TSTP Solution File: SET914+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET914+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 : n005.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 18:22:44 EDT 2022

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   43 (   7 unt;   0 def)
%            Number of atoms       :  218 (  81 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  274 (  99   ~;  99   |;  62   &)
%                                         (  10 <=>;   4  =>;   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    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  119 (  99   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f106,plain,
    $false,
    inference(subsumption_resolution,[],[f89,f56]) ).

fof(f56,plain,
    in(sK2,sK4),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ( in(sK2,sK4)
    & disjoint(unordered_pair(sK2,sK3),sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f33,f34]) ).

fof(f34,plain,
    ( ? [X0,X1,X2] :
        ( in(X0,X2)
        & disjoint(unordered_pair(X0,X1),X2) )
   => ( in(sK2,sK4)
      & disjoint(unordered_pair(sK2,sK3),sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ? [X0,X1,X2] :
      ( in(X0,X2)
      & disjoint(unordered_pair(X0,X1),X2) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ? [X0,X2,X1] :
      ( in(X0,X1)
      & disjoint(unordered_pair(X0,X2),X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ~ ! [X2,X0,X1] :
        ~ ( in(X0,X1)
          & disjoint(unordered_pair(X0,X2),X1) ),
    inference(rectify,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ~ ( in(X0,X2)
          & disjoint(unordered_pair(X0,X1),X2) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X0,X2,X1] :
      ~ ( in(X0,X2)
        & disjoint(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).

fof(f89,plain,
    ~ in(sK2,sK4),
    inference(resolution,[],[f83,f67]) ).

fof(f67,plain,
    ! [X3,X1] : in(X3,unordered_pair(X3,X1)),
    inference(equality_resolution,[],[f66]) ).

fof(f66,plain,
    ! [X3,X0,X1] :
      ( in(X3,X0)
      | unordered_pair(X3,X1) != X0 ),
    inference(equality_resolution,[],[f47]) ).

fof(f47,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | X2 != X3
      | unordered_pair(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) )
            & ( X1 = X3
              | X2 = X3
              | ~ in(X3,X0) ) )
        | unordered_pair(X2,X1) != X0 )
      & ( unordered_pair(X2,X1) = X0
        | ( ( ( sK0(X0,X1,X2) != X1
              & sK0(X0,X1,X2) != X2 )
            | ~ in(sK0(X0,X1,X2),X0) )
          & ( sK0(X0,X1,X2) = X1
            | sK0(X0,X1,X2) = X2
            | in(sK0(X0,X1,X2),X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f25,f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ( X1 != X4
              & X2 != X4 )
            | ~ in(X4,X0) )
          & ( X1 = X4
            | X2 = X4
            | in(X4,X0) ) )
     => ( ( ( sK0(X0,X1,X2) != X1
            & sK0(X0,X1,X2) != X2 )
          | ~ in(sK0(X0,X1,X2),X0) )
        & ( sK0(X0,X1,X2) = X1
          | sK0(X0,X1,X2) = X2
          | in(sK0(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) )
            & ( X1 = X3
              | X2 = X3
              | ~ in(X3,X0) ) )
        | unordered_pair(X2,X1) != X0 )
      & ( unordered_pair(X2,X1) = X0
        | ? [X4] :
            ( ( ( X1 != X4
                & X2 != X4 )
              | ~ in(X4,X0) )
            & ( X1 = X4
              | X2 = X4
              | in(X4,X0) ) ) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X1,X2,X0] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) )
            & ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) ) )
        | unordered_pair(X0,X2) != X1 )
      & ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ( X2 != X3
                & X0 != X3 )
              | ~ in(X3,X1) )
            & ( X2 = X3
              | X0 = X3
              | in(X3,X1) ) ) ) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X1,X2,X0] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) )
            & ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) ) )
        | unordered_pair(X0,X2) != X1 )
      & ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ( X2 != X3
                & X0 != X3 )
              | ~ in(X3,X1) )
            & ( X2 = X3
              | X0 = X3
              | in(X3,X1) ) ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X1,X2,X0] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> ( X2 = X3
            | X0 = X3 ) )
    <=> unordered_pair(X0,X2) = X1 ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( ( X1 = X3
            | X0 = X3 )
        <=> in(X3,X2) )
    <=> unordered_pair(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f83,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sK2,sK3))
      | ~ in(X0,sK4) ),
    inference(subsumption_resolution,[],[f78,f72]) ).

fof(f72,plain,
    ! [X1] : ~ in(X1,empty_set),
    inference(equality_resolution,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | in(sK5(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f39,f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ? [X2] : in(X2,X0)
     => in(sK5(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X2] : in(X2,X0) ) ),
    inference(rectify,[],[f38]) ).

fof(f38,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(f78,plain,
    ! [X0] :
      ( ~ in(X0,sK4)
      | ~ in(X0,unordered_pair(sK2,sK3))
      | in(X0,empty_set) ),
    inference(superposition,[],[f71,f74]) ).

fof(f74,plain,
    empty_set = set_intersection2(unordered_pair(sK2,sK3),sK4),
    inference(resolution,[],[f55,f58]) ).

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

fof(f37,plain,
    ! [X0,X1] :
      ( ( disjoint(X0,X1)
        | set_intersection2(X0,X1) != empty_set )
      & ( set_intersection2(X0,X1) = empty_set
        | ~ disjoint(X0,X1) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> set_intersection2(X0,X1) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

fof(f55,plain,
    disjoint(unordered_pair(sK2,sK3),sK4),
    inference(cnf_transformation,[],[f35]) ).

fof(f71,plain,
    ! [X2,X1,X4] :
      ( in(X4,set_intersection2(X1,X2))
      | ~ in(X4,X2)
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f49]) ).

fof(f49,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | ~ in(X4,X1)
      | set_intersection2(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X1,X2) = X0
        | ( ( ~ in(sK1(X0,X1,X2),X0)
            | ~ in(sK1(X0,X1,X2),X2)
            | ~ in(sK1(X0,X1,X2),X1) )
          & ( in(sK1(X0,X1,X2),X0)
            | ( in(sK1(X0,X1,X2),X2)
              & in(sK1(X0,X1,X2),X1) ) ) ) )
      & ( ! [X4] :
            ( ( ( in(X4,X2)
                & in(X4,X1) )
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ~ in(X4,X2)
              | ~ in(X4,X1) ) )
        | set_intersection2(X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f30,f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ~ in(X3,X2)
            | ~ in(X3,X1) )
          & ( in(X3,X0)
            | ( in(X3,X2)
              & in(X3,X1) ) ) )
     => ( ( ~ in(sK1(X0,X1,X2),X0)
          | ~ in(sK1(X0,X1,X2),X2)
          | ~ in(sK1(X0,X1,X2),X1) )
        & ( in(sK1(X0,X1,X2),X0)
          | ( in(sK1(X0,X1,X2),X2)
            & in(sK1(X0,X1,X2),X1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( in(X3,X0)
              | ( in(X3,X2)
                & in(X3,X1) ) ) ) )
      & ( ! [X4] :
            ( ( ( in(X4,X2)
                & in(X4,X1) )
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ~ in(X4,X2)
              | ~ in(X4,X1) ) )
        | set_intersection2(X1,X2) != X0 ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ! [X1,X2,X0] :
      ( ( set_intersection2(X2,X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | ( in(X3,X0)
                & in(X3,X2) ) ) ) )
      & ( ! [X3] :
            ( ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_intersection2(X2,X0) != X1 ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X1,X2,X0] :
      ( ( set_intersection2(X2,X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | ( in(X3,X0)
                & in(X3,X2) ) ) ) )
      & ( ! [X3] :
            ( ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_intersection2(X2,X0) != X1 ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X2,X0] :
      ( set_intersection2(X2,X0) = X1
    <=> ! [X3] :
          ( ( in(X3,X0)
            & in(X3,X2) )
        <=> in(X3,X1) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X2,X0] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X0)
            & in(X3,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % 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 : n005.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 16:08:18 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.44  % (12953)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.47  % (12953)First to succeed.
% 0.19/0.47  % (12953)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Theorem for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48  % (12953)------------------------------
% 0.19/0.48  % (12953)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (12953)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (12953)Termination reason: Refutation
% 0.19/0.48  
% 0.19/0.48  % (12953)Memory used [KB]: 6012
% 0.19/0.48  % (12953)Time elapsed: 0.088 s
% 0.19/0.48  % (12953)Instructions burned: 3 (million)
% 0.19/0.48  % (12953)------------------------------
% 0.19/0.48  % (12953)------------------------------
% 0.19/0.48  % (12950)Success in time 0.128 s
%------------------------------------------------------------------------------