TSTP Solution File: SYN056+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYN056+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 : n018.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 19:36:42 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   97 (   1 unt;   0 def)
%            Number of atoms       :  282 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  327 ( 142   ~; 128   |;  20   &)
%                                         (  26 <=>;  10  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   23 (  22 usr;  19 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   77 (  61   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f121,plain,
    $false,
    inference(avatar_sat_refutation,[],[f45,f53,f61,f69,f74,f78,f86,f91,f92,f93,f101,f102,f104,f106,f108,f111,f112,f114,f117,f120]) ).

fof(f120,plain,
    ( spl7_2
    | ~ spl7_8
    | ~ spl7_13 ),
    inference(avatar_contradiction_clause,[],[f119]) ).

fof(f119,plain,
    ( $false
    | spl7_2
    | ~ spl7_8
    | ~ spl7_13 ),
    inference(subsumption_resolution,[],[f118,f90]) ).

fof(f90,plain,
    ( big_q(sK1)
    | ~ spl7_13 ),
    inference(avatar_component_clause,[],[f88]) ).

fof(f88,plain,
    ( spl7_13
  <=> big_q(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).

fof(f118,plain,
    ( ~ big_q(sK1)
    | spl7_2
    | ~ spl7_8 ),
    inference(resolution,[],[f68,f44]) ).

fof(f44,plain,
    ( ~ big_s(sK1)
    | spl7_2 ),
    inference(avatar_component_clause,[],[f42]) ).

fof(f42,plain,
    ( spl7_2
  <=> big_s(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f68,plain,
    ( ! [X1] :
        ( big_s(X1)
        | ~ big_q(X1) )
    | ~ spl7_8 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f67,plain,
    ( spl7_8
  <=> ! [X1] :
        ( ~ big_q(X1)
        | big_s(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).

fof(f117,plain,
    ( spl7_1
    | ~ spl7_9
    | ~ spl7_12 ),
    inference(avatar_contradiction_clause,[],[f116]) ).

fof(f116,plain,
    ( $false
    | spl7_1
    | ~ spl7_9
    | ~ spl7_12 ),
    inference(subsumption_resolution,[],[f115,f73]) ).

fof(f73,plain,
    ( big_p(sK0)
    | ~ spl7_9 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f71,plain,
    ( spl7_9
  <=> big_p(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).

fof(f115,plain,
    ( ~ big_p(sK0)
    | spl7_1
    | ~ spl7_12 ),
    inference(resolution,[],[f85,f40]) ).

fof(f40,plain,
    ( ~ big_r(sK0)
    | spl7_1 ),
    inference(avatar_component_clause,[],[f38]) ).

fof(f38,plain,
    ( spl7_1
  <=> big_r(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f85,plain,
    ( ! [X2] :
        ( big_r(X2)
        | ~ big_p(X2) )
    | ~ spl7_12 ),
    inference(avatar_component_clause,[],[f84]) ).

fof(f84,plain,
    ( spl7_12
  <=> ! [X2] :
        ( big_r(X2)
        | ~ big_p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).

fof(f114,plain,
    ( ~ spl7_4
    | ~ spl7_13 ),
    inference(avatar_contradiction_clause,[],[f113]) ).

fof(f113,plain,
    ( $false
    | ~ spl7_4
    | ~ spl7_13 ),
    inference(subsumption_resolution,[],[f90,f52]) ).

fof(f52,plain,
    ( ! [X1] : ~ big_q(X1)
    | ~ spl7_4 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f51,plain,
    ( spl7_4
  <=> ! [X1] : ~ big_q(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).

fof(f112,plain,
    ( ~ spl7_3
    | ~ spl7_15 ),
    inference(avatar_contradiction_clause,[],[f110]) ).

fof(f110,plain,
    ( $false
    | ~ spl7_3
    | ~ spl7_15 ),
    inference(resolution,[],[f100,f49]) ).

fof(f49,plain,
    ( big_p(sK2)
    | ~ spl7_3 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f47,plain,
    ( spl7_3
  <=> big_p(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).

fof(f100,plain,
    ( ! [X3] : ~ big_p(X3)
    | ~ spl7_15 ),
    inference(avatar_component_clause,[],[f99]) ).

fof(f99,plain,
    ( spl7_15
  <=> ! [X3] : ~ big_p(X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_15])]) ).

fof(f111,plain,
    ( ~ spl7_9
    | ~ spl7_15 ),
    inference(avatar_contradiction_clause,[],[f109]) ).

fof(f109,plain,
    ( $false
    | ~ spl7_9
    | ~ spl7_15 ),
    inference(resolution,[],[f100,f73]) ).

fof(f108,plain,
    ( spl7_15
    | ~ spl7_10
    | ~ spl7_12 ),
    inference(avatar_split_clause,[],[f107,f84,f76,f99]) ).

fof(f76,plain,
    ( spl7_10
  <=> ! [X0] :
        ( ~ big_p(X0)
        | ~ big_r(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).

fof(f107,plain,
    ( ! [X0] : ~ big_p(X0)
    | ~ spl7_10
    | ~ spl7_12 ),
    inference(subsumption_resolution,[],[f77,f85]) ).

fof(f77,plain,
    ( ! [X0] :
        ( ~ big_p(X0)
        | ~ big_r(X0) )
    | ~ spl7_10 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f106,plain,
    ( ~ spl7_4
    | ~ spl7_14 ),
    inference(avatar_contradiction_clause,[],[f105]) ).

fof(f105,plain,
    ( $false
    | ~ spl7_4
    | ~ spl7_14 ),
    inference(resolution,[],[f97,f52]) ).

fof(f97,plain,
    ( big_q(sK3)
    | ~ spl7_14 ),
    inference(avatar_component_clause,[],[f95]) ).

fof(f95,plain,
    ( spl7_14
  <=> big_q(sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_14])]) ).

fof(f104,plain,
    ( spl7_4
    | ~ spl7_6
    | ~ spl7_8 ),
    inference(avatar_split_clause,[],[f103,f67,f59,f51]) ).

fof(f59,plain,
    ( spl7_6
  <=> ! [X1] :
        ( ~ big_q(X1)
        | ~ big_s(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).

fof(f103,plain,
    ( ! [X1] : ~ big_q(X1)
    | ~ spl7_6
    | ~ spl7_8 ),
    inference(subsumption_resolution,[],[f68,f60]) ).

fof(f60,plain,
    ( ! [X1] :
        ( ~ big_s(X1)
        | ~ big_q(X1) )
    | ~ spl7_6 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f102,plain,
    ( spl7_12
    | spl7_5 ),
    inference(avatar_split_clause,[],[f35,f55,f84]) ).

fof(f55,plain,
    ( spl7_5
  <=> sP6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).

fof(f35,plain,
    ! [X0] :
      ( sP6
      | big_r(X0)
      | ~ big_p(X0) ),
    inference(cnf_transformation,[],[f35_D]) ).

fof(f35_D,plain,
    ( ! [X0] :
        ( big_r(X0)
        | ~ big_p(X0) )
  <=> ~ sP6 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP6])]) ).

fof(f101,plain,
    ( spl7_14
    | spl7_15 ),
    inference(avatar_split_clause,[],[f27,f99,f95]) ).

fof(f27,plain,
    ! [X3] :
      ( ~ big_p(X3)
      | big_q(sK3) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ( ( big_p(sK2)
      | ! [X1] : ~ big_q(X1) )
    & ( big_q(sK3)
      | ! [X3] : ~ big_p(X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f16,f18,f17]) ).

fof(f17,plain,
    ( ? [X0] : big_p(X0)
   => big_p(sK2) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ( ? [X2] : big_q(X2)
   => big_q(sK3) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ( ( ? [X0] : big_p(X0)
      | ! [X1] : ~ big_q(X1) )
    & ( ? [X2] : big_q(X2)
      | ! [X3] : ~ big_p(X3) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ( ( ? [X1] : big_p(X1)
      | ! [X0] : ~ big_q(X0) )
    & ( ? [X0] : big_q(X0)
      | ! [X1] : ~ big_p(X1) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,plain,
    ( ? [X1] : big_p(X1)
  <=> ? [X0] : big_q(X0) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ( ? [X1] : big_q(X1)
  <=> ? [X0] : big_p(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_1) ).

fof(f93,plain,
    ( spl7_13
    | spl7_9 ),
    inference(avatar_split_clause,[],[f24,f71,f88]) ).

fof(f24,plain,
    ( big_p(sK0)
    | big_q(sK1) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ( ( ( ~ big_r(sK0)
        & big_p(sK0) )
      | ( big_q(sK1)
        & ~ big_s(sK1) ) )
    & ( ! [X2] :
          ( big_r(X2)
          | ~ big_p(X2) )
      | ! [X3] :
          ( ~ big_q(X3)
          | big_s(X3) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13,f12]) ).

fof(f12,plain,
    ( ? [X0] :
        ( ~ big_r(X0)
        & big_p(X0) )
   => ( ~ big_r(sK0)
      & big_p(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ( ? [X1] :
        ( big_q(X1)
        & ~ big_s(X1) )
   => ( big_q(sK1)
      & ~ big_s(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ( ( ? [X0] :
          ( ~ big_r(X0)
          & big_p(X0) )
      | ? [X1] :
          ( big_q(X1)
          & ~ big_s(X1) ) )
    & ( ! [X2] :
          ( big_r(X2)
          | ~ big_p(X2) )
      | ! [X3] :
          ( ~ big_q(X3)
          | big_s(X3) ) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ( ( ? [X0] :
          ( ~ big_r(X0)
          & big_p(X0) )
      | ? [X1] :
          ( big_q(X1)
          & ~ big_s(X1) ) )
    & ( ! [X0] :
          ( big_r(X0)
          | ~ big_p(X0) )
      | ! [X1] :
          ( ~ big_q(X1)
          | big_s(X1) ) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ( ! [X1] :
        ( ~ big_q(X1)
        | big_s(X1) )
  <~> ! [X0] :
        ( big_r(X0)
        | ~ big_p(X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,negated_conjecture,
    ~ ( ! [X1] :
          ( big_q(X1)
         => big_s(X1) )
    <=> ! [X0] :
          ( big_p(X0)
         => big_r(X0) ) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f3,conjecture,
    ( ! [X1] :
        ( big_q(X1)
       => big_s(X1) )
  <=> ! [X0] :
        ( big_p(X0)
       => big_r(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26) ).

fof(f92,plain,
    ( ~ spl7_11
    | spl7_8 ),
    inference(avatar_split_clause,[],[f32,f67,f80]) ).

fof(f80,plain,
    ( spl7_11
  <=> sP4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).

fof(f32,plain,
    ! [X3] :
      ( big_s(X3)
      | ~ sP4
      | ~ big_q(X3) ),
    inference(general_splitting,[],[f22,f31_D]) ).

fof(f31,plain,
    ! [X2] :
      ( big_r(X2)
      | sP4
      | ~ big_p(X2) ),
    inference(cnf_transformation,[],[f31_D]) ).

fof(f31_D,plain,
    ( ! [X2] :
        ( big_r(X2)
        | ~ big_p(X2) )
  <=> ~ sP4 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).

fof(f22,plain,
    ! [X2,X3] :
      ( big_r(X2)
      | ~ big_p(X2)
      | ~ big_q(X3)
      | big_s(X3) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f91,plain,
    ( spl7_13
    | ~ spl7_1 ),
    inference(avatar_split_clause,[],[f26,f38,f88]) ).

fof(f26,plain,
    ( ~ big_r(sK0)
    | big_q(sK1) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f86,plain,
    ( spl7_11
    | spl7_12 ),
    inference(avatar_split_clause,[],[f31,f84,f80]) ).

fof(f78,plain,
    ( spl7_7
    | spl7_10 ),
    inference(avatar_split_clause,[],[f33,f76,f63]) ).

fof(f63,plain,
    ( spl7_7
  <=> sP5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).

fof(f33,plain,
    ! [X0] :
      ( ~ big_p(X0)
      | sP5
      | ~ big_r(X0) ),
    inference(cnf_transformation,[],[f33_D]) ).

fof(f33_D,plain,
    ( ! [X0] :
        ( ~ big_p(X0)
        | ~ big_r(X0) )
  <=> ~ sP5 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).

fof(f74,plain,
    ( spl7_9
    | ~ spl7_2 ),
    inference(avatar_split_clause,[],[f23,f42,f71]) ).

fof(f23,plain,
    ( ~ big_s(sK1)
    | big_p(sK0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f69,plain,
    ( ~ spl7_7
    | spl7_8 ),
    inference(avatar_split_clause,[],[f34,f67,f63]) ).

fof(f34,plain,
    ! [X1] :
      ( ~ big_q(X1)
      | big_s(X1)
      | ~ sP5 ),
    inference(general_splitting,[],[f30,f33_D]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ big_p(X0)
      | big_s(X1)
      | ~ big_r(X0)
      | ~ big_q(X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ big_p(X0)
      | ( ( big_s(X1)
          | ~ big_r(X0) )
        & ( big_r(X0)
          | ~ big_s(X1) ) )
      | ~ big_q(X1) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( ~ big_p(X1)
      | ( ( big_s(X0)
          | ~ big_r(X1) )
        & ( big_r(X1)
          | ~ big_s(X0) ) )
      | ~ big_q(X0) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ! [X1,X0] :
      ( ~ big_p(X1)
      | ( big_s(X0)
      <=> big_r(X1) )
      | ~ big_q(X0) ),
    inference(flattening,[],[f7]) ).

fof(f7,plain,
    ! [X0,X1] :
      ( ( big_s(X0)
      <=> big_r(X1) )
      | ~ big_q(X0)
      | ~ big_p(X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,plain,
    ! [X0,X1] :
      ( ( big_q(X0)
        & big_p(X1) )
     => ( big_s(X0)
      <=> big_r(X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ( big_q(X1)
        & big_p(X0) )
     => ( big_r(X0)
      <=> big_s(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_2) ).

fof(f61,plain,
    ( ~ spl7_5
    | spl7_6 ),
    inference(avatar_split_clause,[],[f36,f59,f55]) ).

fof(f36,plain,
    ! [X1] :
      ( ~ big_q(X1)
      | ~ sP6
      | ~ big_s(X1) ),
    inference(general_splitting,[],[f29,f35_D]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ~ big_p(X0)
      | big_r(X0)
      | ~ big_s(X1)
      | ~ big_q(X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f53,plain,
    ( spl7_3
    | spl7_4 ),
    inference(avatar_split_clause,[],[f28,f51,f47]) ).

fof(f28,plain,
    ! [X1] :
      ( ~ big_q(X1)
      | big_p(sK2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f45,plain,
    ( ~ spl7_1
    | ~ spl7_2 ),
    inference(avatar_split_clause,[],[f25,f42,f38]) ).

fof(f25,plain,
    ( ~ big_s(sK1)
    | ~ big_r(sK0) ),
    inference(cnf_transformation,[],[f14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SYN056+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 21:33:40 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (11659)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/99Mi)
% 0.19/0.49  % (11667)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/138Mi)
% 0.19/0.49  % (11667)First to succeed.
% 0.19/0.50  % (11667)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (11667)------------------------------
% 0.19/0.50  % (11667)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (11667)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (11667)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (11667)Memory used [KB]: 5373
% 0.19/0.50  % (11667)Time elapsed: 0.099 s
% 0.19/0.50  % (11667)Instructions burned: 2 (million)
% 0.19/0.50  % (11667)------------------------------
% 0.19/0.50  % (11667)------------------------------
% 0.19/0.50  % (11645)Success in time 0.147 s
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