TSTP Solution File: SWC036+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC036+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 : 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 : Sun May  5 09:52:21 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   74 (  53 unt;   0 def)
%            Number of atoms       :  195 (  90 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  162 (  41   ~;  21   |;  78   &)
%                                         (  10 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   21 (  19 usr;  11 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   32 (   8   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f812,plain,
    $false,
    inference(avatar_sat_refutation,[],[f765,f770,f775,f780,f785,f790,f795,f800,f805,f810,f811]) ).

fof(f811,plain,
    spl69_10,
    inference(avatar_split_clause,[],[f697,f807]) ).

fof(f807,plain,
    ( spl69_10
  <=> sK20 = sK21 ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_10])]) ).

fof(f697,plain,
    sK20 = sK21,
    inference(trivial_inequality_removal,[],[f601]) ).

fof(f601,plain,
    ( sK21 != sK21
    | sK20 = sK21 ),
    inference(definition_unfolding,[],[f382,f600,f600]) ).

fof(f600,plain,
    nil = sK21,
    inference(definition_unfolding,[],[f378,f379]) ).

fof(f379,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ( ( nil != sK21
      | nil = sK20 )
    & nil != sK18
    & sK18 = sK20
    & sK19 = sK21
    & nil = sK19
    & 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] :
                    ( ( nil != X3
                      | nil = X2 )
                    & nil != X0
                    & X0 = X2
                    & X1 = X3
                    & nil = X1
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & nil != sK18
                  & sK18 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

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

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

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

fof(f382,plain,
    ( nil != sK21
    | nil = sK20 ),
    inference(cnf_transformation,[],[f254]) ).

fof(f810,plain,
    ~ spl69_10,
    inference(avatar_split_clause,[],[f602,f807]) ).

fof(f602,plain,
    sK20 != sK21,
    inference(definition_unfolding,[],[f381,f600,f380]) ).

fof(f380,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f254]) ).

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

fof(f805,plain,
    spl69_9,
    inference(avatar_split_clause,[],[f707,f802]) ).

fof(f802,plain,
    ( spl69_9
  <=> totalorderedP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_9])]) ).

fof(f707,plain,
    totalorderedP(sK20),
    inference(forward_demodulation,[],[f612,f697]) ).

fof(f612,plain,
    totalorderedP(sK21),
    inference(definition_unfolding,[],[f390,f600]) ).

fof(f390,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).

fof(f800,plain,
    spl69_8,
    inference(avatar_split_clause,[],[f706,f797]) ).

fof(f797,plain,
    ( spl69_8
  <=> strictorderedP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_8])]) ).

fof(f706,plain,
    strictorderedP(sK20),
    inference(forward_demodulation,[],[f611,f697]) ).

fof(f611,plain,
    strictorderedP(sK21),
    inference(definition_unfolding,[],[f389,f600]) ).

fof(f389,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f69]) ).

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

fof(f795,plain,
    spl69_7,
    inference(avatar_split_clause,[],[f705,f792]) ).

fof(f792,plain,
    ( spl69_7
  <=> totalorderP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_7])]) ).

fof(f705,plain,
    totalorderP(sK20),
    inference(forward_demodulation,[],[f610,f697]) ).

fof(f610,plain,
    totalorderP(sK21),
    inference(definition_unfolding,[],[f388,f600]) ).

fof(f388,plain,
    totalorderP(nil),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    totalorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).

fof(f790,plain,
    spl69_6,
    inference(avatar_split_clause,[],[f704,f787]) ).

fof(f787,plain,
    ( spl69_6
  <=> strictorderP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_6])]) ).

fof(f704,plain,
    strictorderP(sK20),
    inference(forward_demodulation,[],[f609,f697]) ).

fof(f609,plain,
    strictorderP(sK21),
    inference(definition_unfolding,[],[f387,f600]) ).

fof(f387,plain,
    strictorderP(nil),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    strictorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).

fof(f785,plain,
    spl69_5,
    inference(avatar_split_clause,[],[f703,f782]) ).

fof(f782,plain,
    ( spl69_5
  <=> cyclefreeP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_5])]) ).

fof(f703,plain,
    cyclefreeP(sK20),
    inference(forward_demodulation,[],[f608,f697]) ).

fof(f608,plain,
    cyclefreeP(sK21),
    inference(definition_unfolding,[],[f386,f600]) ).

fof(f386,plain,
    cyclefreeP(nil),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    cyclefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).

fof(f780,plain,
    spl69_4,
    inference(avatar_split_clause,[],[f702,f777]) ).

fof(f777,plain,
    ( spl69_4
  <=> duplicatefreeP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_4])]) ).

fof(f702,plain,
    duplicatefreeP(sK20),
    inference(forward_demodulation,[],[f607,f697]) ).

fof(f607,plain,
    duplicatefreeP(sK21),
    inference(definition_unfolding,[],[f385,f600]) ).

fof(f385,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).

fof(f775,plain,
    spl69_3,
    inference(avatar_split_clause,[],[f701,f772]) ).

fof(f772,plain,
    ( spl69_3
  <=> equalelemsP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_3])]) ).

fof(f701,plain,
    equalelemsP(sK20),
    inference(forward_demodulation,[],[f606,f697]) ).

fof(f606,plain,
    equalelemsP(sK21),
    inference(definition_unfolding,[],[f384,f600]) ).

fof(f384,plain,
    equalelemsP(nil),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,axiom,
    equalelemsP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).

fof(f770,plain,
    ~ spl69_2,
    inference(avatar_split_clause,[],[f700,f767]) ).

fof(f767,plain,
    ( spl69_2
  <=> singletonP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_2])]) ).

fof(f700,plain,
    ~ singletonP(sK20),
    inference(forward_demodulation,[],[f605,f697]) ).

fof(f605,plain,
    ~ singletonP(sK21),
    inference(definition_unfolding,[],[f383,f600]) ).

fof(f383,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f765,plain,
    spl69_1,
    inference(avatar_split_clause,[],[f698,f762]) ).

fof(f762,plain,
    ( spl69_1
  <=> ssList(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_1])]) ).

fof(f698,plain,
    ssList(sK20),
    inference(forward_demodulation,[],[f377,f697]) ).

fof(f377,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f254]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWC036+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 20:31:08 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (5813)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (5818)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)
% 0.14/0.38  % (5816)WARNING: value z3 for option sas not known
% 0.14/0.38  % (5815)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (5817)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (5816)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)
% 0.14/0.38  % (5814)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (5819)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)
% 0.14/0.38  % (5820)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)
% 0.14/0.39  % (5818)First to succeed.
% 0.14/0.39  % (5818)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5813"
% 0.14/0.39  % (5818)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (5818)------------------------------
% 0.14/0.39  % (5818)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (5818)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (5818)Memory used [KB]: 1256
% 0.14/0.39  % (5818)Time elapsed: 0.012 s
% 0.14/0.39  % (5818)Instructions burned: 19 (million)
% 0.14/0.39  % (5813)Success in time 0.019 s
%------------------------------------------------------------------------------