TSTP Solution File: NUM385+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUM385+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 : 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 18:04:57 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   45 (  15 unt;   0 def)
%            Number of atoms       :  175 (  59 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  209 (  79   ~;  77   |;  40   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   86 (  73   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f289,plain,
    $false,
    inference(subsumption_resolution,[],[f288,f278]) ).

fof(f278,plain,
    in(sK1,sK0),
    inference(subsumption_resolution,[],[f269,f215]) ).

fof(f215,plain,
    ~ in(sK1,singleton(sK0)),
    inference(extensionality_resolution,[],[f170,f109]) ).

fof(f109,plain,
    sK1 != sK0,
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ( sK1 != sK0
    & succ(sK0) = succ(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f69]) ).

fof(f69,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & succ(X0) = succ(X1) )
   => ( sK1 != sK0
      & succ(sK0) = succ(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ? [X0,X1] :
      ( X0 != X1
      & succ(X0) = succ(X1) ),
    inference(rectify,[],[f65]) ).

fof(f65,plain,
    ? [X1,X0] :
      ( X0 != X1
      & succ(X0) = succ(X1) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ~ ! [X1,X0] :
        ( succ(X0) = succ(X1)
       => X0 = X1 ),
    inference(rectify,[],[f30]) ).

fof(f30,negated_conjecture,
    ~ ! [X1,X0] :
        ( succ(X0) = succ(X1)
       => X0 = X1 ),
    inference(negated_conjecture,[],[f29]) ).

fof(f29,conjecture,
    ! [X1,X0] :
      ( succ(X0) = succ(X1)
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_ordinal1) ).

fof(f170,plain,
    ! [X2,X1] :
      ( ~ in(X2,singleton(X1))
      | X1 = X2 ),
    inference(equality_resolution,[],[f144]) ).

fof(f144,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | ~ in(X2,X0)
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X0)
              | X1 != X2 )
            & ( X1 = X2
              | ~ in(X2,X0) ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ( ( sK9(X0,X1) != X1
            | ~ in(sK9(X0,X1),X0) )
          & ( sK9(X0,X1) = X1
            | in(sK9(X0,X1),X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f92,f93]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( X1 != X3
            | ~ in(X3,X0) )
          & ( X1 = X3
            | in(X3,X0) ) )
     => ( ( sK9(X0,X1) != X1
          | ~ in(sK9(X0,X1),X0) )
        & ( sK9(X0,X1) = X1
          | in(sK9(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X0)
              | X1 != X2 )
            & ( X1 = X2
              | ~ in(X2,X0) ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X3] :
            ( ( X1 != X3
              | ~ in(X3,X0) )
            & ( X1 = X3
              | in(X3,X0) ) ) ) ),
    inference(rectify,[],[f91]) ).

fof(f91,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f269,plain,
    ( in(sK1,sK0)
    | in(sK1,singleton(sK0)) ),
    inference(resolution,[],[f167,f193]) ).

fof(f193,plain,
    in(sK1,set_union2(sK0,singleton(sK0))),
    inference(superposition,[],[f164,f162]) ).

fof(f162,plain,
    set_union2(sK0,singleton(sK0)) = set_union2(sK1,singleton(sK1)),
    inference(definition_unfolding,[],[f108,f114,f114]) ).

fof(f114,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(f108,plain,
    succ(sK0) = succ(sK1),
    inference(cnf_transformation,[],[f70]) ).

fof(f164,plain,
    ! [X0] : in(X0,set_union2(X0,singleton(X0))),
    inference(definition_unfolding,[],[f161,f114]) ).

fof(f161,plain,
    ! [X0] : in(X0,succ(X0)),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).

fof(f167,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,set_union2(X0,X1))
      | in(X3,X0)
      | in(X3,X1) ),
    inference(equality_resolution,[],[f129]) ).

fof(f129,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | in(X3,X0)
      | ~ in(X3,X2)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 )
      & ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK5(X0,X1,X2),X1)
              & ~ in(sK5(X0,X1,X2),X0) )
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( in(sK5(X0,X1,X2),X1)
            | in(sK5(X0,X1,X2),X0)
            | in(sK5(X0,X1,X2),X2) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f80,f81]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ( ~ in(X4,X1)
              & ~ in(X4,X0) )
            | ~ in(X4,X2) )
          & ( in(X4,X1)
            | in(X4,X0)
            | in(X4,X2) ) )
     => ( ( ( ~ in(sK5(X0,X1,X2),X1)
            & ~ in(sK5(X0,X1,X2),X0) )
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( in(sK5(X0,X1,X2),X1)
          | in(sK5(X0,X1,X2),X0)
          | in(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 )
      & ( set_union2(X0,X1) = X2
        | ? [X4] :
            ( ( ( ~ in(X4,X1)
                & ~ in(X4,X0) )
              | ~ in(X4,X2) )
            & ( in(X4,X1)
              | in(X4,X0)
              | in(X4,X2) ) ) ) ),
    inference(rectify,[],[f79]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | ( ~ in(X3,X0)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X2)
              | ~ in(X3,X1) ) )
        | set_union2(X2,X0) != X1 )
      & ( set_union2(X2,X0) = X1
        | ? [X3] :
            ( ( ( ~ in(X3,X0)
                & ~ in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X0)
              | in(X3,X2)
              | in(X3,X1) ) ) ) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X2,X0,X1] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | ( ~ in(X3,X0)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X2)
              | ~ in(X3,X1) ) )
        | set_union2(X2,X0) != X1 )
      & ( set_union2(X2,X0) = X1
        | ? [X3] :
            ( ( ( ~ in(X3,X0)
                & ~ in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X0)
              | in(X3,X2)
              | in(X3,X1) ) ) ) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> ( in(X3,X0)
            | in(X3,X2) ) )
    <=> set_union2(X2,X0) = X1 ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X2,X0] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X0)
            | in(X3,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f288,plain,
    ~ in(sK1,sK0),
    inference(resolution,[],[f285,f133]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ in(X1,X0) ),
    inference(rectify,[],[f66]) ).

fof(f66,plain,
    ! [X1,X0] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f285,plain,
    in(sK0,sK1),
    inference(subsumption_resolution,[],[f284,f164]) ).

fof(f284,plain,
    ( ~ in(sK0,set_union2(sK0,singleton(sK0)))
    | in(sK0,sK1) ),
    inference(resolution,[],[f271,f214]) ).

fof(f214,plain,
    ~ in(sK0,singleton(sK1)),
    inference(extensionality_resolution,[],[f170,f109]) ).

fof(f271,plain,
    ! [X0] :
      ( in(X0,singleton(sK1))
      | in(X0,sK1)
      | ~ in(X0,set_union2(sK0,singleton(sK0))) ),
    inference(superposition,[],[f167,f162]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM385+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_sat --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 06:39:48 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (10364)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51  % (10363)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.51  % (10352)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51  % (10370)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51  % (10352)Refutation not found, incomplete strategy% (10352)------------------------------
% 0.19/0.51  % (10352)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (10374)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.52  % (10352)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (10357)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (10374)First to succeed.
% 0.19/0.52  % (10352)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (10352)Memory used [KB]: 5500
% 0.19/0.52  % (10352)Time elapsed: 0.117 s
% 0.19/0.52  % (10352)Instructions burned: 6 (million)
% 0.19/0.52  % (10352)------------------------------
% 0.19/0.52  % (10352)------------------------------
% 0.19/0.52  % (10353)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.52  % (10365)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.52  % (10375)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.53  % (10372)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.53  TRYING [1]
% 0.19/0.53  TRYING [2]
% 0.19/0.53  % (10356)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.53  % (10355)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (10353)Also succeeded, but the first one will report.
% 0.19/0.53  % (10374)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Theorem for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (10374)------------------------------
% 0.19/0.53  % (10374)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (10374)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (10374)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (10374)Memory used [KB]: 1023
% 0.19/0.53  % (10374)Time elapsed: 0.122 s
% 0.19/0.53  % (10374)Instructions burned: 8 (million)
% 0.19/0.53  % (10374)------------------------------
% 0.19/0.53  % (10374)------------------------------
% 0.19/0.53  % (10348)Success in time 0.179 s
%------------------------------------------------------------------------------