TSTP Solution File: SET867+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET867+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_sat --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 18:25:58 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   24 (   8 unt;   0 def)
%            Number of atoms       :   99 (  22 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  119 (  44   ~;  41   |;  27   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   60 (  45   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f50,plain,
    $false,
    inference(subsumption_resolution,[],[f48,f38]) ).

fof(f38,plain,
    empty_set != union(empty_set),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
    empty_set != union(empty_set),
    inference(flattening,[],[f8]) ).

fof(f8,negated_conjecture,
    empty_set != union(empty_set),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    empty_set = union(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).

fof(f48,plain,
    empty_set = union(empty_set),
    inference(resolution,[],[f46,f29]) ).

fof(f29,plain,
    ! [X0] :
      ( in(sK1(X0),X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK1(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f16]) ).

fof(f16,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK1(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f46,plain,
    ! [X0] : ~ in(X0,union(empty_set)),
    inference(resolution,[],[f41,f39]) ).

fof(f39,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f28]) ).

fof(f28,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f41,plain,
    ! [X1,X5] :
      ( in(sK5(X1,X5),X1)
      | ~ in(X5,union(X1)) ),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X5] :
      ( in(sK5(X1,X5),X1)
      | ~ in(X5,X0)
      | union(X1) != X0 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( union(X1) = X0
        | ( ( ~ in(sK3(X0,X1),X0)
            | ! [X3] :
                ( ~ in(sK3(X0,X1),X3)
                | ~ in(X3,X1) ) )
          & ( in(sK3(X0,X1),X0)
            | ( in(sK3(X0,X1),sK4(X0,X1))
              & in(sK4(X0,X1),X1) ) ) ) )
      & ( ! [X5] :
            ( ( ( in(X5,sK5(X1,X5))
                & in(sK5(X1,X5),X1) )
              | ~ in(X5,X0) )
            & ( in(X5,X0)
              | ! [X7] :
                  ( ~ in(X5,X7)
                  | ~ in(X7,X1) ) ) )
        | union(X1) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f21,f24,f23,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X0)
            | ! [X3] :
                ( ~ in(X2,X3)
                | ~ in(X3,X1) ) )
          & ( in(X2,X0)
            | ? [X4] :
                ( in(X2,X4)
                & in(X4,X1) ) ) )
     => ( ( ~ in(sK3(X0,X1),X0)
          | ! [X3] :
              ( ~ in(sK3(X0,X1),X3)
              | ~ in(X3,X1) ) )
        & ( in(sK3(X0,X1),X0)
          | ? [X4] :
              ( in(sK3(X0,X1),X4)
              & in(X4,X1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( in(sK3(X0,X1),X4)
          & in(X4,X1) )
     => ( in(sK3(X0,X1),sK4(X0,X1))
        & in(sK4(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X1,X5] :
      ( ? [X6] :
          ( in(X5,X6)
          & in(X6,X1) )
     => ( in(X5,sK5(X1,X5))
        & in(sK5(X1,X5),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( union(X1) = X0
        | ? [X2] :
            ( ( ~ in(X2,X0)
              | ! [X3] :
                  ( ~ in(X2,X3)
                  | ~ in(X3,X1) ) )
            & ( in(X2,X0)
              | ? [X4] :
                  ( in(X2,X4)
                  & in(X4,X1) ) ) ) )
      & ( ! [X5] :
            ( ( ? [X6] :
                  ( in(X5,X6)
                  & in(X6,X1) )
              | ~ in(X5,X0) )
            & ( in(X5,X0)
              | ! [X7] :
                  ( ~ in(X5,X7)
                  | ~ in(X7,X1) ) ) )
        | union(X1) != X0 ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ~ in(X2,X1)
              | ! [X3] :
                  ( ~ in(X2,X3)
                  | ~ in(X3,X0) ) )
            & ( in(X2,X1)
              | ? [X3] :
                  ( in(X2,X3)
                  & in(X3,X0) ) ) ) )
      & ( ! [X2] :
            ( ( ? [X3] :
                  ( in(X2,X3)
                  & in(X3,X0) )
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | ! [X3] :
                  ( ~ in(X2,X3)
                  | ~ in(X3,X0) ) ) )
        | union(X0) != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( union(X0) = X1
    <=> ! [X2] :
          ( ? [X3] :
              ( in(X2,X3)
              & in(X3,X0) )
        <=> in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n007.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 14:12:46 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  % (23972)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/191324Mi)
% 0.20/0.50  % (23992)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/176Mi)
% 0.20/0.50  TRYING [1]
% 0.20/0.50  TRYING [2]
% 0.20/0.50  TRYING [3]
% 0.20/0.50  TRYING [4]
% 0.20/0.51  % (23984)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.20/0.51  TRYING [5]
% 0.20/0.51  % (23992)First to succeed.
% 0.20/0.51  % (23992)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  % (23992)------------------------------
% 0.20/0.51  % (23992)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (23992)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (23992)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (23992)Memory used [KB]: 5373
% 0.20/0.52  % (23992)Time elapsed: 0.113 s
% 0.20/0.52  % (23992)Instructions burned: 2 (million)
% 0.20/0.52  % (23992)------------------------------
% 0.20/0.52  % (23992)------------------------------
% 0.20/0.52  % (23971)Success in time 0.156 s
%------------------------------------------------------------------------------