TSTP Solution File: SEU177+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU177+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_sat --cores 0 -t %d %s

% Computer : n015.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 18:32:21 EDT 2022

% Result   : Theorem 0.21s 0.56s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   53 (  12 unt;   0 def)
%            Number of atoms       :  200 (  24 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  235 (  88   ~;  85   |;  37   &)
%                                         (  10 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   3 con; 0-2 aty)
%            Number of variables   :  141 ( 103   !;  38   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f159,plain,
    $false,
    inference(avatar_sat_refutation,[],[f123,f149,f158]) ).

fof(f158,plain,
    spl13_1,
    inference(avatar_contradiction_clause,[],[f157]) ).

fof(f157,plain,
    ( $false
    | spl13_1 ),
    inference(subsumption_resolution,[],[f156,f97]) ).

fof(f97,plain,
    relation(sK10),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ( in(ordered_pair(sK11,sK12),sK10)
    & relation(sK10)
    & ( ~ in(sK12,relation_rng(sK10))
      | ~ in(sK11,relation_dom(sK10)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f69,f70]) ).

fof(f70,plain,
    ( ? [X0,X1,X2] :
        ( in(ordered_pair(X1,X2),X0)
        & relation(X0)
        & ( ~ in(X2,relation_rng(X0))
          | ~ in(X1,relation_dom(X0)) ) )
   => ( in(ordered_pair(sK11,sK12),sK10)
      & relation(sK10)
      & ( ~ in(sK12,relation_rng(sK10))
        | ~ in(sK11,relation_dom(sK10)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ? [X0,X1,X2] :
      ( in(ordered_pair(X1,X2),X0)
      & relation(X0)
      & ( ~ in(X2,relation_rng(X0))
        | ~ in(X1,relation_dom(X0)) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ? [X0,X2,X1] :
      ( in(ordered_pair(X2,X1),X0)
      & relation(X0)
      & ( ~ in(X1,relation_rng(X0))
        | ~ in(X2,relation_dom(X0)) ) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ? [X1,X2,X0] :
      ( ( ~ in(X1,relation_rng(X0))
        | ~ in(X2,relation_dom(X0)) )
      & in(ordered_pair(X2,X1),X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,plain,
    ~ ! [X1,X2,X0] :
        ( relation(X0)
       => ( in(ordered_pair(X2,X1),X0)
         => ( in(X1,relation_rng(X0))
            & in(X2,relation_dom(X0)) ) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,negated_conjecture,
    ~ ! [X2,X1,X0] :
        ( relation(X2)
       => ( in(ordered_pair(X0,X1),X2)
         => ( in(X1,relation_rng(X2))
            & in(X0,relation_dom(X2)) ) ) ),
    inference(negated_conjecture,[],[f24]) ).

fof(f24,conjecture,
    ! [X2,X1,X0] :
      ( relation(X2)
     => ( in(ordered_pair(X0,X1),X2)
       => ( in(X1,relation_rng(X2))
          & in(X0,relation_dom(X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).

fof(f156,plain,
    ( ~ relation(sK10)
    | spl13_1 ),
    inference(subsumption_resolution,[],[f153,f118]) ).

fof(f118,plain,
    ( ~ in(sK12,relation_rng(sK10))
    | spl13_1 ),
    inference(avatar_component_clause,[],[f116]) ).

fof(f116,plain,
    ( spl13_1
  <=> in(sK12,relation_rng(sK10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

fof(f153,plain,
    ( in(sK12,relation_rng(sK10))
    | ~ relation(sK10) ),
    inference(resolution,[],[f144,f134]) ).

fof(f134,plain,
    in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),sK10),
    inference(forward_demodulation,[],[f110,f95]) ).

fof(f95,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(f110,plain,
    in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),sK10),
    inference(definition_unfolding,[],[f98,f82]) ).

fof(f82,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f98,plain,
    in(ordered_pair(sK11,sK12),sK10),
    inference(cnf_transformation,[],[f71]) ).

fof(f144,plain,
    ! [X2,X0,X4] :
      ( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X2)),X0)
      | ~ relation(X0)
      | in(X2,relation_rng(X0)) ),
    inference(forward_demodulation,[],[f114,f95]) ).

fof(f114,plain,
    ! [X2,X0,X4] :
      ( ~ relation(X0)
      | ~ in(unordered_pair(unordered_pair(X4,X2),singleton(X4)),X0)
      | in(X2,relation_rng(X0)) ),
    inference(equality_resolution,[],[f107]) ).

fof(f107,plain,
    ! [X2,X0,X1,X4] :
      ( in(X2,X1)
      | ~ in(unordered_pair(unordered_pair(X4,X2),singleton(X4)),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f93,f82]) ).

fof(f93,plain,
    ! [X2,X0,X1,X4] :
      ( in(X2,X1)
      | ~ in(ordered_pair(X4,X2),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(ordered_pair(sK7(X0,X2),X2),X0)
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X4] : ~ in(ordered_pair(X4,X2),X0) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ( ( ~ in(sK8(X0,X1),X1)
                | ! [X6] : ~ in(ordered_pair(X6,sK8(X0,X1)),X0) )
              & ( in(sK8(X0,X1),X1)
                | in(ordered_pair(sK9(X0,X1),sK8(X0,X1)),X0) ) ) ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f64,f67,f66,f65]) ).

fof(f65,plain,
    ! [X0,X2] :
      ( ? [X3] : in(ordered_pair(X3,X2),X0)
     => in(ordered_pair(sK7(X0,X2),X2),X0) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ( ~ in(X5,X1)
            | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
          & ( in(X5,X1)
            | ? [X7] : in(ordered_pair(X7,X5),X0) ) )
     => ( ( ~ in(sK8(X0,X1),X1)
          | ! [X6] : ~ in(ordered_pair(X6,sK8(X0,X1)),X0) )
        & ( in(sK8(X0,X1),X1)
          | ? [X7] : in(ordered_pair(X7,sK8(X0,X1)),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ? [X7] : in(ordered_pair(X7,sK8(X0,X1)),X0)
     => in(ordered_pair(sK9(X0,X1),sK8(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X4] : ~ in(ordered_pair(X4,X2),X0) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ? [X5] :
                ( ( ~ in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(X5,X1)
                  | ? [X7] : in(ordered_pair(X7,X5),X0) ) ) ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( in(X2,X1)
                  | ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ? [X3] : in(ordered_pair(X3,X2),X0)
            <=> in(X2,X1) )
        <=> relation_rng(X0) = X1 )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( ! [X2] :
              ( ? [X3] : in(ordered_pair(X3,X2),X0)
            <=> in(X2,X1) )
        <=> relation_rng(X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f149,plain,
    spl13_2,
    inference(avatar_split_clause,[],[f148,f120]) ).

fof(f120,plain,
    ( spl13_2
  <=> in(sK11,relation_dom(sK10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

fof(f148,plain,
    in(sK11,relation_dom(sK10)),
    inference(subsumption_resolution,[],[f145,f97]) ).

fof(f145,plain,
    ( in(sK11,relation_dom(sK10))
    | ~ relation(sK10) ),
    inference(resolution,[],[f143,f134]) ).

fof(f143,plain,
    ! [X2,X3,X0] :
      ( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)
      | in(X2,relation_dom(X0))
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f111,f95]) ).

fof(f111,plain,
    ! [X2,X3,X0] :
      ( ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
      | ~ relation(X0)
      | in(X2,relation_dom(X0)) ),
    inference(equality_resolution,[],[f102]) ).

fof(f102,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X1)
      | ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f90,f82]) ).

fof(f90,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X1)
      | ~ in(ordered_pair(X2,X3),X0)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( in(ordered_pair(X2,sK4(X0,X2)),X0)
                  | ~ in(X2,X1) ) )
            | relation_dom(X0) != X1 )
          & ( relation_dom(X0) = X1
            | ( ( ! [X6] : ~ in(ordered_pair(sK5(X0,X1),X6),X0)
                | ~ in(sK5(X0,X1),X1) )
              & ( in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
                | in(sK5(X0,X1),X1) ) ) ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f58,f61,f60,f59]) ).

fof(f59,plain,
    ! [X0,X2] :
      ( ? [X4] : in(ordered_pair(X2,X4),X0)
     => in(ordered_pair(X2,sK4(X0,X2)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
            | ~ in(X5,X1) )
          & ( ? [X7] : in(ordered_pair(X5,X7),X0)
            | in(X5,X1) ) )
     => ( ( ! [X6] : ~ in(ordered_pair(sK5(X0,X1),X6),X0)
          | ~ in(sK5(X0,X1),X1) )
        & ( ? [X7] : in(ordered_pair(sK5(X0,X1),X7),X0)
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ? [X7] : in(ordered_pair(sK5(X0,X1),X7),X0)
     => in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( ? [X4] : in(ordered_pair(X2,X4),X0)
                  | ~ in(X2,X1) ) )
            | relation_dom(X0) != X1 )
          & ( relation_dom(X0) = X1
            | ? [X5] :
                ( ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
                  | ~ in(X5,X1) )
                & ( ? [X7] : in(ordered_pair(X5,X7),X0)
                  | in(X5,X1) ) ) ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) ) )
            | relation_dom(X0) != X1 )
          & ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | in(X2,X1) ) ) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) )
        <=> relation_dom(X0) = X1 )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) )
        <=> relation_dom(X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

fof(f123,plain,
    ( ~ spl13_1
    | ~ spl13_2 ),
    inference(avatar_split_clause,[],[f96,f120,f116]) ).

fof(f96,plain,
    ( ~ in(sK11,relation_dom(sK10))
    | ~ in(sK12,relation_rng(sK10)) ),
    inference(cnf_transformation,[],[f71]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% 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
% 0.14/0.34  % Computer : n015.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 14:58:21 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.53  % (5601)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 (2999ds/48Mi)
% 0.21/0.55  % (5601)First to succeed.
% 0.21/0.56  % (5617)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.56  % (5601)Refutation found. Thanks to Tanya!
% 0.21/0.56  % SZS status Theorem for theBenchmark
% 0.21/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.56  % (5601)------------------------------
% 0.21/0.56  % (5601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.56  % (5601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.56  % (5601)Termination reason: Refutation
% 0.21/0.56  
% 0.21/0.56  % (5601)Memory used [KB]: 5500
% 0.21/0.56  % (5601)Time elapsed: 0.135 s
% 0.21/0.56  % (5601)Instructions burned: 4 (million)
% 0.21/0.56  % (5601)------------------------------
% 0.21/0.56  % (5601)------------------------------
% 0.21/0.56  % (5595)Success in time 0.208 s
%------------------------------------------------------------------------------