TSTP Solution File: SWC287+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC287+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.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 : Tue Apr 30 16:17:37 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   33 (   8 unt;   0 def)
%            Number of atoms       :  213 (  81 equ)
%            Maximal formula atoms :   20 (   6 avg)
%            Number of connectives :  245 (  65   ~;  63   |; 105   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   65 (  34   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f760,plain,
    $false,
    inference(resolution,[],[f750,f399]) ).

fof(f399,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).

fof(f750,plain,
    ~ strictorderedP(nil),
    inference(backward_demodulation,[],[f643,f746]) ).

fof(f746,plain,
    nil = sK22,
    inference(duplicate_literal_removal,[],[f744]) ).

fof(f744,plain,
    ( nil = sK22
    | nil = sK22 ),
    inference(resolution,[],[f743,f391]) ).

fof(f391,plain,
    ( sP0(sK23,sK22)
    | nil = sK22 ),
    inference(cnf_transformation,[],[f259]) ).

fof(f259,plain,
    ( ( ( nil = sK22
        & nil = sK23 )
      | sP0(sK23,sK22) )
    & ~ strictorderedP(sK20)
    & sK20 = sK22
    & sK21 = sK23
    & ssList(sK23)
    & ssList(sK22)
    & ssList(sK21)
    & ssList(sK20) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f223,f258,f257,f256,f255]) ).

fof(f255,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | sP0(X3,X2) )
                    & ~ strictorderedP(X0)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | sP0(X3,X2) )
                  & ~ strictorderedP(sK20)
                  & sK20 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f256,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | sP0(X3,X2) )
                & ~ strictorderedP(sK20)
                & sK20 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | sP0(X3,X2) )
              & ~ strictorderedP(sK20)
              & sK20 = X2
              & sK21 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f257,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | sP0(X3,X2) )
            & ~ strictorderedP(sK20)
            & sK20 = X2
            & sK21 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK22
              & nil = X3 )
            | sP0(X3,sK22) )
          & ~ strictorderedP(sK20)
          & sK20 = sK22
          & sK21 = X3
          & ssList(X3) )
      & ssList(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f258,plain,
    ( ? [X3] :
        ( ( ( nil = sK22
            & nil = X3 )
          | sP0(X3,sK22) )
        & ~ strictorderedP(sK20)
        & sK20 = sK22
        & sK21 = X3
        & ssList(X3) )
   => ( ( ( nil = sK22
          & nil = sK23 )
        | sP0(sK23,sK22) )
      & ~ strictorderedP(sK20)
      & sK20 = sK22
      & sK21 = sK23
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | sP0(X3,X2) )
                  & ~ strictorderedP(X0)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f98,f222]) ).

fof(f222,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ! [X5] :
              ( ~ leq(X5,X4)
              | ~ memberP(X3,X5)
              | X4 = X5
              | ~ ssItem(X5) )
          & memberP(X3,X4)
          & cons(X4,nil) = X2
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X5,X4)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ~ strictorderedP(X0)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

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

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

fof(f743,plain,
    ( ~ sP0(sK23,sK22)
    | nil = sK22 ),
    inference(resolution,[],[f740,f379]) ).

fof(f379,plain,
    ! [X0,X1] :
      ( ssItem(sK19(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ! [X0,X1] :
      ( ( ! [X3] :
            ( ~ leq(X3,sK19(X0,X1))
            | ~ memberP(X0,X3)
            | sK19(X0,X1) = X3
            | ~ ssItem(X3) )
        & memberP(X0,sK19(X0,X1))
        & cons(sK19(X0,X1),nil) = X1
        & ssItem(sK19(X0,X1)) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f252,f253]) ).

fof(f253,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ~ leq(X3,X2)
              | ~ memberP(X0,X3)
              | X2 = X3
              | ~ ssItem(X3) )
          & memberP(X0,X2)
          & cons(X2,nil) = X1
          & ssItem(X2) )
     => ( ! [X3] :
            ( ~ leq(X3,sK19(X0,X1))
            | ~ memberP(X0,X3)
            | sK19(X0,X1) = X3
            | ~ ssItem(X3) )
        & memberP(X0,sK19(X0,X1))
        & cons(sK19(X0,X1),nil) = X1
        & ssItem(sK19(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ~ leq(X3,X2)
              | ~ memberP(X0,X3)
              | X2 = X3
              | ~ ssItem(X3) )
          & memberP(X0,X2)
          & cons(X2,nil) = X1
          & ssItem(X2) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f251]) ).

fof(f251,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ! [X5] :
              ( ~ leq(X5,X4)
              | ~ memberP(X3,X5)
              | X4 = X5
              | ~ ssItem(X5) )
          & memberP(X3,X4)
          & cons(X4,nil) = X2
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    inference(nnf_transformation,[],[f222]) ).

fof(f740,plain,
    ( ~ ssItem(sK19(sK23,sK22))
    | nil = sK22 ),
    inference(resolution,[],[f735,f643]) ).

fof(f735,plain,
    ( strictorderedP(sK22)
    | ~ ssItem(sK19(sK23,sK22))
    | nil = sK22 ),
    inference(superposition,[],[f411,f727]) ).

fof(f727,plain,
    ( sK22 = cons(sK19(sK23,sK22),nil)
    | nil = sK22 ),
    inference(resolution,[],[f380,f391]) ).

fof(f380,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | cons(sK19(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f411,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).

fof(f643,plain,
    ~ strictorderedP(sK22),
    inference(forward_demodulation,[],[f389,f388]) ).

fof(f388,plain,
    sK20 = sK22,
    inference(cnf_transformation,[],[f259]) ).

fof(f389,plain,
    ~ strictorderedP(sK20),
    inference(cnf_transformation,[],[f259]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC287+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 04:34:29 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (6866)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (6872)WARNING: value z3 for option sas not known
% 0.15/0.38  % (6871)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (6870)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (6872)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (6874)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38  % (6875)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38  % (6876)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38  % (6873)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (6875)First to succeed.
% 0.15/0.39  TRYING [1]
% 0.15/0.39  % (6875)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (6875)------------------------------
% 0.15/0.39  % (6875)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39  % (6875)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (6875)Memory used [KB]: 1393
% 0.15/0.39  % (6875)Time elapsed: 0.017 s
% 0.15/0.39  % (6875)Instructions burned: 27 (million)
% 0.15/0.39  % (6875)------------------------------
% 0.15/0.39  % (6875)------------------------------
% 0.15/0.39  % (6866)Success in time 0.036 s
%------------------------------------------------------------------------------