TSTP Solution File: SWC406+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC406+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : n011.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 18:41:00 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (   7 unt;   0 def)
%            Number of atoms       :  347 (  64 equ)
%            Maximal formula atoms :   44 (  15 avg)
%            Number of connectives :  458 ( 134   ~; 113   |; 187   &)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  12 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :  103 (  45   !;  58   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f657,plain,
    $false,
    inference(subsumption_resolution,[],[f656,f473]) ).

fof(f473,plain,
    ssItem(sK29),
    inference(cnf_transformation,[],[f292]) ).

fof(f292,plain,
    ( ssItem(sK29)
    & memberP(sK25,sK29)
    & ~ memberP(sK26,sK29)
    & sK28 = sK26
    & ssList(sK28)
    & sK27 = sK25
    & ! [X5] :
        ( ~ ssItem(X5)
        | ( ( ( ssItem(sK30(X5))
              & sK30(X5) != X5
              & leq(sK30(X5),X5)
              & memberP(sK28,sK30(X5)) )
            | ~ memberP(sK28,X5)
            | memberP(sK27,X5) )
          & ( ( ! [X7] :
                  ( ~ memberP(sK28,X7)
                  | ~ ssItem(X7)
                  | ~ leq(X7,X5)
                  | X5 = X7 )
              & memberP(sK28,X5) )
            | ~ memberP(sK27,X5) ) ) )
    & ssList(sK27)
    & ssList(sK26)
    & ssList(sK25) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27,sK28,sK29,sK30])],[f285,f291,f290,f289,f288,f287,f286]) ).

fof(f286,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ssItem(X4)
                        & memberP(X0,X4)
                        & ~ memberP(X1,X4) )
                    & X1 = X3
                    & ssList(X3)
                    & X0 = X2
                    & ! [X5] :
                        ( ~ ssItem(X5)
                        | ( ( ? [X6] :
                                ( ssItem(X6)
                                & X5 != X6
                                & leq(X6,X5)
                                & memberP(X3,X6) )
                            | ~ memberP(X3,X5)
                            | memberP(X2,X5) )
                          & ( ( ! [X7] :
                                  ( ~ memberP(X3,X7)
                                  | ~ ssItem(X7)
                                  | ~ leq(X7,X5)
                                  | X5 = X7 )
                              & memberP(X3,X5) )
                            | ~ memberP(X2,X5) ) ) ) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ssItem(X4)
                      & memberP(sK25,X4)
                      & ~ memberP(X1,X4) )
                  & X1 = X3
                  & ssList(X3)
                  & sK25 = X2
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ( ( ? [X6] :
                              ( ssItem(X6)
                              & X5 != X6
                              & leq(X6,X5)
                              & memberP(X3,X6) )
                          | ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ( ! [X7] :
                                ( ~ memberP(X3,X7)
                                | ~ ssItem(X7)
                                | ~ leq(X7,X5)
                                | X5 = X7 )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) ) ) ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK25) ) ),
    introduced(choice_axiom,[]) ).

fof(f287,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ssItem(X4)
                    & memberP(sK25,X4)
                    & ~ memberP(X1,X4) )
                & X1 = X3
                & ssList(X3)
                & sK25 = X2
                & ! [X5] :
                    ( ~ ssItem(X5)
                    | ( ( ? [X6] :
                            ( ssItem(X6)
                            & X5 != X6
                            & leq(X6,X5)
                            & memberP(X3,X6) )
                        | ~ memberP(X3,X5)
                        | memberP(X2,X5) )
                      & ( ( ! [X7] :
                              ( ~ memberP(X3,X7)
                              | ~ ssItem(X7)
                              | ~ leq(X7,X5)
                              | X5 = X7 )
                          & memberP(X3,X5) )
                        | ~ memberP(X2,X5) ) ) ) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ssItem(X4)
                  & memberP(sK25,X4)
                  & ~ memberP(sK26,X4) )
              & sK26 = X3
              & ssList(X3)
              & sK25 = X2
              & ! [X5] :
                  ( ~ ssItem(X5)
                  | ( ( ? [X6] :
                          ( ssItem(X6)
                          & X5 != X6
                          & leq(X6,X5)
                          & memberP(X3,X6) )
                      | ~ memberP(X3,X5)
                      | memberP(X2,X5) )
                    & ( ( ! [X7] :
                            ( ~ memberP(X3,X7)
                            | ~ ssItem(X7)
                            | ~ leq(X7,X5)
                            | X5 = X7 )
                        & memberP(X3,X5) )
                      | ~ memberP(X2,X5) ) ) ) )
          & ssList(X2) )
      & ssList(sK26) ) ),
    introduced(choice_axiom,[]) ).

fof(f288,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( ssItem(X4)
                & memberP(sK25,X4)
                & ~ memberP(sK26,X4) )
            & sK26 = X3
            & ssList(X3)
            & sK25 = X2
            & ! [X5] :
                ( ~ ssItem(X5)
                | ( ( ? [X6] :
                        ( ssItem(X6)
                        & X5 != X6
                        & leq(X6,X5)
                        & memberP(X3,X6) )
                    | ~ memberP(X3,X5)
                    | memberP(X2,X5) )
                  & ( ( ! [X7] :
                          ( ~ memberP(X3,X7)
                          | ~ ssItem(X7)
                          | ~ leq(X7,X5)
                          | X5 = X7 )
                      & memberP(X3,X5) )
                    | ~ memberP(X2,X5) ) ) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ? [X4] :
              ( ssItem(X4)
              & memberP(sK25,X4)
              & ~ memberP(sK26,X4) )
          & sK26 = X3
          & ssList(X3)
          & sK27 = sK25
          & ! [X5] :
              ( ~ ssItem(X5)
              | ( ( ? [X6] :
                      ( ssItem(X6)
                      & X5 != X6
                      & leq(X6,X5)
                      & memberP(X3,X6) )
                  | ~ memberP(X3,X5)
                  | memberP(sK27,X5) )
                & ( ( ! [X7] :
                        ( ~ memberP(X3,X7)
                        | ~ ssItem(X7)
                        | ~ leq(X7,X5)
                        | X5 = X7 )
                    & memberP(X3,X5) )
                  | ~ memberP(sK27,X5) ) ) ) )
      & ssList(sK27) ) ),
    introduced(choice_axiom,[]) ).

fof(f289,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( ssItem(X4)
            & memberP(sK25,X4)
            & ~ memberP(sK26,X4) )
        & sK26 = X3
        & ssList(X3)
        & sK27 = sK25
        & ! [X5] :
            ( ~ ssItem(X5)
            | ( ( ? [X6] :
                    ( ssItem(X6)
                    & X5 != X6
                    & leq(X6,X5)
                    & memberP(X3,X6) )
                | ~ memberP(X3,X5)
                | memberP(sK27,X5) )
              & ( ( ! [X7] :
                      ( ~ memberP(X3,X7)
                      | ~ ssItem(X7)
                      | ~ leq(X7,X5)
                      | X5 = X7 )
                  & memberP(X3,X5) )
                | ~ memberP(sK27,X5) ) ) ) )
   => ( ? [X4] :
          ( ssItem(X4)
          & memberP(sK25,X4)
          & ~ memberP(sK26,X4) )
      & sK28 = sK26
      & ssList(sK28)
      & sK27 = sK25
      & ! [X5] :
          ( ~ ssItem(X5)
          | ( ( ? [X6] :
                  ( ssItem(X6)
                  & X5 != X6
                  & leq(X6,X5)
                  & memberP(sK28,X6) )
              | ~ memberP(sK28,X5)
              | memberP(sK27,X5) )
            & ( ( ! [X7] :
                    ( ~ memberP(sK28,X7)
                    | ~ ssItem(X7)
                    | ~ leq(X7,X5)
                    | X5 = X7 )
                & memberP(sK28,X5) )
              | ~ memberP(sK27,X5) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f290,plain,
    ( ? [X4] :
        ( ssItem(X4)
        & memberP(sK25,X4)
        & ~ memberP(sK26,X4) )
   => ( ssItem(sK29)
      & memberP(sK25,sK29)
      & ~ memberP(sK26,sK29) ) ),
    introduced(choice_axiom,[]) ).

fof(f291,plain,
    ! [X5] :
      ( ? [X6] :
          ( ssItem(X6)
          & X5 != X6
          & leq(X6,X5)
          & memberP(sK28,X6) )
     => ( ssItem(sK30(X5))
        & sK30(X5) != X5
        & leq(sK30(X5),X5)
        & memberP(sK28,sK30(X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f285,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ssItem(X4)
                      & memberP(X0,X4)
                      & ~ memberP(X1,X4) )
                  & X1 = X3
                  & ssList(X3)
                  & X0 = X2
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ( ( ? [X6] :
                              ( ssItem(X6)
                              & X5 != X6
                              & leq(X6,X5)
                              & memberP(X3,X6) )
                          | ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ( ! [X7] :
                                ( ~ memberP(X3,X7)
                                | ~ ssItem(X7)
                                | ~ leq(X7,X5)
                                | X5 = X7 )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) ) ) ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(rectify,[],[f135]) ).

fof(f135,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ssItem(X4)
                      & memberP(X0,X4)
                      & ~ memberP(X1,X4) )
                  & X1 = X3
                  & ssList(X3)
                  & X0 = X2
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ( ( ? [X7] :
                              ( ssItem(X7)
                              & X5 != X7
                              & leq(X7,X5)
                              & memberP(X3,X7) )
                          | ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ( ! [X6] :
                                ( ~ memberP(X3,X6)
                                | ~ ssItem(X6)
                                | ~ leq(X6,X5)
                                | X5 = X6 )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) ) ) ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f134]) ).

fof(f134,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( memberP(X0,X4)
                      & ~ memberP(X1,X4)
                      & ssItem(X4) )
                  & X1 = X3
                  & X0 = X2
                  & ! [X5] :
                      ( ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5)
                          | ? [X7] :
                              ( leq(X7,X5)
                              & memberP(X3,X7)
                              & X5 != X7
                              & ssItem(X7) ) )
                        & ( ( ! [X6] :
                                ( ~ memberP(X3,X6)
                                | ~ ssItem(X6)
                                | ~ leq(X6,X5)
                                | X5 = X6 )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) ) )
                      | ~ ssItem(X5) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ! [X4] :
                          ( ssItem(X4)
                         => ( ~ memberP(X0,X4)
                            | memberP(X1,X4) ) )
                      | X1 != X3
                      | X0 != X2
                      | ? [X5] :
                          ( ( ( memberP(X3,X5)
                              & ~ memberP(X2,X5)
                              & ! [X7] :
                                  ( ssItem(X7)
                                 => ( ~ leq(X7,X5)
                                    | ~ memberP(X3,X7)
                                    | X5 = X7 ) ) )
                            | ( memberP(X2,X5)
                              & ( ? [X6] :
                                    ( ssItem(X6)
                                    & X5 != X6
                                    & leq(X6,X5)
                                    & memberP(X3,X6) )
                                | ~ memberP(X3,X5) ) ) )
                          & ssItem(X5) ) ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ! [X6] :
                          ( ssItem(X6)
                         => ( ~ memberP(X0,X6)
                            | memberP(X1,X6) ) )
                      | X1 != X3
                      | ? [X4] :
                          ( ssItem(X4)
                          & ( ( ( ~ memberP(X3,X4)
                                | ? [X5] :
                                    ( memberP(X3,X5)
                                    & leq(X5,X4)
                                    & X4 != X5
                                    & ssItem(X5) ) )
                              & memberP(X2,X4) )
                            | ( ~ memberP(X2,X4)
                              & memberP(X3,X4)
                              & ! [X5] :
                                  ( ssItem(X5)
                                 => ( ~ leq(X5,X4)
                                    | X4 = X5
                                    | ~ memberP(X3,X5) ) ) ) ) )
                      | X0 != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ! [X6] :
                        ( ssItem(X6)
                       => ( ~ memberP(X0,X6)
                          | memberP(X1,X6) ) )
                    | X1 != X3
                    | ? [X4] :
                        ( ssItem(X4)
                        & ( ( ( ~ memberP(X3,X4)
                              | ? [X5] :
                                  ( memberP(X3,X5)
                                  & leq(X5,X4)
                                  & X4 != X5
                                  & ssItem(X5) ) )
                            & memberP(X2,X4) )
                          | ( ~ memberP(X2,X4)
                            & memberP(X3,X4)
                            & ! [X5] :
                                ( ssItem(X5)
                               => ( ~ leq(X5,X4)
                                  | X4 = X5
                                  | ~ memberP(X3,X5) ) ) ) ) )
                    | X0 != X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f656,plain,
    ~ ssItem(sK29),
    inference(subsumption_resolution,[],[f655,f472]) ).

fof(f472,plain,
    memberP(sK25,sK29),
    inference(cnf_transformation,[],[f292]) ).

fof(f655,plain,
    ( ~ memberP(sK25,sK29)
    | ~ ssItem(sK29) ),
    inference(resolution,[],[f572,f471]) ).

fof(f471,plain,
    ~ memberP(sK26,sK29),
    inference(cnf_transformation,[],[f292]) ).

fof(f572,plain,
    ! [X5] :
      ( memberP(sK26,X5)
      | ~ ssItem(X5)
      | ~ memberP(sK25,X5) ),
    inference(definition_unfolding,[],[f462,f470,f468]) ).

fof(f468,plain,
    sK27 = sK25,
    inference(cnf_transformation,[],[f292]) ).

fof(f470,plain,
    sK28 = sK26,
    inference(cnf_transformation,[],[f292]) ).

fof(f462,plain,
    ! [X5] :
      ( ~ ssItem(X5)
      | memberP(sK28,X5)
      | ~ memberP(sK27,X5) ),
    inference(cnf_transformation,[],[f292]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWC406+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13  % 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 : n011.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 18:51:40 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (26043)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.51  % (26050)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)
% 0.19/0.52  % (26058)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)
% 0.19/0.52  % (26058)Instruction limit reached!
% 0.19/0.52  % (26058)------------------------------
% 0.19/0.52  % (26058)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (26043)First to succeed.
% 0.19/0.53  % (26046)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (26047)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)
% 0.19/0.53  % (26058)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (26068)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.53  % (26058)Termination reason: Unknown
% 0.19/0.53  % (26058)Termination phase: Function definition elimination
% 0.19/0.53  
% 0.19/0.53  % (26058)Memory used [KB]: 1791
% 0.19/0.53  % (26058)Time elapsed: 0.006 s
% 0.19/0.53  % (26058)Instructions burned: 8 (million)
% 0.19/0.53  % (26058)------------------------------
% 0.19/0.53  % (26058)------------------------------
% 0.19/0.53  % (26043)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Theorem for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (26043)------------------------------
% 0.19/0.53  % (26043)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (26043)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (26043)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (26043)Memory used [KB]: 6396
% 0.19/0.53  % (26043)Time elapsed: 0.105 s
% 0.19/0.53  % (26043)Instructions burned: 14 (million)
% 0.19/0.53  % (26043)------------------------------
% 0.19/0.53  % (26043)------------------------------
% 0.19/0.53  % (26042)Success in time 0.182 s
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