TSTP Solution File: KRS113+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : KRS113+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : n015.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 17:29:44 EDT 2022

% Result   : Unsatisfiable 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   71 (  13 unt;   0 def)
%            Number of atoms       :  277 (  20 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  312 ( 106   ~;  94   |;  84   &)
%                                         (  16 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-1 aty)
%            Number of variables   :  150 ( 111   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f247,plain,
    $false,
    inference(subsumption_resolution,[],[f240,f181]) ).

fof(f181,plain,
    ca_Vx2(sK5(i2003_11_14_17_21_22376)),
    inference(resolution,[],[f140,f176]) ).

fof(f176,plain,
    sP0(i2003_11_14_17_21_22376),
    inference(resolution,[],[f147,f126]) ).

fof(f126,plain,
    cUnsatisfiable(i2003_11_14_17_21_22376),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    cUnsatisfiable(i2003_11_14_17_21_22376),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

fof(f147,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ~ cUnsatisfiable(X0) )
      & ( cUnsatisfiable(X0)
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0] :
      ( sP0(X0)
    <=> cUnsatisfiable(X0) ),
    inference(definition_folding,[],[f71,f82]) ).

fof(f82,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ( ! [X2,X3] :
            ( X2 = X3
            | ~ rr(X0,X3)
            | ~ rr(X0,X2) )
        & ? [X1] :
            ( rr(X0,X1)
            & ca_Vx2(X1) )
        & cpxcomp(X0)
        & ? [X4] :
            ( cp(X4)
            & rs(X0,X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f71,plain,
    ! [X0] :
      ( ( ! [X2,X3] :
            ( X2 = X3
            | ~ rr(X0,X3)
            | ~ rr(X0,X2) )
        & ? [X1] :
            ( rr(X0,X1)
            & ca_Vx2(X1) )
        & cpxcomp(X0)
        & ? [X4] :
            ( cp(X4)
            & rs(X0,X4) ) )
    <=> cUnsatisfiable(X0) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X4] :
            ( cp(X4)
            & rs(X0,X4) )
        & cpxcomp(X0)
        & ? [X1] :
            ( rr(X0,X1)
            & ca_Vx2(X1) )
        & ! [X2,X3] :
            ( X2 = X3
            | ~ rr(X0,X2)
            | ~ rr(X0,X3) ) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X4] :
            ( cp(X4)
            & rs(X0,X4) )
        & cpxcomp(X0)
        & ? [X1] :
            ( rr(X0,X1)
            & ca_Vx2(X1) )
        & ! [X2,X3] :
            ( ( rr(X0,X2)
              & rr(X0,X3) )
           => X2 = X3 ) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,axiom,
    ! [X3] :
      ( ( cpxcomp(X3)
        & ? [X6] :
            ( rr(X3,X6)
            & ca_Vx2(X6) )
        & ! [X5,X4] :
            ( ( rr(X3,X4)
              & rr(X3,X5) )
           => X4 = X5 )
        & ? [X6] :
            ( rs(X3,X6)
            & cp(X6) ) )
    <=> cUnsatisfiable(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f140,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | ca_Vx2(sK5(X0)) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( sK4(X0) != sK3(X0)
          & rr(X0,sK4(X0))
          & rr(X0,sK3(X0)) )
        | ! [X3] :
            ( ~ rr(X0,X3)
            | ~ ca_Vx2(X3) )
        | ~ cpxcomp(X0)
        | ! [X4] :
            ( ~ cp(X4)
            | ~ rs(X0,X4) ) )
      & ( ( ! [X5,X6] :
              ( X5 = X6
              | ~ rr(X0,X6)
              | ~ rr(X0,X5) )
          & rr(X0,sK5(X0))
          & ca_Vx2(sK5(X0))
          & cpxcomp(X0)
          & cp(sK6(X0))
          & rs(X0,sK6(X0)) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f105,f108,f107,f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & rr(X0,X2)
          & rr(X0,X1) )
     => ( sK4(X0) != sK3(X0)
        & rr(X0,sK4(X0))
        & rr(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0] :
      ( ? [X7] :
          ( rr(X0,X7)
          & ca_Vx2(X7) )
     => ( rr(X0,sK5(X0))
        & ca_Vx2(sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ! [X0] :
      ( ? [X8] :
          ( cp(X8)
          & rs(X0,X8) )
     => ( cp(sK6(X0))
        & rs(X0,sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rr(X0,X2)
            & rr(X0,X1) )
        | ! [X3] :
            ( ~ rr(X0,X3)
            | ~ ca_Vx2(X3) )
        | ~ cpxcomp(X0)
        | ! [X4] :
            ( ~ cp(X4)
            | ~ rs(X0,X4) ) )
      & ( ( ! [X5,X6] :
              ( X5 = X6
              | ~ rr(X0,X6)
              | ~ rr(X0,X5) )
          & ? [X7] :
              ( rr(X0,X7)
              & ca_Vx2(X7) )
          & cpxcomp(X0)
          & ? [X8] :
              ( cp(X8)
              & rs(X0,X8) ) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X2,X3] :
            ( X2 != X3
            & rr(X0,X3)
            & rr(X0,X2) )
        | ! [X1] :
            ( ~ rr(X0,X1)
            | ~ ca_Vx2(X1) )
        | ~ cpxcomp(X0)
        | ! [X4] :
            ( ~ cp(X4)
            | ~ rs(X0,X4) ) )
      & ( ( ! [X2,X3] :
              ( X2 = X3
              | ~ rr(X0,X3)
              | ~ rr(X0,X2) )
          & ? [X1] :
              ( rr(X0,X1)
              & ca_Vx2(X1) )
          & cpxcomp(X0)
          & ? [X4] :
              ( cp(X4)
              & rs(X0,X4) ) )
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X2,X3] :
            ( X2 != X3
            & rr(X0,X3)
            & rr(X0,X2) )
        | ! [X1] :
            ( ~ rr(X0,X1)
            | ~ ca_Vx2(X1) )
        | ~ cpxcomp(X0)
        | ! [X4] :
            ( ~ cp(X4)
            | ~ rs(X0,X4) ) )
      & ( ( ! [X2,X3] :
              ( X2 = X3
              | ~ rr(X0,X3)
              | ~ rr(X0,X2) )
          & ? [X1] :
              ( rr(X0,X1)
              & ca_Vx2(X1) )
          & cpxcomp(X0)
          & ? [X4] :
              ( cp(X4)
              & rs(X0,X4) ) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f82]) ).

fof(f240,plain,
    ~ ca_Vx2(sK5(i2003_11_14_17_21_22376)),
    inference(backward_demodulation,[],[f192,f235]) ).

fof(f235,plain,
    sK6(i2003_11_14_17_21_22376) = sK5(i2003_11_14_17_21_22376),
    inference(subsumption_resolution,[],[f233,f176]) ).

fof(f233,plain,
    ( sK6(i2003_11_14_17_21_22376) = sK5(i2003_11_14_17_21_22376)
    | ~ sP0(i2003_11_14_17_21_22376) ),
    inference(resolution,[],[f194,f190]) ).

fof(f190,plain,
    rr(i2003_11_14_17_21_22376,sK6(i2003_11_14_17_21_22376)),
    inference(resolution,[],[f155,f185]) ).

fof(f185,plain,
    rs(i2003_11_14_17_21_22376,sK6(i2003_11_14_17_21_22376)),
    inference(resolution,[],[f137,f176]) ).

fof(f137,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | rs(X0,sK6(X0)) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( ~ rs(X0,X1)
      | rr(X0,X1) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rs(X0,X1) ),
    inference(rectify,[],[f79]) ).

fof(f79,plain,
    ! [X1,X0] :
      ( rr(X1,X0)
      | ~ rs(X1,X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0] :
      ( rs(X1,X0)
     => rr(X1,X0) ),
    inference(rectify,[],[f25]) ).

fof(f25,axiom,
    ! [X6,X3] :
      ( rs(X3,X6)
     => rr(X3,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

fof(f194,plain,
    ! [X0,X1] :
      ( ~ rr(X0,X1)
      | ~ sP0(X0)
      | sK5(X0) = X1 ),
    inference(duplicate_literal_removal,[],[f193]) ).

fof(f193,plain,
    ! [X0,X1] :
      ( ~ sP0(X0)
      | ~ sP0(X0)
      | sK5(X0) = X1
      | ~ rr(X0,X1) ),
    inference(resolution,[],[f142,f141]) ).

fof(f141,plain,
    ! [X0] :
      ( rr(X0,sK5(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f142,plain,
    ! [X0,X6,X5] :
      ( ~ rr(X0,X6)
      | ~ rr(X0,X5)
      | ~ sP0(X0)
      | X5 = X6 ),
    inference(cnf_transformation,[],[f109]) ).

fof(f192,plain,
    ~ ca_Vx2(sK6(i2003_11_14_17_21_22376)),
    inference(subsumption_resolution,[],[f191,f184]) ).

fof(f184,plain,
    ~ cp(i2003_11_14_17_21_22376),
    inference(resolution,[],[f182,f178]) ).

fof(f178,plain,
    cpxcomp(i2003_11_14_17_21_22376),
    inference(resolution,[],[f176,f139]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | cpxcomp(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f182,plain,
    ! [X0] :
      ( ~ cpxcomp(X0)
      | ~ cp(X0) ),
    inference(resolution,[],[f119,f152]) ).

fof(f152,plain,
    ! [X2,X0] :
      ( ~ ra_Px1(X0,X2)
      | ~ cp(X0) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( ( cp(X0)
        | ra_Px1(X0,sK7(X0)) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cp(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f113,f114]) ).

fof(f114,plain,
    ! [X0] :
      ( ? [X1] : ra_Px1(X0,X1)
     => ra_Px1(X0,sK7(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ! [X0] :
      ( ( cp(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cp(X0) ) ),
    inference(rectify,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ( cp(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X1] : ~ ra_Px1(X0,X1)
        | ~ cp(X0) ) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( cp(X0)
    <=> ! [X1] : ~ ra_Px1(X0,X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ~ ? [X1] : ra_Px1(X0,X1)
    <=> cp(X0) ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X3] :
      ( ~ ? [X6] : ra_Px1(X3,X6)
    <=> cp(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f119,plain,
    ! [X0] :
      ( ra_Px1(X0,sK1(X0))
      | ~ cpxcomp(X0) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ( ra_Px1(X0,sK1(X0))
        | ~ cpxcomp(X0) )
      & ( cpxcomp(X0)
        | ! [X2] : ~ ra_Px1(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f85,f86]) ).

fof(f86,plain,
    ! [X0] :
      ( ? [X1] : ra_Px1(X0,X1)
     => ra_Px1(X0,sK1(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ! [X0] :
      ( ( ? [X1] : ra_Px1(X0,X1)
        | ~ cpxcomp(X0) )
      & ( cpxcomp(X0)
        | ! [X2] : ~ ra_Px1(X0,X2) ) ),
    inference(rectify,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ( ? [X1] : ra_Px1(X0,X1)
        | ~ cpxcomp(X0) )
      & ( cpxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) ) ),
    inference(nnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ? [X1] : ra_Px1(X0,X1)
    <=> cpxcomp(X0) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X3] :
      ( cpxcomp(X3)
    <=> ? [X4] : ra_Px1(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f191,plain,
    ( ~ ca_Vx2(sK6(i2003_11_14_17_21_22376))
    | cp(i2003_11_14_17_21_22376) ),
    inference(resolution,[],[f123,f186]) ).

fof(f186,plain,
    rinvS(sK6(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376),
    inference(resolution,[],[f185,f122]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ~ rs(X1,X0)
      | rinvS(X0,X1) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ( rinvS(X0,X1)
        | ~ rs(X1,X0) )
      & ( rs(X1,X0)
        | ~ rinvS(X0,X1) ) ),
    inference(rectify,[],[f89]) ).

fof(f89,plain,
    ! [X1,X0] :
      ( ( rinvS(X1,X0)
        | ~ rs(X0,X1) )
      & ( rs(X0,X1)
        | ~ rinvS(X1,X0) ) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X1,X0] :
      ( rinvS(X1,X0)
    <=> rs(X0,X1) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X6,X3] :
      ( rinvS(X3,X6)
    <=> rs(X6,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

fof(f123,plain,
    ! [X2,X0] :
      ( ~ rinvS(X0,X2)
      | ~ ca_Vx2(X0)
      | cp(X2) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0] :
      ( ( ca_Vx2(X0)
        | ( ~ cp(sK2(X0))
          & rinvS(X0,sK2(X0)) ) )
      & ( ! [X2] :
            ( cp(X2)
            | ~ rinvS(X0,X2) )
        | ~ ca_Vx2(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f92,f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ cp(X1)
          & rinvS(X0,X1) )
     => ( ~ cp(sK2(X0))
        & rinvS(X0,sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ! [X0] :
      ( ( ca_Vx2(X0)
        | ? [X1] :
            ( ~ cp(X1)
            & rinvS(X0,X1) ) )
      & ( ! [X2] :
            ( cp(X2)
            | ~ rinvS(X0,X2) )
        | ~ ca_Vx2(X0) ) ),
    inference(rectify,[],[f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ( ca_Vx2(X0)
        | ? [X1] :
            ( ~ cp(X1)
            & rinvS(X0,X1) ) )
      & ( ! [X1] :
            ( cp(X1)
            | ~ rinvS(X0,X1) )
        | ~ ca_Vx2(X0) ) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ca_Vx2(X0)
    <=> ! [X1] :
          ( cp(X1)
          | ~ rinvS(X0,X1) ) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ca_Vx2(X0)
    <=> ! [X1] :
          ( rinvS(X0,X1)
         => cp(X1) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X3] :
      ( ca_Vx2(X3)
    <=> ! [X6] :
          ( rinvS(X3,X6)
         => cp(X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : KRS113+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34  % Computer : n015.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 00:45:20 EDT 2022
% 0.20/0.35  % CPUTime    : 
% 0.20/0.49  % (20906)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.50  % (20914)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)
% 0.20/0.51  % (20914)Refutation not found, incomplete strategy% (20914)------------------------------
% 0.20/0.51  % (20914)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (20906)First to succeed.
% 0.20/0.51  % (20906)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (20906)------------------------------
% 0.20/0.51  % (20906)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (20906)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (20906)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (20906)Memory used [KB]: 6012
% 0.20/0.51  % (20906)Time elapsed: 0.060 s
% 0.20/0.51  % (20906)Instructions burned: 4 (million)
% 0.20/0.51  % (20906)------------------------------
% 0.20/0.51  % (20906)------------------------------
% 0.20/0.51  % (20890)Success in time 0.154 s
%------------------------------------------------------------------------------