TSTP Solution File: SWW629_2 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWW629_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n015.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 : Fri Sep  1 00:39:58 EDT 2023

% Result   : Theorem 27.09s 4.21s
% Output   : CNFRefutation 27.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   45 (  11 unt;   0 typ;   0 def)
%            Number of atoms       : 1910 ( 194 equ)
%            Maximal formula atoms :   50 (  42 avg)
%            Number of connectives :  578 (  98   ~;  89   |; 334   &)
%                                         (   5 <=>;  52  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   9 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       : 1385 (1385 fml;   0 var)
%            Number arithmetic     :   68 (  10 atm;  16 fun;  42 num;   0 var)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   26 (  23 usr;  17 prp; 0-3 aty)
%            Number of functors    :    3 (   0 usr;   2 con; 0-2 aty)
%            Number of variables   :  211 (   0 sgn;  75   !; 118   ?; 193   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f45,axiom,
    ! [X0: ty,X14: uni,X13: uni,X15: uni] :
      ( permut(X0,X14,X13)
     => ( permut(X0,X13,X15)
       => permut(X0,X14,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_trans) ).

tff(f50,axiom,
    ! [X0: ty,X14: uni,X13: uni,X16: uni,X17: uni] :
      ( permut(X0,X14,X16)
     => ( permut(X0,X13,X17)
       => permut(X0,infix_plpl(X0,X14,X13),infix_plpl(X0,X16,X17)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_append) ).

tff(f74,conjecture,
    ! [X18: list_elt] :
      ( $less(1,length2(elt,t2tb(X18)))
     => ! [X21: list_elt] :
          ( ( tb2t(nil(elt)) = X21 )
         => ! [X22: list_elt] :
              ( ( tb2t(nil(elt)) = X22 )
             => ! [X23: list_elt,X24: list_elt,X25: list_elt] :
                  ( ( ( ( ( length2(elt,t2tb(X24)) = $sum(length2(elt,t2tb(X23)),1) )
                        & ( 0 = length2(elt,t2tb(X25)) ) )
                      | ( length2(elt,t2tb(X24)) = length2(elt,t2tb(X23)) ) )
                    & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X25)),t2tb(X18)) )
                 => ! [X26: bool1] :
                      ( ( ( true1 = X26 )
                      <=> ( tb2t(nil(elt)) = X25 ) )
                     => ( ( true1 = X26 )
                       => ( ( tb2t(nil(elt)) = X25 )
                         => ( permut(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X18))
                           => ! [X27: list_elt] :
                                ( ( permut(elt,t2tb(X27),t2tb(X24))
                                  & sorted1(X27) )
                               => ! [X28: list_elt] :
                                    ( ( permut(elt,t2tb(X28),t2tb(X23))
                                      & sorted1(X28) )
                                   => ( ( sorted1(X28)
                                        & sorted1(X27)
                                        & ( tb2t(nil(elt)) = X25 ) )
                                     => ! [X29: list_elt] :
                                          ( ( permut(elt,t2tb(X29),infix_plpl(elt,t2tb(X27),t2tb(X28)))
                                            & sorted1(X29) )
                                         => ( permut(elt,t2tb(X29),t2tb(X18))
                                            & sorted1(X29) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_mergesort) ).

tff(f75,negated_conjecture,
    ~ ! [X18: list_elt] :
        ( $less(1,length2(elt,t2tb(X18)))
       => ! [X21: list_elt] :
            ( ( tb2t(nil(elt)) = X21 )
           => ! [X22: list_elt] :
                ( ( tb2t(nil(elt)) = X22 )
               => ! [X23: list_elt,X24: list_elt,X25: list_elt] :
                    ( ( ( ( ( length2(elt,t2tb(X24)) = $sum(length2(elt,t2tb(X23)),1) )
                          & ( 0 = length2(elt,t2tb(X25)) ) )
                        | ( length2(elt,t2tb(X24)) = length2(elt,t2tb(X23)) ) )
                      & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X25)),t2tb(X18)) )
                   => ! [X26: bool1] :
                        ( ( ( true1 = X26 )
                        <=> ( tb2t(nil(elt)) = X25 ) )
                       => ( ( true1 = X26 )
                         => ( ( tb2t(nil(elt)) = X25 )
                           => ( permut(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X18))
                             => ! [X27: list_elt] :
                                  ( ( permut(elt,t2tb(X27),t2tb(X24))
                                    & sorted1(X27) )
                                 => ! [X28: list_elt] :
                                      ( ( permut(elt,t2tb(X28),t2tb(X23))
                                        & sorted1(X28) )
                                     => ( ( sorted1(X28)
                                          & sorted1(X27)
                                          & ( tb2t(nil(elt)) = X25 ) )
                                       => ! [X29: list_elt] :
                                            ( ( permut(elt,t2tb(X29),infix_plpl(elt,t2tb(X27),t2tb(X28)))
                                              & sorted1(X29) )
                                           => ( permut(elt,t2tb(X29),t2tb(X18))
                                              & sorted1(X29) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f74]) ).

tff(f127,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni] :
      ( permut(X0,X1,X2)
     => ( permut(X0,X2,X3)
       => permut(X0,X1,X3) ) ),
    inference(rectify,[],[f45]) ).

tff(f132,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
      ( permut(X0,X1,X3)
     => ( permut(X0,X2,X4)
       => permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4)) ) ),
    inference(rectify,[],[f50]) ).

tff(f153,plain,
    ~ ! [X0: list_elt] :
        ( $less(1,length2(elt,t2tb(X0)))
       => ! [X1: list_elt] :
            ( ( tb2t(nil(elt)) = X1 )
           => ! [X2: list_elt] :
                ( ( tb2t(nil(elt)) = X2 )
               => ! [X3: list_elt,X4: list_elt,X5: list_elt] :
                    ( ( ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                          & ( 0 = length2(elt,t2tb(X5)) ) )
                        | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
                      & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
                   => ! [X6: bool1] :
                        ( ( ( true1 = X6 )
                        <=> ( tb2t(nil(elt)) = X5 ) )
                       => ( ( true1 = X6 )
                         => ( ( tb2t(nil(elt)) = X5 )
                           => ( permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
                             => ! [X7: list_elt] :
                                  ( ( permut(elt,t2tb(X7),t2tb(X4))
                                    & sorted1(X7) )
                                 => ! [X8: list_elt] :
                                      ( ( permut(elt,t2tb(X8),t2tb(X3))
                                        & sorted1(X8) )
                                     => ( ( sorted1(X8)
                                          & sorted1(X7)
                                          & ( tb2t(nil(elt)) = X5 ) )
                                       => ! [X9: list_elt] :
                                            ( ( permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                                              & sorted1(X9) )
                                           => ( permut(elt,t2tb(X9),t2tb(X0))
                                              & sorted1(X9) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f75]) ).

tff(f166,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni] :
      ( permut(X0,X1,X3)
      | ~ permut(X0,X2,X3)
      | ~ permut(X0,X1,X2) ),
    inference(ennf_transformation,[],[f127]) ).

tff(f167,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni] :
      ( permut(X0,X1,X3)
      | ~ permut(X0,X2,X3)
      | ~ permut(X0,X1,X2) ),
    inference(flattening,[],[f166]) ).

tff(f169,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
      ( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
      | ~ permut(X0,X2,X4)
      | ~ permut(X0,X1,X3) ),
    inference(ennf_transformation,[],[f132]) ).

tff(f170,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
      ( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
      | ~ permut(X0,X2,X4)
      | ~ permut(X0,X1,X3) ),
    inference(flattening,[],[f169]) ).

tff(f184,plain,
    ? [X0: list_elt] :
      ( ? [X1: list_elt] :
          ( ? [X2: list_elt] :
              ( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
                  ( ? [X6: bool1] :
                      ( ? [X7: list_elt] :
                          ( ? [X8: list_elt] :
                              ( ? [X9: list_elt] :
                                  ( ( ~ permut(elt,t2tb(X9),t2tb(X0))
                                    | ~ sorted1(X9) )
                                  & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                                  & sorted1(X9) )
                              & sorted1(X8)
                              & sorted1(X7)
                              & ( tb2t(nil(elt)) = X5 )
                              & permut(elt,t2tb(X8),t2tb(X3))
                              & sorted1(X8) )
                          & permut(elt,t2tb(X7),t2tb(X4))
                          & sorted1(X7) )
                      & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
                      & ( tb2t(nil(elt)) = X5 )
                      & ( true1 = X6 )
                      & ( ( true1 = X6 )
                      <=> ( tb2t(nil(elt)) = X5 ) ) )
                  & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                      & ( 0 = length2(elt,t2tb(X5)) ) )
                    | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
                  & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
              & ( tb2t(nil(elt)) = X2 ) )
          & ( tb2t(nil(elt)) = X1 ) )
      & $less(1,length2(elt,t2tb(X0))) ),
    inference(ennf_transformation,[],[f153]) ).

tff(f185,plain,
    ? [X0: list_elt] :
      ( ? [X1: list_elt] :
          ( ? [X2: list_elt] :
              ( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
                  ( ? [X6: bool1] :
                      ( ? [X7: list_elt] :
                          ( ? [X8: list_elt] :
                              ( ? [X9: list_elt] :
                                  ( ( ~ permut(elt,t2tb(X9),t2tb(X0))
                                    | ~ sorted1(X9) )
                                  & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                                  & sorted1(X9) )
                              & sorted1(X8)
                              & sorted1(X7)
                              & ( tb2t(nil(elt)) = X5 )
                              & permut(elt,t2tb(X8),t2tb(X3))
                              & sorted1(X8) )
                          & permut(elt,t2tb(X7),t2tb(X4))
                          & sorted1(X7) )
                      & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
                      & ( tb2t(nil(elt)) = X5 )
                      & ( true1 = X6 )
                      & ( ( true1 = X6 )
                      <=> ( tb2t(nil(elt)) = X5 ) ) )
                  & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                      & ( 0 = length2(elt,t2tb(X5)) ) )
                    | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
                  & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
              & ( tb2t(nil(elt)) = X2 ) )
          & ( tb2t(nil(elt)) = X1 ) )
      & $less(1,length2(elt,t2tb(X0))) ),
    inference(flattening,[],[f184]) ).

tff(f210,plain,
    ? [X0: list_elt] :
      ( ? [X1: list_elt] :
          ( ? [X2: list_elt] :
              ( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
                  ( ? [X6: bool1] :
                      ( ? [X7: list_elt] :
                          ( ? [X8: list_elt] :
                              ( ? [X9: list_elt] :
                                  ( ( ~ permut(elt,t2tb(X9),t2tb(X0))
                                    | ~ sorted1(X9) )
                                  & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                                  & sorted1(X9) )
                              & sorted1(X8)
                              & sorted1(X7)
                              & ( tb2t(nil(elt)) = X5 )
                              & permut(elt,t2tb(X8),t2tb(X3))
                              & sorted1(X8) )
                          & permut(elt,t2tb(X7),t2tb(X4))
                          & sorted1(X7) )
                      & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
                      & ( tb2t(nil(elt)) = X5 )
                      & ( true1 = X6 )
                      & ( ( true1 = X6 )
                        | ( tb2t(nil(elt)) != X5 ) )
                      & ( ( tb2t(nil(elt)) = X5 )
                        | ( true1 != X6 ) ) )
                  & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                      & ( 0 = length2(elt,t2tb(X5)) ) )
                    | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
                  & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
              & ( tb2t(nil(elt)) = X2 ) )
          & ( tb2t(nil(elt)) = X1 ) )
      & $less(1,length2(elt,t2tb(X0))) ),
    inference(nnf_transformation,[],[f185]) ).

tff(f211,plain,
    ? [X0: list_elt] :
      ( ? [X1: list_elt] :
          ( ? [X2: list_elt] :
              ( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
                  ( ? [X6: bool1] :
                      ( ? [X7: list_elt] :
                          ( ? [X8: list_elt] :
                              ( ? [X9: list_elt] :
                                  ( ( ~ permut(elt,t2tb(X9),t2tb(X0))
                                    | ~ sorted1(X9) )
                                  & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                                  & sorted1(X9) )
                              & sorted1(X8)
                              & sorted1(X7)
                              & ( tb2t(nil(elt)) = X5 )
                              & permut(elt,t2tb(X8),t2tb(X3))
                              & sorted1(X8) )
                          & permut(elt,t2tb(X7),t2tb(X4))
                          & sorted1(X7) )
                      & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
                      & ( tb2t(nil(elt)) = X5 )
                      & ( true1 = X6 )
                      & ( ( true1 = X6 )
                        | ( tb2t(nil(elt)) != X5 ) )
                      & ( ( tb2t(nil(elt)) = X5 )
                        | ( true1 != X6 ) ) )
                  & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                      & ( 0 = length2(elt,t2tb(X5)) ) )
                    | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
                  & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
              & ( tb2t(nil(elt)) = X2 ) )
          & ( tb2t(nil(elt)) = X1 ) )
      & $less(1,length2(elt,t2tb(X0))) ),
    inference(flattening,[],[f210]) ).

tff(f212,plain,
    ( ? [X0: list_elt] :
        ( ? [X1: list_elt] :
            ( ? [X2: list_elt] :
                ( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
                    ( ? [X6: bool1] :
                        ( ? [X7: list_elt] :
                            ( ? [X8: list_elt] :
                                ( ? [X9: list_elt] :
                                    ( ( ~ permut(elt,t2tb(X9),t2tb(X0))
                                      | ~ sorted1(X9) )
                                    & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                                    & sorted1(X9) )
                                & sorted1(X8)
                                & sorted1(X7)
                                & ( tb2t(nil(elt)) = X5 )
                                & permut(elt,t2tb(X8),t2tb(X3))
                                & sorted1(X8) )
                            & permut(elt,t2tb(X7),t2tb(X4))
                            & sorted1(X7) )
                        & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
                        & ( tb2t(nil(elt)) = X5 )
                        & ( true1 = X6 )
                        & ( ( true1 = X6 )
                          | ( tb2t(nil(elt)) != X5 ) )
                        & ( ( tb2t(nil(elt)) = X5 )
                          | ( true1 != X6 ) ) )
                    & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                        & ( 0 = length2(elt,t2tb(X5)) ) )
                      | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
                    & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
                & ( tb2t(nil(elt)) = X2 ) )
            & ( tb2t(nil(elt)) = X1 ) )
        & $less(1,length2(elt,t2tb(X0))) )
   => ( ? [X1: list_elt] :
          ( ? [X2: list_elt] :
              ( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
                  ( ? [X6: bool1] :
                      ( ? [X7: list_elt] :
                          ( ? [X8: list_elt] :
                              ( ? [X9: list_elt] :
                                  ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                                    | ~ sorted1(X9) )
                                  & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                                  & sorted1(X9) )
                              & sorted1(X8)
                              & sorted1(X7)
                              & ( tb2t(nil(elt)) = X5 )
                              & permut(elt,t2tb(X8),t2tb(X3))
                              & sorted1(X8) )
                          & permut(elt,t2tb(X7),t2tb(X4))
                          & sorted1(X7) )
                      & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
                      & ( tb2t(nil(elt)) = X5 )
                      & ( true1 = X6 )
                      & ( ( true1 = X6 )
                        | ( tb2t(nil(elt)) != X5 ) )
                      & ( ( tb2t(nil(elt)) = X5 )
                        | ( true1 != X6 ) ) )
                  & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                      & ( 0 = length2(elt,t2tb(X5)) ) )
                    | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
                  & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
              & ( tb2t(nil(elt)) = X2 ) )
          & ( tb2t(nil(elt)) = X1 ) )
      & $less(1,length2(elt,t2tb(sK10))) ) ),
    introduced(choice_axiom,[]) ).

tff(f213,plain,
    ( ? [X1: list_elt] :
        ( ? [X2: list_elt] :
            ( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
                ( ? [X6: bool1] :
                    ( ? [X7: list_elt] :
                        ( ? [X8: list_elt] :
                            ( ? [X9: list_elt] :
                                ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                                  | ~ sorted1(X9) )
                                & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                                & sorted1(X9) )
                            & sorted1(X8)
                            & sorted1(X7)
                            & ( tb2t(nil(elt)) = X5 )
                            & permut(elt,t2tb(X8),t2tb(X3))
                            & sorted1(X8) )
                        & permut(elt,t2tb(X7),t2tb(X4))
                        & sorted1(X7) )
                    & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
                    & ( tb2t(nil(elt)) = X5 )
                    & ( true1 = X6 )
                    & ( ( true1 = X6 )
                      | ( tb2t(nil(elt)) != X5 ) )
                    & ( ( tb2t(nil(elt)) = X5 )
                      | ( true1 != X6 ) ) )
                & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                    & ( 0 = length2(elt,t2tb(X5)) ) )
                  | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
                & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
            & ( tb2t(nil(elt)) = X2 ) )
        & ( tb2t(nil(elt)) = X1 ) )
   => ( ? [X2: list_elt] :
          ( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
              ( ? [X6: bool1] :
                  ( ? [X7: list_elt] :
                      ( ? [X8: list_elt] :
                          ( ? [X9: list_elt] :
                              ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                                | ~ sorted1(X9) )
                              & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                              & sorted1(X9) )
                          & sorted1(X8)
                          & sorted1(X7)
                          & ( tb2t(nil(elt)) = X5 )
                          & permut(elt,t2tb(X8),t2tb(X3))
                          & sorted1(X8) )
                      & permut(elt,t2tb(X7),t2tb(X4))
                      & sorted1(X7) )
                  & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
                  & ( tb2t(nil(elt)) = X5 )
                  & ( true1 = X6 )
                  & ( ( true1 = X6 )
                    | ( tb2t(nil(elt)) != X5 ) )
                  & ( ( tb2t(nil(elt)) = X5 )
                    | ( true1 != X6 ) ) )
              & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                  & ( 0 = length2(elt,t2tb(X5)) ) )
                | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
              & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
          & ( tb2t(nil(elt)) = X2 ) )
      & ( tb2t(nil(elt)) = sK11 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f214,plain,
    ( ? [X2: list_elt] :
        ( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
            ( ? [X6: bool1] :
                ( ? [X7: list_elt] :
                    ( ? [X8: list_elt] :
                        ( ? [X9: list_elt] :
                            ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                              | ~ sorted1(X9) )
                            & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                            & sorted1(X9) )
                        & sorted1(X8)
                        & sorted1(X7)
                        & ( tb2t(nil(elt)) = X5 )
                        & permut(elt,t2tb(X8),t2tb(X3))
                        & sorted1(X8) )
                    & permut(elt,t2tb(X7),t2tb(X4))
                    & sorted1(X7) )
                & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
                & ( tb2t(nil(elt)) = X5 )
                & ( true1 = X6 )
                & ( ( true1 = X6 )
                  | ( tb2t(nil(elt)) != X5 ) )
                & ( ( tb2t(nil(elt)) = X5 )
                  | ( true1 != X6 ) ) )
            & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
                & ( 0 = length2(elt,t2tb(X5)) ) )
              | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
            & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
        & ( tb2t(nil(elt)) = X2 ) )
   => ( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
          ( ? [X6: bool1] :
              ( ? [X7: list_elt] :
                  ( ? [X8: list_elt] :
                      ( ? [X9: list_elt] :
                          ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                            | ~ sorted1(X9) )
                          & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                          & sorted1(X9) )
                      & sorted1(X8)
                      & sorted1(X7)
                      & ( tb2t(nil(elt)) = X5 )
                      & permut(elt,t2tb(X8),t2tb(X3))
                      & sorted1(X8) )
                  & permut(elt,t2tb(X7),t2tb(X4))
                  & sorted1(X7) )
              & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
              & ( tb2t(nil(elt)) = X5 )
              & ( true1 = X6 )
              & ( ( true1 = X6 )
                | ( tb2t(nil(elt)) != X5 ) )
              & ( ( tb2t(nil(elt)) = X5 )
                | ( true1 != X6 ) ) )
          & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
              & ( 0 = length2(elt,t2tb(X5)) ) )
            | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
          & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
      & ( tb2t(nil(elt)) = sK12 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f215,plain,
    ( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
        ( ? [X6: bool1] :
            ( ? [X7: list_elt] :
                ( ? [X8: list_elt] :
                    ( ? [X9: list_elt] :
                        ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                          | ~ sorted1(X9) )
                        & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                        & sorted1(X9) )
                    & sorted1(X8)
                    & sorted1(X7)
                    & ( tb2t(nil(elt)) = X5 )
                    & permut(elt,t2tb(X8),t2tb(X3))
                    & sorted1(X8) )
                & permut(elt,t2tb(X7),t2tb(X4))
                & sorted1(X7) )
            & permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
            & ( tb2t(nil(elt)) = X5 )
            & ( true1 = X6 )
            & ( ( true1 = X6 )
              | ( tb2t(nil(elt)) != X5 ) )
            & ( ( tb2t(nil(elt)) = X5 )
              | ( true1 != X6 ) ) )
        & ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
            & ( 0 = length2(elt,t2tb(X5)) ) )
          | ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
        & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
   => ( ? [X6: bool1] :
          ( ? [X7: list_elt] :
              ( ? [X8: list_elt] :
                  ( ? [X9: list_elt] :
                      ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                        | ~ sorted1(X9) )
                      & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                      & sorted1(X9) )
                  & sorted1(X8)
                  & sorted1(X7)
                  & ( tb2t(nil(elt)) = sK15 )
                  & permut(elt,t2tb(X8),t2tb(sK13))
                  & sorted1(X8) )
              & permut(elt,t2tb(X7),t2tb(sK14))
              & sorted1(X7) )
          & permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
          & ( tb2t(nil(elt)) = sK15 )
          & ( true1 = X6 )
          & ( ( true1 = X6 )
            | ( tb2t(nil(elt)) != sK15 ) )
          & ( ( tb2t(nil(elt)) = sK15 )
            | ( true1 != X6 ) ) )
      & ( ( ( length2(elt,t2tb(sK14)) = $sum(length2(elt,t2tb(sK13)),1) )
          & ( 0 = length2(elt,t2tb(sK15)) ) )
        | ( length2(elt,t2tb(sK14)) = length2(elt,t2tb(sK13)) ) )
      & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK15)),t2tb(sK10)) ) ),
    introduced(choice_axiom,[]) ).

tff(f216,plain,
    ( ? [X6: bool1] :
        ( ? [X7: list_elt] :
            ( ? [X8: list_elt] :
                ( ? [X9: list_elt] :
                    ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                      | ~ sorted1(X9) )
                    & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                    & sorted1(X9) )
                & sorted1(X8)
                & sorted1(X7)
                & ( tb2t(nil(elt)) = sK15 )
                & permut(elt,t2tb(X8),t2tb(sK13))
                & sorted1(X8) )
            & permut(elt,t2tb(X7),t2tb(sK14))
            & sorted1(X7) )
        & permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
        & ( tb2t(nil(elt)) = sK15 )
        & ( true1 = X6 )
        & ( ( true1 = X6 )
          | ( tb2t(nil(elt)) != sK15 ) )
        & ( ( tb2t(nil(elt)) = sK15 )
          | ( true1 != X6 ) ) )
   => ( ? [X7: list_elt] :
          ( ? [X8: list_elt] :
              ( ? [X9: list_elt] :
                  ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                    | ~ sorted1(X9) )
                  & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                  & sorted1(X9) )
              & sorted1(X8)
              & sorted1(X7)
              & ( tb2t(nil(elt)) = sK15 )
              & permut(elt,t2tb(X8),t2tb(sK13))
              & sorted1(X8) )
          & permut(elt,t2tb(X7),t2tb(sK14))
          & sorted1(X7) )
      & permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
      & ( tb2t(nil(elt)) = sK15 )
      & ( true1 = sK16 )
      & ( ( true1 = sK16 )
        | ( tb2t(nil(elt)) != sK15 ) )
      & ( ( tb2t(nil(elt)) = sK15 )
        | ( true1 != sK16 ) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f217,plain,
    ( ? [X7: list_elt] :
        ( ? [X8: list_elt] :
            ( ? [X9: list_elt] :
                ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                  | ~ sorted1(X9) )
                & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
                & sorted1(X9) )
            & sorted1(X8)
            & sorted1(X7)
            & ( tb2t(nil(elt)) = sK15 )
            & permut(elt,t2tb(X8),t2tb(sK13))
            & sorted1(X8) )
        & permut(elt,t2tb(X7),t2tb(sK14))
        & sorted1(X7) )
   => ( ? [X8: list_elt] :
          ( ? [X9: list_elt] :
              ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
                | ~ sorted1(X9) )
              & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(X8)))
              & sorted1(X9) )
          & sorted1(X8)
          & sorted1(sK17)
          & ( tb2t(nil(elt)) = sK15 )
          & permut(elt,t2tb(X8),t2tb(sK13))
          & sorted1(X8) )
      & permut(elt,t2tb(sK17),t2tb(sK14))
      & sorted1(sK17) ) ),
    introduced(choice_axiom,[]) ).

tff(f218,plain,
    ( ? [X8: list_elt] :
        ( ? [X9: list_elt] :
            ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
              | ~ sorted1(X9) )
            & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(X8)))
            & sorted1(X9) )
        & sorted1(X8)
        & sorted1(sK17)
        & ( tb2t(nil(elt)) = sK15 )
        & permut(elt,t2tb(X8),t2tb(sK13))
        & sorted1(X8) )
   => ( ? [X9: list_elt] :
          ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
            | ~ sorted1(X9) )
          & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
          & sorted1(X9) )
      & sorted1(sK18)
      & sorted1(sK17)
      & ( tb2t(nil(elt)) = sK15 )
      & permut(elt,t2tb(sK18),t2tb(sK13))
      & sorted1(sK18) ) ),
    introduced(choice_axiom,[]) ).

tff(f219,plain,
    ( ? [X9: list_elt] :
        ( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
          | ~ sorted1(X9) )
        & permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
        & sorted1(X9) )
   => ( ( ~ permut(elt,t2tb(sK19),t2tb(sK10))
        | ~ sorted1(sK19) )
      & permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
      & sorted1(sK19) ) ),
    introduced(choice_axiom,[]) ).

tff(f220,plain,
    ( ( ~ permut(elt,t2tb(sK19),t2tb(sK10))
      | ~ sorted1(sK19) )
    & permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
    & sorted1(sK19)
    & sorted1(sK18)
    & sorted1(sK17)
    & ( tb2t(nil(elt)) = sK15 )
    & permut(elt,t2tb(sK18),t2tb(sK13))
    & sorted1(sK18)
    & permut(elt,t2tb(sK17),t2tb(sK14))
    & sorted1(sK17)
    & permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
    & ( tb2t(nil(elt)) = sK15 )
    & ( true1 = sK16 )
    & ( ( true1 = sK16 )
      | ( tb2t(nil(elt)) != sK15 ) )
    & ( ( tb2t(nil(elt)) = sK15 )
      | ( true1 != sK16 ) )
    & ( ( ( length2(elt,t2tb(sK14)) = $sum(length2(elt,t2tb(sK13)),1) )
        & ( 0 = length2(elt,t2tb(sK15)) ) )
      | ( length2(elt,t2tb(sK14)) = length2(elt,t2tb(sK13)) ) )
    & permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK15)),t2tb(sK10))
    & ( tb2t(nil(elt)) = sK12 )
    & ( tb2t(nil(elt)) = sK11 )
    & $less(1,length2(elt,t2tb(sK10))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19])],[f211,f219,f218,f217,f216,f215,f214,f213,f212]) ).

tff(f282,plain,
    ! [X2: uni,X3: uni,X0: ty,X1: uni] :
      ( permut(X0,X1,X3)
      | ~ permut(X0,X2,X3)
      | ~ permut(X0,X1,X2) ),
    inference(cnf_transformation,[],[f167]) ).

tff(f287,plain,
    ! [X2: uni,X3: uni,X0: ty,X1: uni,X4: uni] :
      ( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
      | ~ permut(X0,X2,X4)
      | ~ permut(X0,X1,X3) ),
    inference(cnf_transformation,[],[f170]) ).

tff(f331,plain,
    permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10)),
    inference(cnf_transformation,[],[f220]) ).

tff(f333,plain,
    permut(elt,t2tb(sK17),t2tb(sK14)),
    inference(cnf_transformation,[],[f220]) ).

tff(f335,plain,
    permut(elt,t2tb(sK18),t2tb(sK13)),
    inference(cnf_transformation,[],[f220]) ).

tff(f339,plain,
    sorted1(sK19),
    inference(cnf_transformation,[],[f220]) ).

tff(f340,plain,
    permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18))),
    inference(cnf_transformation,[],[f220]) ).

tff(f341,plain,
    ( ~ permut(elt,t2tb(sK19),t2tb(sK10))
    | ~ sorted1(sK19) ),
    inference(cnf_transformation,[],[f220]) ).

cnf(c_128,plain,
    ( ~ permut(X0_14,X0_13,X1_13)
    | ~ permut(X0_14,X2_13,X0_13)
    | permut(X0_14,X2_13,X1_13) ),
    inference(cnf_transformation,[],[f282]) ).

cnf(c_133,plain,
    ( ~ permut(X0_14,X0_13,X1_13)
    | ~ permut(X0_14,X2_13,X3_13)
    | permut(X0_14,infix_plpl(X0_14,X2_13,X0_13),infix_plpl(X0_14,X3_13,X1_13)) ),
    inference(cnf_transformation,[],[f287]) ).

cnf(c_166,negated_conjecture,
    ( ~ permut(elt,t2tb(sK19),t2tb(sK10))
    | ~ sorted1(sK19) ),
    inference(cnf_transformation,[],[f341]) ).

cnf(c_167,negated_conjecture,
    permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18))),
    inference(cnf_transformation,[],[f340]) ).

cnf(c_168,negated_conjecture,
    sorted1(sK19),
    inference(cnf_transformation,[],[f339]) ).

cnf(c_172,negated_conjecture,
    permut(elt,t2tb(sK18),t2tb(sK13)),
    inference(cnf_transformation,[],[f335]) ).

cnf(c_174,negated_conjecture,
    permut(elt,t2tb(sK17),t2tb(sK14)),
    inference(cnf_transformation,[],[f333]) ).

cnf(c_176,negated_conjecture,
    permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10)),
    inference(cnf_transformation,[],[f331]) ).

cnf(c_7021,plain,
    ( ~ permut(elt,infix_plpl(elt,t2tb(sK17),t2tb(sK18)),X0_13)
    | permut(elt,t2tb(sK19),X0_13) ),
    inference(resolution,[status(thm)],[c_128,c_167]) ).

cnf(c_8535,plain,
    ( ~ permut(X0_14,infix_plpl(X0_14,X0_13,X1_13),X2_13)
    | ~ permut(X0_14,X3_13,X1_13)
    | ~ permut(X0_14,X4_13,X0_13)
    | permut(X0_14,infix_plpl(X0_14,X4_13,X3_13),X2_13) ),
    inference(resolution,[status(thm)],[c_133,c_128]) ).

cnf(c_44408,plain,
    ( ~ permut(elt,X0_13,t2tb(sK14))
    | ~ permut(elt,X1_13,t2tb(sK13))
    | permut(elt,infix_plpl(elt,X0_13,X1_13),t2tb(sK10)) ),
    inference(resolution,[status(thm)],[c_8535,c_176]) ).

cnf(c_45400,plain,
    ( ~ permut(elt,t2tb(sK17),t2tb(sK14))
    | ~ permut(elt,t2tb(sK18),t2tb(sK13))
    | permut(elt,t2tb(sK19),t2tb(sK10)) ),
    inference(resolution,[status(thm)],[c_44408,c_7021]) ).

cnf(c_45401,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_45400,c_166,c_172,c_174,c_168]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW629_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.36  % Computer : n015.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Sun Aug 27 22:00:24 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.21/0.48  Running TFA theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.09/4.21  % SZS status Started for theBenchmark.p
% 27.09/4.21  % SZS status Theorem for theBenchmark.p
% 27.09/4.21  
% 27.09/4.21  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 27.09/4.21  
% 27.09/4.21  ------  iProver source info
% 27.09/4.21  
% 27.09/4.21  git: date: 2023-05-31 18:12:56 +0000
% 27.09/4.21  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 27.09/4.21  git: non_committed_changes: false
% 27.09/4.21  git: last_make_outside_of_git: false
% 27.09/4.21  
% 27.09/4.21  ------ Parsing...
% 27.09/4.21  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 27.09/4.21  
% 27.09/4.21  ------ Preprocessing... sup_sim: 8  sf_s  rm: 4 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 27.09/4.21  
% 27.09/4.21  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 27.09/4.21  
% 27.09/4.21  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 27.09/4.21  ------ Proving...
% 27.09/4.21  ------ Problem Properties 
% 27.09/4.21  
% 27.09/4.21  
% 27.09/4.21  clauses                                 125
% 27.09/4.21  conjectures                             20
% 27.09/4.21  EPR                                     16
% 27.09/4.21  Horn                                    107
% 27.09/4.21  unary                                   67
% 27.09/4.21  binary                                  35
% 27.09/4.21  lits                                    217
% 27.09/4.21  lits eq                                 69
% 27.09/4.21  fd_pure                                 1
% 27.09/4.21  fd_pseudo                               0
% 27.09/4.21  fd_cond                                 0
% 27.09/4.21  fd_pseudo_cond                          5
% 27.09/4.21  AC symbols                              2
% 27.09/4.21  
% 27.09/4.21  ------ Input Options Time Limit: Unbounded
% 27.09/4.21  
% 27.09/4.21  
% 27.09/4.21  ------ 
% 27.09/4.21  Current options:
% 27.09/4.21  ------ 
% 27.09/4.21  
% 27.09/4.21  
% 27.09/4.21  
% 27.09/4.21  
% 27.09/4.21  ------ Proving...
% 27.09/4.21  
% 27.09/4.21  
% 27.09/4.21  % SZS status Theorem for theBenchmark.p
% 27.09/4.21  
% 27.09/4.21  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.09/4.22  
% 27.09/4.22  
%------------------------------------------------------------------------------