TSTP Solution File: NUN081+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN081+1 : 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 : 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 18:08:08 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   38 (   6 unt;   0 def)
%            Number of atoms       :  172 (   0 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  154 (  20   ~;  15   |; 106   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   0 con; 1-2 aty)
%            Number of variables   :  155 (  69   !;  86   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f139,plain,
    $false,
    inference(unit_resulting_resolution,[],[f98,f107,f107,f132,f127,f129,f103]) ).

fof(f103,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ r3(X0,X2,X1)
      | ~ r1(X6)
      | ~ r2(X4,X3)
      | ~ r2(X5,X4)
      | ~ r2(X6,X5)
      | ~ id(X1,X3) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ~ id(X1,X3)
          | ! [X4] :
              ( ! [X5] :
                  ( ~ r2(X5,X4)
                  | ! [X6] :
                      ( ~ r2(X6,X5)
                      | ~ r1(X6) ) )
              | ~ r2(X4,X3) ) )
      | ~ r3(X0,X2,X1) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( ~ id(X0,X3)
          | ! [X4] :
              ( ! [X5] :
                  ( ~ r2(X5,X4)
                  | ! [X6] :
                      ( ~ r2(X6,X5)
                      | ~ r1(X6) ) )
              | ~ r2(X4,X3) ) )
      | ~ r3(X2,X1,X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ~ ? [X1,X2,X0] :
        ( r3(X2,X1,X0)
        & ? [X3] :
            ( id(X0,X3)
            & ? [X4] :
                ( r2(X4,X3)
                & ? [X5] :
                    ( r2(X5,X4)
                    & ? [X6] :
                        ( r2(X6,X5)
                        & r1(X6) ) ) ) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ? [X46,X45,X62] :
        ( ? [X39] :
            ( id(X46,X39)
            & ? [X40] :
                ( r2(X40,X39)
                & ? [X48] :
                    ( r2(X48,X40)
                    & ? [X42] :
                        ( r1(X42)
                        & r2(X42,X48) ) ) ) )
        & r3(X62,X45,X46) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ? [X46,X45,X62] :
      ( ? [X39] :
          ( id(X46,X39)
          & ? [X40] :
              ( r2(X40,X39)
              & ? [X48] :
                  ( r2(X48,X40)
                  & ? [X42] :
                      ( r1(X42)
                      & r2(X42,X48) ) ) ) )
      & r3(X62,X45,X46) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xplusyidthree) ).

fof(f129,plain,
    ! [X0] : r3(X0,sK15(X0),sK14(X0)),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( r3(X0,sK15(X0),sK14(X0))
      & r1(sK15(X0))
      & id(sK14(X0),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f22,f68,f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) )
          & id(X1,X0) )
     => ( ? [X2] :
            ( r3(X0,X2,sK14(X0))
            & r1(X2) )
        & id(sK14(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK14(X0))
          & r1(X2) )
     => ( r3(X0,sK15(X0),sK14(X0))
        & r1(sK15(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) )
      & id(X1,X0) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X53] :
    ? [X54] :
      ( ? [X55] :
          ( r1(X55)
          & r3(X53,X55,X54) )
      & id(X54,X53) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).

fof(f127,plain,
    ! [X0] : id(sK14(X0),X0),
    inference(cnf_transformation,[],[f69]) ).

fof(f132,plain,
    ! [X0,X1] : r2(X0,sK18(X0,X1)),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( id(sK17(X0,X1),sK16(X0,X1))
      & r4(X1,sK18(X0,X1),sK17(X0,X1))
      & r2(X0,sK18(X0,X1))
      & r4(X1,X0,sK19(X0,X1))
      & r3(sK19(X0,X1),X1,sK16(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f70,f74,f73,f72,f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( id(X3,X2)
              & ? [X4] :
                  ( r4(X1,X4,X3)
                  & r2(X0,X4) ) )
          & ? [X5] :
              ( r4(X1,X0,X5)
              & r3(X5,X1,X2) ) )
     => ( ? [X3] :
            ( id(X3,sK16(X0,X1))
            & ? [X4] :
                ( r4(X1,X4,X3)
                & r2(X0,X4) ) )
        & ? [X5] :
            ( r4(X1,X0,X5)
            & r3(X5,X1,sK16(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( id(X3,sK16(X0,X1))
          & ? [X4] :
              ( r4(X1,X4,X3)
              & r2(X0,X4) ) )
     => ( id(sK17(X0,X1),sK16(X0,X1))
        & ? [X4] :
            ( r4(X1,X4,sK17(X0,X1))
            & r2(X0,X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r4(X1,X4,sK17(X0,X1))
          & r2(X0,X4) )
     => ( r4(X1,sK18(X0,X1),sK17(X0,X1))
        & r2(X0,sK18(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X1,X0,X5)
          & r3(X5,X1,sK16(X0,X1)) )
     => ( r4(X1,X0,sK19(X0,X1))
        & r3(sK19(X0,X1),X1,sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( id(X3,X2)
          & ? [X4] :
              ( r4(X1,X4,X3)
              & r2(X0,X4) ) )
      & ? [X5] :
          ( r4(X1,X0,X5)
          & r3(X5,X1,X2) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ? [X3] :
          ( id(X3,X2)
          & ? [X4] :
              ( r4(X0,X4,X3)
              & r2(X1,X4) ) )
      & ? [X5] :
          ( r4(X0,X1,X5)
          & r3(X5,X0,X2) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X43,X44] :
    ? [X45] :
      ( ? [X46] :
          ( id(X46,X45)
          & ? [X47] :
              ( r2(X44,X47)
              & r4(X43,X47,X46) ) )
      & ? [X48] :
          ( r4(X43,X44,X48)
          & r3(X48,X43,X45) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).

fof(f107,plain,
    ! [X0,X1] : r2(X1,sK7(X0,X1)),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( id(sK6(X0,X1),sK5(X0,X1))
      & r2(X1,sK7(X0,X1))
      & r3(X0,sK7(X0,X1),sK6(X0,X1))
      & r3(X0,X1,sK8(X0,X1))
      & r2(sK8(X0,X1),sK5(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f37,f55,f54,f53,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( id(X3,X2)
              & ? [X4] :
                  ( r2(X1,X4)
                  & r3(X0,X4,X3) ) )
          & ? [X5] :
              ( r3(X0,X1,X5)
              & r2(X5,X2) ) )
     => ( ? [X3] :
            ( id(X3,sK5(X0,X1))
            & ? [X4] :
                ( r2(X1,X4)
                & r3(X0,X4,X3) ) )
        & ? [X5] :
            ( r3(X0,X1,X5)
            & r2(X5,sK5(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( id(X3,sK5(X0,X1))
          & ? [X4] :
              ( r2(X1,X4)
              & r3(X0,X4,X3) ) )
     => ( id(sK6(X0,X1),sK5(X0,X1))
        & ? [X4] :
            ( r2(X1,X4)
            & r3(X0,X4,sK6(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r2(X1,X4)
          & r3(X0,X4,sK6(X0,X1)) )
     => ( r2(X1,sK7(X0,X1))
        & r3(X0,sK7(X0,X1),sK6(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,sK5(X0,X1)) )
     => ( r3(X0,X1,sK8(X0,X1))
        & r2(sK8(X0,X1),sK5(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( id(X3,X2)
          & ? [X4] :
              ( r2(X1,X4)
              & r3(X0,X4,X3) ) )
      & ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,X2) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X37,X38] :
    ? [X39] :
      ( ? [X40] :
          ( ? [X41] :
              ( r3(X37,X41,X40)
              & r2(X38,X41) )
          & id(X40,X39) )
      & ? [X42] :
          ( r3(X37,X38,X42)
          & r2(X42,X39) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).

fof(f98,plain,
    ! [X0] : r1(sK4(X0)),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( r4(X0,sK3(X0),sK2(X0))
      & r1(sK3(X0))
      & r1(sK4(X0))
      & id(sK2(X0),sK4(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f23,f48,f47,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r4(X0,X2,X1)
              & r1(X2) )
          & ? [X3] :
              ( r1(X3)
              & id(X1,X3) ) )
     => ( ? [X2] :
            ( r4(X0,X2,sK2(X0))
            & r1(X2) )
        & ? [X3] :
            ( r1(X3)
            & id(sK2(X0),X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0] :
      ( ? [X2] :
          ( r4(X0,X2,sK2(X0))
          & r1(X2) )
     => ( r4(X0,sK3(X0),sK2(X0))
        & r1(sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0] :
      ( ? [X3] :
          ( r1(X3)
          & id(sK2(X0),X3) )
     => ( r1(sK4(X0))
        & id(sK2(X0),sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r4(X0,X2,X1)
          & r1(X2) )
      & ? [X3] :
          ( r1(X3)
          & id(X1,X3) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X56] :
    ? [X57] :
      ( ? [X58] :
          ( r4(X56,X58,X57)
          & r1(X58) )
      & ? [X59] :
          ( r1(X59)
          & id(X57,X59) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : NUN081+1 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n015.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   : Tue Aug 30 09:59:05 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.48  % (28919)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)
% 0.19/0.48  % (28898)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.48  % (28911)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)
% 0.19/0.48  % (28898)First to succeed.
% 0.19/0.49  % (28898)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (28898)------------------------------
% 0.19/0.49  % (28898)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (28898)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (28898)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (28898)Memory used [KB]: 5500
% 0.19/0.49  % (28898)Time elapsed: 0.087 s
% 0.19/0.49  % (28898)Instructions burned: 6 (million)
% 0.19/0.49  % (28898)------------------------------
% 0.19/0.49  % (28898)------------------------------
% 0.19/0.49  % (28896)Success in time 0.146 s
%------------------------------------------------------------------------------