TSTP Solution File: SET009+3 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Tue Apr 30 15:03:56 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   31 (   8 unt;   0 def)
%            Number of atoms       :   83 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   86 (  34   ~;  27   |;  17   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   59 (  50   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f40,plain,
    $false,
    inference(subsumption_resolution,[],[f38,f27]) ).

fof(f27,plain,
    ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK1),
    inference(resolution,[],[f23,f25]) ).

fof(f25,plain,
    member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,sK1)),
    inference(resolution,[],[f20,f17]) ).

fof(f17,plain,
    ~ subset(difference(sK2,sK1),difference(sK2,sK0)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
    ( ~ subset(difference(sK2,sK1),difference(sK2,sK0))
    & subset(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8]) ).

fof(f8,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(difference(X2,X1),difference(X2,X0))
        & subset(X0,X1) )
   => ( ~ subset(difference(sK2,sK1),difference(sK2,sK0))
      & subset(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f6,plain,
    ? [X0,X1,X2] :
      ( ~ subset(difference(X2,X1),difference(X2,X0))
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( subset(X0,X1)
       => subset(difference(X2,X1),difference(X2,X0)) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
     => subset(difference(X2,X1),difference(X2,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_difference) ).

fof(f20,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK3(X0,X1),X1)
          & member(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f11,f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

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

fof(f23,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(flattening,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,difference(X0,X1))
    <=> ( ~ member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).

fof(f38,plain,
    member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK1),
    inference(resolution,[],[f37,f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ~ member(X0,sK0)
      | member(X0,sK1) ),
    inference(resolution,[],[f19,f16]) ).

fof(f16,plain,
    subset(sK0,sK1),
    inference(cnf_transformation,[],[f9]) ).

fof(f19,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ member(X3,X0)
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f37,plain,
    member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK0),
    inference(subsumption_resolution,[],[f33,f17]) ).

fof(f33,plain,
    ( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK0)
    | subset(difference(sK2,sK1),difference(sK2,sK0)) ),
    inference(resolution,[],[f32,f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ member(sK3(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f32,plain,
    ! [X0] :
      ( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,X0))
      | member(sK3(difference(sK2,sK1),difference(sK2,sK0)),X0) ),
    inference(resolution,[],[f24,f26]) ).

fof(f26,plain,
    member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK2),
    inference(resolution,[],[f22,f25]) ).

fof(f22,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X0)
      | member(X2,X1)
      | member(X2,difference(X0,X1)) ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET009+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n005.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 01:40:41 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (10861)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (10864)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.38  % (10867)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  % (10866)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (10863)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (10866)First to succeed.
% 0.14/0.38  % (10865)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38  % (10862)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  TRYING [1,1]
% 0.14/0.38  TRYING [2,1]
% 0.14/0.38  TRYING [1,1]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [3,1]
% 0.14/0.38  TRYING [2,1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  % (10866)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (10866)------------------------------
% 0.14/0.38  % (10866)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38  % (10866)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (10866)Memory used [KB]: 748
% 0.14/0.38  % (10866)Time elapsed: 0.003 s
% 0.14/0.38  % (10866)Instructions burned: 3 (million)
% 0.14/0.38  % (10866)------------------------------
% 0.14/0.38  % (10866)------------------------------
% 0.14/0.38  % (10861)Success in time 0.017 s
%------------------------------------------------------------------------------