TSTP Solution File: SEU208+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU208+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n024.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 18:27:26 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   55 (   6 unt;   0 def)
%            Number of atoms       :  167 (  16 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  193 (  81   ~;  76   |;  12   &)
%                                         (  17 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   97 (  85   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f340,plain,
    $false,
    inference(avatar_sat_refutation,[],[f123,f128,f134,f155,f337]) ).

fof(f337,plain,
    ( ~ spl15_1
    | ~ spl15_3 ),
    inference(avatar_contradiction_clause,[],[f328]) ).

fof(f328,plain,
    ( $false
    | ~ spl15_1
    | ~ spl15_3 ),
    inference(unit_resulting_resolution,[],[f165,f300]) ).

fof(f300,plain,
    ( ! [X0] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK7(sK3,sK2,sK1))),sK3)
    | ~ spl15_1
    | ~ spl15_3 ),
    inference(forward_demodulation,[],[f298,f68]) ).

fof(f68,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f298,plain,
    ( ! [X0] : ~ in(unordered_pair(unordered_pair(X0,sK7(sK3,sK2,sK1)),singleton(X0)),sK3)
    | ~ spl15_1
    | ~ spl15_3 ),
    inference(unit_resulting_resolution,[],[f60,f260,f108]) ).

fof(f108,plain,
    ! [X2,X3,X0] :
      ( ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
      | in(X2,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f103]) ).

fof(f103,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X1)
      | ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f79,f70]) ).

fof(f70,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f79,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X1)
      | ~ in(ordered_pair(X3,X2),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( ? [X3] : in(ordered_pair(X3,X2),X0)
            <=> in(X2,X1) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( ? [X3] : in(ordered_pair(X3,X2),X0)
            <=> in(X2,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f260,plain,
    ( ~ in(sK7(sK3,sK2,sK1),relation_rng(sK3))
    | ~ spl15_1
    | ~ spl15_3 ),
    inference(unit_resulting_resolution,[],[f157,f165,f122]) ).

fof(f122,plain,
    ( ! [X3] :
        ( ~ in(unordered_pair(singleton(sK1),unordered_pair(sK1,X3)),sK3)
        | ~ in(X3,sK2)
        | ~ in(X3,relation_rng(sK3)) )
    | ~ spl15_3 ),
    inference(avatar_component_clause,[],[f121]) ).

fof(f121,plain,
    ( spl15_3
  <=> ! [X3] :
        ( ~ in(X3,sK2)
        | ~ in(unordered_pair(singleton(sK1),unordered_pair(sK1,X3)),sK3)
        | ~ in(X3,relation_rng(sK3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).

fof(f157,plain,
    ( in(sK7(sK3,sK2,sK1),sK2)
    | ~ spl15_1 ),
    inference(unit_resulting_resolution,[],[f60,f113,f107]) ).

fof(f107,plain,
    ! [X2,X3,X0] :
      ( in(sK7(X0,X2,X3),X2)
      | ~ in(X3,relation_inverse_image(X0,X2))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f75]) ).

fof(f75,plain,
    ! [X2,X3,X0,X1] :
      ( in(sK7(X0,X2,X3),X2)
      | ~ in(X3,X1)
      | relation_inverse_image(X0,X2) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( relation_inverse_image(X0,X2) = X1
        <=> ! [X3] :
              ( in(X3,X1)
            <=> ? [X4] :
                  ( in(ordered_pair(X3,X4),X0)
                  & in(X4,X2) ) ) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( relation(X0)
     => ! [X1,X2] :
          ( relation_inverse_image(X0,X2) = X1
        <=> ! [X3] :
              ( in(X3,X1)
            <=> ? [X4] :
                  ( in(ordered_pair(X3,X4),X0)
                  & in(X4,X2) ) ) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X3,X4),X0) ) )
        <=> relation_inverse_image(X0,X1) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).

fof(f113,plain,
    ( in(sK1,relation_inverse_image(sK3,sK2))
    | ~ spl15_1 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f111,plain,
    ( spl15_1
  <=> in(sK1,relation_inverse_image(sK3,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).

fof(f60,plain,
    relation(sK3),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ? [X2,X1,X0] :
      ( ( ? [X3] :
            ( in(X3,X1)
            & in(X3,relation_rng(X0))
            & in(ordered_pair(X2,X3),X0) )
      <~> in(X2,relation_inverse_image(X0,X1)) )
      & relation(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,plain,
    ~ ! [X0,X2,X1] :
        ( relation(X0)
       => ( ? [X3] :
              ( in(X3,X1)
              & in(X3,relation_rng(X0))
              & in(ordered_pair(X2,X3),X0) )
        <=> in(X2,relation_inverse_image(X0,X1)) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,negated_conjecture,
    ~ ! [X2,X1,X0] :
        ( relation(X2)
       => ( ? [X3] :
              ( in(ordered_pair(X0,X3),X2)
              & in(X3,relation_rng(X2))
              & in(X3,X1) )
        <=> in(X0,relation_inverse_image(X2,X1)) ) ),
    inference(negated_conjecture,[],[f26]) ).

fof(f26,conjecture,
    ! [X2,X1,X0] :
      ( relation(X2)
     => ( ? [X3] :
            ( in(ordered_pair(X0,X3),X2)
            & in(X3,relation_rng(X2))
            & in(X3,X1) )
      <=> in(X0,relation_inverse_image(X2,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).

fof(f165,plain,
    ( in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK7(sK3,sK2,sK1))),sK3)
    | ~ spl15_1 ),
    inference(forward_demodulation,[],[f156,f68]) ).

fof(f156,plain,
    ( in(unordered_pair(unordered_pair(sK1,sK7(sK3,sK2,sK1)),singleton(sK1)),sK3)
    | ~ spl15_1 ),
    inference(unit_resulting_resolution,[],[f60,f113,f106]) ).

fof(f106,plain,
    ! [X2,X3,X0] :
      ( in(unordered_pair(unordered_pair(X3,sK7(X0,X2,X3)),singleton(X3)),X0)
      | ~ in(X3,relation_inverse_image(X0,X2))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f98]) ).

fof(f98,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(unordered_pair(X3,sK7(X0,X2,X3)),singleton(X3)),X0)
      | ~ in(X3,X1)
      | relation_inverse_image(X0,X2) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f76,f70]) ).

fof(f76,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X3,sK7(X0,X2,X3)),X0)
      | ~ in(X3,X1)
      | relation_inverse_image(X0,X2) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f155,plain,
    ( ~ spl15_5
    | spl15_1
    | ~ spl15_4 ),
    inference(avatar_split_clause,[],[f154,f125,f111,f131]) ).

fof(f131,plain,
    ( spl15_5
  <=> in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK4)),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).

fof(f125,plain,
    ( spl15_4
  <=> in(sK4,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).

fof(f154,plain,
    ( ~ in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK4)),sK3)
    | spl15_1
    | ~ spl15_4 ),
    inference(forward_demodulation,[],[f153,f68]) ).

fof(f153,plain,
    ( ~ in(unordered_pair(unordered_pair(sK1,sK4),singleton(sK1)),sK3)
    | spl15_1
    | ~ spl15_4 ),
    inference(unit_resulting_resolution,[],[f60,f127,f112,f105]) ).

fof(f105,plain,
    ! [X2,X3,X0,X4] :
      ( ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
      | in(X3,relation_inverse_image(X0,X2))
      | ~ in(X4,X2)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f97]) ).

fof(f97,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,X2)
      | ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
      | in(X3,X1)
      | relation_inverse_image(X0,X2) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f77,f70]) ).

fof(f77,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,X2)
      | ~ in(ordered_pair(X3,X4),X0)
      | in(X3,X1)
      | relation_inverse_image(X0,X2) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f112,plain,
    ( ~ in(sK1,relation_inverse_image(sK3,sK2))
    | spl15_1 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f127,plain,
    ( in(sK4,sK2)
    | ~ spl15_4 ),
    inference(avatar_component_clause,[],[f125]) ).

fof(f134,plain,
    ( spl15_5
    | spl15_1 ),
    inference(avatar_split_clause,[],[f129,f111,f131]) ).

fof(f129,plain,
    ( in(sK1,relation_inverse_image(sK3,sK2))
    | in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK4)),sK3) ),
    inference(forward_demodulation,[],[f94,f68]) ).

fof(f94,plain,
    ( in(sK1,relation_inverse_image(sK3,sK2))
    | in(unordered_pair(unordered_pair(sK1,sK4),singleton(sK1)),sK3) ),
    inference(definition_unfolding,[],[f57,f70]) ).

fof(f57,plain,
    ( in(sK1,relation_inverse_image(sK3,sK2))
    | in(ordered_pair(sK1,sK4),sK3) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f128,plain,
    ( spl15_4
    | spl15_1 ),
    inference(avatar_split_clause,[],[f59,f111,f125]) ).

fof(f59,plain,
    ( in(sK1,relation_inverse_image(sK3,sK2))
    | in(sK4,sK2) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f123,plain,
    ( spl15_3
    | ~ spl15_1 ),
    inference(avatar_split_clause,[],[f119,f111,f121]) ).

fof(f119,plain,
    ! [X3] :
      ( ~ in(sK1,relation_inverse_image(sK3,sK2))
      | ~ in(X3,sK2)
      | ~ in(X3,relation_rng(sK3))
      | ~ in(unordered_pair(singleton(sK1),unordered_pair(sK1,X3)),sK3) ),
    inference(forward_demodulation,[],[f95,f68]) ).

fof(f95,plain,
    ! [X3] :
      ( ~ in(X3,relation_rng(sK3))
      | ~ in(sK1,relation_inverse_image(sK3,sK2))
      | ~ in(X3,sK2)
      | ~ in(unordered_pair(unordered_pair(sK1,X3),singleton(sK1)),sK3) ),
    inference(definition_unfolding,[],[f56,f70]) ).

fof(f56,plain,
    ! [X3] :
      ( ~ in(sK1,relation_inverse_image(sK3,sK2))
      | ~ in(ordered_pair(sK1,X3),sK3)
      | ~ in(X3,relation_rng(sK3))
      | ~ in(X3,sK2) ),
    inference(cnf_transformation,[],[f51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEU208+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 14:53:34 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (24252)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.49  % (24259)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.49  % (24259)Instruction limit reached!
% 0.19/0.49  % (24259)------------------------------
% 0.19/0.49  % (24259)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (24252)First to succeed.
% 0.19/0.50  % (24259)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (24259)Termination reason: Unknown
% 0.19/0.50  % (24259)Termination phase: Saturation
% 0.19/0.50  
% 0.19/0.50  % (24259)Memory used [KB]: 6012
% 0.19/0.50  % (24259)Time elapsed: 0.092 s
% 0.19/0.50  % (24259)Instructions burned: 7 (million)
% 0.19/0.50  % (24259)------------------------------
% 0.19/0.50  % (24259)------------------------------
% 0.19/0.50  % (24267)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.51  % (24246)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51  % (24268)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51  % (24248)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (24252)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (24252)------------------------------
% 0.19/0.51  % (24252)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (24252)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (24252)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (24252)Memory used [KB]: 6140
% 0.19/0.51  % (24252)Time elapsed: 0.096 s
% 0.19/0.51  % (24252)Instructions burned: 12 (million)
% 0.19/0.51  % (24252)------------------------------
% 0.19/0.51  % (24252)------------------------------
% 0.19/0.51  % (24243)Success in time 0.159 s
%------------------------------------------------------------------------------