TSTP Solution File: SYN078+1 by SnakeForV-SAT---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : n004.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 19:36:50 EDT 2022

% Result   : Theorem 0.18s 0.46s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   50 (   3 unt;   0 def)
%            Number of atoms       :  155 (  23 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  168 (  63   ~;  62   |;  23   &)
%                                         (  10 <=>;   9  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   8 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :   39 (  25   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f68,plain,
    $false,
    inference(avatar_sat_refutation,[],[f28,f37,f42,f47,f48,f53,f54,f61,f65,f67]) ).

fof(f67,plain,
    ( spl5_4
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(avatar_split_clause,[],[f66,f58,f50,f39]) ).

fof(f39,plain,
    ( spl5_4
  <=> big_p(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f50,plain,
    ( spl5_6
  <=> sF4 = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

fof(f58,plain,
    ( spl5_7
  <=> big_p(sF4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

fof(f66,plain,
    ( big_p(sK1)
    | ~ spl5_6
    | ~ spl5_7 ),
    inference(forward_demodulation,[],[f60,f52]) ).

fof(f52,plain,
    ( sF4 = sK1
    | ~ spl5_6 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f60,plain,
    ( big_p(sF4)
    | ~ spl5_7 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f65,plain,
    ( ~ spl5_3
    | ~ spl5_1
    | spl5_5 ),
    inference(avatar_split_clause,[],[f62,f44,f26,f34]) ).

fof(f34,plain,
    ( spl5_3
  <=> big_p(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f26,plain,
    ( spl5_1
  <=> ! [X5] :
        ( ~ big_p(X5)
        | big_p(f(X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f44,plain,
    ( spl5_5
  <=> big_p(sF3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f62,plain,
    ( ~ big_p(sK0)
    | ~ spl5_1
    | spl5_5 ),
    inference(subsumption_resolution,[],[f55,f46]) ).

fof(f46,plain,
    ( ~ big_p(sF3)
    | spl5_5 ),
    inference(avatar_component_clause,[],[f44]) ).

fof(f55,plain,
    ( big_p(sF3)
    | ~ big_p(sK0)
    | ~ spl5_1 ),
    inference(superposition,[],[f27,f19]) ).

fof(f19,plain,
    f(sK0) = sF3,
    introduced(function_definition,[]) ).

fof(f27,plain,
    ( ! [X5] :
        ( big_p(f(X5))
        | ~ big_p(X5) )
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f26]) ).

fof(f61,plain,
    ( ~ spl5_2
    | spl5_7
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f56,f26,f58,f30]) ).

fof(f30,plain,
    ( spl5_2
  <=> big_p(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f56,plain,
    ( big_p(sF4)
    | ~ big_p(sK2)
    | ~ spl5_1 ),
    inference(superposition,[],[f27,f20]) ).

fof(f20,plain,
    sF4 = f(sK2),
    introduced(function_definition,[]) ).

fof(f54,plain,
    ( spl5_3
    | spl5_6 ),
    inference(avatar_split_clause,[],[f24,f50,f34]) ).

fof(f24,plain,
    ( sF4 = sK1
    | big_p(sK0) ),
    inference(definition_folding,[],[f14,f20]) ).

fof(f14,plain,
    ( big_p(sK0)
    | f(sK2) = sK1 ),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ( ( ( ~ big_p(f(sK0))
        & big_p(sK0) )
      | ( f(sK2) = sK1
        & big_p(sK2)
        & ~ big_p(sK1) ) )
    & ( ! [X3] :
          ( big_p(f(X3))
          | ~ big_p(X3) )
      | ! [X4] :
          ( ! [X5] :
              ( f(X5) != X4
              | ~ big_p(X5) )
          | big_p(X4) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f9,f8,f7]) ).

fof(f7,plain,
    ( ? [X0] :
        ( ~ big_p(f(X0))
        & big_p(X0) )
   => ( ~ big_p(f(sK0))
      & big_p(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( f(X2) = X1
            & big_p(X2) )
        & ~ big_p(X1) )
   => ( ? [X2] :
          ( f(X2) = sK1
          & big_p(X2) )
      & ~ big_p(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ( ? [X2] :
        ( f(X2) = sK1
        & big_p(X2) )
   => ( f(sK2) = sK1
      & big_p(sK2) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

fof(f2,negated_conjecture,
    ~ ( ! [X2] :
          ( big_p(X2)
         => big_p(f(X2)) )
    <=> ! [X0] :
          ( ? [X1] :
              ( f(X1) = X0
              & big_p(X1) )
         => big_p(X0) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ( ! [X2] :
        ( big_p(X2)
       => big_p(f(X2)) )
  <=> ! [X0] :
        ( ? [X1] :
            ( f(X1) = X0
            & big_p(X1) )
       => big_p(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel56) ).

fof(f53,plain,
    ( ~ spl5_5
    | spl5_6 ),
    inference(avatar_split_clause,[],[f21,f50,f44]) ).

fof(f21,plain,
    ( sF4 = sK1
    | ~ big_p(sF3) ),
    inference(definition_folding,[],[f17,f20,f19]) ).

fof(f17,plain,
    ( ~ big_p(f(sK0))
    | f(sK2) = sK1 ),
    inference(cnf_transformation,[],[f10]) ).

fof(f48,plain,
    ( ~ spl5_5
    | spl5_2 ),
    inference(avatar_split_clause,[],[f22,f30,f44]) ).

fof(f22,plain,
    ( big_p(sK2)
    | ~ big_p(sF3) ),
    inference(definition_folding,[],[f16,f19]) ).

fof(f16,plain,
    ( ~ big_p(f(sK0))
    | big_p(sK2) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f47,plain,
    ( ~ spl5_4
    | ~ spl5_5 ),
    inference(avatar_split_clause,[],[f23,f44,f39]) ).

fof(f23,plain,
    ( ~ big_p(sF3)
    | ~ big_p(sK1) ),
    inference(definition_folding,[],[f15,f19]) ).

fof(f15,plain,
    ( ~ big_p(f(sK0))
    | ~ big_p(sK1) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f42,plain,
    ( spl5_3
    | ~ spl5_4 ),
    inference(avatar_split_clause,[],[f12,f39,f34]) ).

fof(f12,plain,
    ( ~ big_p(sK1)
    | big_p(sK0) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f37,plain,
    ( spl5_2
    | spl5_3 ),
    inference(avatar_split_clause,[],[f13,f34,f30]) ).

fof(f13,plain,
    ( big_p(sK0)
    | big_p(sK2) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f28,plain,
    ( spl5_1
    | spl5_1 ),
    inference(avatar_split_clause,[],[f18,f26,f26]) ).

fof(f18,plain,
    ! [X3,X5] :
      ( ~ big_p(X3)
      | big_p(f(X3))
      | ~ big_p(X5)
      | big_p(f(X5)) ),
    inference(equality_resolution,[],[f11]) ).

fof(f11,plain,
    ! [X3,X4,X5] :
      ( big_p(f(X3))
      | ~ big_p(X3)
      | f(X5) != X4
      | ~ big_p(X5)
      | big_p(X4) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem    : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% 0.02/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.11/0.33  % Computer : n004.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Tue Aug 30 21:25:19 EDT 2022
% 0.11/0.33  % CPUTime    : 
% 0.18/0.44  % (9519)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.18/0.44  % (9519)First to succeed.
% 0.18/0.46  % (9510)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.18/0.46  % (9519)Refutation found. Thanks to Tanya!
% 0.18/0.46  % SZS status Theorem for theBenchmark
% 0.18/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46  % (9519)------------------------------
% 0.18/0.46  % (9519)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.46  % (9519)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.46  % (9519)Termination reason: Refutation
% 0.18/0.46  
% 0.18/0.46  % (9519)Memory used [KB]: 5373
% 0.18/0.46  % (9519)Time elapsed: 0.076 s
% 0.18/0.46  % (9519)Instructions burned: 1 (million)
% 0.18/0.46  % (9519)------------------------------
% 0.18/0.46  % (9519)------------------------------
% 0.18/0.46  % (9503)Success in time 0.125 s
%------------------------------------------------------------------------------