TSTP Solution File: SWC018+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC018+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_sat --cores 0 -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 : Wed Aug 31 18:41:14 EDT 2022

% Result   : Theorem 1.63s 0.60s
% Output   : Refutation 1.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   76 (  21 unt;   0 def)
%            Number of atoms       :  504 ( 190 equ)
%            Maximal formula atoms :   46 (   6 avg)
%            Number of connectives :  669 ( 241   ~; 218   |; 180   &)
%                                         (   6 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :  165 ( 112   !;  53   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f892,plain,
    $false,
    inference(subsumption_resolution,[],[f891,f532]) ).

fof(f532,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f891,plain,
    ~ ssList(nil),
    inference(resolution,[],[f885,f595]) ).

fof(f595,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f574]) ).

fof(f574,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f438]) ).

fof(f438,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f282]) ).

fof(f282,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f141]) ).

fof(f141,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( neq(X0,X1)
          <=> X0 != 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(f885,plain,
    neq(nil,nil),
    inference(forward_demodulation,[],[f865,f867]) ).

fof(f867,plain,
    nil = sK33,
    inference(backward_demodulation,[],[f466,f866]) ).

fof(f866,plain,
    nil = sK35,
    inference(trivial_inequality_removal,[],[f851]) ).

fof(f851,plain,
    ( nil = sK35
    | nil != nil ),
    inference(backward_demodulation,[],[f606,f846]) ).

fof(f846,plain,
    nil = sK32,
    inference(subsumption_resolution,[],[f845,f607]) ).

fof(f607,plain,
    ssList(sK32),
    inference(backward_demodulation,[],[f458,f464]) ).

fof(f464,plain,
    sK34 = sK32,
    inference(cnf_transformation,[],[f297]) ).

fof(f297,plain,
    ( ssList(sK32)
    & ( ( ! [X4] :
            ( ~ neq(X4,nil)
            | ~ frontsegP(sK32,X4)
            | ~ frontsegP(sK33,X4)
            | ~ ssList(X4) )
        & neq(sK33,nil) )
      | ( nil = sK33
        & nil != sK32 ) )
    & sK35 = sK33
    & ( nil != sK34
      | nil = sK35 )
    & sK34 = sK32
    & ssList(sK36)
    & app(sK34,sK36) = sK35
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ~ ssList(X8)
                | sK34 != app(X8,cons(X6,nil)) )
            | app(cons(X6,nil),X7) != sK36
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & equalelemsP(sK34)
    & ssList(sK35)
    & ssList(sK34)
    & ssList(sK33) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35,sK36])],[f291,f296,f295,f294,f293,f292]) ).

fof(f292,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ! [X4] :
                            ( ~ neq(X4,nil)
                            | ~ frontsegP(X0,X4)
                            | ~ frontsegP(X1,X4)
                            | ~ ssList(X4) )
                        & neq(X1,nil) )
                      | ( nil = X1
                        & nil != X0 ) )
                    & X1 = X3
                    & ( nil != X2
                      | nil = X3 )
                    & X0 = X2
                    & ? [X5] :
                        ( ssList(X5)
                        & app(X2,X5) = X3
                        & ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ~ ssList(X8)
                                    | app(X8,cons(X6,nil)) != X2 )
                                | app(cons(X6,nil),X7) != X5
                                | ~ ssList(X7) )
                            | ~ ssItem(X6) )
                        & equalelemsP(X2) )
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK32)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ~ neq(X4,nil)
                          | ~ frontsegP(sK32,X4)
                          | ~ frontsegP(X1,X4)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil = X1
                      & nil != sK32 ) )
                  & X1 = X3
                  & ( nil != X2
                    | nil = X3 )
                  & sK32 = X2
                  & ? [X5] :
                      ( ssList(X5)
                      & app(X2,X5) = X3
                      & ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ~ ssList(X8)
                                  | app(X8,cons(X6,nil)) != X2 )
                              | app(cons(X6,nil),X7) != X5
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & equalelemsP(X2) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f293,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ! [X4] :
                        ( ~ neq(X4,nil)
                        | ~ frontsegP(sK32,X4)
                        | ~ frontsegP(X1,X4)
                        | ~ ssList(X4) )
                    & neq(X1,nil) )
                  | ( nil = X1
                    & nil != sK32 ) )
                & X1 = X3
                & ( nil != X2
                  | nil = X3 )
                & sK32 = X2
                & ? [X5] :
                    ( ssList(X5)
                    & app(X2,X5) = X3
                    & ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ~ ssList(X8)
                                | app(X8,cons(X6,nil)) != X2 )
                            | app(cons(X6,nil),X7) != X5
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & equalelemsP(X2) )
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ! [X4] :
                      ( ~ neq(X4,nil)
                      | ~ frontsegP(sK32,X4)
                      | ~ frontsegP(sK33,X4)
                      | ~ ssList(X4) )
                  & neq(sK33,nil) )
                | ( nil = sK33
                  & nil != sK32 ) )
              & sK33 = X3
              & ( nil != X2
                | nil = X3 )
              & sK32 = X2
              & ? [X5] :
                  ( ssList(X5)
                  & app(X2,X5) = X3
                  & ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ~ ssList(X8)
                              | app(X8,cons(X6,nil)) != X2 )
                          | app(cons(X6,nil),X7) != X5
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & equalelemsP(X2) )
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK33) ) ),
    introduced(choice_axiom,[]) ).

fof(f294,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ! [X4] :
                    ( ~ neq(X4,nil)
                    | ~ frontsegP(sK32,X4)
                    | ~ frontsegP(sK33,X4)
                    | ~ ssList(X4) )
                & neq(sK33,nil) )
              | ( nil = sK33
                & nil != sK32 ) )
            & sK33 = X3
            & ( nil != X2
              | nil = X3 )
            & sK32 = X2
            & ? [X5] :
                ( ssList(X5)
                & app(X2,X5) = X3
                & ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ~ ssList(X8)
                            | app(X8,cons(X6,nil)) != X2 )
                        | app(cons(X6,nil),X7) != X5
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & equalelemsP(X2) )
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ! [X4] :
                  ( ~ neq(X4,nil)
                  | ~ frontsegP(sK32,X4)
                  | ~ frontsegP(sK33,X4)
                  | ~ ssList(X4) )
              & neq(sK33,nil) )
            | ( nil = sK33
              & nil != sK32 ) )
          & sK33 = X3
          & ( nil != sK34
            | nil = X3 )
          & sK34 = sK32
          & ? [X5] :
              ( ssList(X5)
              & app(sK34,X5) = X3
              & ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ~ ssList(X8)
                          | sK34 != app(X8,cons(X6,nil)) )
                      | app(cons(X6,nil),X7) != X5
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & equalelemsP(sK34) )
          & ssList(X3) )
      & ssList(sK34) ) ),
    introduced(choice_axiom,[]) ).

fof(f295,plain,
    ( ? [X3] :
        ( ( ( ! [X4] :
                ( ~ neq(X4,nil)
                | ~ frontsegP(sK32,X4)
                | ~ frontsegP(sK33,X4)
                | ~ ssList(X4) )
            & neq(sK33,nil) )
          | ( nil = sK33
            & nil != sK32 ) )
        & sK33 = X3
        & ( nil != sK34
          | nil = X3 )
        & sK34 = sK32
        & ? [X5] :
            ( ssList(X5)
            & app(sK34,X5) = X3
            & ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ~ ssList(X8)
                        | sK34 != app(X8,cons(X6,nil)) )
                    | app(cons(X6,nil),X7) != X5
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & equalelemsP(sK34) )
        & ssList(X3) )
   => ( ( ( ! [X4] :
              ( ~ neq(X4,nil)
              | ~ frontsegP(sK32,X4)
              | ~ frontsegP(sK33,X4)
              | ~ ssList(X4) )
          & neq(sK33,nil) )
        | ( nil = sK33
          & nil != sK32 ) )
      & sK35 = sK33
      & ( nil != sK34
        | nil = sK35 )
      & sK34 = sK32
      & ? [X5] :
          ( ssList(X5)
          & app(sK34,X5) = sK35
          & ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ~ ssList(X8)
                      | sK34 != app(X8,cons(X6,nil)) )
                  | app(cons(X6,nil),X7) != X5
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & equalelemsP(sK34) )
      & ssList(sK35) ) ),
    introduced(choice_axiom,[]) ).

fof(f296,plain,
    ( ? [X5] :
        ( ssList(X5)
        & app(sK34,X5) = sK35
        & ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ ssList(X8)
                    | sK34 != app(X8,cons(X6,nil)) )
                | app(cons(X6,nil),X7) != X5
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & equalelemsP(sK34) )
   => ( ssList(sK36)
      & app(sK34,sK36) = sK35
      & ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ~ ssList(X8)
                  | sK34 != app(X8,cons(X6,nil)) )
              | app(cons(X6,nil),X7) != sK36
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & equalelemsP(sK34) ) ),
    introduced(choice_axiom,[]) ).

fof(f291,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ~ neq(X4,nil)
                          | ~ frontsegP(X0,X4)
                          | ~ frontsegP(X1,X4)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil = X1
                      & nil != X0 ) )
                  & X1 = X3
                  & ( nil != X2
                    | nil = X3 )
                  & X0 = X2
                  & ? [X5] :
                      ( ssList(X5)
                      & app(X2,X5) = X3
                      & ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ~ ssList(X8)
                                  | app(X8,cons(X6,nil)) != X2 )
                              | app(cons(X6,nil),X7) != X5
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & equalelemsP(X2) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(rectify,[],[f110]) ).

fof(f110,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X8] :
                          ( ~ neq(X8,nil)
                          | ~ frontsegP(X0,X8)
                          | ~ frontsegP(X1,X8)
                          | ~ ssList(X8) )
                      & neq(X1,nil) )
                    | ( nil = X1
                      & nil != X0 ) )
                  & X1 = X3
                  & ( nil != X2
                    | nil = X3 )
                  & X0 = X2
                  & ? [X4] :
                      ( ssList(X4)
                      & app(X2,X4) = X3
                      & ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(X7,cons(X5,nil)) != X2 )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & equalelemsP(X2) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(flattening,[],[f109]) ).

fof(f109,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(X7,cons(X5,nil)) != X2 )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & app(X2,X4) = X3
                      & equalelemsP(X2)
                      & ssList(X4) )
                  & X0 = X2
                  & ( ( ! [X8] :
                          ( ~ neq(X8,nil)
                          | ~ frontsegP(X0,X8)
                          | ~ frontsegP(X1,X8)
                          | ~ ssList(X8) )
                      & neq(X1,nil) )
                    | ( nil = X1
                      & nil != X0 ) )
                  & 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)
                   => ( ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ( ? [X5] :
                                ( ? [X6] :
                                    ( ? [X7] :
                                        ( ssList(X7)
                                        & app(X7,cons(X5,nil)) = X2 )
                                    & ssList(X6)
                                    & app(cons(X5,nil),X6) = X4 )
                                & ssItem(X5) )
                            | app(X2,X4) != X3
                            | ~ equalelemsP(X2) ) )
                      | X0 != X2
                      | ( ( ? [X8] :
                              ( ssList(X8)
                              & frontsegP(X0,X8)
                              & frontsegP(X1,X8)
                              & neq(X8,nil) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ( ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( ssList(X7)
                                      & app(X7,cons(X5,nil)) = X2 )
                                  & ssList(X6)
                                  & app(cons(X5,nil),X6) = X4 )
                              & ssItem(X5) )
                          | app(X2,X4) != X3
                          | ~ equalelemsP(X2) ) )
                    | X0 != X2
                    | ( ( ? [X8] :
                            ( ssList(X8)
                            & frontsegP(X0,X8)
                            & frontsegP(X1,X8)
                            & neq(X8,nil) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f458,plain,
    ssList(sK34),
    inference(cnf_transformation,[],[f297]) ).

fof(f845,plain,
    ( ~ ssList(sK32)
    | nil = sK32 ),
    inference(duplicate_literal_removal,[],[f844]) ).

fof(f844,plain,
    ( ~ ssList(sK32)
    | nil = sK32
    | nil = sK32 ),
    inference(resolution,[],[f839,f562]) ).

fof(f562,plain,
    ! [X0] :
      ( ~ frontsegP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f349,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( frontsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ frontsegP(nil,X0) ) ) ),
    inference(nnf_transformation,[],[f210]) ).

fof(f210,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( frontsegP(nil,X0)
      <=> nil = X0 ) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( frontsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).

fof(f839,plain,
    ( frontsegP(nil,sK32)
    | nil = sK32 ),
    inference(superposition,[],[f722,f830]) ).

fof(f830,plain,
    ( nil = sK33
    | nil = sK32 ),
    inference(subsumption_resolution,[],[f829,f607]) ).

fof(f829,plain,
    ( ~ ssList(sK32)
    | nil = sK33
    | nil = sK32 ),
    inference(resolution,[],[f826,f424]) ).

fof(f424,plain,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | frontsegP(X0,X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).

fof(f826,plain,
    ( ~ frontsegP(sK32,sK32)
    | nil = sK33
    | nil = sK32 ),
    inference(subsumption_resolution,[],[f825,f607]) ).

fof(f825,plain,
    ( nil = sK32
    | nil = sK33
    | ~ frontsegP(sK32,sK32)
    | ~ ssList(sK32) ),
    inference(subsumption_resolution,[],[f822,f532]) ).

fof(f822,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK32)
    | nil = sK33
    | ~ frontsegP(sK32,sK32)
    | nil = sK32 ),
    inference(resolution,[],[f439,f724]) ).

fof(f724,plain,
    ( ~ neq(sK32,nil)
    | nil = sK33
    | ~ frontsegP(sK32,sK32) ),
    inference(subsumption_resolution,[],[f723,f607]) ).

fof(f723,plain,
    ( ~ ssList(sK32)
    | ~ neq(sK32,nil)
    | nil = sK33
    | ~ frontsegP(sK32,sK32) ),
    inference(resolution,[],[f722,f470]) ).

fof(f470,plain,
    ! [X4] :
      ( ~ frontsegP(sK33,X4)
      | ~ neq(X4,nil)
      | ~ frontsegP(sK32,X4)
      | ~ ssList(X4)
      | nil = sK33 ),
    inference(cnf_transformation,[],[f297]) ).

fof(f439,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X0)
      | X0 = X1
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f282]) ).

fof(f722,plain,
    frontsegP(sK33,sK32),
    inference(subsumption_resolution,[],[f721,f607]) ).

fof(f721,plain,
    ( ~ ssList(sK32)
    | frontsegP(sK33,sK32) ),
    inference(subsumption_resolution,[],[f716,f463]) ).

fof(f463,plain,
    ssList(sK36),
    inference(cnf_transformation,[],[f297]) ).

fof(f716,plain,
    ( ~ ssList(sK36)
    | ~ ssList(sK32)
    | frontsegP(sK33,sK32) ),
    inference(superposition,[],[f605,f609]) ).

fof(f609,plain,
    app(sK32,sK36) = sK33,
    inference(backward_demodulation,[],[f602,f464]) ).

fof(f602,plain,
    app(sK34,sK36) = sK33,
    inference(backward_demodulation,[],[f600,f466]) ).

fof(f600,plain,
    app(sK34,sK36) = sK35,
    inference(forward_demodulation,[],[f591,f592]) ).

fof(f592,plain,
    sF58 = sK35,
    inference(definition_folding,[],[f462,f591]) ).

fof(f462,plain,
    app(sK34,sK36) = sK35,
    inference(cnf_transformation,[],[f297]) ).

fof(f591,plain,
    app(sK34,sK36) = sF58,
    introduced(function_definition,[]) ).

fof(f605,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1) ),
    inference(subsumption_resolution,[],[f582,f456]) ).

fof(f456,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X0)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f194,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ssList(app(X0,X1)) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f582,plain,
    ! [X2,X1] :
      ( ~ ssList(app(X1,X2))
      | ~ ssList(X2)
      | frontsegP(app(X1,X2),X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f514]) ).

fof(f514,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f321]) ).

fof(f321,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK46(X0,X1)) = X0
                & ssList(sK46(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f319,f320]) ).

fof(f320,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK46(X0,X1)) = X0
        & ssList(sK46(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f319,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X1,X3) = X0
                  & ssList(X3) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f318]) ).

fof(f318,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

fof(f606,plain,
    ( nil != sK32
    | nil = sK35 ),
    inference(backward_demodulation,[],[f465,f464]) ).

fof(f465,plain,
    ( nil != sK34
    | nil = sK35 ),
    inference(cnf_transformation,[],[f297]) ).

fof(f466,plain,
    sK35 = sK33,
    inference(cnf_transformation,[],[f297]) ).

fof(f865,plain,
    neq(sK33,nil),
    inference(trivial_inequality_removal,[],[f848]) ).

fof(f848,plain,
    ( neq(sK33,nil)
    | nil != nil ),
    inference(backward_demodulation,[],[f467,f846]) ).

fof(f467,plain,
    ( neq(sK33,nil)
    | nil != sK32 ),
    inference(cnf_transformation,[],[f297]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC018+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 18:05:49 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.52  % (26084)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.53  % (26084)Instruction limit reached!
% 0.20/0.53  % (26084)------------------------------
% 0.20/0.53  % (26084)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (26084)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (26084)Termination reason: Unknown
% 0.20/0.53  % (26084)Termination phase: Preprocessing 2
% 0.20/0.53  
% 0.20/0.53  % (26084)Memory used [KB]: 1023
% 0.20/0.53  % (26084)Time elapsed: 0.004 s
% 0.20/0.53  % (26084)Instructions burned: 2 (million)
% 0.20/0.53  % (26084)------------------------------
% 0.20/0.53  % (26084)------------------------------
% 0.20/0.53  % (26092)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53  % (26099)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.53  % (26100)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.53  % (26083)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.54  % (26083)Instruction limit reached!
% 0.20/0.54  % (26083)------------------------------
% 0.20/0.54  % (26083)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (26083)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (26083)Termination reason: Unknown
% 0.20/0.54  % (26083)Termination phase: Property scanning
% 0.20/0.54  
% 0.20/0.54  % (26083)Memory used [KB]: 1279
% 0.20/0.54  % (26083)Time elapsed: 0.004 s
% 0.20/0.54  % (26083)Instructions burned: 7 (million)
% 0.20/0.54  % (26083)------------------------------
% 0.20/0.54  % (26083)------------------------------
% 0.20/0.54  % (26093)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.54  % (26091)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.54  % (26085)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.48/0.55  % (26081)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.48/0.55  % (26078)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.48/0.55  % (26090)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.48/0.55  % (26101)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.48/0.55  % (26089)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.48/0.55  % (26079)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.48/0.56  % (26097)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.48/0.56  % (26102)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.48/0.56  % (26076)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.48/0.56  % (26087)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)
% 1.48/0.56  % (26086)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.48/0.56  % (26082)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.63/0.57  % (26094)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.63/0.57  % (26077)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.63/0.57  % (26095)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)
% 1.63/0.58  % (26098)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.63/0.58  % (26103)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)
% 1.63/0.58  % (26105)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.63/0.59  TRYING [1]
% 1.63/0.59  % (26077)Refutation not found, incomplete strategy% (26077)------------------------------
% 1.63/0.59  % (26077)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.63/0.59  % (26077)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.63/0.59  % (26077)Termination reason: Refutation not found, incomplete strategy
% 1.63/0.59  
% 1.63/0.59  % (26077)Memory used [KB]: 6140
% 1.63/0.59  % (26077)Time elapsed: 0.142 s
% 1.63/0.59  % (26077)Instructions burned: 22 (million)
% 1.63/0.59  % (26077)------------------------------
% 1.63/0.59  % (26077)------------------------------
% 1.63/0.60  % (26078)Instruction limit reached!
% 1.63/0.60  % (26078)------------------------------
% 1.63/0.60  % (26078)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.63/0.60  TRYING [2]
% 1.63/0.60  % (26104)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.63/0.60  % (26091)First to succeed.
% 1.63/0.60  % (26080)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.63/0.60  % (26091)Refutation found. Thanks to Tanya!
% 1.63/0.60  % SZS status Theorem for theBenchmark
% 1.63/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.63/0.60  % (26091)------------------------------
% 1.63/0.60  % (26091)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.63/0.60  % (26091)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.63/0.60  % (26091)Termination reason: Refutation
% 1.63/0.60  
% 1.63/0.60  % (26091)Memory used [KB]: 1663
% 1.63/0.60  % (26091)Time elapsed: 0.174 s
% 1.63/0.60  % (26091)Instructions burned: 32 (million)
% 1.63/0.60  % (26091)------------------------------
% 1.63/0.60  % (26091)------------------------------
% 1.63/0.60  % (26075)Success in time 0.247 s
%------------------------------------------------------------------------------