TSTP Solution File: SYN075+1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SYN075+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n018.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 20:01:12 EDT 2024

% Result   : Theorem 0.21s 0.42s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   45 (   5 unt;   0 def)
%            Number of atoms       :  176 ( 100 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  211 (  80   ~;  86   |;  30   &)
%                                         (  10 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   90 (  61   !;  29   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f121,plain,
    $false,
    inference(avatar_sat_refutation,[],[f85,f109,f120]) ).

fof(f120,plain,
    spl5_3,
    inference(avatar_contradiction_clause,[],[f119]) ).

fof(f119,plain,
    ( $false
    | spl5_3 ),
    inference(subsumption_resolution,[],[f117,f25]) ).

fof(f25,plain,
    big_f(sK3,sK4),
    inference(equality_resolution,[],[f24]) ).

fof(f24,plain,
    ! [X2] :
      ( big_f(X2,sK4)
      | sK3 != X2 ),
    inference(equality_resolution,[],[f22]) ).

fof(f22,plain,
    ! [X2,X3] :
      ( big_f(X2,X3)
      | sK4 != X3
      | sK3 != X2 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | sK4 != X3
        | sK3 != X2 )
      & ( ( sK4 = X3
          & sK3 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f13,f14]) ).

fof(f14,plain,
    ( ? [X0,X1] :
      ! [X2,X3] :
        ( ( big_f(X2,X3)
          | X1 != X3
          | X0 != X2 )
        & ( ( X1 = X3
            & X0 = X2 )
          | ~ big_f(X2,X3) ) )
   => ! [X3,X2] :
        ( ( big_f(X2,X3)
          | sK4 != X3
          | sK3 != X2 )
        & ( ( sK4 = X3
            & sK3 = X2 )
          | ~ big_f(X2,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1] :
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | X1 != X3
        | X0 != X2 )
      & ( ( X1 = X3
          & X0 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ? [X0,X1] :
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | X1 != X3
        | X0 != X2 )
      & ( ( X1 = X3
          & X0 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ? [X0,X1] :
    ! [X2,X3] :
      ( big_f(X2,X3)
    <=> ( X1 = X3
        & X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f117,plain,
    ( ~ big_f(sK3,sK4)
    | spl5_3 ),
    inference(superposition,[],[f80,f36]) ).

fof(f36,plain,
    sK4 = sK0(sK4),
    inference(equality_resolution,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( sK4 != X0
      | sK0(X0) = X0 ),
    inference(equality_factoring,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( sK0(X0) = sK4
      | sK0(X0) = X0 ),
    inference(resolution,[],[f23,f21]) ).

fof(f21,plain,
    ! [X2,X3] :
      ( ~ big_f(X2,X3)
      | sK4 = X3 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f23,plain,
    ! [X0] :
      ( big_f(sK2(X0),sK0(X0))
      | sK0(X0) = X0 ),
    inference(equality_resolution,[],[f17]) ).

fof(f17,plain,
    ! [X0,X5] :
      ( sK0(X0) = X0
      | big_f(X5,sK0(X0))
      | sK2(X0) != X5 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0] :
      ( ( sK0(X0) != X0
        | ! [X2] :
            ( ( sK1(X0,X2) != X2
              | ~ big_f(sK1(X0,X2),sK0(X0)) )
            & ( sK1(X0,X2) = X2
              | big_f(sK1(X0,X2),sK0(X0)) ) ) )
      & ( sK0(X0) = X0
        | ! [X5] :
            ( ( big_f(X5,sK0(X0))
              | sK2(X0) != X5 )
            & ( sK2(X0) = X5
              | ~ big_f(X5,sK0(X0)) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8]) ).

fof(f8,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( X0 != X1
            | ! [X2] :
              ? [X3] :
                ( ( X2 != X3
                  | ~ big_f(X3,X1) )
                & ( X2 = X3
                  | big_f(X3,X1) ) ) )
          & ( X0 = X1
            | ? [X4] :
              ! [X5] :
                ( ( big_f(X5,X1)
                  | X4 != X5 )
                & ( X4 = X5
                  | ~ big_f(X5,X1) ) ) ) )
     => ( ( sK0(X0) != X0
          | ! [X2] :
            ? [X3] :
              ( ( X2 != X3
                | ~ big_f(X3,sK0(X0)) )
              & ( X2 = X3
                | big_f(X3,sK0(X0)) ) ) )
        & ( sK0(X0) = X0
          | ? [X4] :
            ! [X5] :
              ( ( big_f(X5,sK0(X0))
                | X4 != X5 )
              & ( X4 = X5
                | ~ big_f(X5,sK0(X0)) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X0,X2] :
      ( ? [X3] :
          ( ( X2 != X3
            | ~ big_f(X3,sK0(X0)) )
          & ( X2 = X3
            | big_f(X3,sK0(X0)) ) )
     => ( ( sK1(X0,X2) != X2
          | ~ big_f(sK1(X0,X2),sK0(X0)) )
        & ( sK1(X0,X2) = X2
          | big_f(sK1(X0,X2),sK0(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ! [X0] :
      ( ? [X4] :
        ! [X5] :
          ( ( big_f(X5,sK0(X0))
            | X4 != X5 )
          & ( X4 = X5
            | ~ big_f(X5,sK0(X0)) ) )
     => ! [X5] :
          ( ( big_f(X5,sK0(X0))
            | sK2(X0) != X5 )
          & ( sK2(X0) = X5
            | ~ big_f(X5,sK0(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f7,plain,
    ! [X0] :
    ? [X1] :
      ( ( X0 != X1
        | ! [X2] :
          ? [X3] :
            ( ( X2 != X3
              | ~ big_f(X3,X1) )
            & ( X2 = X3
              | big_f(X3,X1) ) ) )
      & ( X0 = X1
        | ? [X4] :
          ! [X5] :
            ( ( big_f(X5,X1)
              | X4 != X5 )
            & ( X4 = X5
              | ~ big_f(X5,X1) ) ) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,plain,
    ! [X0] :
    ? [X1] :
      ( ( X0 != X1
        | ! [X2] :
          ? [X3] :
            ( ( X2 != X3
              | ~ big_f(X3,X1) )
            & ( X2 = X3
              | big_f(X3,X1) ) ) )
      & ( X0 = X1
        | ? [X2] :
          ! [X3] :
            ( ( big_f(X3,X1)
              | X2 != X3 )
            & ( X2 = X3
              | ~ big_f(X3,X1) ) ) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
        ! [X3] :
          ( big_f(X3,X1)
        <=> X2 = X3 )
    <~> X0 = X1 ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,plain,
    ~ ? [X0] :
      ! [X1] :
        ( ? [X2] :
          ! [X3] :
            ( big_f(X3,X1)
          <=> X2 = X3 )
      <=> X0 = X1 ),
    inference(rectify,[],[f3]) ).

fof(f3,negated_conjecture,
    ~ ? [X1] :
      ! [X3] :
        ( ? [X0] :
          ! [X2] :
            ( big_f(X2,X3)
          <=> X0 = X2 )
      <=> X1 = X3 ),
    inference(negated_conjecture,[],[f2]) ).

fof(f2,conjecture,
    ? [X1] :
    ! [X3] :
      ( ? [X0] :
        ! [X2] :
          ( big_f(X2,X3)
        <=> X0 = X2 )
    <=> X1 = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f80,plain,
    ( ~ big_f(sK3,sK0(sK4))
    | spl5_3 ),
    inference(avatar_component_clause,[],[f78]) ).

fof(f78,plain,
    ( spl5_3
  <=> big_f(sK3,sK0(sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f109,plain,
    ( ~ spl5_3
    | ~ spl5_4 ),
    inference(avatar_split_clause,[],[f108,f82,f78]) ).

fof(f82,plain,
    ( spl5_4
  <=> ! [X0] :
        ( sK3 != X0
        | sK1(sK4,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f108,plain,
    ( ~ big_f(sK3,sK0(sK4))
    | ~ spl5_4 ),
    inference(subsumption_resolution,[],[f107,f36]) ).

fof(f107,plain,
    ( sK4 != sK0(sK4)
    | ~ big_f(sK3,sK0(sK4))
    | ~ spl5_4 ),
    inference(trivial_inequality_removal,[],[f106]) ).

fof(f106,plain,
    ( sK3 != sK3
    | sK4 != sK0(sK4)
    | ~ big_f(sK3,sK0(sK4))
    | ~ spl5_4 ),
    inference(superposition,[],[f19,f91]) ).

fof(f91,plain,
    ( sK3 = sK1(sK4,sK3)
    | ~ spl5_4 ),
    inference(equality_resolution,[],[f83]) ).

fof(f83,plain,
    ( ! [X0] :
        ( sK3 != X0
        | sK1(sK4,X0) = X0 )
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f82]) ).

fof(f19,plain,
    ! [X2,X0] :
      ( sK1(X0,X2) != X2
      | sK0(X0) != X0
      | ~ big_f(sK1(X0,X2),sK0(X0)) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f85,plain,
    spl5_4,
    inference(avatar_split_clause,[],[f75,f82]) ).

fof(f75,plain,
    ! [X0] :
      ( sK3 != X0
      | sK1(sK4,X0) = X0 ),
    inference(equality_factoring,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( sK3 = sK1(sK4,X0)
      | sK1(sK4,X0) = X0 ),
    inference(resolution,[],[f43,f20]) ).

fof(f20,plain,
    ! [X2,X3] :
      ( ~ big_f(X2,X3)
      | sK3 = X2 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f43,plain,
    ! [X0] :
      ( big_f(sK1(sK4,X0),sK4)
      | sK1(sK4,X0) = X0 ),
    inference(trivial_inequality_removal,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( sK4 != sK4
      | sK1(sK4,X0) = X0
      | big_f(sK1(sK4,X0),sK4) ),
    inference(superposition,[],[f18,f36]) ).

fof(f18,plain,
    ! [X2,X0] :
      ( sK0(X0) != X0
      | sK1(X0,X2) = X2
      | big_f(sK1(X0,X2),sK0(X0)) ),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN075+1 : TPTP v8.2.0. Released v2.0.0.
% 0.07/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n018.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   : Sun Jun 23 23:17:24 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.36  Running first-order theorem proving
% 0.12/0.36  Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.42  % (4410)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4417)lrs+1010_1:1_to=lpo:sil=2000:sos=on:fd=off:i=117:bd=off_0 on theBenchmark for (2999ds/117Mi)
% 0.21/0.42  % (4410)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4411)ott+4_40_av=off:bce=on:fsd=off:fde=unused:nm=4:nwc=1.1:sos=all:sp=frequency:i=69040_0 on theBenchmark for (2999ds/69040Mi)
% 0.21/0.42  % (4410)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4414)lrs+21_2461:262144_anc=none:drc=off:sil=2000:sp=occurrence:nwc=6.0:updr=off:st=3.0:i=109:sd=2:afp=4000:erml=3:nm=14:afq=2.0:uhcvi=on:ss=included:er=filter:abs=on:nicw=on:ile=on:sims=off:s2a=on:s2agt=50:s2at=-1.0:plsq=on:plsql=on:plsqc=2:plsqr=1,32:newcnf=on:bd=off:to=lpo_0 on theBenchmark for (2999ds/109Mi)
% 0.21/0.42  % (4410)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4412)lrs+1011_8:1_sil=128000:tgt=ground:fde=unused:sp=frequency:nwc=5.0:lwlo=on:i=105338:awrs=converge:awrsf=1385:av=off_0 on theBenchmark for (2999ds/105338Mi)
% 0.21/0.42  % (4410)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4416)ott-1011_16:1_sil=2000:sp=const_max:urr=on:lsd=20:st=3.0:i=117:ss=axioms:gsp=on:rp=on:sos=on:fd=off:aac=none_0 on theBenchmark for (2999ds/117Mi)
% 0.21/0.42  % (4410)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4415)lrs-1011_37821:262144_bsr=unit_only:sil=2000:fde=none:plsq=on:plsqr=43543,131072:bce=on:rnwc=on:plsql=on:rp=on:nwc=10.0:newcnf=on:i=109:awrs=decay:awrsf=10:ep=R:mep=off:amm=sco_0 on theBenchmark for (2999ds/109Mi)
% 0.21/0.42  % (4417)First to succeed.
% 0.21/0.42  % (4410)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4413)dis+1011_1:99_anc=none:fde=unused:plsqc=2:bsd=on:plsq=on:plsqr=109,504:sp=reverse_frequency:spb=intro:rp=on:alpa=random:s2a=on:i=257151:s2at=-1.0:aac=none:nm=16:rawr=on:sil=256000:acc=model_0 on theBenchmark for (2999ds/257151Mi)
% 0.21/0.42  % (4415)Refutation not found, incomplete strategy% (4415)------------------------------
% 0.21/0.42  % (4415)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.42  % (4415)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.42  % (4415)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42  
% 0.21/0.42  % (4415)Memory used [KB]: 1052
% 0.21/0.42  % (4415)Time elapsed: 0.003 s
% 0.21/0.42  % (4415)Instructions burned: 2 (million)
% 0.21/0.42  % (4417)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4410"
% 0.21/0.42  % (4415)------------------------------
% 0.21/0.42  % (4415)------------------------------
% 0.21/0.42  % (4410)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4417)Refutation found. Thanks to Tanya!
% 0.21/0.42  % SZS status Theorem for theBenchmark
% 0.21/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.42  % (4417)------------------------------
% 0.21/0.42  % (4417)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.42  % (4417)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.42  % (4417)Termination reason: Refutation
% 0.21/0.42  
% 0.21/0.42  % (4417)Memory used [KB]: 1163
% 0.21/0.42  % (4417)Time elapsed: 0.006 s
% 0.21/0.42  % (4417)Instructions burned: 5 (million)
% 0.21/0.42  % (4417)------------------------------
% 0.21/0.42  % (4417)------------------------------
% 0.21/0.42  % (4410)Success in time 0.063 s
%------------------------------------------------------------------------------