TSTP Solution File: SWC048+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC048+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 : n008.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 : Sun May  5 09:52:25 EDT 2024

% Result   : Theorem 0.22s 0.39s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   54 (  10 unt;   0 def)
%            Number of atoms       :  322 ( 117 equ)
%            Maximal formula atoms :   34 (   5 avg)
%            Number of connectives :  393 ( 125   ~; 127   |; 121   &)
%                                         (   4 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   64 (  38   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f758,plain,
    $false,
    inference(resolution,[],[f757,f396]) ).

fof(f396,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f757,plain,
    ~ ssList(nil),
    inference(resolution,[],[f755,f633]) ).

fof(f633,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f626]) ).

fof(f626,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f575]) ).

fof(f575,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f355,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f755,plain,
    neq(nil,nil),
    inference(trivial_inequality_removal,[],[f752]) ).

fof(f752,plain,
    ( nil != nil
    | neq(nil,nil) ),
    inference(backward_demodulation,[],[f740,f747]) ).

fof(f747,plain,
    nil = sK20,
    inference(resolution,[],[f746,f376]) ).

fof(f376,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ( ( ( rearsegP(sK21,sK20)
        & neq(sK20,nil) )
      | ( nil = sK20
        & nil = sK21 ) )
    & ( ( ! [X4] :
            ( ~ rearsegP(sK18,X4)
            | ~ rearsegP(sK19,X4)
            | ~ neq(X4,nil)
            | ~ ssList(X4) )
        & neq(sK19,nil) )
      | ( nil != sK18
        & nil = sK19 ) )
    & sK18 = sK20
    & sK19 = sK21
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f99,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( rearsegP(X3,X2)
                        & neq(X2,nil) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & ( ( ! [X4] :
                            ( ~ rearsegP(X0,X4)
                            | ~ rearsegP(X1,X4)
                            | ~ neq(X4,nil)
                            | ~ ssList(X4) )
                        & neq(X1,nil) )
                      | ( nil != X0
                        & nil = X1 ) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( rearsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ( ( ! [X4] :
                          ( ~ rearsegP(sK18,X4)
                          | ~ rearsegP(X1,X4)
                          | ~ neq(X4,nil)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != sK18
                      & nil = X1 ) )
                  & sK18 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( rearsegP(X3,X2)
                    & neq(X2,nil) )
                  | ( nil = X2
                    & nil = X3 ) )
                & ( ( ! [X4] :
                        ( ~ rearsegP(sK18,X4)
                        | ~ rearsegP(X1,X4)
                        | ~ neq(X4,nil)
                        | ~ ssList(X4) )
                    & neq(X1,nil) )
                  | ( nil != sK18
                    & nil = X1 ) )
                & sK18 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( rearsegP(X3,X2)
                  & neq(X2,nil) )
                | ( nil = X2
                  & nil = X3 ) )
              & ( ( ! [X4] :
                      ( ~ rearsegP(sK18,X4)
                      | ~ rearsegP(sK19,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & neq(sK19,nil) )
                | ( nil != sK18
                  & nil = sK19 ) )
              & sK18 = X2
              & sK19 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( rearsegP(X3,X2)
                & neq(X2,nil) )
              | ( nil = X2
                & nil = X3 ) )
            & ( ( ! [X4] :
                    ( ~ rearsegP(sK18,X4)
                    | ~ rearsegP(sK19,X4)
                    | ~ neq(X4,nil)
                    | ~ ssList(X4) )
                & neq(sK19,nil) )
              | ( nil != sK18
                & nil = sK19 ) )
            & sK18 = X2
            & sK19 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( rearsegP(X3,sK20)
              & neq(sK20,nil) )
            | ( nil = sK20
              & nil = X3 ) )
          & ( ( ! [X4] :
                  ( ~ rearsegP(sK18,X4)
                  | ~ rearsegP(sK19,X4)
                  | ~ neq(X4,nil)
                  | ~ ssList(X4) )
              & neq(sK19,nil) )
            | ( nil != sK18
              & nil = sK19 ) )
          & sK18 = sK20
          & sK19 = X3
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( ( ( rearsegP(X3,sK20)
            & neq(sK20,nil) )
          | ( nil = sK20
            & nil = X3 ) )
        & ( ( ! [X4] :
                ( ~ rearsegP(sK18,X4)
                | ~ rearsegP(sK19,X4)
                | ~ neq(X4,nil)
                | ~ ssList(X4) )
            & neq(sK19,nil) )
          | ( nil != sK18
            & nil = sK19 ) )
        & sK18 = sK20
        & sK19 = X3
        & ssList(X3) )
   => ( ( ( rearsegP(sK21,sK20)
          & neq(sK20,nil) )
        | ( nil = sK20
          & nil = sK21 ) )
      & ( ( ! [X4] :
              ( ~ rearsegP(sK18,X4)
              | ~ rearsegP(sK19,X4)
              | ~ neq(X4,nil)
              | ~ ssList(X4) )
          & neq(sK19,nil) )
        | ( nil != sK18
          & nil = sK19 ) )
      & sK18 = sK20
      & sK19 = sK21
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( rearsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ( ( ! [X4] :
                          ( ~ rearsegP(X0,X4)
                          | ~ rearsegP(X1,X4)
                          | ~ neq(X4,nil)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( rearsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ( ( ! [X4] :
                          ( ~ rearsegP(X0,X4)
                          | ~ rearsegP(X1,X4)
                          | ~ neq(X4,nil)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & 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] :
                    ( ssList(X3)
                   => ( ( ( ~ rearsegP(X3,X2)
                          | ~ neq(X2,nil) )
                        & ( nil != X2
                          | nil != X3 ) )
                      | ( ( ? [X4] :
                              ( rearsegP(X0,X4)
                              & rearsegP(X1,X4)
                              & neq(X4,nil)
                              & ssList(X4) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f746,plain,
    ( ~ ssList(sK20)
    | nil = sK20 ),
    inference(duplicate_literal_removal,[],[f745]) ).

fof(f745,plain,
    ( nil = sK20
    | nil = sK20
    | ~ ssList(sK20) ),
    inference(resolution,[],[f738,f556]) ).

fof(f556,plain,
    ! [X0] :
      ( ~ rearsegP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f349,plain,
    ! [X0] :
      ( ( ( rearsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ rearsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ( rearsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( rearsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).

fof(f738,plain,
    ( rearsegP(nil,sK20)
    | nil = sK20 ),
    inference(backward_demodulation,[],[f639,f736]) ).

fof(f736,plain,
    nil = sK19,
    inference(resolution,[],[f735,f376]) ).

fof(f735,plain,
    ( ~ ssList(sK20)
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f733]) ).

fof(f733,plain,
    ( ~ ssList(sK20)
    | nil = sK19
    | nil = sK19 ),
    inference(resolution,[],[f732,f641]) ).

fof(f641,plain,
    ( rearsegP(sK19,sK20)
    | nil = sK19 ),
    inference(forward_demodulation,[],[f640,f378]) ).

fof(f378,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f254]) ).

fof(f640,plain,
    ( rearsegP(sK19,sK20)
    | nil = sK21 ),
    inference(forward_demodulation,[],[f386,f378]) ).

fof(f386,plain,
    ( rearsegP(sK21,sK20)
    | nil = sK21 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f732,plain,
    ( ~ rearsegP(sK19,sK20)
    | ~ ssList(sK20)
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f731]) ).

fof(f731,plain,
    ( ~ rearsegP(sK19,sK20)
    | ~ ssList(sK20)
    | nil = sK19
    | ~ ssList(sK20) ),
    inference(resolution,[],[f729,f457]) ).

fof(f457,plain,
    ! [X0] :
      ( rearsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0] :
      ( rearsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,axiom,
    ! [X0] :
      ( ssList(X0)
     => rearsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).

fof(f729,plain,
    ( ~ rearsegP(sK20,sK20)
    | ~ rearsegP(sK19,sK20)
    | ~ ssList(sK20)
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f727]) ).

fof(f727,plain,
    ( ~ rearsegP(sK19,sK20)
    | ~ rearsegP(sK20,sK20)
    | ~ ssList(sK20)
    | nil = sK19
    | nil = sK19 ),
    inference(resolution,[],[f646,f642]) ).

fof(f642,plain,
    ( neq(sK20,nil)
    | nil = sK19 ),
    inference(forward_demodulation,[],[f384,f378]) ).

fof(f384,plain,
    ( neq(sK20,nil)
    | nil = sK21 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f646,plain,
    ! [X4] :
      ( ~ neq(X4,nil)
      | ~ rearsegP(sK19,X4)
      | ~ rearsegP(sK20,X4)
      | ~ ssList(X4)
      | nil = sK19 ),
    inference(forward_demodulation,[],[f382,f379]) ).

fof(f379,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f254]) ).

fof(f382,plain,
    ! [X4] :
      ( ~ rearsegP(sK18,X4)
      | ~ rearsegP(sK19,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil = sK19 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f639,plain,
    ( rearsegP(sK19,sK20)
    | nil = sK20 ),
    inference(forward_demodulation,[],[f387,f378]) ).

fof(f387,plain,
    ( rearsegP(sK21,sK20)
    | nil = sK20 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f740,plain,
    ( neq(nil,nil)
    | nil != sK20 ),
    inference(backward_demodulation,[],[f647,f736]) ).

fof(f647,plain,
    ( nil != sK20
    | neq(sK19,nil) ),
    inference(forward_demodulation,[],[f381,f379]) ).

fof(f381,plain,
    ( neq(sK19,nil)
    | nil != sK18 ),
    inference(cnf_transformation,[],[f254]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SWC048+1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n008.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   : Fri May  3 20:35:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.22/0.36  % (10552)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.37  % (10555)WARNING: value z3 for option sas not known
% 0.22/0.38  % (10555)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)
% 0.22/0.38  % (10559)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)
% 0.22/0.38  % (10554)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38  % (10556)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38  % (10557)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)
% 0.22/0.38  % (10558)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)
% 0.22/0.38  % (10553)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39  % (10558)First to succeed.
% 0.22/0.39  TRYING [1]
% 0.22/0.39  % (10558)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10552"
% 0.22/0.39  TRYING [2]
% 0.22/0.39  % (10558)Refutation found. Thanks to Tanya!
% 0.22/0.39  % SZS status Theorem for theBenchmark
% 0.22/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39  % (10558)------------------------------
% 0.22/0.39  % (10558)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.39  % (10558)Termination reason: Refutation
% 0.22/0.39  
% 0.22/0.39  % (10558)Memory used [KB]: 1394
% 0.22/0.39  % (10558)Time elapsed: 0.015 s
% 0.22/0.39  % (10558)Instructions burned: 27 (million)
% 0.22/0.39  % (10552)Success in time 0.033 s
%------------------------------------------------------------------------------