TSTP Solution File: NUN059+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% 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 : Wed Aug 31 18:07:36 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   45 (  17 unt;   0 def)
%            Number of atoms       :  129 (  32 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  124 (  40   ~;  26   |;  51   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   2 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  110 (  66   !;  44   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f270,plain,
    $false,
    inference(avatar_sat_refutation,[],[f257,f269]) ).

fof(f269,plain,
    ~ spl20_1,
    inference(avatar_contradiction_clause,[],[f268]) ).

fof(f268,plain,
    ( $false
    | ~ spl20_1 ),
    inference(resolution,[],[f256,f121]) ).

fof(f121,plain,
    ! [X0] : r4(X0,sK2,sK2),
    inference(backward_demodulation,[],[f117,f115]) ).

fof(f115,plain,
    ! [X1] : sK8(X1) = sK2,
    inference(resolution,[],[f63,f99]) ).

fof(f99,plain,
    ! [X0] : r1(sK8(X0)),
    inference(definition_unfolding,[],[f77,f78]) ).

fof(f78,plain,
    ! [X0] : sK10(X0) = sK8(X0),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( r4(X0,sK9(X0),sK8(X0))
      & r1(sK9(X0))
      & sK10(X0) = sK8(X0)
      & r1(sK10(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f18,f43,f42,f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r4(X0,X2,X1)
              & r1(X2) )
          & ? [X3] :
              ( X1 = X3
              & r1(X3) ) )
     => ( ? [X2] :
            ( r4(X0,X2,sK8(X0))
            & r1(X2) )
        & ? [X3] :
            ( sK8(X0) = X3
            & r1(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0] :
      ( ? [X2] :
          ( r4(X0,X2,sK8(X0))
          & r1(X2) )
     => ( r4(X0,sK9(X0),sK8(X0))
        & r1(sK9(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0] :
      ( ? [X3] :
          ( sK8(X0) = X3
          & r1(X3) )
     => ( sK10(X0) = sK8(X0)
        & r1(sK10(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r4(X0,X2,X1)
          & r1(X2) )
      & ? [X3] :
          ( X1 = X3
          & r1(X3) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X32] :
    ? [X33] :
      ( ? [X34] :
          ( r4(X32,X34,X33)
          & r1(X34) )
      & ? [X35] :
          ( X33 = X35
          & r1(X35) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).

fof(f77,plain,
    ! [X0] : r1(sK10(X0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f63,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK2 = X1 ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X1] :
      ( ( r1(X1)
        & sK2 = X1 )
      | ( sK2 != X1
        & ~ r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f1,f30]) ).

fof(f30,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( r1(X1)
          & X0 = X1 )
        | ( X0 != X1
          & ~ r1(X1) ) )
   => ! [X1] :
        ( ( r1(X1)
          & sK2 = X1 )
        | ( sK2 != X1
          & ~ r1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( r1(X1)
        & X0 = X1 )
      | ( X0 != X1
        & ~ r1(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

fof(f117,plain,
    ! [X0] : r4(X0,sK2,sK8(X0)),
    inference(backward_demodulation,[],[f80,f116]) ).

fof(f116,plain,
    ! [X2] : sK2 = sK9(X2),
    inference(resolution,[],[f63,f79]) ).

fof(f79,plain,
    ! [X0] : r1(sK9(X0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f80,plain,
    ! [X0] : r4(X0,sK9(X0),sK8(X0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f256,plain,
    ( ! [X0] : ~ r4(X0,X0,sK2)
    | ~ spl20_1 ),
    inference(avatar_component_clause,[],[f255]) ).

fof(f255,plain,
    ( spl20_1
  <=> ! [X0] : ~ r4(X0,X0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).

fof(f257,plain,
    ( spl20_1
    | spl20_1 ),
    inference(avatar_split_clause,[],[f250,f255,f255]) ).

fof(f250,plain,
    ! [X0,X1] :
      ( ~ r4(X1,X1,sK2)
      | ~ r4(X0,X0,sK2) ),
    inference(resolution,[],[f156,f119]) ).

fof(f119,plain,
    ! [X0] : r3(X0,sK2,X0),
    inference(backward_demodulation,[],[f112,f113]) ).

fof(f113,plain,
    ! [X0] : sK1(X0) = sK2,
    inference(resolution,[],[f63,f60]) ).

fof(f60,plain,
    ! [X0] : r1(sK1(X0)),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( sK0(X0) = X0
      & r1(sK1(X0))
      & r3(X0,sK1(X0),sK0(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f27,f26]) ).

fof(f26,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r1(X2)
              & r3(X0,X2,X1) ) )
     => ( sK0(X0) = X0
        & ? [X2] :
            ( r1(X2)
            & r3(X0,X2,sK0(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0] :
      ( ? [X2] :
          ( r1(X2)
          & r3(X0,X2,sK0(X0)) )
     => ( r1(sK1(X0))
        & r3(X0,sK1(X0),sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0] :
    ? [X1] :
      ( X0 = X1
      & ? [X2] :
          ( r1(X2)
          & r3(X0,X2,X1) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X29] :
    ? [X30] :
      ( X29 = X30
      & ? [X31] :
          ( r1(X31)
          & r3(X29,X31,X30) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).

fof(f112,plain,
    ! [X0] : r3(X0,sK1(X0),X0),
    inference(backward_demodulation,[],[f59,f61]) ).

fof(f61,plain,
    ! [X0] : sK0(X0) = X0,
    inference(cnf_transformation,[],[f28]) ).

fof(f59,plain,
    ! [X0] : r3(X0,sK1(X0),sK0(X0)),
    inference(cnf_transformation,[],[f28]) ).

fof(f156,plain,
    ! [X2,X3,X0,X1] :
      ( ~ r3(sK2,X1,X3)
      | ~ r4(X0,X0,X1)
      | ~ r4(X2,X2,X3) ),
    inference(resolution,[],[f102,f121]) ).

fof(f102,plain,
    ! [X2,X0,X1,X6,X4,X5] :
      ( ~ r4(X1,X1,X6)
      | ~ r4(X0,X0,X5)
      | ~ r4(X2,X2,X4)
      | ~ r3(X6,X5,X4) ),
    inference(equality_resolution,[],[f62]) ).

fof(f62,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ r4(X2,X2,X4)
      | X3 != X4
      | ~ r4(X1,X1,X6)
      | ~ r3(X6,X5,X3)
      | ~ r4(X0,X0,X5) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( ! [X4] :
          ( ~ r4(X2,X2,X4)
          | X3 != X4 )
      | ! [X5] :
          ( ! [X6] :
              ( ~ r4(X1,X1,X6)
              | ~ r3(X6,X5,X3) )
          | ~ r4(X0,X0,X5) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X2,X0,X1,X3] :
      ( ! [X6] :
          ( ~ r4(X1,X1,X6)
          | X3 != X6 )
      | ! [X4] :
          ( ! [X5] :
              ( ~ r4(X0,X0,X5)
              | ~ r3(X5,X4,X3) )
          | ~ r4(X2,X2,X4) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ? [X3,X2,X0,X1] :
        ( ? [X6] :
            ( r4(X1,X1,X6)
            & X3 = X6 )
        & ? [X4] :
            ( ? [X5] :
                ( r4(X0,X0,X5)
                & r3(X5,X4,X3) )
            & r4(X2,X2,X4) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ? [X38,X21,X22,X15] :
        ( ? [X24] :
            ( ? [X18] :
                ( r4(X38,X38,X18)
                & r3(X18,X24,X15) )
            & r4(X22,X22,X24) )
        & ? [X16] :
            ( X15 = X16
            & r4(X21,X21,X16) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ? [X38,X21,X22,X15] :
      ( ? [X24] :
          ( ? [X18] :
              ( r4(X38,X38,X18)
              & r3(X18,X24,X15) )
          & r4(X22,X22,X24) )
      & ? [X16] :
          ( X15 = X16
          & r4(X21,X21,X16) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fermattothepoweroftwo) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 09:46:10 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.47  % (17468)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.47  % (17468)Refutation not found, incomplete strategy% (17468)------------------------------
% 0.19/0.47  % (17468)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (17468)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (17468)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47  
% 0.19/0.47  % (17468)Memory used [KB]: 6012
% 0.19/0.47  % (17468)Time elapsed: 0.079 s
% 0.19/0.47  % (17468)Instructions burned: 3 (million)
% 0.19/0.47  % (17468)------------------------------
% 0.19/0.47  % (17468)------------------------------
% 0.19/0.49  % (17476)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.50  % (17488)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.50  % (17491)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.50  % (17493)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.51  % (17493)First to succeed.
% 0.19/0.51  % (17470)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (17491)Refutation not found, incomplete strategy% (17491)------------------------------
% 0.19/0.51  % (17491)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (17491)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (17491)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (17491)Memory used [KB]: 1535
% 0.19/0.51  % (17491)Time elapsed: 0.062 s
% 0.19/0.51  % (17491)Instructions burned: 4 (million)
% 0.19/0.51  % (17491)------------------------------
% 0.19/0.51  % (17491)------------------------------
% 0.19/0.51  % (17493)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (17493)------------------------------
% 0.19/0.51  % (17493)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (17493)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (17493)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (17493)Memory used [KB]: 6140
% 0.19/0.51  % (17493)Time elapsed: 0.115 s
% 0.19/0.51  % (17493)Instructions burned: 8 (million)
% 0.19/0.51  % (17493)------------------------------
% 0.19/0.51  % (17493)------------------------------
% 0.19/0.51  % (17463)Success in time 0.156 s
%------------------------------------------------------------------------------