TSTP Solution File: SEU153+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU153+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_uns --cores 0 -t %d %s

% Computer : n022.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 18:26:56 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   47 (   9 unt;   0 def)
%            Number of atoms       :  195 (  56 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  231 (  83   ~;  82   |;  50   &)
%                                         (  11 <=>;   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    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :  107 (  91   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f110,plain,
    $false,
    inference(subsumption_resolution,[],[f109,f79]) ).

fof(f79,plain,
    ! [X1] : ~ in(X1,empty_set),
    inference(equality_resolution,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | in(sK5(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f44,f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ? [X2] : in(X2,X0)
     => in(sK5(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X2] : in(X2,X0) ) ),
    inference(rectify,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X1] : in(X1,X0) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ! [X1] : ~ in(X1,X0)
    <=> empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f109,plain,
    in(sK3,empty_set),
    inference(backward_demodulation,[],[f83,f103]) ).

fof(f103,plain,
    empty_set = set_intersection2(sK4,singleton(sK3)),
    inference(unit_resulting_resolution,[],[f98,f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = empty_set
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ( set_intersection2(X0,X1) = empty_set
        | ~ disjoint(X0,X1) )
      & ( disjoint(X0,X1)
        | set_intersection2(X0,X1) != empty_set ) ),
    inference(rectify,[],[f41]) ).

fof(f41,plain,
    ! [X1,X0] :
      ( ( set_intersection2(X1,X0) = empty_set
        | ~ disjoint(X1,X0) )
      & ( disjoint(X1,X0)
        | set_intersection2(X1,X0) != empty_set ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( set_intersection2(X1,X0) = empty_set
    <=> disjoint(X1,X0) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X0] :
      ( disjoint(X0,X1)
    <=> set_intersection2(X0,X1) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

fof(f98,plain,
    disjoint(sK4,singleton(sK3)),
    inference(unit_resulting_resolution,[],[f66,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(X1,X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X1,X0] :
      ( disjoint(X0,X1)
     => disjoint(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

fof(f66,plain,
    disjoint(singleton(sK3),sK4),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( disjoint(singleton(sK3),sK4)
    & in(sK3,sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f38,f39]) ).

fof(f39,plain,
    ( ? [X0,X1] :
        ( disjoint(singleton(X0),X1)
        & in(X0,X1) )
   => ( disjoint(singleton(sK3),sK4)
      & in(sK3,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ? [X0,X1] :
      ( disjoint(singleton(X0),X1)
      & in(X0,X1) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ? [X1,X0] :
      ( disjoint(singleton(X1),X0)
      & in(X1,X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ~ ! [X0,X1] :
        ~ ( disjoint(singleton(X1),X0)
          & in(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X1,X0] :
        ~ ( disjoint(singleton(X0),X1)
          & in(X0,X1) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X1,X0] :
      ~ ( disjoint(singleton(X0),X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).

fof(f83,plain,
    in(sK3,set_intersection2(sK4,singleton(sK3))),
    inference(unit_resulting_resolution,[],[f75,f65,f78]) ).

fof(f78,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,X0)
      | in(X3,set_intersection2(X0,X2))
      | ~ in(X3,X2) ),
    inference(equality_resolution,[],[f58]) ).

fof(f58,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X2)
      | ~ in(X3,X0)
      | set_intersection2(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( ( in(X3,X2)
                & in(X3,X0) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X2)
              | ~ in(X3,X0) ) )
        | set_intersection2(X0,X2) != X1 )
      & ( set_intersection2(X0,X2) = X1
        | ( ( ~ in(sK2(X0,X1,X2),X1)
            | ~ in(sK2(X0,X1,X2),X2)
            | ~ in(sK2(X0,X1,X2),X0) )
          & ( in(sK2(X0,X1,X2),X1)
            | ( in(sK2(X0,X1,X2),X2)
              & in(sK2(X0,X1,X2),X0) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f35,f36]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X1)
            | ~ in(X4,X2)
            | ~ in(X4,X0) )
          & ( in(X4,X1)
            | ( in(X4,X2)
              & in(X4,X0) ) ) )
     => ( ( ~ in(sK2(X0,X1,X2),X1)
          | ~ in(sK2(X0,X1,X2),X2)
          | ~ in(sK2(X0,X1,X2),X0) )
        & ( in(sK2(X0,X1,X2),X1)
          | ( in(sK2(X0,X1,X2),X2)
            & in(sK2(X0,X1,X2),X0) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( ( in(X3,X2)
                & in(X3,X0) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X2)
              | ~ in(X3,X0) ) )
        | set_intersection2(X0,X2) != X1 )
      & ( set_intersection2(X0,X2) = X1
        | ? [X4] :
            ( ( ~ in(X4,X1)
              | ~ in(X4,X2)
              | ~ in(X4,X0) )
            & ( in(X4,X1)
              | ( in(X4,X2)
                & in(X4,X0) ) ) ) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_intersection2(X2,X0) != X1 )
      & ( set_intersection2(X2,X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | ( in(X3,X0)
                & in(X3,X2) ) ) ) ) ),
    inference(flattening,[],[f33]) ).

fof(f33,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_intersection2(X2,X0) != X1 )
      & ( set_intersection2(X2,X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | ( in(X3,X0)
                & in(X3,X2) ) ) ) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X2,X1,X0] :
      ( ! [X3] :
          ( ( in(X3,X0)
            & in(X3,X2) )
        <=> in(X3,X1) )
    <=> set_intersection2(X2,X0) = X1 ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X2,X0] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X0)
            & in(X3,X1) ) )
    <=> set_intersection2(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f65,plain,
    in(sK3,sK4),
    inference(cnf_transformation,[],[f40]) ).

fof(f75,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f74]) ).

fof(f74,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f50]) ).

fof(f50,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( ~ in(sK0(X0,X1),X1)
            | sK0(X0,X1) != X0 )
          & ( in(sK0(X0,X1),X1)
            | sK0(X0,X1) = X0 ) ) )
      & ( ! [X3] :
            ( ( X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | X0 != X3 ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f28,f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | X0 != X2 )
          & ( in(X2,X1)
            | X0 = X2 ) )
     => ( ( ~ in(sK0(X0,X1),X1)
          | sK0(X0,X1) != X0 )
        & ( in(sK0(X0,X1),X1)
          | sK0(X0,X1) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( ~ in(X2,X1)
              | X0 != X2 )
            & ( in(X2,X1)
              | X0 = X2 ) ) )
      & ( ! [X3] :
            ( ( X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | X0 != X3 ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0] :
      ( ( singleton(X1) = X0
        | ? [X2] :
            ( ( ~ in(X2,X0)
              | X1 != X2 )
            & ( in(X2,X0)
              | X1 = X2 ) ) )
      & ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X1,X0] :
      ( singleton(X1) = X0
    <=> ! [X2] :
          ( X1 = X2
        <=> in(X2,X0) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( X0 = X2
        <=> in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEU153+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13  % 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 : n022.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 14:43:26 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.48  % (23094)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.49  % (23087)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (23094)First to succeed.
% 0.19/0.50  % (23094)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (23094)------------------------------
% 0.19/0.50  % (23094)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (23094)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (23094)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (23094)Memory used [KB]: 6012
% 0.19/0.50  % (23094)Time elapsed: 0.097 s
% 0.19/0.50  % (23094)Instructions burned: 3 (million)
% 0.19/0.50  % (23094)------------------------------
% 0.19/0.50  % (23094)------------------------------
% 0.19/0.50  % (23083)Success in time 0.151 s
%------------------------------------------------------------------------------