TSTP Solution File: NUN073+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% 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 : n008.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 18:08:05 EDT 2022

% Result   : Theorem 1.34s 0.53s
% Output   : Refutation 1.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   63 (  25 unt;   3 typ;   0 def)
%            Number of atoms       :  176 (  53 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  191 (  75   ~;  54   |;  55   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-1 aty)
%            Number of variables   :  105 (  73   !;  32   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_6,type,
    sQ26_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_7,type,
    sQ27_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_8,type,
    sQ28_eqProxy: ( $real * $real ) > $o ).

fof(f329,plain,
    $false,
    inference(subsumption_resolution,[],[f324,f245]) ).

fof(f245,plain,
    ! [X1] : ~ r2(X1,sK0),
    inference(backward_demodulation,[],[f224,f231]) ).

fof(f231,plain,
    sK0 = sK3,
    inference(resolution,[],[f155,f141]) ).

fof(f141,plain,
    r1(sK3),
    inference(literal_reordering,[],[f75]) ).

fof(f75,plain,
    r1(sK3),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ( r2(sK3,sK2)
    & r1(sK3)
    & sK1 = sK2
    & r2(sK5,sK4)
    & r1(sK5)
    & r2(sK4,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f28,f33,f32,f31,f30,f29]) ).

fof(f29,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( r2(X2,X1)
                & r1(X2) )
            & X0 = X1 )
        & ? [X3] :
            ( ? [X4] :
                ( r2(X4,X3)
                & r1(X4) )
            & r2(X3,X0) ) )
   => ( ? [X1] :
          ( ? [X2] :
              ( r2(X2,X1)
              & r1(X2) )
          & sK1 = X1 )
      & ? [X3] :
          ( ? [X4] :
              ( r2(X4,X3)
              & r1(X4) )
          & r2(X3,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( r2(X2,X1)
            & r1(X2) )
        & sK1 = X1 )
   => ( ? [X2] :
          ( r2(X2,sK2)
          & r1(X2) )
      & sK1 = sK2 ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ( ? [X2] :
        ( r2(X2,sK2)
        & r1(X2) )
   => ( r2(sK3,sK2)
      & r1(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( r2(X4,X3)
            & r1(X4) )
        & r2(X3,sK1) )
   => ( ? [X4] :
          ( r2(X4,sK4)
          & r1(X4) )
      & r2(sK4,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ( ? [X4] :
        ( r2(X4,sK4)
        & r1(X4) )
   => ( r2(sK5,sK4)
      & r1(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r2(X2,X1)
              & r1(X2) )
          & X0 = X1 )
      & ? [X3] :
          ( ? [X4] :
              ( r2(X4,X3)
              & r1(X4) )
          & r2(X3,X0) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ? [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( r2(X4,X3)
              & r1(X4) )
          & X0 = X3 )
      & ? [X1] :
          ( ? [X2] :
              ( r2(X2,X1)
              & r1(X2) )
          & r2(X1,X0) ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ! [X0] :
        ( ! [X3] :
            ( ! [X4] :
                ( ~ r1(X4)
                | ~ r2(X4,X3) )
            | X0 != X3 )
        | ! [X1] :
            ( ! [X2] :
                ( ~ r2(X2,X1)
                | ~ r1(X2) )
            | ~ r2(X1,X0) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X38] :
        ( ! [X22] :
            ( ~ r2(X22,X38)
            | ! [X16] :
                ( ~ r2(X16,X22)
                | ~ r1(X16) ) )
        | ! [X21] :
            ( ! [X15] :
                ( ~ r1(X15)
                | ~ r2(X15,X21) )
            | X21 != X38 ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X38] :
      ( ! [X22] :
          ( ~ r2(X22,X38)
          | ! [X16] :
              ( ~ r2(X16,X22)
              | ~ r1(X16) ) )
      | ! [X21] :
          ( ! [X15] :
              ( ~ r1(X15)
              | ~ r2(X15,X21) )
          | X21 != X38 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneuneqtwo) ).

fof(f155,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK0 = X1 ),
    inference(literal_reordering,[],[f68]) ).

fof(f68,plain,
    ! [X1] :
      ( sK0 = X1
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X1] :
      ( ( r1(X1)
        & sK0 = X1 )
      | ( ~ r1(X1)
        & sK0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1,f26]) ).

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

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

fof(f224,plain,
    ! [X1] : ~ r2(X1,sK3),
    inference(resolution,[],[f143,f141]) ).

fof(f143,plain,
    ! [X2,X1] :
      ( ~ r1(X2)
      | ~ r2(X1,X2) ),
    inference(literal_reordering,[],[f119]) ).

fof(f119,plain,
    ! [X2,X1] :
      ( ~ r2(X1,X2)
      | ~ r1(X2) ),
    inference(equality_resolution,[],[f83]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X1,X0)
      | X0 != X2
      | ~ r1(X2) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ~ r2(X1,X0)
      | ! [X2] :
          ( X0 != X2
          | ~ r1(X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X41,X40] :
      ( ! [X42] :
          ( X41 != X42
          | ~ r1(X42) )
      | ~ r2(X40,X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).

fof(f324,plain,
    r2(sK0,sK0),
    inference(backward_demodulation,[],[f293,f321]) ).

fof(f321,plain,
    sK0 = sK16(sK0),
    inference(resolution,[],[f300,f293]) ).

fof(f300,plain,
    ! [X8] :
      ( ~ r2(X8,sK16(sK0))
      | sK0 = X8 ),
    inference(forward_demodulation,[],[f289,f257]) ).

fof(f257,plain,
    sK4 = sK16(sK0),
    inference(resolution,[],[f254,f131]) ).

fof(f131,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | sK16(X0) = X2 ),
    inference(literal_reordering,[],[f97]) ).

fof(f97,plain,
    ! [X2,X0] :
      ( sK16(X0) = X2
      | ~ r2(X0,X2) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X2] :
      ( ( sK16(X0) != X2
        & ~ r2(X0,X2) )
      | ( r2(X0,X2)
        & sK16(X0) = X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f23,f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 != X2
            & ~ r2(X0,X2) )
          | ( r2(X0,X2)
            & X1 = X2 ) )
     => ! [X2] :
          ( ( sK16(X0) != X2
            & ~ r2(X0,X2) )
          | ( r2(X0,X2)
            & sK16(X0) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( X1 != X2
        & ~ r2(X0,X2) )
      | ( r2(X0,X2)
        & X1 = X2 ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( ~ r2(X2,X4)
        & X3 != X4 )
      | ( X3 = X4
        & r2(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f254,plain,
    r2(sK0,sK4),
    inference(backward_demodulation,[],[f129,f232]) ).

fof(f232,plain,
    sK0 = sK5,
    inference(resolution,[],[f155,f162]) ).

fof(f162,plain,
    r1(sK5),
    inference(literal_reordering,[],[f72]) ).

fof(f72,plain,
    r1(sK5),
    inference(cnf_transformation,[],[f34]) ).

fof(f129,plain,
    r2(sK5,sK4),
    inference(literal_reordering,[],[f73]) ).

fof(f73,plain,
    r2(sK5,sK4),
    inference(cnf_transformation,[],[f34]) ).

fof(f289,plain,
    ! [X8] :
      ( ~ r2(X8,sK4)
      | sK0 = X8 ),
    inference(resolution,[],[f160,f254]) ).

fof(f160,plain,
    ! [X3,X0,X1] :
      ( ~ r2(X0,X3)
      | X0 = X1
      | ~ r2(X1,X3) ),
    inference(literal_reordering,[],[f118]) ).

fof(f118,plain,
    ! [X3,X0,X1] :
      ( ~ r2(X1,X3)
      | X0 = X1
      | ~ r2(X0,X3) ),
    inference(equality_resolution,[],[f77]) ).

fof(f77,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X0,X2)
      | ~ r2(X1,X3)
      | X2 != X3 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ! [X2] :
          ( ~ r2(X0,X2)
          | ! [X3] :
              ( ~ r2(X1,X3)
              | X2 != X3 ) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( X0 = X1
      | ! [X2] :
          ( ~ r2(X1,X2)
          | ! [X3] :
              ( ~ r2(X0,X3)
              | X2 != X3 ) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X25,X26] :
      ( ! [X27] :
          ( ~ r2(X26,X27)
          | ! [X28] :
              ( ~ r2(X25,X28)
              | X27 != X28 ) )
      | X25 = X26 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).

fof(f293,plain,
    r2(sK16(sK0),sK16(sK0)),
    inference(backward_demodulation,[],[f267,f257]) ).

fof(f267,plain,
    r2(sK4,sK16(sK0)),
    inference(backward_demodulation,[],[f154,f249]) ).

fof(f249,plain,
    sK16(sK0) = sK2,
    inference(resolution,[],[f246,f131]) ).

fof(f246,plain,
    r2(sK0,sK2),
    inference(backward_demodulation,[],[f152,f231]) ).

fof(f152,plain,
    r2(sK3,sK2),
    inference(literal_reordering,[],[f76]) ).

fof(f76,plain,
    r2(sK3,sK2),
    inference(cnf_transformation,[],[f34]) ).

fof(f154,plain,
    r2(sK4,sK2),
    inference(literal_reordering,[],[f112]) ).

fof(f112,plain,
    r2(sK4,sK2),
    inference(definition_unfolding,[],[f71,f74]) ).

fof(f74,plain,
    sK1 = sK2,
    inference(cnf_transformation,[],[f34]) ).

fof(f71,plain,
    r2(sK4,sK1),
    inference(cnf_transformation,[],[f34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% 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 : n008.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 11:17:55 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (17808)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)
% 0.19/0.51  % (17800)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)
% 0.19/0.51  % (17792)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)
% 0.19/0.52  TRYING [1]
% 1.34/0.52  TRYING [2]
% 1.34/0.52  % (17800)First to succeed.
% 1.34/0.52  TRYING [3]
% 1.34/0.53  % (17800)Refutation found. Thanks to Tanya!
% 1.34/0.53  % SZS status Theorem for theBenchmark
% 1.34/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.34/0.53  % (17800)------------------------------
% 1.34/0.53  % (17800)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.34/0.53  % (17800)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.34/0.53  % (17800)Termination reason: Refutation
% 1.34/0.53  
% 1.34/0.53  % (17800)Memory used [KB]: 5884
% 1.34/0.53  % (17800)Time elapsed: 0.015 s
% 1.34/0.53  % (17800)Instructions burned: 9 (million)
% 1.34/0.53  % (17800)------------------------------
% 1.34/0.53  % (17800)------------------------------
% 1.34/0.53  % (17784)Success in time 0.178 s
%------------------------------------------------------------------------------