%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEV421_1 : TPTP v8.1.0. Released v5.0.0.
% 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 18:35:57 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   40 (   5 unt;  15 typ;   0 def)
%            Number of atoms       :   80 (  69 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :   90 (  35   ~;  22   |;  23   &)
%                                         (   4 <=>;   4  =>;   0  <=;   2 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :   39 (   0 atm;   0 fun;  31 num;   8 var)
%            Number of types       :    4 (   2 usr;   1 ari)
%            Number of type conns  :   14 (   9   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :   28 (  13   !;  15   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    set: $tType ).

tff(type_def_6,type,
    element: $tType ).

tff(func_def_0,type,
    empty_set: set ).

tff(func_def_1,type,
    singleton: element > set ).

tff(func_def_2,type,
    intersection: ( set * set ) > set ).

tff(func_def_3,type,
    union: ( set * set ) > set ).

tff(func_def_4,type,
    difference: ( set * set ) > set ).

tff(func_def_5,type,
    complement: set > set ).

tff(func_def_6,type,
    cardinality: set > $int ).

tff(func_def_11,type,
    sK0: element ).

tff(func_def_12,type,
    sK1: set ).

tff(func_def_13,type,
    sK2: $int ).

tff(func_def_14,type,
    sK3: set > element ).

tff(pred_def_1,type,
    member: ( element * set ) > $o ).

tff(pred_def_2,type,
    subset: ( set * set ) > $o ).

tff(f125,plain,
    $false,
    inference(subsumption_resolution,[],[f124,f95]) ).

tff(f95,plain,
    0 = cardinality(empty_set),
    inference(equality_resolution,[],[f78]) ).

tff(f78,plain,
    ! [X0: set] :
      ( ( cardinality(X0) = 0 )
      | ( empty_set != X0 ) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f50,plain,
    ! [X0: set] :
      ( ( ( empty_set = X0 )
        | ( cardinality(X0) != 0 ) )
      & ( ( cardinality(X0) = 0 )
        | ( empty_set != X0 ) ) ),
    inference(nnf_transformation,[],[f8]) ).

tff(f8,axiom,
    ! [X0: set] :
      ( ( empty_set = X0 )
    <=> ( cardinality(X0) = 0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cardinality_empty_set) ).

tff(f124,plain,
    0 != cardinality(empty_set),
    inference(subsumption_resolution,[],[f122,f118]) ).

tff(f118,plain,
    empty_set = sK1,
    inference(trivial_inequality_removal,[],[f117]) ).

tff(f117,plain,
    ( ( 0 != 0 )
    | ( empty_set = sK1 ) ),
    inference(duplicate_literal_removal,[],[f115]) ).

tff(f115,plain,
    ( ( empty_set = sK1 )
    | ( 0 != 0 )
    | ( empty_set = sK1 ) ),
    inference(superposition,[],[f79,f98]) ).

tff(f98,plain,
    ( ( 0 = cardinality(sK1) )
    | ( empty_set = sK1 ) ),
    inference(superposition,[],[f89,f88]) ).

tff(f88,plain,
    cardinality(sK1) = sK2,
    inference(cnf_transformation,[],[f60]) ).

tff(f60,plain,
    ( ( ( empty_set != sK1 )
      | ( 0 != sK2 ) )
    & ( ( empty_set = sK1 )
      | ( 0 = sK2 ) )
    & ( cardinality(sK1) = sK2 )
    & ~ member(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f58,f59]) ).

tff(f59,plain,
    ( ? [X0: element,X1: set,X2: $int] :
        ( ( ( empty_set != X1 )
          | ( 0 != X2 ) )
        & ( ( empty_set = X1 )
          | ( 0 = X2 ) )
        & ( cardinality(X1) = X2 )
        & ~ member(X0,X1) )
   => ( ( ( empty_set != sK1 )
        | ( 0 != sK2 ) )
      & ( ( empty_set = sK1 )
        | ( 0 = sK2 ) )
      & ( cardinality(sK1) = sK2 )
      & ~ member(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f58,plain,
    ? [X0: element,X1: set,X2: $int] :
      ( ( ( empty_set != X1 )
        | ( 0 != X2 ) )
      & ( ( empty_set = X1 )
        | ( 0 = X2 ) )
      & ( cardinality(X1) = X2 )
      & ~ member(X0,X1) ),
    inference(flattening,[],[f57]) ).

tff(f57,plain,
    ? [X0: element,X1: set,X2: $int] :
      ( ( ( empty_set != X1 )
        | ( 0 != X2 ) )
      & ( ( empty_set = X1 )
        | ( 0 = X2 ) )
      & ( cardinality(X1) = X2 )
      & ~ member(X0,X1) ),
    inference(nnf_transformation,[],[f38]) ).

tff(f38,plain,
    ? [X0: element,X1: set,X2: $int] :
      ( ( ( 0 = X2 )
      <~> ( empty_set = X1 ) )
      & ( cardinality(X1) = X2 )
      & ~ member(X0,X1) ),
    inference(flattening,[],[f37]) ).

tff(f37,plain,
    ? [X1: set,X0: element,X2: $int] :
      ( ( ( 0 = X2 )
      <~> ( empty_set = X1 ) )
      & ( cardinality(X1) = X2 )
      & ~ member(X0,X1) ),
    inference(ennf_transformation,[],[f31]) ).

tff(f31,plain,
    ~ ! [X1: set,X0: element,X2: $int] :
        ( ( ( cardinality(X1) = X2 )
          & ~ member(X0,X1) )
       => ( ( empty_set = X1 )
        <=> ( 0 = X2 ) ) ),
    inference(rectify,[],[f14]) ).

tff(f14,negated_conjecture,
    ~ ! [X1: element,X6: set,X7: $int] :
        ( ( ( cardinality(X6) = X7 )
          & ~ member(X1,X6) )
       => ( ( 0 = X7 )
        <=> ( empty_set = X6 ) ) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    ! [X1: element,X6: set,X7: $int] :
      ( ( ( cardinality(X6) = X7 )
        & ~ member(X1,X6) )
     => ( ( 0 = X7 )
      <=> ( empty_set = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vc1) ).

tff(f89,plain,
    ( ( 0 = sK2 )
    | ( empty_set = sK1 ) ),
    inference(cnf_transformation,[],[f60]) ).

tff(f79,plain,
    ! [X0: set] :
      ( ( cardinality(X0) != 0 )
      | ( empty_set = X0 ) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f122,plain,
    ( ( empty_set != sK1 )
    | ( 0 != cardinality(empty_set) ) ),
    inference(backward_demodulation,[],[f101,f118]) ).

tff(f101,plain,
    ( ( 0 != cardinality(sK1) )
    | ( empty_set != sK1 ) ),
    inference(superposition,[],[f90,f88]) ).

tff(f90,plain,
    ( ( 0 != sK2 )
    | ( empty_set != sK1 ) ),
    inference(cnf_transformation,[],[f60]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEV421=1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13  % 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 : n007.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 16:56:16 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (15563)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.49  % (15571)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.49  % (15571)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.49  % (15571)Terminated due to inappropriate strategy.
% 0.20/0.49  % (15571)------------------------------
% 0.20/0.49  % (15571)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (15571)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (15571)Termination reason: Inappropriate
% 0.20/0.49  
% 0.20/0.49  % (15571)Memory used [KB]: 895
% 0.20/0.49  % (15571)Time elapsed: 0.002 s
% 0.20/0.49  % (15571)Instructions burned: 2 (million)
% 0.20/0.49  % (15571)------------------------------
% 0.20/0.49  % (15571)------------------------------
% 0.20/0.50  % (15576)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)
% 0.20/0.50  % (15576)First to succeed.
% 0.20/0.51  % (15560)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)
% 0.20/0.51  % (15568)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)
% 0.20/0.51  % (15562)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51  % (15576)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  % (15576)------------------------------
% 0.20/0.51  % (15576)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (15576)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (15576)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (15576)Memory used [KB]: 1023
% 0.20/0.51  % (15576)Time elapsed: 0.067 s
% 0.20/0.51  % (15576)Instructions burned: 4 (million)
% 0.20/0.51  % (15576)------------------------------
% 0.20/0.51  % (15576)------------------------------
% 0.20/0.51  % (15553)Success in time 0.158 s
%------------------------------------------------------------------------------