! [X0] :
          ( g(f(X0)) != X0
          | ? [X1] :
              ( X0 != X1
              & g(f(X1)) = X1 ) )
      | ! [X2] :
          ( f(g(X2)) != X2
          | ? [X3] :
              ( X2 != X3
              & f(g(X3)) = X3 ) ) )
    & ( ? [X4] :
          ( g(f(X4)) = X4
          & ! [X5] :
              ( X4 = X5
              | g(f(X5)) != X5 ) )
      | ? [X6] :
          ( f(g(X6)) = X6
          & ! [X7] :
              ( X6 = X7
              | f(g(X7)) != X7 ) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f7,plain,
    ( ( ! [X0] :
          ( g(f(X0)) != X0
          | ( sK0(X0) != X0
            & sK0(X0) = g(f(sK0(X0))) ) )
      | ! [X2] :
          ( f(g(X2)) != X2
          | ( sK1(X2) != X2
            & sK1(X2) = f(g(sK1(X2))) ) ) )
    & ( ( sK2 = g(f(sK2))
        & ! [X5] :
            ( sK2 = X5
            | g(f(X5)) != X5 ) )
      | ( sK3 = f(g(sK3))
        & ! [X7] :
            ( sK3 = X7
            | f(g(X7)) != X7 ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X1,sK0(X0)),skolemize(X3,sK1(X2)),skolemize(X4,sK2),skolemize(X6,sK3)],[f6]) ).

fof(f8,plain,
    ! [X7,X5] :
      ( sK2 = X5
      | g(f(X5)) != X5
      | sK3 = X7
      | f(g(X7)) != X7 ),
    inference(cnf_transformation,[],[f7]) ).

fof(f9,plain,
    ! [X5] :
      ( sK2 = X5
      | g(f(X5)) != X5
      | sK3 = f(g(sK3)) ),
    inference(cnf_transformation,[],[f7]) ).

fof(f10,plain,
    ! [X7] :
      ( sK2 = g(f(sK2))
      | sK3 = X7
      | f(g(X7)) != X7 ),
    inference(cnf_transformation,[],[f7]) ).

fof(f11,plain,
    ( sK2 = g(f(sK2))
    | sK3 = f(g(sK3)) ),
    inference(cnf_transformation,[],[f7]) ).

fof(f12,plain,
    ! [X2,X0] :
      ( g(f(X0)) != X0
      | sK0(X0) = g(f(sK0(X0)))
      | f(g(X2)) != X2
      | sK1(X2) = f(g(sK1(X2))) ),
    inference(cnf_transformation,[],[f7]) ).

fof(f13,plain,
    ! [X2,X0] :
      ( g(f(X0)) != X0
      | sK0(X0) = g(f(sK0(X0)))
      | f(g(X2)) != X2
      | sK1(X2) != X2 ),
    inference(cnf_transformation,[],[f7]) ).

fof(f14,plain,
    ! [X2,X0] :
      ( g(f(X0)) != X0
      | sK0(X0) != X0
      | f(g(X2)) != X2
      | sK1(X2) = f(g(sK1(X2))) ),
    inference(cnf_transformation,[],[f7]) ).

fof(f15,plain,
    ! [X2,X0] :
      ( g(f(X0)) != X0
      | sK0(X0) != X0
      | f(g(X2)) != X2
      | sK1(X2) != X2 ),
    inference(cnf_transformation,[],[f7]) ).

fof(f17,definition,
    ( spl4_1
  <=> ! [X7] :
        ( sK3 = X7
        | f(g(X7)) != X7 ) ),
    introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).

fof(f18,plain,
    ( ! [X7] :
        ( f(g(X7)) != X7
        | sK3 = X7 )
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f17]) ).

fof(f20,definition,
    ( spl4_2
  <=> ! [X5] :
        ( sK2 = X5
        | g(f(X5)) != X5 ) ),
    introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).

fof(f21,plain,
    ( ! [X5] :
        ( g(f(X5)) != X5
        | sK2 = X5 )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f20]) ).

fof(f22,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f8,f20,f17]) ).

fof(f24,definition,
    ( spl4_3
  <=> sK3 = f(g(sK3)) ),
    introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).

fof(f26,plain,
    ( sK3 = f(g(sK3))
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f24]) ).

fof(f27,plain,
    ( spl4_3
    | spl4_2 ),
    inference(avatar_split_clause,[],[f9,f20,f24]) ).

fof(f29,definition,
    ( spl4_4
  <=> sK2 = g(f(sK2)) ),
    introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).

fof(f30,plain,
    ( sK2 != g(f(sK2))
    | spl4_4 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f31,plain,
    ( sK2 = g(f(sK2))
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f32,plain,
    ( spl4_1
    | spl4_4 ),
    inference(avatar_split_clause,[],[f10,f29,f17]) ).

fof(f33,plain,
    ( spl4_3
    | spl4_4 ),
    inference(avatar_split_clause,[],[f11,f29,f24]) ).

fof(f35,definition,
    ( spl4_5
  <=> ! [X2] :
        ( f(g(X2)) != X2
        | sK1(X2) = f(g(sK1(X2))) ) ),
    introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).

fof(f36,plain,
    ( ! [X2] :
        ( f(g(X2)) != X2
        | sK1(X2) = f(g(sK1(X2))) )
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f38,definition,
    ( spl4_6
  <=> ! [X0] :
        ( g(f(X0)) != X0
        | sK0(X0) = g(f(sK0(X0))) ) ),
    introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).

fof(f39,plain,
    ( ! [X0] :
        ( g(f(X0)) != X0
        | sK0(X0) = g(f(sK0(X0))) )
    | ~ spl4_6 ),
    inference(avatar_component_clause,[],[f38]) ).

fof(f40,plain,
    ( spl4_5
    | spl4_6 ),
    inference(avatar_split_clause,[],[f12,f38,f35]) ).

fof(f42,definition,
    ( spl4_7
  <=> ! [X2] :
        ( f(g(X2)) != X2
        | sK1(X2) != X2 ) ),
    introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).

fof(f43,plain,
    ( ! [X2] :
        ( sK1(X2) != X2
        | f(g(X2)) != X2 )
    | ~ spl4_7 ),
    inference(avatar_component_clause,[],[f42]) ).

fof(f44,plain,
    ( spl4_7
    | spl4_6 ),
    inference(avatar_split_clause,[],[f13,f38,f42]) ).

fof(f46,definition,
    ( spl4_8
  <=> ! [X0] :
        ( g(f(X0)) != X0
        | sK0(X0) != X0 ) ),
    introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).

fof(f47,plain,
    ( ! [X0] :
        ( sK0(X0) != X0
        | g(f(X0)) != X0 )
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f48,plain,
    ( spl4_5
    | spl4_8 ),
    inference(avatar_split_clause,[],[f14,f46,f35]) ).

fof(f49,plain,
    ( spl4_7
    | spl4_8 ),
    inference(avatar_split_clause,[],[f15,f46,f42]) ).

fof(f50,plain,
    ( f(sK2) != f(sK2)
    | sK1(f(sK2)) = f(g(sK1(f(sK2))))
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(superposition,[],[f36,f31]) ).

fof(f51,plain,
    ( sK1(f(sK2)) = f(g(sK1(f(sK2))))
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f50]) ).

fof(f53,plain,
    ( g(sK1(f(sK2))) != g(sK1(f(sK2)))
    | sK2 = g(sK1(f(sK2)))
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(superposition,[],[f21,f51]) ).

fof(f54,plain,
    ( sK2 = g(sK1(f(sK2)))
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f53]) ).

fof(f56,plain,
    ( f(sK2) = sK1(f(sK2))
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(superposition,[],[f51,f54]) ).

fof(f60,plain,
    ( f(sK2) != f(sK2)
    | f(sK2) != f(g(f(sK2)))
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(superposition,[],[f43,f56]) ).

fof(f61,plain,
    ( f(sK2) != f(g(f(sK2)))
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f60]) ).

fof(f62,plain,
    ( f(sK2) != f(sK2)
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(forward_demodulation,[],[f61,f31]) ).

fof(f63,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f62]) ).

fof(f64,plain,
    ( ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(avatar_contradiction_clause,[],[f63]) ).

fof(f65,plain,
    ( sK2 != sK2
    | sK0(sK2) = g(f(sK0(sK2)))
    | ~ spl4_4
    | ~ spl4_6 ),
    inference(superposition,[],[f39,f31]) ).

fof(f66,plain,
    ( sK0(sK2) = g(f(sK0(sK2)))
    | ~ spl4_4
    | ~ spl4_6 ),
    inference(trivial_inequality_removal,[],[f65]) ).

fof(f68,plain,
    ( sK0(sK2) != sK0(sK2)
    | sK2 = sK0(sK2)
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_6 ),
    inference(superposition,[],[f21,f66]) ).

fof(f69,plain,
    ( sK2 = sK0(sK2)
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_6 ),
    inference(trivial_inequality_removal,[],[f68]) ).

fof(f73,plain,
    ( sK2 != sK2
    | sK2 != g(f(sK2))
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(superposition,[],[f47,f69]) ).

fof(f74,plain,
    ( sK2 != g(f(sK2))
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f73]) ).

fof(f75,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(forward_subsumption_resolution,[],[f74,f31]) ).

fof(f76,plain,
    ( ~ spl4_2
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(avatar_contradiction_clause,[],[f75]) ).

fof(f77,plain,
    ( g(sK3) != g(sK3)
    | sK0(g(sK3)) = g(f(sK0(g(sK3))))
    | ~ spl4_3
    | ~ spl4_6 ),
    inference(superposition,[],[f39,f26]) ).

fof(f78,plain,
    ( g(sK3) != g(sK3)
    | sK2 = g(sK3)
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(superposition,[],[f21,f26]) ).

fof(f79,plain,
    ( sK2 = g(sK3)
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(trivial_inequality_removal,[],[f78]) ).

fof(f80,plain,
    ( sK0(g(sK3)) = g(f(sK0(g(sK3))))
    | ~ spl4_3
    | ~ spl4_6 ),
    inference(trivial_inequality_removal,[],[f77]) ).

fof(f82,plain,
    ( f(sK2) = sK3
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(superposition,[],[f26,f79]) ).

fof(f83,plain,
    ( sK2 = g(f(sK2))
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(superposition,[],[f79,f82]) ).

fof(f85,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_3
    | spl4_4 ),
    inference(forward_subsumption_resolution,[],[f83,f30]) ).

fof(f86,plain,
    ( ~ spl4_2
    | ~ spl4_3
    | spl4_4 ),
    inference(avatar_contradiction_clause,[],[f85]) ).

fof(f88,plain,
    ( f(sK0(g(sK3))) != f(sK0(g(sK3)))
    | sK3 = f(sK0(g(sK3)))
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6 ),
    inference(superposition,[],[f18,f80]) ).

fof(f89,plain,
    ( sK3 = f(sK0(g(sK3)))
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6 ),
    inference(trivial_inequality_removal,[],[f88]) ).

fof(f91,plain,
    ( g(sK3) = sK0(g(sK3))
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6 ),
    inference(superposition,[],[f80,f89]) ).

fof(f95,plain,
    ( g(sK3) != g(sK3)
    | g(sK3) != g(f(g(sK3)))
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(superposition,[],[f47,f91]) ).

fof(f96,plain,
    ( g(sK3) != g(f(g(sK3)))
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f95]) ).

fof(f97,plain,
    ( g(sK3) != g(sK3)
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(forward_demodulation,[],[f96,f26]) ).

fof(f98,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f97]) ).

fof(f99,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(avatar_contradiction_clause,[],[f98]) ).

fof(f100,plain,
    ( sK3 != sK3
    | sK1(sK3) = f(g(sK1(sK3)))
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(superposition,[],[f36,f26]) ).

fof(f101,plain,
    ( sK1(sK3) = f(g(sK1(sK3)))
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f100]) ).

fof(f103,plain,
    ( sK1(sK3) != sK1(sK3)
    | sK3 = sK1(sK3)
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(superposition,[],[f18,f101]) ).

fof(f104,plain,
    ( sK3 = sK1(sK3)
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f103]) ).

fof(f108,plain,
    ( sK3 != sK3
    | sK3 != f(g(sK3))
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(superposition,[],[f43,f104]) ).

fof(f109,plain,
    ( sK3 != f(g(sK3))
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f108]) ).

fof(f110,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(forward_subsumption_resolution,[],[f109,f26]) ).

fof(f111,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(avatar_contradiction_clause,[],[f110]) ).

cnf(s1,plain,
    ( spl4_1
    | spl4_2 ),
    inference(sat_conversion,[],[f22]) ).

cnf(s2,plain,
    ( spl4_2
    | spl4_3 ),
    inference(sat_conversion,[],[f27]) ).

cnf(s3,plain,
    ( spl4_1
    | spl4_4 ),
    inference(sat_conversion,[],[f32]) ).

cnf(s4,plain,
    ( spl4_3
    | spl4_4 ),
    inference(sat_conversion,[],[f33]) ).

cnf(s5,plain,
    ( spl4_5
    | spl4_6 ),
    inference(sat_conversion,[],[f40]) ).

cnf(s6,plain,
    ( spl4_6
    | spl4_7 ),
    inference(sat_conversion,[],[f44]) ).

cnf(s7,plain,
    ( spl4_5
    | spl4_8 ),
    inference(sat_conversion,[],[f48]) ).

cnf(s8,plain,
    ( spl4_7
    | spl4_8 ),
    inference(sat_conversion,[],[f49]) ).

cnf(s9,plain,
    ( ~ spl4_2
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(sat_conversion,[],[f64]) ).

cnf(s10,plain,
    ( ~ spl4_2
    | ~ spl4_4
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(sat_conversion,[],[f76]) ).

cnf(s11,plain,
    ( ~ spl4_2
    | ~ spl4_3
    | spl4_4 ),
    inference(sat_conversion,[],[f86]) ).

cnf(s12,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_6
    | ~ spl4_8 ),
    inference(sat_conversion,[],[f99]) ).

cnf(s13,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_5
    | ~ spl4_7 ),
    inference(sat_conversion,[],[f111]) ).

cnf(s14,plain,
    ( spl4_5
    | spl4_1 ),
    inference(rat,[],[s10,s5,s7,s3,s1]) ).

cnf(s15,plain,
    ( ~ spl4_5
    | ~ spl4_2
    | ~ spl4_4 ),
    inference(rat,[],[s10,s6,s8,s9]) ).

cnf(s16,plain,
    spl4_1,
    inference(rat,[],[s15,s14,s1,s3]) ).

cnf(s17,plain,
    ( ~ spl4_4
    | ~ spl4_2 ),
    inference(rat,[],[s10,s5,s7,s15]) ).

cnf(s18,plain,
    ~ spl4_2,
    inference(rat,[],[s11,s4,s17]) ).

cnf(s19,plain,
    spl4_3,
    inference(rat,[],[s2,s18]) ).

cnf(s20,plain,
    spl4_5,
    inference(rat,[],[s12,s5,s7,s16,s19]) ).

cnf(s21,plain,
    ~ spl4_7,
    inference(rat,[],[s13,s19,s16,s20]) ).

cnf(s22,plain,
    spl4_8,
    inference(rat,[],[s8,s21]) ).

cnf(s23,plain,
    spl4_6,
    inference(rat,[],[s6,s21]) ).

cnf(s24,plain,
    $false,
    inference(rat,[],[s12,s19,s16,s22,s23]) ).

fof(f112,plain,
    $false,
    inference(avatar_sat_refutation,[],[s24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SYN417+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17  % Computer : n007.cluster.edu
% 0.08/0.17  % Model    : x86_64 x86_64
% 0.08/0.17  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17  % Memory   : 8046.5625MB
% 0.08/0.17  % OS       : Linux 6.8.0-71-generic
% 0.08/0.17  % CPULimit : 300
% 0.08/0.17  % WCLimit  : 300
% 0.08/0.17  % DateTime : Mon Sep 28 15:53:10 UTC 2026
% 0.08/0.17  % CPUTime  : 
% 0.08/0.17  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20  Running first-order model finding
% 0.08/0.20  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
% 0.08/0.24  % (2521303)Will run a generic schedule for satisfiability detection.
% 0.08/0.24  % (2521322)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=248562788:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.24  % (2521322) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2521303-2521322"...
% 0.08/0.24  % (2521322)...printing done.
% 0.08/0.24  % (2521322)Refutation found. Thanks to Tanya!
% 0.08/0.24  % SZS status Theorem for theBenchmark
% 0.08/0.24  % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.24  % (2521322)------------------------------
% 0.08/0.24  % (2521322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24  % (2521322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24  % (2521322)CaDiCaL version: 2.1.3
% 0.08/0.24  % (2521322)Termination reason: Refutation
% 0.08/0.24  % (2521322)Time elapsed: 0.003 s
% 0.08/0.24  % (2521322)Peak memory usage: 12 MB
% 0.08/0.24  % (2521322)Instructions burned: 5 (million)
% 0.08/0.24  % (2521303)Success in time 0.035 s
% 0.08/0.24  % Vampire exiting
%------------------------------------------------------------------------------