TSTP Solution File: SWC057+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC057+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n003.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 : Sat Sep  2 12:38:48 EDT 2023

% Result   : Theorem 27.17s 4.31s
% Output   : Refutation 27.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   87 (  13 unt;   0 def)
%            Number of atoms       :  477 ( 154 equ)
%            Maximal formula atoms :   34 (   5 avg)
%            Number of connectives :  604 ( 214   ~; 221   |; 139   &)
%                                         (   8 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  125 (;  86   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f73790,plain,
    $false,
    inference(resolution,[],[f73788,f395]) ).

fof(f395,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/tmp/tmp.W8IlV0ALqE/Vampire---4.8_514',ax17) ).

fof(f73788,plain,
    ~ ssList(nil),
    inference(resolution,[],[f69653,f925]) ).

fof(f925,plain,
    ! [X0] :
      ( ~ neq(X0,X0)
      | ~ ssList(X0) ),
    inference(duplicate_literal_removal,[],[f924]) ).

fof(f924,plain,
    ! [X0] :
      ( ~ neq(X0,X0)
      | ~ ssList(X0)
      | ~ ssList(X0) ),
    inference(equality_resolution,[],[f574]) ).

fof(f574,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f354]) ).

fof(f354,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f197]) ).

fof(f197,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/sandbox/tmp/tmp.W8IlV0ALqE/Vampire---4.8_514',ax15) ).

fof(f69653,plain,
    neq(nil,nil),
    inference(trivial_inequality_removal,[],[f69238]) ).

fof(f69238,plain,
    ( nil != nil
    | neq(nil,nil) ),
    inference(backward_demodulation,[],[f35089,f66254]) ).

fof(f66254,plain,
    nil = sK20,
    inference(resolution,[],[f66252,f375]) ).

fof(f375,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f253]) ).

fof(f253,plain,
    ( ( ( frontsegP(sK21,sK20)
        & neq(sK20,nil) )
      | ( nil = sK20
        & nil = sK21 ) )
    & ( ( ! [X4] :
            ( ~ segmentP(sK18,X4)
            | ~ segmentP(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])],[f98,f252,f251,f250,f249]) ).

fof(f249,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( frontsegP(X3,X2)
                        & neq(X2,nil) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & ( ( ! [X4] :
                            ( ~ segmentP(X0,X4)
                            | ~ segmentP(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] :
                  ( ( ( frontsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ( ( ! [X4] :
                          ( ~ segmentP(sK18,X4)
                          | ~ segmentP(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(f250,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( frontsegP(X3,X2)
                    & neq(X2,nil) )
                  | ( nil = X2
                    & nil = X3 ) )
                & ( ( ! [X4] :
                        ( ~ segmentP(sK18,X4)
                        | ~ segmentP(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] :
              ( ( ( frontsegP(X3,X2)
                  & neq(X2,nil) )
                | ( nil = X2
                  & nil = X3 ) )
              & ( ( ! [X4] :
                      ( ~ segmentP(sK18,X4)
                      | ~ segmentP(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(f251,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( frontsegP(X3,X2)
                & neq(X2,nil) )
              | ( nil = X2
                & nil = X3 ) )
            & ( ( ! [X4] :
                    ( ~ segmentP(sK18,X4)
                    | ~ segmentP(sK19,X4)
                    | ~ neq(X4,nil)
                    | ~ ssList(X4) )
                & neq(sK19,nil) )
              | ( nil != sK18
                & nil = sK19 ) )
            & sK18 = X2
            & sK19 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( frontsegP(X3,sK20)
              & neq(sK20,nil) )
            | ( nil = sK20
              & nil = X3 ) )
          & ( ( ! [X4] :
                  ( ~ segmentP(sK18,X4)
                  | ~ segmentP(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(f252,plain,
    ( ? [X3] :
        ( ( ( frontsegP(X3,sK20)
            & neq(sK20,nil) )
          | ( nil = sK20
            & nil = X3 ) )
        & ( ( ! [X4] :
                ( ~ segmentP(sK18,X4)
                | ~ segmentP(sK19,X4)
                | ~ neq(X4,nil)
                | ~ ssList(X4) )
            & neq(sK19,nil) )
          | ( nil != sK18
            & nil = sK19 ) )
        & sK18 = sK20
        & sK19 = X3
        & ssList(X3) )
   => ( ( ( frontsegP(sK21,sK20)
          & neq(sK20,nil) )
        | ( nil = sK20
          & nil = sK21 ) )
      & ( ( ! [X4] :
              ( ~ segmentP(sK18,X4)
              | ~ segmentP(sK19,X4)
              | ~ neq(X4,nil)
              | ~ ssList(X4) )
          & neq(sK19,nil) )
        | ( nil != sK18
          & nil = sK19 ) )
      & sK18 = sK20
      & sK19 = sK21
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( ( ~ frontsegP(X3,X2)
                      | ~ neq(X2,nil) )
                    & ( nil != X2
                      | nil != X3 ) )
                  | ( ( ? [X4] :
                          ( segmentP(X0,X4)
                          & segmentP(X1,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      | ~ neq(X1,nil) )
                    & ( nil = X0
                      | nil != X1 ) )
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.W8IlV0ALqE/Vampire---4.8_514',co1) ).

fof(f66252,plain,
    ( ~ ssList(sK20)
    | nil = sK20 ),
    inference(duplicate_literal_removal,[],[f66241]) ).

fof(f66241,plain,
    ( nil = sK20
    | nil = sK20
    | ~ ssList(sK20) ),
    inference(resolution,[],[f35091,f555]) ).

fof(f555,plain,
    ! [X0] :
      ( ~ frontsegP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f348,plain,
    ! [X0] :
      ( ( ( frontsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ frontsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f176,plain,
    ! [X0] :
      ( ( frontsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( frontsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox/tmp/tmp.W8IlV0ALqE/Vampire---4.8_514',ax46) ).

fof(f35091,plain,
    ( frontsegP(nil,sK20)
    | nil = sK20 ),
    inference(backward_demodulation,[],[f610,f35087]) ).

fof(f35087,plain,
    nil = sK19,
    inference(resolution,[],[f35086,f395]) ).

fof(f35086,plain,
    ( ~ ssList(nil)
    | nil = sK19 ),
    inference(resolution,[],[f35085,f612]) ).

fof(f612,plain,
    ssList(sK19),
    inference(forward_demodulation,[],[f376,f377]) ).

fof(f377,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f253]) ).

fof(f376,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f253]) ).

fof(f35085,plain,
    ( ~ ssList(sK19)
    | nil = sK19
    | ~ ssList(nil) ),
    inference(resolution,[],[f35084,f375]) ).

fof(f35084,plain,
    ( ~ ssList(sK20)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f35078]) ).

fof(f35078,plain,
    ( ~ ssList(sK20)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ ssList(nil)
    | nil = sK19 ),
    inference(resolution,[],[f35077,f611]) ).

fof(f611,plain,
    ( frontsegP(sK19,sK20)
    | nil = sK19 ),
    inference(forward_demodulation,[],[f609,f377]) ).

fof(f609,plain,
    ( nil = sK19
    | frontsegP(sK21,sK20) ),
    inference(backward_demodulation,[],[f385,f377]) ).

fof(f385,plain,
    ( frontsegP(sK21,sK20)
    | nil = sK21 ),
    inference(cnf_transformation,[],[f253]) ).

fof(f35077,plain,
    ( ~ frontsegP(sK19,sK20)
    | ~ ssList(sK20)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f35076]) ).

fof(f35076,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK20)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ frontsegP(sK19,sK20)
    | ~ ssList(sK20)
    | ~ ssList(sK19) ),
    inference(resolution,[],[f35075,f583]) ).

fof(f583,plain,
    ! [X0,X1] :
      ( ssList(sK66(X0,X1))
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f367]) ).

fof(f367,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK66(X0,X1)) = X0
                & ssList(sK66(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f365,f366]) ).

fof(f366,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK66(X0,X1)) = X0
        & ssList(sK66(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f365,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,[],[f364]) ).

fof(f364,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,[],[f200]) ).

fof(f200,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/sandbox/tmp/tmp.W8IlV0ALqE/Vampire---4.8_514',ax5) ).

fof(f35075,plain,
    ( ~ ssList(sK66(sK19,sK20))
    | ~ ssList(nil)
    | ~ ssList(sK20)
    | ~ ssList(sK19)
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f35054]) ).

fof(f35054,plain,
    ( ~ ssList(sK66(sK19,sK20))
    | ~ ssList(nil)
    | ~ ssList(sK20)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ ssList(sK20)
    | nil = sK19 ),
    inference(resolution,[],[f14443,f701]) ).

fof(f701,plain,
    ( ~ segmentP(sK19,sK20)
    | ~ ssList(sK20)
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f700]) ).

fof(f700,plain,
    ( ~ segmentP(sK19,sK20)
    | ~ ssList(sK20)
    | nil = sK19
    | ~ ssList(sK20) ),
    inference(resolution,[],[f698,f456]) ).

fof(f456,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.W8IlV0ALqE/Vampire---4.8_514',ax55) ).

fof(f698,plain,
    ( ~ segmentP(sK20,sK20)
    | ~ segmentP(sK19,sK20)
    | ~ ssList(sK20)
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f696]) ).

fof(f696,plain,
    ( ~ segmentP(sK19,sK20)
    | ~ segmentP(sK20,sK20)
    | ~ ssList(sK20)
    | nil = sK19
    | nil = sK19 ),
    inference(resolution,[],[f606,f608]) ).

fof(f608,plain,
    ( neq(sK20,nil)
    | nil = sK19 ),
    inference(backward_demodulation,[],[f383,f377]) ).

fof(f383,plain,
    ( neq(sK20,nil)
    | nil = sK21 ),
    inference(cnf_transformation,[],[f253]) ).

fof(f606,plain,
    ! [X4] :
      ( ~ neq(X4,nil)
      | ~ segmentP(sK19,X4)
      | ~ segmentP(sK20,X4)
      | ~ ssList(X4)
      | nil = sK19 ),
    inference(backward_demodulation,[],[f381,f378]) ).

fof(f378,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f253]) ).

fof(f381,plain,
    ! [X4] :
      ( ~ segmentP(sK18,X4)
      | ~ segmentP(sK19,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil = sK19 ),
    inference(cnf_transformation,[],[f253]) ).

fof(f14443,plain,
    ( segmentP(sK19,sK20)
    | ~ ssList(sK66(sK19,sK20))
    | ~ ssList(nil)
    | ~ ssList(sK20)
    | ~ ssList(sK19)
    | nil = sK19 ),
    inference(superposition,[],[f14428,f1902]) ).

fof(f1902,plain,
    ( sK19 = app(sK20,sK66(sK19,sK20))
    | nil = sK19 ),
    inference(resolution,[],[f1901,f612]) ).

fof(f1901,plain,
    ( ~ ssList(sK19)
    | sK19 = app(sK20,sK66(sK19,sK20))
    | nil = sK19 ),
    inference(resolution,[],[f1813,f375]) ).

fof(f1813,plain,
    ( ~ ssList(sK20)
    | sK19 = app(sK20,sK66(sK19,sK20))
    | ~ ssList(sK19)
    | nil = sK19 ),
    inference(resolution,[],[f584,f611]) ).

fof(f584,plain,
    ! [X0,X1] :
      ( ~ frontsegP(X0,X1)
      | app(X1,sK66(X0,X1)) = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f367]) ).

fof(f14428,plain,
    ! [X0] :
      ( segmentP(app(sK20,X0),sK20)
      | ~ ssList(X0)
      | ~ ssList(nil)
      | ~ ssList(sK20)
      | ~ ssList(app(sK20,X0)) ),
    inference(equality_resolution,[],[f4643]) ).

fof(f4643,plain,
    ! [X42,X43] :
      ( app(sK20,X42) != X43
      | segmentP(X43,sK20)
      | ~ ssList(X42)
      | ~ ssList(nil)
      | ~ ssList(sK20)
      | ~ ssList(X43) ),
    inference(superposition,[],[f582,f641]) ).

fof(f641,plain,
    sK20 = app(nil,sK20),
    inference(resolution,[],[f458,f375]) ).

fof(f458,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox/tmp/tmp.W8IlV0ALqE/Vampire---4.8_514',ax28) ).

fof(f582,plain,
    ! [X2,X3,X0,X1] :
      ( app(app(X2,X1),X3) != X0
      | segmentP(X0,X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f363]) ).

fof(f363,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
                & ssList(sK65(X0,X1))
                & ssList(sK64(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f360,f362,f361]) ).

fof(f361,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK64(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK64(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f362,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK64(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
        & ssList(sK65(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f360,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f359]) ).

fof(f359,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.W8IlV0ALqE/Vampire---4.8_514',ax7) ).

fof(f610,plain,
    ( frontsegP(sK19,sK20)
    | nil = sK20 ),
    inference(backward_demodulation,[],[f386,f377]) ).

fof(f386,plain,
    ( frontsegP(sK21,sK20)
    | nil = sK20 ),
    inference(cnf_transformation,[],[f253]) ).

fof(f35089,plain,
    ( nil != sK20
    | neq(nil,nil) ),
    inference(backward_demodulation,[],[f605,f35087]) ).

fof(f605,plain,
    ( nil != sK20
    | neq(sK19,nil) ),
    inference(backward_demodulation,[],[f380,f378]) ).

fof(f380,plain,
    ( neq(sK19,nil)
    | nil != sK18 ),
    inference(cnf_transformation,[],[f253]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SWC057+1 : TPTP v8.1.2. Released v2.4.0.
% 0.16/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37  % Computer : n003.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Wed Aug 30 17:21:11 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.22/0.43  % (803)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (826)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.43  % (827)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.43  % (829)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43  % (828)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 Vampire---4 for (569ds/0Mi)
% 0.22/0.43  % (830)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 Vampire---4 for (531ds/0Mi)
% 0.22/0.43  % (831)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 Vampire---4 for (522ds/0Mi)
% 0.22/0.44  % (832)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 Vampire---4 for (497ds/0Mi)
% 0.22/0.44  TRYING [1]
% 0.22/0.44  TRYING [1]
% 0.22/0.45  TRYING [2]
% 0.22/0.45  TRYING [2]
% 0.22/0.45  TRYING [3]
% 0.22/0.46  TRYING [3]
% 0.22/0.49  TRYING [4]
% 0.22/0.49  TRYING [4]
% 0.22/0.58  TRYING [5]
% 0.22/0.59  TRYING [5]
% 2.24/0.75  TRYING [6]
% 2.24/0.76  TRYING [6]
% 4.34/1.05  TRYING [7]
% 4.34/1.10  TRYING [7]
% 6.65/1.41  TRYING [1]
% 6.65/1.41  TRYING [2]
% 7.07/1.41  TRYING [3]
% 7.07/1.43  TRYING [4]
% 7.41/1.50  TRYING [5]
% 8.02/1.57  TRYING [8]
% 8.73/1.65  TRYING [6]
% 9.48/1.85  TRYING [8]
% 10.87/1.99  TRYING [7]
% 15.55/2.63  TRYING [9]
% 15.55/2.68  TRYING [8]
% 18.28/3.00  TRYING [9]
% 25.69/4.08  TRYING [9]
% 27.17/4.30  % (831)First to succeed.
% 27.17/4.31  % (831)Refutation found. Thanks to Tanya!
% 27.17/4.31  % SZS status Theorem for Vampire---4
% 27.17/4.31  % SZS output start Proof for Vampire---4
% See solution above
% 27.17/4.31  % (831)------------------------------
% 27.17/4.31  % (831)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 27.17/4.31  % (831)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 27.17/4.31  % (831)Termination reason: Refutation
% 27.17/4.31  
% 27.17/4.31  % (831)Memory used [KB]: 74327
% 27.17/4.31  % (831)Time elapsed: 3.870 s
% 27.17/4.31  % (831)------------------------------
% 27.17/4.31  % (831)------------------------------
% 27.17/4.31  % (803)Success in time 3.93 s
% 27.17/4.31  % Vampire---4.8 exiting
%------------------------------------------------------------------------------