TSTP Solution File: SEV517+1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV517+1 : TPTP v8.2.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n028.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 : Mon Jun 24 16:04:13 EDT 2024

% Result   : Theorem 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   44 (   7 unt;   0 def)
%            Number of atoms       :  177 (  16 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  206 (  73   ~;  60   |;  49   &)
%                                         (   6 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  126 ( 102   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f281,plain,
    $false,
    inference(subsumption_resolution,[],[f280,f133]) ).

fof(f133,plain,
    member(sK0,sK1),
    inference(resolution,[],[f117,f80]) ).

fof(f80,plain,
    member(sK0,difference(sK1,sK2)),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ( ! [X4] :
        ( ~ member(sK0,X4)
        | ~ member(X4,difference(sK3,singleton(sK2))) )
    & partition(sK3,sK1)
    & member(sK0,difference(sK1,sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f41,f46]) ).

fof(f46,plain,
    ( ? [X0,X1,X2,X3] :
        ( ! [X4] :
            ( ~ member(X0,X4)
            | ~ member(X4,difference(X3,singleton(X2))) )
        & partition(X3,X1)
        & member(X0,difference(X1,X2)) )
   => ( ! [X4] :
          ( ~ member(sK0,X4)
          | ~ member(X4,difference(sK3,singleton(sK2))) )
      & partition(sK3,sK1)
      & member(sK0,difference(sK1,sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ? [X0,X1,X2,X3] :
      ( ! [X4] :
          ( ~ member(X0,X4)
          | ~ member(X4,difference(X3,singleton(X2))) )
      & partition(X3,X1)
      & member(X0,difference(X1,X2)) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ? [X0,X1,X2,X3] :
      ( ! [X4] :
          ( ~ member(X0,X4)
          | ~ member(X4,difference(X3,singleton(X2))) )
      & partition(X3,X1)
      & member(X0,difference(X1,X2)) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( partition(X3,X1)
          & member(X0,difference(X1,X2)) )
       => ? [X4] :
            ( member(X0,X4)
            & member(X4,difference(X3,singleton(X2))) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X2,X0,X1,X10] :
        ( ( partition(X10,X0)
          & member(X2,difference(X0,X1)) )
       => ? [X11] :
            ( member(X2,X11)
            & member(X11,difference(X10,singleton(X1))) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X2,X0,X1,X10] :
      ( ( partition(X10,X0)
        & member(X2,difference(X0,X1)) )
     => ? [X11] :
          ( member(X2,X11)
          & member(X11,difference(X10,singleton(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f117,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f280,plain,
    ~ member(sK0,sK1),
    inference(resolution,[],[f203,f81]) ).

fof(f81,plain,
    partition(sK3,sK1),
    inference(cnf_transformation,[],[f47]) ).

fof(f203,plain,
    ! [X0] :
      ( ~ partition(sK3,X0)
      | ~ member(sK0,X0) ),
    inference(subsumption_resolution,[],[f201,f134]) ).

fof(f134,plain,
    ~ member(sK0,sK2),
    inference(resolution,[],[f118,f80]) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f201,plain,
    ! [X0] :
      ( member(sK0,sK2)
      | ~ member(sK0,X0)
      | ~ partition(sK3,X0) ),
    inference(superposition,[],[f89,f187]) ).

fof(f187,plain,
    sK2 = sK5(sK3,sK0),
    inference(subsumption_resolution,[],[f186,f133]) ).

fof(f186,plain,
    ( ~ member(sK0,sK1)
    | sK2 = sK5(sK3,sK0) ),
    inference(resolution,[],[f185,f81]) ).

fof(f185,plain,
    ! [X0] :
      ( ~ partition(sK3,X0)
      | ~ member(sK0,X0)
      | sK2 = sK5(sK3,sK0) ),
    inference(subsumption_resolution,[],[f184,f133]) ).

fof(f184,plain,
    ! [X0] :
      ( ~ member(sK0,sK1)
      | sK2 = sK5(sK3,sK0)
      | ~ member(sK0,X0)
      | ~ partition(sK3,X0) ),
    inference(resolution,[],[f164,f89]) ).

fof(f164,plain,
    ! [X0] :
      ( ~ member(sK0,sK5(sK3,X0))
      | ~ member(X0,sK1)
      | sK2 = sK5(sK3,X0) ),
    inference(resolution,[],[f163,f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ( member(X0,singleton(X1))
        | X0 != X1 )
      & ( X0 = X1
        | ~ member(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
    <=> X0 = X1 ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X2,X0] :
      ( member(X2,singleton(X0))
    <=> X0 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f163,plain,
    ! [X0] :
      ( member(sK5(sK3,X0),singleton(sK2))
      | ~ member(sK0,sK5(sK3,X0))
      | ~ member(X0,sK1) ),
    inference(resolution,[],[f159,f145]) ).

fof(f145,plain,
    ! [X0] :
      ( member(sK5(sK3,X0),sK3)
      | ~ member(X0,sK1) ),
    inference(resolution,[],[f88,f81]) ).

fof(f88,plain,
    ! [X0,X1,X5] :
      ( ~ partition(X0,X1)
      | ~ member(X5,X1)
      | member(sK5(X0,X5),X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3] :
            ( X2 = X3
            | ! [X4] :
                ( ~ member(X4,X3)
                | ~ member(X4,X2) )
            | ~ member(X3,X0)
            | ~ member(X2,X0) )
        & ! [X5] :
            ( ( member(X5,sK5(X0,X5))
              & member(sK5(X0,X5),X0) )
            | ~ member(X5,X1) )
        & ! [X7] :
            ( subset(X7,X1)
            | ~ member(X7,X0) ) )
      | ~ partition(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f44,f52]) ).

fof(f52,plain,
    ! [X0,X5] :
      ( ? [X6] :
          ( member(X5,X6)
          & member(X6,X0) )
     => ( member(X5,sK5(X0,X5))
        & member(sK5(X0,X5),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3] :
            ( X2 = X3
            | ! [X4] :
                ( ~ member(X4,X3)
                | ~ member(X4,X2) )
            | ~ member(X3,X0)
            | ~ member(X2,X0) )
        & ! [X5] :
            ( ? [X6] :
                ( member(X5,X6)
                & member(X6,X0) )
            | ~ member(X5,X1) )
        & ! [X7] :
            ( subset(X7,X1)
            | ~ member(X7,X0) ) )
      | ~ partition(X0,X1) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3] :
            ( X2 = X3
            | ! [X4] :
                ( ~ member(X4,X3)
                | ~ member(X4,X2) )
            | ~ member(X3,X0)
            | ~ member(X2,X0) )
        & ! [X5] :
            ( ? [X6] :
                ( member(X5,X6)
                & member(X6,X0) )
            | ~ member(X5,X1) )
        & ! [X7] :
            ( subset(X7,X1)
            | ~ member(X7,X0) ) )
      | ~ partition(X0,X1) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( partition(X0,X1)
     => ( ! [X2,X3] :
            ( ( member(X3,X0)
              & member(X2,X0) )
           => ( ? [X4] :
                  ( member(X4,X3)
                  & member(X4,X2) )
             => X2 = X3 ) )
        & ! [X5] :
            ( member(X5,X1)
           => ? [X6] :
                ( member(X5,X6)
                & member(X6,X0) ) )
        & ! [X7] :
            ( member(X7,X0)
           => subset(X7,X1) ) ) ),
    inference(unused_predicate_definition_removal,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( partition(X0,X1)
    <=> ( ! [X2,X3] :
            ( ( member(X3,X0)
              & member(X2,X0) )
           => ( ? [X4] :
                  ( member(X4,X3)
                  & member(X4,X2) )
             => X2 = X3 ) )
        & ! [X5] :
            ( member(X5,X1)
           => ? [X6] :
                ( member(X5,X6)
                & member(X6,X0) ) )
        & ! [X7] :
            ( member(X7,X0)
           => subset(X7,X1) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X3] :
      ( partition(X0,X3)
    <=> ( ! [X2,X4] :
            ( ( member(X4,X0)
              & member(X2,X0) )
           => ( ? [X5] :
                  ( member(X5,X4)
                  & member(X5,X2) )
             => X2 = X4 ) )
        & ! [X2] :
            ( member(X2,X3)
           => ? [X4] :
                ( member(X2,X4)
                & member(X4,X0) ) )
        & ! [X2] :
            ( member(X2,X0)
           => subset(X2,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f159,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | member(X0,singleton(sK2))
      | ~ member(sK0,X0) ),
    inference(resolution,[],[f119,f82]) ).

fof(f82,plain,
    ! [X4] :
      ( ~ member(X4,difference(sK3,singleton(sK2)))
      | ~ member(sK0,X4) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f119,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f89,plain,
    ! [X0,X1,X5] :
      ( member(X5,sK5(X0,X5))
      | ~ member(X5,X1)
      | ~ partition(X0,X1) ),
    inference(cnf_transformation,[],[f53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEV517+1 : TPTP v8.2.0. Released v7.3.0.
% 0.06/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 21 18:36:39 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.35  Running first-order theorem proving
% 0.12/0.35  Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42  % (18263)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (18267)lrs+1002_74:59_drc=off:tgt=full:sos=all:cond=fast:i=124987:kws=inv_frequency:afp=300:afq=2.0744697298148953:rawr=on:urr=full:sil=128000:si=on:rtra=on:random_seed=3250543_0 on theBenchmark for (2999ds/124987Mi)
% 0.20/0.42  % (18263)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (18271)lrs+1011_1:1_sil=32000:rnwc=on:nwc=10.0:lwlo=on:i=121:bd=off:av=off_0 on theBenchmark for (2999ds/121Mi)
% 0.20/0.42  % (18263)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (18266)lrs+2_5:39_bsr=unit_only:to=lpo:drc=off:sil=128000:plsq=on:plsqr=2,19:sp=frequency:lcm=reverse:fd=preordered:s2a=on:i=38749:s2at=-1.0:fsr=off:uhcvi=on:rawr=on:aer=off:lwlo=on:add=off:bce=on:acc=model:afr=on_0 on theBenchmark for (2999ds/38749Mi)
% 0.20/0.42  % (18263)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (18269)lrs+1011_1:1_sil=2000:i=103:ep=RS:nm=32:ss=axioms:sos=on_0 on theBenchmark for (2999ds/103Mi)
% 0.20/0.42  % (18269)Refutation not found, incomplete strategy% (18269)------------------------------
% 0.20/0.42  % (18269)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.42  % (18269)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.42  % (18269)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.42  
% 0.20/0.42  % (18269)Memory used [KB]: 1168
% 0.20/0.42  % (18269)Time elapsed: 0.004 s
% 0.20/0.42  % (18269)Instructions burned: 2 (million)
% 0.20/0.42  % (18263)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (18272)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=113:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2999ds/113Mi)
% 0.20/0.42  % (18269)------------------------------
% 0.20/0.42  % (18269)------------------------------
% 0.20/0.42  % (18263)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (18273)lrs+1010_1:1_to=lpo:sil=2000:plsq=on:plsqr=32,1:sp=reverse_arity:sos=on:spb=goal_then_units:i=128:ss=axioms:sgt=50:bd=off:sd=3_0 on theBenchmark for (2999ds/128Mi)
% 0.20/0.43  % (18272)Refutation not found, incomplete strategy% (18272)------------------------------
% 0.20/0.43  % (18272)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.43  % (18272)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.43  % (18272)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.43  
% 0.20/0.43  % (18272)Memory used [KB]: 1185
% 0.20/0.43  % (18272)Time elapsed: 0.005 s
% 0.20/0.43  % (18272)Instructions burned: 4 (million)
% 0.20/0.43  % (18263)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (18268)lrs+11_1:16_to=lpo:drc=off:bsd=on:sp=frequency:i=172350:bs=on:av=off:fsd=on:sil=256000:fdi=50_0 on theBenchmark for (2999ds/172350Mi)
% 0.20/0.43  % (18272)------------------------------
% 0.20/0.43  % (18272)------------------------------
% 0.20/0.43  % (18271)First to succeed.
% 0.20/0.43  % (18271)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18263"
% 0.20/0.43  % (18263)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (18271)Refutation found. Thanks to Tanya!
% 0.20/0.43  % SZS status Theorem for theBenchmark
% 0.20/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.43  % (18271)------------------------------
% 0.20/0.43  % (18271)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.43  % (18271)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.43  % (18271)Termination reason: Refutation
% 0.20/0.43  
% 0.20/0.43  % (18271)Memory used [KB]: 1240
% 0.20/0.43  % (18271)Time elapsed: 0.013 s
% 0.20/0.43  % (18271)Instructions burned: 15 (million)
% 0.20/0.43  % (18271)------------------------------
% 0.20/0.43  % (18271)------------------------------
% 0.20/0.43  % (18263)Success in time 0.072 s
%------------------------------------------------------------------------------