TSTP Solution File: SEU133+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU133+2 : 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 : n023.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 18:26:48 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   30 (  11 unt;   0 def)
%            Number of atoms       :  129 (  11 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  160 (  61   ~;  53   |;  34   &)
%                                         (   7 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   77 (  64   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f403,plain,
    $false,
    inference(subsumption_resolution,[],[f391,f263]) ).

fof(f263,plain,
    ~ in(sK9(set_difference(sK4,sK5),sK4),sK4),
    inference(resolution,[],[f171,f199]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK9(X0,X1),X1) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( ~ in(sK9(X0,X1),X1)
          & in(sK9(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f132,f133]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ in(X3,X1)
          & in(X3,X0) )
     => ( ~ in(sK9(X0,X1),X1)
        & in(sK9(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    inference(rectify,[],[f131]) ).

fof(f131,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( in(X2,X0)
            | ~ in(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( ~ in(X2,X0)
            & in(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
          | ~ in(X2,X1) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f171,plain,
    ~ subset(set_difference(sK4,sK5),sK4),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ~ subset(set_difference(sK4,sK5),sK4),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f107,f108]) ).

fof(f108,plain,
    ( ? [X0,X1] : ~ subset(set_difference(X0,X1),X0)
   => ~ subset(set_difference(sK4,sK5),sK4) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ? [X0,X1] : ~ subset(set_difference(X0,X1),X0),
    inference(rectify,[],[f71]) ).

fof(f71,plain,
    ? [X1,X0] : ~ subset(set_difference(X1,X0),X1),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,plain,
    ~ ! [X1,X0] : subset(set_difference(X1,X0),X1),
    inference(rectify,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ! [X1,X0] : subset(set_difference(X0,X1),X0),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ! [X1,X0] : subset(set_difference(X0,X1),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).

fof(f391,plain,
    in(sK9(set_difference(sK4,sK5),sK4),sK4),
    inference(resolution,[],[f262,f219]) ).

fof(f219,plain,
    ! [X2,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,set_difference(X1,X2)) ),
    inference(equality_resolution,[],[f175]) ).

fof(f175,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X0)
      | set_difference(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X1,X2) = X0
        | ( ( ~ in(sK6(X0,X1,X2),X0)
            | ~ in(sK6(X0,X1,X2),X1)
            | in(sK6(X0,X1,X2),X2) )
          & ( in(sK6(X0,X1,X2),X0)
            | ( in(sK6(X0,X1,X2),X1)
              & ~ in(sK6(X0,X1,X2),X2) ) ) ) )
      & ( ! [X4] :
            ( ( ( in(X4,X1)
                & ~ in(X4,X2) )
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ~ in(X4,X1)
              | in(X4,X2) ) )
        | set_difference(X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f113,f114]) ).

fof(f114,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ~ in(X3,X1)
            | in(X3,X2) )
          & ( in(X3,X0)
            | ( in(X3,X1)
              & ~ in(X3,X2) ) ) )
     => ( ( ~ in(sK6(X0,X1,X2),X0)
          | ~ in(sK6(X0,X1,X2),X1)
          | in(sK6(X0,X1,X2),X2) )
        & ( in(sK6(X0,X1,X2),X0)
          | ( in(sK6(X0,X1,X2),X1)
            & ~ in(sK6(X0,X1,X2),X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X1)
              | in(X3,X2) )
            & ( in(X3,X0)
              | ( in(X3,X1)
                & ~ in(X3,X2) ) ) ) )
      & ( ! [X4] :
            ( ( ( in(X4,X1)
                & ~ in(X4,X2) )
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ~ in(X4,X1)
              | in(X4,X2) ) )
        | set_difference(X1,X2) != X0 ) ),
    inference(rectify,[],[f112]) ).

fof(f112,plain,
    ! [X2,X1,X0] :
      ( ( set_difference(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | in(X3,X0) )
            & ( in(X3,X2)
              | ( in(X3,X1)
                & ~ in(X3,X0) ) ) ) )
      & ( ! [X3] :
            ( ( ( in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ~ in(X3,X1)
              | in(X3,X0) ) )
        | set_difference(X1,X0) != X2 ) ),
    inference(flattening,[],[f111]) ).

fof(f111,plain,
    ! [X2,X1,X0] :
      ( ( set_difference(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | in(X3,X0) )
            & ( in(X3,X2)
              | ( in(X3,X1)
                & ~ in(X3,X0) ) ) ) )
      & ( ! [X3] :
            ( ( ( in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ~ in(X3,X1)
              | in(X3,X0) ) )
        | set_difference(X1,X0) != X2 ) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X2,X1,X0] :
      ( set_difference(X1,X0) = X2
    <=> ! [X3] :
          ( ( in(X3,X1)
            & ~ in(X3,X0) )
        <=> in(X3,X2) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0,X2] :
      ( set_difference(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X0)
            & ~ in(X3,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f262,plain,
    in(sK9(set_difference(sK4,sK5),sK4),set_difference(sK4,sK5)),
    inference(resolution,[],[f171,f198]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( in(sK9(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f134]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU133+2 : 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_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 15:02:35 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  % (11574)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.48  % (11566)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.49  % (11566)First to succeed.
% 0.20/0.49  % (11574)Instruction limit reached!
% 0.20/0.49  % (11574)------------------------------
% 0.20/0.49  % (11574)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (11574)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (11574)Termination reason: Unknown
% 0.20/0.49  % (11574)Termination phase: Saturation
% 0.20/0.49  
% 0.20/0.49  % (11574)Memory used [KB]: 1535
% 0.20/0.49  % (11574)Time elapsed: 0.005 s
% 0.20/0.49  % (11574)Instructions burned: 3 (million)
% 0.20/0.49  % (11574)------------------------------
% 0.20/0.49  % (11574)------------------------------
% 0.20/0.49  % (11566)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (11566)------------------------------
% 0.20/0.49  % (11566)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (11566)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (11566)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (11566)Memory used [KB]: 6140
% 0.20/0.49  % (11566)Time elapsed: 0.072 s
% 0.20/0.49  % (11566)Instructions burned: 7 (million)
% 0.20/0.49  % (11566)------------------------------
% 0.20/0.49  % (11566)------------------------------
% 0.20/0.49  % (11555)Success in time 0.134 s
%------------------------------------------------------------------------------