TSTP Solution File: LCL686+1.001 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : LCL686+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 : n007.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 17:49:42 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   38 (   6 unt;   0 def)
%            Number of atoms       :  307 (   0 equ)
%            Maximal formula atoms :   38 (   8 avg)
%            Number of connectives :  462 ( 193   ~; 152   |; 110   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-1 aty)
%            Number of variables   :  120 (  74   !;  46   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f111,plain,
    $false,
    inference(subsumption_resolution,[],[f110,f36]) ).

fof(f36,plain,
    ! [X0] : r1(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : r1(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

fof(f110,plain,
    ~ r1(sK3,sK3),
    inference(subsumption_resolution,[],[f109,f104]) ).

fof(f104,plain,
    ~ p1(sK6(sK3)),
    inference(subsumption_resolution,[],[f103,f36]) ).

fof(f103,plain,
    ( ~ p1(sK6(sK3))
    | ~ r1(sK3,sK3) ),
    inference(duplicate_literal_removal,[],[f102]) ).

fof(f102,plain,
    ( ~ p1(sK6(sK3))
    | ~ p1(sK6(sK3))
    | ~ r1(sK3,sK3) ),
    inference(resolution,[],[f83,f39]) ).

fof(f39,plain,
    ! [X4] :
      ( ~ p2(sK6(X4))
      | ~ r1(sK3,X4)
      | ~ p1(sK6(X4)) ),
    inference(consistent_polarity_flipping,[],[f28]) ).

fof(f28,plain,
    ! [X4] :
      ( p1(sK6(X4))
      | p2(sK6(X4))
      | ~ r1(sK3,X4) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ( r1(sK0,sK1)
    & p1(sK2)
    & r1(sK1,sK2)
    & p3(sK1)
    & ! [X4] :
        ( ~ r1(sK3,X4)
        | ( ~ p3(sK4(X4))
          & r1(X4,sK4(X4))
          & r1(X4,sK5(X4))
          & ( p1(sK6(X4))
            | p2(sK6(X4)) )
          & r1(X4,sK6(X4))
          & ( ~ p2(sK6(X4))
            | ~ p1(sK6(X4)) )
          & ! [X8] :
              ( ( ( ~ p2(X8)
                  | p1(X8) )
                & ( p2(X8)
                  | ~ p1(X8) ) )
              | ~ r1(X4,X8) ) ) )
    & r1(sK0,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f13,f20,f19,f18,f17,f16,f15,f14]) ).

fof(f14,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( r1(X0,X1)
            & ? [X2] :
                ( p1(X2)
                & r1(X1,X2) )
            & p3(X1) )
        & ? [X3] :
            ( ! [X4] :
                ( ~ r1(X3,X4)
                | ( ? [X5] :
                      ( ~ p3(X5)
                      & r1(X4,X5) )
                  & ? [X6] : r1(X4,X6)
                  & ? [X7] :
                      ( ( p1(X7)
                        | p2(X7) )
                      & r1(X4,X7)
                      & ( ~ p2(X7)
                        | ~ p1(X7) ) )
                  & ! [X8] :
                      ( ( ( ~ p2(X8)
                          | p1(X8) )
                        & ( p2(X8)
                          | ~ p1(X8) ) )
                      | ~ r1(X4,X8) ) ) )
            & r1(X0,X3) ) )
   => ( ? [X1] :
          ( r1(sK0,X1)
          & ? [X2] :
              ( p1(X2)
              & r1(X1,X2) )
          & p3(X1) )
      & ? [X3] :
          ( ! [X4] :
              ( ~ r1(X3,X4)
              | ( ? [X5] :
                    ( ~ p3(X5)
                    & r1(X4,X5) )
                & ? [X6] : r1(X4,X6)
                & ? [X7] :
                    ( ( p1(X7)
                      | p2(X7) )
                    & r1(X4,X7)
                    & ( ~ p2(X7)
                      | ~ p1(X7) ) )
                & ! [X8] :
                    ( ( ( ~ p2(X8)
                        | p1(X8) )
                      & ( p2(X8)
                        | ~ p1(X8) ) )
                    | ~ r1(X4,X8) ) ) )
          & r1(sK0,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ( ? [X1] :
        ( r1(sK0,X1)
        & ? [X2] :
            ( p1(X2)
            & r1(X1,X2) )
        & p3(X1) )
   => ( r1(sK0,sK1)
      & ? [X2] :
          ( p1(X2)
          & r1(sK1,X2) )
      & p3(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ( ? [X2] :
        ( p1(X2)
        & r1(sK1,X2) )
   => ( p1(sK2)
      & r1(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ( ? [X3] :
        ( ! [X4] :
            ( ~ r1(X3,X4)
            | ( ? [X5] :
                  ( ~ p3(X5)
                  & r1(X4,X5) )
              & ? [X6] : r1(X4,X6)
              & ? [X7] :
                  ( ( p1(X7)
                    | p2(X7) )
                  & r1(X4,X7)
                  & ( ~ p2(X7)
                    | ~ p1(X7) ) )
              & ! [X8] :
                  ( ( ( ~ p2(X8)
                      | p1(X8) )
                    & ( p2(X8)
                      | ~ p1(X8) ) )
                  | ~ r1(X4,X8) ) ) )
        & r1(sK0,X3) )
   => ( ! [X4] :
          ( ~ r1(sK3,X4)
          | ( ? [X5] :
                ( ~ p3(X5)
                & r1(X4,X5) )
            & ? [X6] : r1(X4,X6)
            & ? [X7] :
                ( ( p1(X7)
                  | p2(X7) )
                & r1(X4,X7)
                & ( ~ p2(X7)
                  | ~ p1(X7) ) )
            & ! [X8] :
                ( ( ( ~ p2(X8)
                    | p1(X8) )
                  & ( p2(X8)
                    | ~ p1(X8) ) )
                | ~ r1(X4,X8) ) ) )
      & r1(sK0,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X4] :
      ( ? [X5] :
          ( ~ p3(X5)
          & r1(X4,X5) )
     => ( ~ p3(sK4(X4))
        & r1(X4,sK4(X4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X4] :
      ( ? [X6] : r1(X4,X6)
     => r1(X4,sK5(X4)) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X4] :
      ( ? [X7] :
          ( ( p1(X7)
            | p2(X7) )
          & r1(X4,X7)
          & ( ~ p2(X7)
            | ~ p1(X7) ) )
     => ( ( p1(sK6(X4))
          | p2(sK6(X4)) )
        & r1(X4,sK6(X4))
        & ( ~ p2(sK6(X4))
          | ~ p1(sK6(X4)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0] :
      ( ? [X1] :
          ( r1(X0,X1)
          & ? [X2] :
              ( p1(X2)
              & r1(X1,X2) )
          & p3(X1) )
      & ? [X3] :
          ( ! [X4] :
              ( ~ r1(X3,X4)
              | ( ? [X5] :
                    ( ~ p3(X5)
                    & r1(X4,X5) )
                & ? [X6] : r1(X4,X6)
                & ? [X7] :
                    ( ( p1(X7)
                      | p2(X7) )
                    & r1(X4,X7)
                    & ( ~ p2(X7)
                      | ~ p1(X7) ) )
                & ! [X8] :
                    ( ( ( ~ p2(X8)
                        | p1(X8) )
                      & ( p2(X8)
                        | ~ p1(X8) ) )
                    | ~ r1(X4,X8) ) ) )
          & r1(X0,X3) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ? [X0] :
      ( ? [X1] :
          ( r1(X0,X1)
          & ? [X2] :
              ( p1(X2)
              & r1(X1,X2) )
          & p3(X1) )
      & ? [X3] :
          ( ! [X4] :
              ( ~ r1(X3,X4)
              | ( ? [X8] :
                    ( ~ p3(X8)
                    & r1(X4,X8) )
                & ? [X5] : r1(X4,X5)
                & ? [X7] :
                    ( ( p1(X7)
                      | p2(X7) )
                    & r1(X4,X7)
                    & ( ~ p2(X7)
                      | ~ p1(X7) ) )
                & ! [X6] :
                    ( ( ( ~ p2(X6)
                        | p1(X6) )
                      & ( p2(X6)
                        | ~ p1(X6) ) )
                    | ~ r1(X4,X6) ) ) )
          & r1(X0,X3) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ? [X0] :
      ~ ( ! [X3] :
            ( ~ ! [X4] :
                  ( ~ ( ! [X8] :
                          ( p3(X8)
                          | ~ r1(X4,X8) )
                      | ~ ! [X6] :
                            ( ~ ( ( ~ p1(X6)
                                  & p2(X6) )
                                | ( ~ p2(X6)
                                  & p1(X6) ) )
                            | ~ r1(X4,X6) )
                      | ! [X5] : ~ r1(X4,X5)
                      | ! [X7] :
                          ( ( p1(X7)
                            & p2(X7) )
                          | ( ~ p1(X7)
                            & ~ p2(X7) )
                          | ~ r1(X4,X7) ) )
                  | ~ r1(X3,X4) )
            | ~ r1(X0,X3) )
        | ! [X1] :
            ( ! [X2] :
                ( ~ p1(X2)
                | ~ r1(X1,X2) )
            | ~ r1(X0,X1)
            | ~ p3(X1) ) ),
    inference(flattening,[],[f6]) ).

fof(f6,plain,
    ~ ~ ? [X0] :
          ~ ( ! [X3] :
                ( ~ ! [X4] :
                      ( ~ ( ! [X8] :
                              ( p3(X8)
                              | ~ r1(X4,X8) )
                          | ~ ! [X6] :
                                ( ~ ( ( ~ p1(X6)
                                      & p2(X6) )
                                    | ( ~ p2(X6)
                                      & p1(X6) ) )
                                | ~ r1(X4,X6) )
                          | ! [X5] : ~ r1(X4,X5)
                          | ! [X7] :
                              ( ( p1(X7)
                                & p2(X7) )
                              | ( ~ p1(X7)
                                & ~ p2(X7) )
                              | ~ r1(X4,X7) ) )
                      | ~ r1(X3,X4) )
                | ~ r1(X0,X3) )
            | ! [X1] :
                ( ! [X2] :
                    ( ~ p1(X2)
                    | ~ r1(X1,X2) )
                | ~ r1(X0,X1)
                | ~ p3(X1) ) ),
    inference(true_and_false_elimination,[],[f5]) ).

fof(f5,plain,
    ~ ~ ? [X0] :
          ~ ( ! [X1] :
                ( ! [X2] :
                    ( ~ p1(X2)
                    | ~ r1(X1,X2) )
                | ~ r1(X0,X1)
                | ~ p3(X1) )
            | ! [X3] :
                ( ~ ! [X4] :
                      ( ~ r1(X3,X4)
                      | ~ ( ! [X5] :
                              ( ~ r1(X4,X5)
                              | $false )
                          | ~ ! [X6] :
                                ( ~ ( ( ~ p1(X6)
                                      & p2(X6) )
                                    | ( ~ p2(X6)
                                      & p1(X6) ) )
                                | ~ r1(X4,X6) )
                          | ! [X7] :
                              ( ( p1(X7)
                                & p2(X7) )
                              | ( ~ p1(X7)
                                & ~ p2(X7) )
                              | ~ r1(X4,X7) )
                          | ! [X8] :
                              ( p3(X8)
                              | ~ r1(X4,X8) ) ) )
                | ~ r1(X0,X3) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,negated_conjecture,
    ~ ~ ? [X0] :
          ~ ( ! [X1] :
                ( ~ p3(X1)
                | ~ r1(X0,X1)
                | ! [X0] :
                    ( ~ r1(X1,X0)
                    | ~ p1(X0) ) )
            | ! [X1] :
                ( ~ ! [X0] :
                      ( ~ r1(X1,X0)
                      | ~ ( ! [X1] :
                              ( ~ r1(X0,X1)
                              | $false )
                          | ~ ! [X1] :
                                ( ~ ( ( p2(X1)
                                      & ~ p1(X1) )
                                    | ( p1(X1)
                                      & ~ p2(X1) ) )
                                | ~ r1(X0,X1) )
                          | ! [X1] :
                              ( ~ r1(X0,X1)
                              | ( ~ p1(X1)
                                & ~ p2(X1) )
                              | ( p2(X1)
                                & p1(X1) ) )
                          | ! [X1] :
                              ( p3(X1)
                              | ~ r1(X0,X1) ) ) )
                | ~ r1(X0,X1) ) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f3,conjecture,
    ~ ? [X0] :
        ~ ( ! [X1] :
              ( ~ p3(X1)
              | ~ r1(X0,X1)
              | ! [X0] :
                  ( ~ r1(X1,X0)
                  | ~ p1(X0) ) )
          | ! [X1] :
              ( ~ ! [X0] :
                    ( ~ r1(X1,X0)
                    | ~ ( ! [X1] :
                            ( ~ r1(X0,X1)
                            | $false )
                        | ~ ! [X1] :
                              ( ~ ( ( p2(X1)
                                    & ~ p1(X1) )
                                  | ( p1(X1)
                                    & ~ p2(X1) ) )
                              | ~ r1(X0,X1) )
                        | ! [X1] :
                            ( ~ r1(X0,X1)
                            | ( ~ p1(X1)
                              & ~ p2(X1) )
                            | ( p2(X1)
                              & p1(X1) ) )
                        | ! [X1] :
                            ( p3(X1)
                            | ~ r1(X0,X1) ) ) )
              | ~ r1(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).

fof(f83,plain,
    ( p2(sK6(sK3))
    | ~ p1(sK6(sK3)) ),
    inference(resolution,[],[f46,f50]) ).

fof(f50,plain,
    r1(sK3,sK6(sK3)),
    inference(resolution,[],[f36,f27]) ).

fof(f27,plain,
    ! [X4] :
      ( ~ r1(sK3,X4)
      | r1(X4,sK6(X4)) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f46,plain,
    ! [X0] :
      ( ~ r1(sK3,X0)
      | ~ p1(X0)
      | p2(X0) ),
    inference(resolution,[],[f36,f43]) ).

fof(f43,plain,
    ! [X8,X4] :
      ( ~ r1(sK3,X4)
      | ~ r1(X4,X8)
      | p2(X8)
      | ~ p1(X8) ),
    inference(consistent_polarity_flipping,[],[f25]) ).

fof(f25,plain,
    ! [X8,X4] :
      ( ~ p2(X8)
      | ~ r1(sK3,X4)
      | p1(X8)
      | ~ r1(X4,X8) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f109,plain,
    ( p1(sK6(sK3))
    | ~ r1(sK3,sK3) ),
    inference(duplicate_literal_removal,[],[f108]) ).

fof(f108,plain,
    ( p1(sK6(sK3))
    | p1(sK6(sK3))
    | ~ r1(sK3,sK3) ),
    inference(resolution,[],[f90,f37]) ).

fof(f37,plain,
    ! [X4] :
      ( p2(sK6(X4))
      | ~ r1(sK3,X4)
      | p1(sK6(X4)) ),
    inference(consistent_polarity_flipping,[],[f26]) ).

fof(f26,plain,
    ! [X4] :
      ( ~ r1(sK3,X4)
      | ~ p1(sK6(X4))
      | ~ p2(sK6(X4)) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f90,plain,
    ( ~ p2(sK6(sK3))
    | p1(sK6(sK3)) ),
    inference(resolution,[],[f47,f50]) ).

fof(f47,plain,
    ! [X1] :
      ( ~ r1(sK3,X1)
      | p1(X1)
      | ~ p2(X1) ),
    inference(resolution,[],[f36,f42]) ).

fof(f42,plain,
    ! [X8,X4] :
      ( ~ r1(sK3,X4)
      | ~ p2(X8)
      | p1(X8)
      | ~ r1(X4,X8) ),
    inference(consistent_polarity_flipping,[],[f24]) ).

fof(f24,plain,
    ! [X8,X4] :
      ( ~ p1(X8)
      | ~ r1(sK3,X4)
      | p2(X8)
      | ~ r1(X4,X8) ),
    inference(cnf_transformation,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : LCL686+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 02:15:30 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (20874)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51  % (20883)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.51  % (20866)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52  % (20874)First to succeed.
% 0.20/0.52  % (20874)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (20874)------------------------------
% 0.20/0.52  % (20874)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (20874)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (20874)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (20874)Memory used [KB]: 895
% 0.20/0.52  % (20874)Time elapsed: 0.121 s
% 0.20/0.52  % (20874)Instructions burned: 3 (million)
% 0.20/0.52  % (20874)------------------------------
% 0.20/0.52  % (20874)------------------------------
% 0.20/0.52  % (20849)Success in time 0.168 s
%------------------------------------------------------------------------------