TSTP Solution File: SYN364+1 by SnakeForV-SAT---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYN364+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 : n016.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 19:37:41 EDT 2022

% Result   : Theorem 0.23s 0.50s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   39 (   2 unt;   0 def)
%            Number of atoms       :  133 (   0 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  153 (  59   ~;  47   |;  30   &)
%                                         (   6 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   81 (  64   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f46,plain,
    $false,
    inference(avatar_sat_refutation,[],[f24,f32,f36,f41,f43,f45]) ).

fof(f45,plain,
    ( ~ spl3_2
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f44]) ).

fof(f44,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(resolution,[],[f31,f23]) ).

fof(f23,plain,
    ( ! [X1] : big_p(X1,X1)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f22]) ).

fof(f22,plain,
    ( spl3_2
  <=> ! [X1] : big_p(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f31,plain,
    ( ! [X4] : ~ big_p(g(sK0),X4)
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f30]) ).

fof(f30,plain,
    ( spl3_4
  <=> ! [X4] : ~ big_p(g(sK0),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f43,plain,
    ( ~ spl3_2
    | spl3_3 ),
    inference(avatar_contradiction_clause,[],[f42]) ).

fof(f42,plain,
    ( $false
    | ~ spl3_2
    | spl3_3 ),
    inference(subsumption_resolution,[],[f28,f23]) ).

fof(f28,plain,
    ( ~ big_p(sK0,sK0)
    | spl3_3 ),
    inference(avatar_component_clause,[],[f26]) ).

fof(f26,plain,
    ( spl3_3
  <=> big_p(sK0,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f41,plain,
    ~ spl3_5,
    inference(avatar_contradiction_clause,[],[f40]) ).

fof(f40,plain,
    ( $false
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f39,f38]) ).

fof(f38,plain,
    ( ! [X7] : ~ big_q(X7)
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f10,f37]) ).

fof(f37,plain,
    ( ! [X5] : big_m(X5)
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f11,f35]) ).

fof(f35,plain,
    ( ! [X2,X0] : ~ big_p(X0,X2)
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f34]) ).

fof(f34,plain,
    ( spl3_5
  <=> ! [X2,X0] : ~ big_p(X0,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f11,plain,
    ! [X5] :
      ( big_p(X5,sK1(X5))
      | big_m(X5) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
    ( ! [X0] :
        ( ! [X1] : big_p(X1,X1)
        | ! [X2] : ~ big_p(X0,X2) )
    & ! [X4] :
        ( ~ big_p(g(sK0),X4)
        | ~ big_p(sK0,sK0) )
    & ! [X5] :
        ( big_p(X5,sK1(X5))
        | ( big_q(f(X5,sK1(X5)))
          & big_m(X5) ) )
    & ! [X7] :
        ( ~ big_m(g(X7))
        | ~ big_q(X7) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).

fof(f7,plain,
    ( ? [X3] :
      ! [X4] :
        ( ~ big_p(g(X3),X4)
        | ~ big_p(X3,X3) )
   => ! [X4] :
        ( ~ big_p(g(sK0),X4)
        | ~ big_p(sK0,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ! [X5] :
      ( ? [X6] :
          ( big_p(X5,X6)
          | ( big_q(f(X5,X6))
            & big_m(X5) ) )
     => ( big_p(X5,sK1(X5))
        | ( big_q(f(X5,sK1(X5)))
          & big_m(X5) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f5,plain,
    ( ! [X0] :
        ( ! [X2] : big_p(X2,X2)
        | ! [X1] : ~ big_p(X0,X1) )
    & ? [X6] :
      ! [X7] :
        ( ~ big_p(g(X6),X7)
        | ~ big_p(X6,X6) )
    & ! [X4] :
      ? [X5] :
        ( big_p(X4,X5)
        | ( big_q(f(X4,X5))
          & big_m(X4) ) )
    & ! [X3] :
        ( ~ big_m(g(X3))
        | ~ big_q(X3) ) ),
    inference(flattening,[],[f4]) ).

fof(f4,plain,
    ( ? [X6] :
      ! [X7] :
        ( ~ big_p(g(X6),X7)
        | ~ big_p(X6,X6) )
    & ! [X3] :
        ( ~ big_m(g(X3))
        | ~ big_q(X3) )
    & ! [X0] :
        ( ! [X2] : big_p(X2,X2)
        | ! [X1] : ~ big_p(X0,X1) )
    & ! [X4] :
      ? [X5] :
        ( big_p(X4,X5)
        | ( big_q(f(X4,X5))
          & big_m(X4) ) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
    ~ ( ( ! [X3] :
            ( big_q(X3)
           => ~ big_m(g(X3)) )
        & ! [X0] :
            ( ? [X1] : big_p(X0,X1)
           => ! [X2] : big_p(X2,X2) )
        & ! [X4] :
          ? [X5] :
            ( big_p(X4,X5)
            | ( big_q(f(X4,X5))
              & big_m(X4) ) ) )
     => ! [X6] :
        ? [X7] :
          ( big_p(g(X6),X7)
          & big_p(X6,X6) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ( ( ! [X0] :
            ( ? [X1] : big_p(X0,X1)
           => ! [X2] : big_p(X2,X2) )
        & ! [X5] :
            ( big_q(X5)
           => ~ big_m(g(X5)) )
        & ! [X3] :
          ? [X4] :
            ( ( big_m(X3)
              & big_q(f(X3,X4)) )
            | big_p(X3,X4) ) )
     => ! [X3] :
        ? [X4] :
          ( big_p(g(X3),X4)
          & big_p(X3,X3) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ( ( ! [X0] :
          ( ? [X1] : big_p(X0,X1)
         => ! [X2] : big_p(X2,X2) )
      & ! [X5] :
          ( big_q(X5)
         => ~ big_m(g(X5)) )
      & ! [X3] :
        ? [X4] :
          ( ( big_m(X3)
            & big_q(f(X3,X4)) )
          | big_p(X3,X4) ) )
   => ! [X3] :
      ? [X4] :
        ( big_p(g(X3),X4)
        & big_p(X3,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2115) ).

fof(f10,plain,
    ! [X7] :
      ( ~ big_m(g(X7))
      | ~ big_q(X7) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f39,plain,
    ( ! [X5] : big_q(f(X5,sK1(X5)))
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f12,f35]) ).

fof(f12,plain,
    ! [X5] :
      ( big_q(f(X5,sK1(X5)))
      | big_p(X5,sK1(X5)) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f36,plain,
    ( spl3_5
    | ~ spl3_1 ),
    inference(avatar_split_clause,[],[f16,f18,f34]) ).

fof(f18,plain,
    ( spl3_1
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f16,plain,
    ! [X2,X0] :
      ( ~ sP2
      | ~ big_p(X0,X2) ),
    inference(general_splitting,[],[f14,f15_D]) ).

fof(f15,plain,
    ! [X1] :
      ( big_p(X1,X1)
      | sP2 ),
    inference(cnf_transformation,[],[f15_D]) ).

fof(f15_D,plain,
    ( ! [X1] : big_p(X1,X1)
  <=> ~ sP2 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).

fof(f14,plain,
    ! [X2,X0,X1] :
      ( big_p(X1,X1)
      | ~ big_p(X0,X2) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f32,plain,
    ( ~ spl3_3
    | spl3_4 ),
    inference(avatar_split_clause,[],[f13,f30,f26]) ).

fof(f13,plain,
    ! [X4] :
      ( ~ big_p(g(sK0),X4)
      | ~ big_p(sK0,sK0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f24,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f15,f22,f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : SYN364+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.36  % Computer : n016.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   : Tue Aug 30 22:10:46 EDT 2022
% 0.14/0.37  % CPUTime    : 
% 0.23/0.49  % (30206)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/48Mi)
% 0.23/0.49  % (30206)First to succeed.
% 0.23/0.50  % (30206)Refutation found. Thanks to Tanya!
% 0.23/0.50  % SZS status Theorem for theBenchmark
% 0.23/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.50  % (30206)------------------------------
% 0.23/0.50  % (30206)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.23/0.50  % (30206)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.23/0.50  % (30206)Termination reason: Refutation
% 0.23/0.50  
% 0.23/0.50  % (30206)Memory used [KB]: 5373
% 0.23/0.50  % (30206)Time elapsed: 0.083 s
% 0.23/0.50  % (30206)Instructions burned: 2 (million)
% 0.23/0.50  % (30206)------------------------------
% 0.23/0.50  % (30206)------------------------------
% 0.23/0.50  % (30200)Success in time 0.123 s
%------------------------------------------------------------------------------