TSTP Solution File: SET950+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET950+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 : n007.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 18:22:50 EDT 2022

% Result   : Theorem 0.21s 0.57s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   48 (   6 unt;   0 def)
%            Number of atoms       :  202 (  47 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  243 (  89   ~;  77   |;  61   &)
%                                         (   8 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :  148 ( 113   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f88,plain,
    $false,
    inference(avatar_sat_refutation,[],[f78,f82,f87]) ).

fof(f87,plain,
    spl9_2,
    inference(avatar_contradiction_clause,[],[f86]) ).

fof(f86,plain,
    ( $false
    | spl9_2 ),
    inference(subsumption_resolution,[],[f85,f41]) ).

fof(f41,plain,
    in(sK7,sK6),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( ! [X4,X5] :
        ( ~ in(X5,sK8)
        | sK7 != ordered_pair(X5,X4)
        | ~ in(X4,sK5) )
    & in(sK7,sK6)
    & subset(sK6,cartesian_product2(sK8,sK5)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f26,f27]) ).

fof(f27,plain,
    ( ? [X0,X1,X2,X3] :
        ( ! [X4,X5] :
            ( ~ in(X5,X3)
            | ordered_pair(X5,X4) != X2
            | ~ in(X4,X0) )
        & in(X2,X1)
        & subset(X1,cartesian_product2(X3,X0)) )
   => ( ! [X5,X4] :
          ( ~ in(X5,sK8)
          | sK7 != ordered_pair(X5,X4)
          | ~ in(X4,sK5) )
      & in(sK7,sK6)
      & subset(sK6,cartesian_product2(sK8,sK5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1,X2,X3] :
      ( ! [X4,X5] :
          ( ~ in(X5,X3)
          | ordered_pair(X5,X4) != X2
          | ~ in(X4,X0) )
      & in(X2,X1)
      & subset(X1,cartesian_product2(X3,X0)) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ? [X2,X3,X1,X0] :
      ( ! [X5,X4] :
          ( ~ in(X4,X0)
          | ordered_pair(X4,X5) != X1
          | ~ in(X5,X2) )
      & in(X1,X3)
      & subset(X3,cartesian_product2(X0,X2)) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ~ ! [X0,X3,X1,X2] :
        ~ ( subset(X3,cartesian_product2(X0,X2))
          & ! [X5,X4] :
              ~ ( in(X4,X0)
                & ordered_pair(X4,X5) = X1
                & in(X5,X2) )
          & in(X1,X3) ),
    inference(rectify,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X1,X3,X2,X0] :
        ~ ( in(X3,X0)
          & ! [X4,X5] :
              ~ ( ordered_pair(X4,X5) = X3
                & in(X5,X2)
                & in(X4,X1) )
          & subset(X0,cartesian_product2(X1,X2)) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X1,X3,X2,X0] :
      ~ ( in(X3,X0)
        & ! [X4,X5] :
            ~ ( ordered_pair(X4,X5) = X3
              & in(X5,X2)
              & in(X4,X1) )
        & subset(X0,cartesian_product2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).

fof(f85,plain,
    ( ~ in(sK7,sK6)
    | spl9_2 ),
    inference(resolution,[],[f84,f51]) ).

fof(f51,plain,
    ! [X0] :
      ( in(X0,cartesian_product2(sK8,sK5))
      | ~ in(X0,sK6) ),
    inference(resolution,[],[f31,f40]) ).

fof(f40,plain,
    subset(sK6,cartesian_product2(sK8,sK5)),
    inference(cnf_transformation,[],[f28]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | ~ in(X2,X1)
      | in(X2,X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) )
      | ~ subset(X1,X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
     => ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    inference(unused_predicate_definition_removal,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f84,plain,
    ( ~ in(sK7,cartesian_product2(sK8,sK5))
    | spl9_2 ),
    inference(resolution,[],[f77,f45]) ).

fof(f45,plain,
    ! [X0,X1,X8] :
      ( in(sK3(X0,X1,X8),X1)
      | ~ in(X8,cartesian_product2(X1,X0)) ),
    inference(equality_resolution,[],[f35]) ).

fof(f35,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK3(X0,X1,X8),X1)
      | ~ in(X8,X2)
      | cartesian_product2(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X1,X0) = X2
        | ( ( ~ in(sK0(X0,X1,X2),X2)
            | ! [X4,X5] :
                ( ~ in(X4,X1)
                | ~ in(X5,X0)
                | ordered_pair(X4,X5) != sK0(X0,X1,X2) ) )
          & ( in(sK0(X0,X1,X2),X2)
            | ( in(sK1(X0,X1,X2),X1)
              & in(sK2(X0,X1,X2),X0)
              & ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2)) = sK0(X0,X1,X2) ) ) ) )
      & ( ! [X8] :
            ( ( ( in(sK3(X0,X1,X8),X1)
                & in(sK4(X0,X1,X8),X0)
                & ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 )
              | ~ in(X8,X2) )
            & ( in(X8,X2)
              | ! [X11,X12] :
                  ( ~ in(X11,X1)
                  | ~ in(X12,X0)
                  | ordered_pair(X11,X12) != X8 ) ) )
        | cartesian_product2(X1,X0) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f24,f23,f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X2)
            | ! [X4,X5] :
                ( ~ in(X4,X1)
                | ~ in(X5,X0)
                | ordered_pair(X4,X5) != X3 ) )
          & ( in(X3,X2)
            | ? [X6,X7] :
                ( in(X6,X1)
                & in(X7,X0)
                & ordered_pair(X6,X7) = X3 ) ) )
     => ( ( ~ in(sK0(X0,X1,X2),X2)
          | ! [X5,X4] :
              ( ~ in(X4,X1)
              | ~ in(X5,X0)
              | ordered_pair(X4,X5) != sK0(X0,X1,X2) ) )
        & ( in(sK0(X0,X1,X2),X2)
          | ? [X7,X6] :
              ( in(X6,X1)
              & in(X7,X0)
              & sK0(X0,X1,X2) = ordered_pair(X6,X7) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( in(X6,X1)
          & in(X7,X0)
          & sK0(X0,X1,X2) = ordered_pair(X6,X7) )
     => ( in(sK1(X0,X1,X2),X1)
        & in(sK2(X0,X1,X2),X0)
        & ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2)) = sK0(X0,X1,X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1,X8] :
      ( ? [X9,X10] :
          ( in(X9,X1)
          & in(X10,X0)
          & ordered_pair(X9,X10) = X8 )
     => ( in(sK3(X0,X1,X8),X1)
        & in(sK4(X0,X1,X8),X0)
        & ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ! [X4,X5] :
                  ( ~ in(X4,X1)
                  | ~ in(X5,X0)
                  | ordered_pair(X4,X5) != X3 ) )
            & ( in(X3,X2)
              | ? [X6,X7] :
                  ( in(X6,X1)
                  & in(X7,X0)
                  & ordered_pair(X6,X7) = X3 ) ) ) )
      & ( ! [X8] :
            ( ( ? [X9,X10] :
                  ( in(X9,X1)
                  & in(X10,X0)
                  & ordered_pair(X9,X10) = X8 )
              | ~ in(X8,X2) )
            & ( in(X8,X2)
              | ! [X11,X12] :
                  ( ~ in(X11,X1)
                  | ~ in(X12,X0)
                  | ordered_pair(X11,X12) != X8 ) ) )
        | cartesian_product2(X1,X0) != X2 ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ! [X5,X4] :
                  ( ~ in(X5,X0)
                  | ~ in(X4,X1)
                  | ordered_pair(X5,X4) != X3 ) )
            & ( in(X3,X2)
              | ? [X5,X4] :
                  ( in(X5,X0)
                  & in(X4,X1)
                  & ordered_pair(X5,X4) = X3 ) ) ) )
      & ( ! [X3] :
            ( ( ? [X5,X4] :
                  ( in(X5,X0)
                  & in(X4,X1)
                  & ordered_pair(X5,X4) = X3 )
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ! [X5,X4] :
                  ( ~ in(X5,X0)
                  | ~ in(X4,X1)
                  | ordered_pair(X5,X4) != X3 ) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( ? [X5,X4] :
              ( in(X5,X0)
              & in(X4,X1)
              & ordered_pair(X5,X4) = X3 )
        <=> in(X3,X2) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( ? [X5,X4] :
              ( ordered_pair(X4,X5) = X3
              & in(X4,X0)
              & in(X5,X1) )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).

fof(f77,plain,
    ( ~ in(sK3(sK5,sK8,sK7),sK8)
    | spl9_2 ),
    inference(avatar_component_clause,[],[f75]) ).

fof(f75,plain,
    ( spl9_2
  <=> in(sK3(sK5,sK8,sK7),sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f82,plain,
    spl9_1,
    inference(avatar_contradiction_clause,[],[f81]) ).

fof(f81,plain,
    ( $false
    | spl9_1 ),
    inference(subsumption_resolution,[],[f80,f41]) ).

fof(f80,plain,
    ( ~ in(sK7,sK6)
    | spl9_1 ),
    inference(resolution,[],[f79,f51]) ).

fof(f79,plain,
    ( ~ in(sK7,cartesian_product2(sK8,sK5))
    | spl9_1 ),
    inference(resolution,[],[f73,f46]) ).

fof(f46,plain,
    ! [X0,X1,X8] :
      ( in(sK4(X0,X1,X8),X0)
      | ~ in(X8,cartesian_product2(X1,X0)) ),
    inference(equality_resolution,[],[f34]) ).

fof(f34,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK4(X0,X1,X8),X0)
      | ~ in(X8,X2)
      | cartesian_product2(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f73,plain,
    ( ~ in(sK4(sK5,sK8,sK7),sK5)
    | spl9_1 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f71,plain,
    ( spl9_1
  <=> in(sK4(sK5,sK8,sK7),sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f78,plain,
    ( ~ spl9_1
    | ~ spl9_2 ),
    inference(avatar_split_clause,[],[f69,f75,f71]) ).

fof(f69,plain,
    ( ~ in(sK3(sK5,sK8,sK7),sK8)
    | ~ in(sK4(sK5,sK8,sK7),sK5) ),
    inference(trivial_inequality_removal,[],[f68]) ).

fof(f68,plain,
    ( sK7 != sK7
    | ~ in(sK4(sK5,sK8,sK7),sK5)
    | ~ in(sK3(sK5,sK8,sK7),sK8) ),
    inference(superposition,[],[f42,f65]) ).

fof(f65,plain,
    sK7 = ordered_pair(sK3(sK5,sK8,sK7),sK4(sK5,sK8,sK7)),
    inference(resolution,[],[f59,f41]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ in(X0,sK6)
      | ordered_pair(sK3(sK5,sK8,X0),sK4(sK5,sK8,X0)) = X0 ),
    inference(resolution,[],[f47,f51]) ).

fof(f47,plain,
    ! [X0,X1,X8] :
      ( ~ in(X8,cartesian_product2(X1,X0))
      | ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 ),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X2,X0,X1,X8] :
      ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f42,plain,
    ! [X4,X5] :
      ( sK7 != ordered_pair(X5,X4)
      | ~ in(X5,sK8)
      | ~ in(X4,sK5) ),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 14:17:01 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.55  % (8470)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)
% 0.21/0.56  % (8466)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)
% 0.21/0.56  % (8479)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.56  % (8482)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.21/0.57  % (8466)First to succeed.
% 0.21/0.57  % (8487)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.21/0.57  % (8466)Refutation found. Thanks to Tanya!
% 0.21/0.57  % SZS status Theorem for theBenchmark
% 0.21/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.57  % (8466)------------------------------
% 0.21/0.57  % (8466)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.57  % (8466)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.57  % (8466)Termination reason: Refutation
% 0.21/0.57  
% 0.21/0.57  % (8466)Memory used [KB]: 6012
% 0.21/0.57  % (8466)Time elapsed: 0.139 s
% 0.21/0.57  % (8466)Instructions burned: 4 (million)
% 0.21/0.57  % (8466)------------------------------
% 0.21/0.57  % (8466)------------------------------
% 0.21/0.57  % (8461)Success in time 0.217 s
%------------------------------------------------------------------------------