TSTP Solution File: NUN060+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUN060+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_uns --cores 0 -t %d %s

% Computer : n024.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      :    6
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   26 (   7 unt;   0 def)
%            Number of atoms       :  112 (   0 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  109 (  23   ~;  18   |;  62   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   0 con; 1-2 aty)
%            Number of variables   :  109 (  53   !;  56   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f113,plain,
    $false,
    inference(unit_resulting_resolution,[],[f59,f73,f73,f73,f73,f66,f71,f93]) ).

fof(f93,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ r3(X0,X3,X2)
      | ~ id(X2,X1)
      | ~ r2(X7,X6)
      | ~ r1(X7)
      | ~ r2(X6,X5)
      | ~ r2(X5,X4)
      | ~ r2(X4,X3) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ~ id(X2,X1)
      | ! [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ~ r2(X5,X4)
                  | ! [X6] :
                      ( ~ r2(X6,X5)
                      | ! [X7] :
                          ( ~ r2(X7,X6)
                          | ~ r1(X7) ) ) )
              | ~ r2(X4,X3) )
          | ~ r3(X0,X3,X2) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ! [X2,X1,X0] :
      ( ~ id(X0,X1)
      | ! [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ~ r2(X5,X4)
                  | ! [X6] :
                      ( ~ r2(X6,X5)
                      | ! [X7] :
                          ( ~ r2(X7,X6)
                          | ~ r1(X7) ) ) )
              | ~ r2(X4,X3) )
          | ~ r3(X2,X3,X0) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ? [X2,X0,X1] :
        ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( r2(X5,X4)
                    & ? [X6] :
                        ( ? [X7] :
                            ( r2(X7,X6)
                            & r1(X7) )
                        & r2(X6,X5) ) )
                & r2(X4,X3) )
            & r3(X2,X3,X0) )
        & id(X0,X1) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ? [X46,X62,X45] :
        ( ? [X39] :
            ( r3(X45,X39,X46)
            & ? [X40] :
                ( ? [X48] :
                    ( r2(X48,X40)
                    & ? [X42] :
                        ( ? [X57] :
                            ( r2(X57,X42)
                            & r1(X57) )
                        & r2(X42,X48) ) )
                & r2(X40,X39) ) )
        & id(X46,X62) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ? [X46,X62,X45] :
      ( ? [X39] :
          ( r3(X45,X39,X46)
          & ? [X40] :
              ( ? [X48] :
                  ( r2(X48,X40)
                  & ? [X42] :
                      ( ? [X57] :
                          ( r2(X57,X42)
                          & r1(X57) )
                      & r2(X42,X48) ) )
              & r2(X40,X39) ) )
      & id(X46,X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greq4id) ).

fof(f71,plain,
    ! [X0,X1] : r3(X1,X0,sK5(X0,X1)),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( id(sK3(X0,X1),sK2(X0,X1))
      & r3(X1,sK4(X0,X1),sK3(X0,X1))
      & r2(X0,sK4(X0,X1))
      & r2(sK5(X0,X1),sK2(X0,X1))
      & r3(X1,X0,sK5(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f41,f45,f44,f43,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( id(X3,X2)
              & ? [X4] :
                  ( r3(X1,X4,X3)
                  & r2(X0,X4) ) )
          & ? [X5] :
              ( r2(X5,X2)
              & r3(X1,X0,X5) ) )
     => ( ? [X3] :
            ( id(X3,sK2(X0,X1))
            & ? [X4] :
                ( r3(X1,X4,X3)
                & r2(X0,X4) ) )
        & ? [X5] :
            ( r2(X5,sK2(X0,X1))
            & r3(X1,X0,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( id(X3,sK2(X0,X1))
          & ? [X4] :
              ( r3(X1,X4,X3)
              & r2(X0,X4) ) )
     => ( id(sK3(X0,X1),sK2(X0,X1))
        & ? [X4] :
            ( r3(X1,X4,sK3(X0,X1))
            & r2(X0,X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r3(X1,X4,sK3(X0,X1))
          & r2(X0,X4) )
     => ( r3(X1,sK4(X0,X1),sK3(X0,X1))
        & r2(X0,sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r2(X5,sK2(X0,X1))
          & r3(X1,X0,X5) )
     => ( r2(sK5(X0,X1),sK2(X0,X1))
        & r3(X1,X0,sK5(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( id(X3,X2)
          & ? [X4] :
              ( r3(X1,X4,X3)
              & r2(X0,X4) ) )
      & ? [X5] :
          ( r2(X5,X2)
          & r3(X1,X0,X5) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ? [X4] :
          ( id(X4,X2)
          & ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) ) )
      & ? [X3] :
          ( r2(X3,X2)
          & r3(X0,X1,X3) ) ),
    inference(rectify,[],[f12]) ).

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

fof(f66,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] : id(X0,X0),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13] : id(X13,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f73,plain,
    ! [X0,X1] : r2(X0,sK4(X0,X1)),
    inference(cnf_transformation,[],[f46]) ).

fof(f59,plain,
    ! [X0] : r1(sK1(X0)),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( id(sK0(X0),X0)
      & r3(X0,sK1(X0),sK0(X0))
      & r1(sK1(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f24,f37,f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ? [X1] :
          ( id(X1,X0)
          & ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) ) )
     => ( id(sK0(X0),X0)
        & ? [X2] :
            ( r3(X0,X2,sK0(X0))
            & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK0(X0))
          & r1(X2) )
     => ( r3(X0,sK1(X0),sK0(X0))
        & r1(sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0] :
    ? [X1] :
      ( id(X1,X0)
      & ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) ) ),
    inference(rectify,[],[f15]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : NUN060+1 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.13  % 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 : n024.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 09:45:34 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.50  % (9700)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.50  % (9693)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (9701)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)
% 0.19/0.51  % (9713)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)
% 0.19/0.51  % (9708)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)
% 0.19/0.51  % (9697)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (9700)First to succeed.
% 0.19/0.51  % (9716)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)
% 0.19/0.51  % (9705)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.51  % (9700)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  % (9700)------------------------------
% 0.19/0.51  % (9700)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (9700)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (9700)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (9700)Memory used [KB]: 6012
% 0.19/0.51  % (9700)Time elapsed: 0.111 s
% 0.19/0.51  % (9700)Instructions burned: 4 (million)
% 0.19/0.51  % (9700)------------------------------
% 0.19/0.51  % (9700)------------------------------
% 0.19/0.51  % (9692)Success in time 0.167 s
%------------------------------------------------------------------------------