TSTP Solution File: SEU062+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n006.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 18:26:31 EDT 2022

% Result   : Theorem 0.18s 0.50s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   41 (   5 unt;   0 def)
%            Number of atoms       :  125 (  16 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  145 (  61   ~;  42   |;  23   &)
%                                         (   9 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   67 (  56   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f238,plain,
    $false,
    inference(avatar_sat_refutation,[],[f184,f193,f237]) ).

fof(f237,plain,
    ~ spl15_3,
    inference(avatar_contradiction_clause,[],[f236]) ).

fof(f236,plain,
    ( $false
    | ~ spl15_3 ),
    inference(resolution,[],[f225,f146]) ).

fof(f146,plain,
    ~ subset(sK12,relation_rng(sK11)),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ( relation(sK11)
    & ! [X2] :
        ( empty_set != relation_inverse_image(sK11,singleton(X2))
        | ~ in(X2,sK12) )
    & ~ subset(sK12,relation_rng(sK11)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f99,f100]) ).

fof(f100,plain,
    ( ? [X0,X1] :
        ( relation(X0)
        & ! [X2] :
            ( empty_set != relation_inverse_image(X0,singleton(X2))
            | ~ in(X2,X1) )
        & ~ subset(X1,relation_rng(X0)) )
   => ( relation(sK11)
      & ! [X2] :
          ( empty_set != relation_inverse_image(sK11,singleton(X2))
          | ~ in(X2,sK12) )
      & ~ subset(sK12,relation_rng(sK11)) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0,X1] :
      ( relation(X0)
      & ! [X2] :
          ( empty_set != relation_inverse_image(X0,singleton(X2))
          | ~ in(X2,X1) )
      & ~ subset(X1,relation_rng(X0)) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ? [X1,X0] :
      ( relation(X1)
      & ! [X2] :
          ( empty_set != relation_inverse_image(X1,singleton(X2))
          | ~ in(X2,X0) )
      & ~ subset(X0,relation_rng(X1)) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ? [X1,X0] :
      ( ~ subset(X0,relation_rng(X1))
      & ! [X2] :
          ( empty_set != relation_inverse_image(X1,singleton(X2))
          | ~ in(X2,X0) )
      & relation(X1) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,negated_conjecture,
    ~ ! [X1,X0] :
        ( relation(X1)
       => ( ! [X2] :
              ~ ( empty_set = relation_inverse_image(X1,singleton(X2))
                & in(X2,X0) )
         => subset(X0,relation_rng(X1)) ) ),
    inference(negated_conjecture,[],[f26]) ).

fof(f26,conjecture,
    ! [X1,X0] :
      ( relation(X1)
     => ( ! [X2] :
            ~ ( empty_set = relation_inverse_image(X1,singleton(X2))
              & in(X2,X0) )
       => subset(X0,relation_rng(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).

fof(f225,plain,
    ( subset(sK12,relation_rng(sK11))
    | ~ spl15_3 ),
    inference(duplicate_literal_removal,[],[f222]) ).

fof(f222,plain,
    ( subset(sK12,relation_rng(sK11))
    | subset(sK12,relation_rng(sK11))
    | ~ spl15_3 ),
    inference(resolution,[],[f198,f135]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( in(sK8(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( in(sK8(X0,X1),X0)
          & ~ in(sK8(X0,X1),X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f89,f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X0)
          & ~ in(X2,X1) )
     => ( in(sK8(X0,X1),X0)
        & ~ in(sK8(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f88]) ).

fof(f88,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( in(X2,X1)
            & ~ in(X2,X0) ) )
      & ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f198,plain,
    ( ! [X5] :
        ( ~ in(sK8(X5,relation_rng(sK11)),sK12)
        | subset(X5,relation_rng(sK11)) )
    | ~ spl15_3 ),
    inference(resolution,[],[f179,f134]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ~ in(sK8(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f179,plain,
    ( ! [X0] :
        ( in(X0,relation_rng(sK11))
        | ~ in(X0,sK12) )
    | ~ spl15_3 ),
    inference(avatar_component_clause,[],[f178]) ).

fof(f178,plain,
    ( spl15_3
  <=> ! [X0] :
        ( ~ in(X0,sK12)
        | in(X0,relation_rng(sK11)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).

fof(f193,plain,
    spl15_4,
    inference(avatar_contradiction_clause,[],[f191]) ).

fof(f191,plain,
    ( $false
    | spl15_4 ),
    inference(resolution,[],[f183,f148]) ).

fof(f148,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f101]) ).

fof(f183,plain,
    ( ~ relation(sK11)
    | spl15_4 ),
    inference(avatar_component_clause,[],[f181]) ).

fof(f181,plain,
    ( spl15_4
  <=> relation(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).

fof(f184,plain,
    ( spl15_3
    | ~ spl15_4 ),
    inference(avatar_split_clause,[],[f165,f181,f178]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ relation(sK11)
      | ~ in(X0,sK12)
      | in(X0,relation_rng(sK11)) ),
    inference(resolution,[],[f161,f159]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( sQ14_eqProxy(empty_set,relation_inverse_image(X0,singleton(X1)))
      | in(X1,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_proxy_replacement,[],[f141,f157]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( sQ14_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ14_eqProxy])]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( in(X1,relation_rng(X0))
      | empty_set = relation_inverse_image(X0,singleton(X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ( ( in(X1,relation_rng(X0))
          | empty_set = relation_inverse_image(X0,singleton(X1)) )
        & ( empty_set != relation_inverse_image(X0,singleton(X1))
          | ~ in(X1,relation_rng(X0)) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( in(X1,relation_rng(X0))
      <=> empty_set != relation_inverse_image(X0,singleton(X1)) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( relation(X0)
     => ( in(X1,relation_rng(X0))
      <=> empty_set != relation_inverse_image(X0,singleton(X1)) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,axiom,
    ! [X1,X0] :
      ( relation(X1)
     => ( empty_set != relation_inverse_image(X1,singleton(X0))
      <=> in(X0,relation_rng(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).

fof(f161,plain,
    ! [X2] :
      ( ~ sQ14_eqProxy(empty_set,relation_inverse_image(sK11,singleton(X2)))
      | ~ in(X2,sK12) ),
    inference(equality_proxy_replacement,[],[f147,f157]) ).

fof(f147,plain,
    ! [X2] :
      ( empty_set != relation_inverse_image(sK11,singleton(X2))
      | ~ in(X2,sK12) ),
    inference(cnf_transformation,[],[f101]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem    : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n006.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 14:34:55 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.18/0.49  % (19932)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.18/0.49  % (19932)First to succeed.
% 0.18/0.49  % (19922)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.18/0.50  % (19932)Refutation found. Thanks to Tanya!
% 0.18/0.50  % SZS status Theorem for theBenchmark
% 0.18/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50  % (19932)------------------------------
% 0.18/0.50  % (19932)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (19932)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (19932)Termination reason: Refutation
% 0.18/0.50  
% 0.18/0.50  % (19932)Memory used [KB]: 6012
% 0.18/0.50  % (19932)Time elapsed: 0.099 s
% 0.18/0.50  % (19932)Instructions burned: 4 (million)
% 0.18/0.50  % (19932)------------------------------
% 0.18/0.50  % (19932)------------------------------
% 0.18/0.50  % (19912)Success in time 0.15 s
%------------------------------------------------------------------------------