TSTP Solution File: SET607+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET607+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n019.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 18:21:35 EDT 2022

% Result   : Theorem 0.18s 0.49s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   47 (  13 unt;   0 def)
%            Number of atoms       :  148 (  18 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  162 (  61   ~;  65   |;  25   &)
%                                         (   9 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   83 (  76   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f79,plain,
    $false,
    inference(subsumption_resolution,[],[f78,f76]) ).

fof(f76,plain,
    member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK2),
    inference(subsumption_resolution,[],[f72,f74]) ).

fof(f74,plain,
    ~ member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK1),
    inference(resolution,[],[f73,f46]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X1,X0))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X1,X0))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X1,X0)) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0,X2,X1] :
      ( ( member(X1,union(X2,X0))
        | ( ~ member(X1,X2)
          & ~ member(X1,X0) ) )
      & ( member(X1,X2)
        | member(X1,X0)
        | ~ member(X1,union(X2,X0)) ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X0,X2,X1] :
      ( ( member(X1,union(X2,X0))
        | ( ~ member(X1,X2)
          & ~ member(X1,X0) ) )
      & ( member(X1,X2)
        | member(X1,X0)
        | ~ member(X1,union(X2,X0)) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X2,X1] :
      ( member(X1,union(X2,X0))
    <=> ( member(X1,X2)
        | member(X1,X0) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X2,X0] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X0)
        | member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(f73,plain,
    ~ member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),union(sK1,difference(sK2,sK1))),
    inference(subsumption_resolution,[],[f71,f61]) ).

fof(f61,plain,
    ~ sQ4_eqProxy(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),
    inference(equality_proxy_replacement,[],[f47,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).

fof(f47,plain,
    union(sK1,difference(sK2,sK1)) != union(sK1,sK2),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    union(sK1,difference(sK2,sK1)) != union(sK1,sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f15,f28]) ).

fof(f28,plain,
    ( ? [X0,X1] : union(X0,X1) != union(X0,difference(X1,X0))
   => union(sK1,difference(sK2,sK1)) != union(sK1,sK2) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0,X1] : union(X0,X1) != union(X0,difference(X1,X0)),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X1] : union(X0,X1) = union(X0,difference(X1,X0)),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0,X1] : union(X0,X1) = union(X0,difference(X1,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th79) ).

fof(f71,plain,
    ( sQ4_eqProxy(union(sK1,difference(sK2,sK1)),union(sK1,sK2))
    | ~ member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),union(sK1,difference(sK2,sK1))) ),
    inference(resolution,[],[f70,f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X1)
      | sQ4_eqProxy(X0,X1)
      | ~ member(sK0(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f37,f57]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK0(X0,X1),X0)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK0(X0,X1),X0)
            | ~ member(sK0(X0,X1),X1) )
          & ( member(sK0(X0,X1),X0)
            | member(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X0)
            | ~ member(X2,X1) )
          & ( member(X2,X0)
            | member(X2,X1) ) )
     => ( ( ~ member(sK0(X0,X1),X0)
          | ~ member(sK0(X0,X1),X1) )
        & ( member(sK0(X0,X1),X0)
          | member(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f70,plain,
    member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),union(sK1,sK2)),
    inference(subsumption_resolution,[],[f68,f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X1,X0))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f68,plain,
    ( member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),union(sK1,sK2))
    | member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK2) ),
    inference(resolution,[],[f67,f41]) ).

fof(f41,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,difference(X0,X2))
      | member(X1,X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,difference(X0,X2))
        | member(X1,X2)
        | ~ member(X1,X0) )
      & ( ( ~ member(X1,X2)
          & member(X1,X0) )
        | ~ member(X1,difference(X0,X2)) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X1,X0,X2] :
      ( ( member(X0,difference(X1,X2))
        | member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( ~ member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,difference(X1,X2)) ) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X1,X0,X2] :
      ( ( member(X0,difference(X1,X2))
        | member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( ~ member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,difference(X1,X2)) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0,X2] :
      ( member(X0,difference(X1,X2))
    <=> ( ~ member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X0,X1] :
      ( ( ~ member(X2,X1)
        & member(X2,X0) )
    <=> member(X2,difference(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).

fof(f67,plain,
    ( member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),difference(sK2,sK1))
    | member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),union(sK1,sK2)) ),
    inference(subsumption_resolution,[],[f66,f46]) ).

fof(f66,plain,
    ( member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),difference(sK2,sK1))
    | member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),union(sK1,sK2))
    | member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK1) ),
    inference(resolution,[],[f65,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X1,X0))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f65,plain,
    ( member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),union(sK1,difference(sK2,sK1)))
    | member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),union(sK1,sK2)) ),
    inference(resolution,[],[f61,f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | member(sK0(X0,X1),X1)
      | member(sK0(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f36,f57]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK0(X0,X1),X0)
      | member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f72,plain,
    ( member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK2)
    | member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK1) ),
    inference(resolution,[],[f70,f44]) ).

fof(f78,plain,
    ~ member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK2),
    inference(subsumption_resolution,[],[f77,f74]) ).

fof(f77,plain,
    ( member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK1)
    | ~ member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),sK2) ),
    inference(resolution,[],[f75,f43]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( member(X1,difference(X0,X2))
      | ~ member(X1,X0)
      | member(X1,X2) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f75,plain,
    ~ member(sK0(union(sK1,difference(sK2,sK1)),union(sK1,sK2)),difference(sK2,sK1)),
    inference(resolution,[],[f73,f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : SET607+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:07:35 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.18/0.42  % (23882)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.18/0.45  % (23907)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.18/0.47  % (23899)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.48  % (23896)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.49  % (23899)Instruction limit reached!
% 0.18/0.49  % (23899)------------------------------
% 0.18/0.49  % (23899)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (23899)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49  % (23899)Termination reason: Unknown
% 0.18/0.49  % (23899)Termination phase: Saturation
% 0.18/0.49  
% 0.18/0.49  % (23899)Memory used [KB]: 6012
% 0.18/0.49  % (23899)Time elapsed: 0.110 s
% 0.18/0.49  % (23899)Instructions burned: 4 (million)
% 0.18/0.49  % (23899)------------------------------
% 0.18/0.49  % (23899)------------------------------
% 0.18/0.49  % (23887)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.18/0.49  % (23896)First to succeed.
% 0.18/0.49  % (23896)Refutation found. Thanks to Tanya!
% 0.18/0.49  % SZS status Theorem for theBenchmark
% 0.18/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49  % (23896)------------------------------
% 0.18/0.49  % (23896)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (23896)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49  % (23896)Termination reason: Refutation
% 0.18/0.49  
% 0.18/0.49  % (23896)Memory used [KB]: 1535
% 0.18/0.49  % (23896)Time elapsed: 0.095 s
% 0.18/0.49  % (23896)Instructions burned: 1 (million)
% 0.18/0.49  % (23896)------------------------------
% 0.18/0.49  % (23896)------------------------------
% 0.18/0.49  % (23876)Success in time 0.146 s
%------------------------------------------------------------------------------