TSTP Solution File: SET956+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET956+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 : 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 18:22:51 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   39 (  12 unt;   0 def)
%            Number of atoms       :  124 (   9 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  131 (  46   ~;  30   |;  41   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  120 (  95   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f105,plain,
    $false,
    inference(subsumption_resolution,[],[f104,f56]) ).

fof(f56,plain,
    in(sK8(sK2,sK3),sK3),
    inference(unit_resulting_resolution,[],[f42,f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( in(sK8(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( in(sK8(X0,X1),X1)
          & ~ in(sK8(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f37,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X1)
          & ~ in(X3,X0) )
     => ( in(sK8(X0,X1),X1)
        & ~ in(sK8(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X0) ) ) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( in(X2,X1)
            & ~ in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f42,plain,
    ~ subset(sK3,sK2),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ( ! [X4,X5] :
        ( in(ordered_pair(X4,X5),sK2)
        | ~ in(ordered_pair(X4,X5),sK3) )
    & ~ subset(sK3,sK2)
    & subset(sK3,cartesian_product2(sK4,sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f25,f26]) ).

fof(f26,plain,
    ( ? [X0,X1,X2,X3] :
        ( ! [X4,X5] :
            ( in(ordered_pair(X4,X5),X1)
            | ~ in(ordered_pair(X4,X5),X2) )
        & ~ subset(X2,X1)
        & subset(X2,cartesian_product2(X3,X0)) )
   => ( ! [X5,X4] :
          ( in(ordered_pair(X4,X5),sK2)
          | ~ in(ordered_pair(X4,X5),sK3) )
      & ~ subset(sK3,sK2)
      & subset(sK3,cartesian_product2(sK4,sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0,X1,X2,X3] :
      ( ! [X4,X5] :
          ( in(ordered_pair(X4,X5),X1)
          | ~ in(ordered_pair(X4,X5),X2) )
      & ~ subset(X2,X1)
      & subset(X2,cartesian_product2(X3,X0)) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ? [X3,X2,X1,X0] :
      ( ! [X4,X5] :
          ( in(ordered_pair(X4,X5),X2)
          | ~ in(ordered_pair(X4,X5),X1) )
      & ~ subset(X1,X2)
      & subset(X1,cartesian_product2(X0,X3)) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ? [X2,X1,X0,X3] :
      ( ~ subset(X1,X2)
      & ! [X4,X5] :
          ( in(ordered_pair(X4,X5),X2)
          | ~ in(ordered_pair(X4,X5),X1) )
      & subset(X1,cartesian_product2(X0,X3)) ),
    inference(ennf_transformation,[],[f12]) ).

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

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

fof(f10,conjecture,
    ! [X1,X0,X3,X2] :
      ( ( ! [X4,X5] :
            ( in(ordered_pair(X4,X5),X0)
           => in(ordered_pair(X4,X5),X3) )
        & subset(X0,cartesian_product2(X1,X2)) )
     => subset(X0,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).

fof(f104,plain,
    ~ in(sK8(sK2,sK3),sK3),
    inference(subsumption_resolution,[],[f102,f55]) ).

fof(f55,plain,
    ~ in(sK8(sK2,sK3),sK2),
    inference(unit_resulting_resolution,[],[f42,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ in(sK8(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f102,plain,
    ( in(sK8(sK2,sK3),sK2)
    | ~ in(sK8(sK2,sK3),sK3) ),
    inference(superposition,[],[f43,f91]) ).

fof(f91,plain,
    sK8(sK2,sK3) = ordered_pair(sK5(sK4,sK1,sK8(sK2,sK3)),sK6(sK4,sK1,sK8(sK2,sK3))),
    inference(unit_resulting_resolution,[],[f63,f49,f47]) ).

fof(f47,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subset(X3,cartesian_product2(X0,X1))
      | ~ in(X2,X3)
      | ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) = X2 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(X2,X3)
      | ~ subset(X3,cartesian_product2(X0,X1))
      | ( in(sK5(X0,X1,X2),X0)
        & ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) = X2
        & in(sK6(X0,X1,X2),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f30,f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ? [X4,X5] :
          ( in(X4,X0)
          & ordered_pair(X4,X5) = X2
          & in(X5,X1) )
     => ( in(sK5(X0,X1,X2),X0)
        & ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) = X2
        & in(sK6(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(X2,X3)
      | ~ subset(X3,cartesian_product2(X0,X1))
      | ? [X4,X5] :
          ( in(X4,X0)
          & ordered_pair(X4,X5) = X2
          & in(X5,X1) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X1,X3,X2,X0] :
      ( ~ in(X2,X0)
      | ~ subset(X0,cartesian_product2(X1,X3))
      | ? [X5,X4] :
          ( in(X5,X1)
          & ordered_pair(X5,X4) = X2
          & in(X4,X3) ) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X3,X2,X1] :
      ~ ( ! [X4,X5] :
            ~ ( in(X5,X1)
              & ordered_pair(X5,X4) = X2
              & in(X4,X3) )
        & in(X2,X0)
        & subset(X0,cartesian_product2(X1,X3)) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X3,X2] :
      ~ ( subset(X0,cartesian_product2(X1,X2))
        & ! [X5,X4] :
            ~ ( in(X5,X2)
              & ordered_pair(X4,X5) = X3
              & in(X4,X1) )
        & in(X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).

fof(f49,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X1] : subset(X1,X1),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X0] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f63,plain,
    in(sK8(sK2,sK3),cartesian_product2(sK4,sK1)),
    inference(unit_resulting_resolution,[],[f56,f41,f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | in(X2,X0)
      | ~ in(X2,X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f41,plain,
    subset(sK3,cartesian_product2(sK4,sK1)),
    inference(cnf_transformation,[],[f27]) ).

fof(f43,plain,
    ! [X4,X5] :
      ( ~ in(ordered_pair(X4,X5),sK3)
      | in(ordered_pair(X4,X5),sK2) ),
    inference(cnf_transformation,[],[f27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.13/0.34  % Computer : n023.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 14:53:35 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (17367)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  % (17375)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.50  % (17367)First to succeed.
% 0.20/0.51  % (17367)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (17367)------------------------------
% 0.20/0.51  % (17367)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (17367)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (17367)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (17367)Memory used [KB]: 6012
% 0.20/0.51  % (17367)Time elapsed: 0.084 s
% 0.20/0.51  % (17367)Instructions burned: 4 (million)
% 0.20/0.51  % (17367)------------------------------
% 0.20/0.51  % (17367)------------------------------
% 0.20/0.51  % (17353)Success in time 0.155 s
%------------------------------------------------------------------------------