TSTP Solution File: SWW637_2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW637_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.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 May  3 03:25:43 EDT 2024

% Result   : Theorem 11.91s 2.09s
% Output   : CNFRefutation 11.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   89 (  21 unt;   0 typ;   0 def)
%            Number of atoms       : 1318 (  10 equ)
%            Maximal formula atoms :   36 (  14 avg)
%            Number of connectives :  508 ( 172   ~; 152   |; 144   &)
%                                         (   2 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  893 ( 893 fml;   0 var)
%            Number arithmetic     :  186 ( 119 atm;   0 fun;   0 num;  67 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   34 (  29 usr;  15 prp; 0-4 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  229 (   0 sgn 151   !;  43   ?; 194   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f35,axiom,
    ! [X0: ty,X12: uni,X11: uni] :
      ( distinct(X0,X12)
     => ( distinct(X0,X11)
       => ( ! [X1: uni] :
              ( sort(X0,X1)
             => ( mem(X0,X1,X12)
               => ~ mem(X0,X1,X11) ) )
         => distinct(X0,infix_plpl(X0,X12,X11)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct_append) ).

tff(f50,axiom,
    ! [X0: ty] :
      ( ! [X1: uni,X2: uni] : ( labels(X0,node(X0,X1,X2)) = infix_plpl(X0,labels(X0,X1),labels(X0,X2)) )
      & ! [X1: uni] : ( cons(X0,X1,nil(X0)) = labels(X0,leaf(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',labels_def) ).

tff(f52,axiom,
    ! [X0: ty,X1: uni,X14: uni,X16: uni] :
      ( mem(X0,X1,labels(X0,node(X0,X14,X16)))
    <=> ( mem(X0,X1,labels(X0,X16))
        | mem(X0,X1,labels(X0,X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',labels_Node) ).

tff(f54,axiom,
    ! [X0: ty,X17: ty,X12: uni,X18: uni,X11: uni,X19: uni] :
      ( same_shape(X17,X0,X12,X11)
     => ( same_shape(X17,X0,X18,X19)
       => same_shape(X17,X0,node(X0,X12,X18),node(X17,X11,X19)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',same_shape_Node) ).

tff(f71,axiom,
    ! [X21: uni] : ( t2tb3(tb2t3(X21)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR3) ).

tff(f72,conjecture,
    ! [X16: $int,X1: tree_a1,X2: tree_a1,X18: $int,X22: tree_int] :
      ( ( ! [X3: $int] :
            ( mem(int,t2tb3(X3),labels(int,t2tb(X22)))
           => ( $lesseq(X3,X18)
              & $less(X16,X3) ) )
        & $lesseq(X16,X18)
        & distinct(int,labels(int,t2tb(X22)))
        & same_shape(int,a1,t2tb2(X2),t2tb(X22)) )
     => ! [X19: $int,X23: tree_int] :
          ( ( ! [X3: $int] :
                ( mem(int,t2tb3(X3),labels(int,t2tb(X23)))
               => ( $lesseq(X3,X19)
                  & $less(X18,X3) ) )
            & $lesseq(X18,X19)
            & distinct(int,labels(int,t2tb(X23)))
            & same_shape(int,a1,t2tb2(X1),t2tb(X23)) )
         => ( ! [X3: $int] :
                ( mem(int,t2tb3(X3),labels(int,node(int,t2tb(X23),t2tb(X22))))
               => ( $lesseq(X3,X19)
                  & $less(X16,X3) ) )
            & $lesseq(X16,X19)
            & distinct(int,labels(int,node(int,t2tb(X23),t2tb(X22))))
            & same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X23),t2tb(X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_relabel) ).

tff(f73,negated_conjecture,
    ~ ! [X16: $int,X1: tree_a1,X2: tree_a1,X18: $int,X22: tree_int] :
        ( ( ! [X3: $int] :
              ( mem(int,t2tb3(X3),labels(int,t2tb(X22)))
             => ( $lesseq(X3,X18)
                & $less(X16,X3) ) )
          & $lesseq(X16,X18)
          & distinct(int,labels(int,t2tb(X22)))
          & same_shape(int,a1,t2tb2(X2),t2tb(X22)) )
       => ! [X19: $int,X23: tree_int] :
            ( ( ! [X3: $int] :
                  ( mem(int,t2tb3(X3),labels(int,t2tb(X23)))
                 => ( $lesseq(X3,X19)
                    & $less(X18,X3) ) )
              & $lesseq(X18,X19)
              & distinct(int,labels(int,t2tb(X23)))
              & same_shape(int,a1,t2tb2(X1),t2tb(X23)) )
           => ( ! [X3: $int] :
                  ( mem(int,t2tb3(X3),labels(int,node(int,t2tb(X23),t2tb(X22))))
                 => ( $lesseq(X3,X19)
                    & $less(X16,X3) ) )
              & $lesseq(X16,X19)
              & distinct(int,labels(int,node(int,t2tb(X23),t2tb(X22))))
              & same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X23),t2tb(X22))) ) ) ),
    inference(negated_conjecture,[],[f72]) ).

tff(f76,plain,
    ~ ! [X16: $int,X1: tree_a1,X2: tree_a1,X18: $int,X22: tree_int] :
        ( ( ! [X3: $int] :
              ( mem(int,t2tb3(X3),labels(int,t2tb(X22)))
             => ( ~ $less(X18,X3)
                & $less(X16,X3) ) )
          & ~ $less(X18,X16)
          & distinct(int,labels(int,t2tb(X22)))
          & same_shape(int,a1,t2tb2(X2),t2tb(X22)) )
       => ! [X19: $int,X23: tree_int] :
            ( ( ! [X3: $int] :
                  ( mem(int,t2tb3(X3),labels(int,t2tb(X23)))
                 => ( ~ $less(X19,X3)
                    & $less(X18,X3) ) )
              & ~ $less(X19,X18)
              & distinct(int,labels(int,t2tb(X23)))
              & same_shape(int,a1,t2tb2(X1),t2tb(X23)) )
           => ( ! [X3: $int] :
                  ( mem(int,t2tb3(X3),labels(int,node(int,t2tb(X23),t2tb(X22))))
                 => ( ~ $less(X19,X3)
                    & $less(X16,X3) ) )
              & ~ $less(X19,X16)
              & distinct(int,labels(int,node(int,t2tb(X23),t2tb(X22))))
              & same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X23),t2tb(X22))) ) ) ),
    inference(theory_normalization,[],[f73]) ).

tff(f83,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_146,[]) ).

tff(f117,plain,
    ! [X0: ty,X1: uni,X2: uni] :
      ( distinct(X0,X1)
     => ( distinct(X0,X2)
       => ( ! [X3: uni] :
              ( sort(X0,X3)
             => ( mem(X0,X3,X1)
               => ~ mem(X0,X3,X2) ) )
         => distinct(X0,infix_plpl(X0,X1,X2)) ) ) ),
    inference(rectify,[],[f35]) ).

tff(f126,plain,
    ! [X0: ty] :
      ( ! [X1: uni,X2: uni] : ( labels(X0,node(X0,X1,X2)) = infix_plpl(X0,labels(X0,X1),labels(X0,X2)) )
      & ! [X3: uni] : ( cons(X0,X3,nil(X0)) = labels(X0,leaf(X0,X3)) ) ),
    inference(rectify,[],[f50]) ).

tff(f128,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni] :
      ( mem(X0,X1,labels(X0,node(X0,X2,X3)))
    <=> ( mem(X0,X1,labels(X0,X3))
        | mem(X0,X1,labels(X0,X2)) ) ),
    inference(rectify,[],[f52]) ).

tff(f130,plain,
    ! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
      ( same_shape(X1,X0,X2,X4)
     => ( same_shape(X1,X0,X3,X5)
       => same_shape(X1,X0,node(X0,X2,X3),node(X1,X4,X5)) ) ),
    inference(rectify,[],[f54]) ).

tff(f145,plain,
    ! [X0: uni] : ( t2tb3(tb2t3(X0)) = X0 ),
    inference(rectify,[],[f71]) ).

tff(f146,plain,
    ~ ! [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
        ( ( ! [X5: $int] :
              ( mem(int,t2tb3(X5),labels(int,t2tb(X4)))
             => ( ~ $less(X3,X5)
                & $less(X0,X5) ) )
          & ~ $less(X3,X0)
          & distinct(int,labels(int,t2tb(X4)))
          & same_shape(int,a1,t2tb2(X2),t2tb(X4)) )
       => ! [X6: $int,X7: tree_int] :
            ( ( ! [X8: $int] :
                  ( mem(int,t2tb3(X8),labels(int,t2tb(X7)))
                 => ( ~ $less(X6,X8)
                    & $less(X3,X8) ) )
              & ~ $less(X6,X3)
              & distinct(int,labels(int,t2tb(X7)))
              & same_shape(int,a1,t2tb2(X1),t2tb(X7)) )
           => ( ! [X9: $int] :
                  ( mem(int,t2tb3(X9),labels(int,node(int,t2tb(X7),t2tb(X4))))
                 => ( ~ $less(X6,X9)
                    & $less(X0,X9) ) )
              & ~ $less(X6,X0)
              & distinct(int,labels(int,node(int,t2tb(X7),t2tb(X4))))
              & same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X7),t2tb(X4))) ) ) ),
    inference(rectify,[],[f76]) ).

tff(f160,plain,
    ! [X0: ty,X1: uni,X2: uni] :
      ( distinct(X0,infix_plpl(X0,X1,X2))
      | ? [X3: uni] :
          ( mem(X0,X3,X2)
          & mem(X0,X3,X1)
          & sort(X0,X3) )
      | ~ distinct(X0,X2)
      | ~ distinct(X0,X1) ),
    inference(ennf_transformation,[],[f117]) ).

tff(f161,plain,
    ! [X0: ty,X1: uni,X2: uni] :
      ( distinct(X0,infix_plpl(X0,X1,X2))
      | ? [X3: uni] :
          ( mem(X0,X3,X2)
          & mem(X0,X3,X1)
          & sort(X0,X3) )
      | ~ distinct(X0,X2)
      | ~ distinct(X0,X1) ),
    inference(flattening,[],[f160]) ).

tff(f167,plain,
    ! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
      ( same_shape(X1,X0,node(X0,X2,X3),node(X1,X4,X5))
      | ~ same_shape(X1,X0,X3,X5)
      | ~ same_shape(X1,X0,X2,X4) ),
    inference(ennf_transformation,[],[f130]) ).

tff(f168,plain,
    ! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
      ( same_shape(X1,X0,node(X0,X2,X3),node(X1,X4,X5))
      | ~ same_shape(X1,X0,X3,X5)
      | ~ same_shape(X1,X0,X2,X4) ),
    inference(flattening,[],[f167]) ).

tff(f173,plain,
    ? [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
      ( ? [X6: $int,X7: tree_int] :
          ( ( ? [X9: $int] :
                ( ( $less(X6,X9)
                  | ~ $less(X0,X9) )
                & mem(int,t2tb3(X9),labels(int,node(int,t2tb(X7),t2tb(X4)))) )
            | $less(X6,X0)
            | ~ distinct(int,labels(int,node(int,t2tb(X7),t2tb(X4))))
            | ~ same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X7),t2tb(X4))) )
          & ! [X8: $int] :
              ( ( ~ $less(X6,X8)
                & $less(X3,X8) )
              | ~ mem(int,t2tb3(X8),labels(int,t2tb(X7))) )
          & ~ $less(X6,X3)
          & distinct(int,labels(int,t2tb(X7)))
          & same_shape(int,a1,t2tb2(X1),t2tb(X7)) )
      & ! [X5: $int] :
          ( ( ~ $less(X3,X5)
            & $less(X0,X5) )
          | ~ mem(int,t2tb3(X5),labels(int,t2tb(X4))) )
      & ~ $less(X3,X0)
      & distinct(int,labels(int,t2tb(X4)))
      & same_shape(int,a1,t2tb2(X2),t2tb(X4)) ),
    inference(ennf_transformation,[],[f146]) ).

tff(f174,plain,
    ? [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
      ( ? [X6: $int,X7: tree_int] :
          ( ( ? [X9: $int] :
                ( ( $less(X6,X9)
                  | ~ $less(X0,X9) )
                & mem(int,t2tb3(X9),labels(int,node(int,t2tb(X7),t2tb(X4)))) )
            | $less(X6,X0)
            | ~ distinct(int,labels(int,node(int,t2tb(X7),t2tb(X4))))
            | ~ same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X7),t2tb(X4))) )
          & ! [X8: $int] :
              ( ( ~ $less(X6,X8)
                & $less(X3,X8) )
              | ~ mem(int,t2tb3(X8),labels(int,t2tb(X7))) )
          & ~ $less(X6,X3)
          & distinct(int,labels(int,t2tb(X7)))
          & same_shape(int,a1,t2tb2(X1),t2tb(X7)) )
      & ! [X5: $int] :
          ( ( ~ $less(X3,X5)
            & $less(X0,X5) )
          | ~ mem(int,t2tb3(X5),labels(int,t2tb(X4))) )
      & ~ $less(X3,X0)
      & distinct(int,labels(int,t2tb(X4)))
      & same_shape(int,a1,t2tb2(X2),t2tb(X4)) ),
    inference(flattening,[],[f173]) ).

tff(f193,plain,
    ! [X0: ty,X1: uni,X2: uni] :
      ( ? [X3: uni] :
          ( mem(X0,X3,X2)
          & mem(X0,X3,X1)
          & sort(X0,X3) )
     => ( mem(X0,sK7(X0,X1,X2),X2)
        & mem(X0,sK7(X0,X1,X2),X1)
        & sort(X0,sK7(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f194,plain,
    ! [X0: ty,X1: uni,X2: uni] :
      ( distinct(X0,infix_plpl(X0,X1,X2))
      | ( mem(X0,sK7(X0,X1,X2),X2)
        & mem(X0,sK7(X0,X1,X2),X1)
        & sort(X0,sK7(X0,X1,X2)) )
      | ~ distinct(X0,X2)
      | ~ distinct(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f161,f193]) ).

tff(f196,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni] :
      ( ( mem(X0,X1,labels(X0,node(X0,X2,X3)))
        | ( ~ mem(X0,X1,labels(X0,X3))
          & ~ mem(X0,X1,labels(X0,X2)) ) )
      & ( mem(X0,X1,labels(X0,X3))
        | mem(X0,X1,labels(X0,X2))
        | ~ mem(X0,X1,labels(X0,node(X0,X2,X3))) ) ),
    inference(nnf_transformation,[],[f128]) ).

tff(f197,plain,
    ! [X0: ty,X1: uni,X2: uni,X3: uni] :
      ( ( mem(X0,X1,labels(X0,node(X0,X2,X3)))
        | ( ~ mem(X0,X1,labels(X0,X3))
          & ~ mem(X0,X1,labels(X0,X2)) ) )
      & ( mem(X0,X1,labels(X0,X3))
        | mem(X0,X1,labels(X0,X2))
        | ~ mem(X0,X1,labels(X0,node(X0,X2,X3))) ) ),
    inference(flattening,[],[f196]) ).

tff(f205,plain,
    ? [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
      ( ? [X5: $int,X6: tree_int] :
          ( ( ? [X7: $int] :
                ( ( $less(X5,X7)
                  | ~ $less(X0,X7) )
                & mem(int,t2tb3(X7),labels(int,node(int,t2tb(X6),t2tb(X4)))) )
            | $less(X5,X0)
            | ~ distinct(int,labels(int,node(int,t2tb(X6),t2tb(X4))))
            | ~ same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X6),t2tb(X4))) )
          & ! [X8: $int] :
              ( ( ~ $less(X5,X8)
                & $less(X3,X8) )
              | ~ mem(int,t2tb3(X8),labels(int,t2tb(X6))) )
          & ~ $less(X5,X3)
          & distinct(int,labels(int,t2tb(X6)))
          & same_shape(int,a1,t2tb2(X1),t2tb(X6)) )
      & ! [X9: $int] :
          ( ( ~ $less(X3,X9)
            & $less(X0,X9) )
          | ~ mem(int,t2tb3(X9),labels(int,t2tb(X4))) )
      & ~ $less(X3,X0)
      & distinct(int,labels(int,t2tb(X4)))
      & same_shape(int,a1,t2tb2(X2),t2tb(X4)) ),
    inference(rectify,[],[f174]) ).

tff(f206,plain,
    ( ? [X0: $int,X1: tree_a1,X2: tree_a1,X3: $int,X4: tree_int] :
        ( ? [X5: $int,X6: tree_int] :
            ( ( ? [X7: $int] :
                  ( ( $less(X5,X7)
                    | ~ $less(X0,X7) )
                  & mem(int,t2tb3(X7),labels(int,node(int,t2tb(X6),t2tb(X4)))) )
              | $less(X5,X0)
              | ~ distinct(int,labels(int,node(int,t2tb(X6),t2tb(X4))))
              | ~ same_shape(int,a1,node(a1,t2tb2(X1),t2tb2(X2)),node(int,t2tb(X6),t2tb(X4))) )
            & ! [X8: $int] :
                ( ( ~ $less(X5,X8)
                  & $less(X3,X8) )
                | ~ mem(int,t2tb3(X8),labels(int,t2tb(X6))) )
            & ~ $less(X5,X3)
            & distinct(int,labels(int,t2tb(X6)))
            & same_shape(int,a1,t2tb2(X1),t2tb(X6)) )
        & ! [X9: $int] :
            ( ( ~ $less(X3,X9)
              & $less(X0,X9) )
            | ~ mem(int,t2tb3(X9),labels(int,t2tb(X4))) )
        & ~ $less(X3,X0)
        & distinct(int,labels(int,t2tb(X4)))
        & same_shape(int,a1,t2tb2(X2),t2tb(X4)) )
   => ( ? [X6: tree_int,X5: $int] :
          ( ( ? [X7: $int] :
                ( ( $less(X5,X7)
                  | ~ $less(sK14,X7) )
                & mem(int,t2tb3(X7),labels(int,node(int,t2tb(X6),t2tb(sK18)))) )
            | $less(X5,sK14)
            | ~ distinct(int,labels(int,node(int,t2tb(X6),t2tb(sK18))))
            | ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(X6),t2tb(sK18))) )
          & ! [X8: $int] :
              ( ( ~ $less(X5,X8)
                & $less(sK17,X8) )
              | ~ mem(int,t2tb3(X8),labels(int,t2tb(X6))) )
          & ~ $less(X5,sK17)
          & distinct(int,labels(int,t2tb(X6)))
          & same_shape(int,a1,t2tb2(sK15),t2tb(X6)) )
      & ! [X9: $int] :
          ( ( ~ $less(sK17,X9)
            & $less(sK14,X9) )
          | ~ mem(int,t2tb3(X9),labels(int,t2tb(sK18))) )
      & ~ $less(sK17,sK14)
      & distinct(int,labels(int,t2tb(sK18)))
      & same_shape(int,a1,t2tb2(sK16),t2tb(sK18)) ) ),
    introduced(choice_axiom,[]) ).

tff(f207,plain,
    ( ? [X6: tree_int,X5: $int] :
        ( ( ? [X7: $int] :
              ( ( $less(X5,X7)
                | ~ $less(sK14,X7) )
              & mem(int,t2tb3(X7),labels(int,node(int,t2tb(X6),t2tb(sK18)))) )
          | $less(X5,sK14)
          | ~ distinct(int,labels(int,node(int,t2tb(X6),t2tb(sK18))))
          | ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(X6),t2tb(sK18))) )
        & ! [X8: $int] :
            ( ( ~ $less(X5,X8)
              & $less(sK17,X8) )
            | ~ mem(int,t2tb3(X8),labels(int,t2tb(X6))) )
        & ~ $less(X5,sK17)
        & distinct(int,labels(int,t2tb(X6)))
        & same_shape(int,a1,t2tb2(sK15),t2tb(X6)) )
   => ( ( ? [X7: $int] :
            ( ( $less(sK19,X7)
              | ~ $less(sK14,X7) )
            & mem(int,t2tb3(X7),labels(int,node(int,t2tb(sK20),t2tb(sK18)))) )
        | $less(sK19,sK14)
        | ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
        | ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) )
      & ! [X8: $int] :
          ( ( ~ $less(sK19,X8)
            & $less(sK17,X8) )
          | ~ mem(int,t2tb3(X8),labels(int,t2tb(sK20))) )
      & ~ $less(sK19,sK17)
      & distinct(int,labels(int,t2tb(sK20)))
      & same_shape(int,a1,t2tb2(sK15),t2tb(sK20)) ) ),
    introduced(choice_axiom,[]) ).

tff(f208,plain,
    ( ? [X7: $int] :
        ( ( $less(sK19,X7)
          | ~ $less(sK14,X7) )
        & mem(int,t2tb3(X7),labels(int,node(int,t2tb(sK20),t2tb(sK18)))) )
   => ( ( $less(sK19,sK21)
        | ~ $less(sK14,sK21) )
      & mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18)))) ) ),
    introduced(choice_axiom,[]) ).

tff(f209,plain,
    ( ( ( ( $less(sK19,sK21)
          | ~ $less(sK14,sK21) )
        & mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18)))) )
      | $less(sK19,sK14)
      | ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
      | ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) )
    & ! [X8: $int] :
        ( ( ~ $less(sK19,X8)
          & $less(sK17,X8) )
        | ~ mem(int,t2tb3(X8),labels(int,t2tb(sK20))) )
    & ~ $less(sK19,sK17)
    & distinct(int,labels(int,t2tb(sK20)))
    & same_shape(int,a1,t2tb2(sK15),t2tb(sK20))
    & ! [X9: $int] :
        ( ( ~ $less(sK17,X9)
          & $less(sK14,X9) )
        | ~ mem(int,t2tb3(X9),labels(int,t2tb(sK18))) )
    & ~ $less(sK17,sK14)
    & distinct(int,labels(int,t2tb(sK18)))
    & same_shape(int,a1,t2tb2(sK16),t2tb(sK18)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21])],[f205,f208,f207,f206]) ).

tff(f261,plain,
    ! [X2: uni,X0: ty,X1: uni] :
      ( distinct(X0,infix_plpl(X0,X1,X2))
      | mem(X0,sK7(X0,X1,X2),X1)
      | ~ distinct(X0,X2)
      | ~ distinct(X0,X1) ),
    inference(cnf_transformation,[],[f194]) ).

tff(f262,plain,
    ! [X2: uni,X0: ty,X1: uni] :
      ( distinct(X0,infix_plpl(X0,X1,X2))
      | mem(X0,sK7(X0,X1,X2),X2)
      | ~ distinct(X0,X2)
      | ~ distinct(X0,X1) ),
    inference(cnf_transformation,[],[f194]) ).

tff(f278,plain,
    ! [X2: uni,X0: ty,X1: uni] : ( labels(X0,node(X0,X1,X2)) = infix_plpl(X0,labels(X0,X1),labels(X0,X2)) ),
    inference(cnf_transformation,[],[f126]) ).

tff(f281,plain,
    ! [X2: uni,X3: uni,X0: ty,X1: uni] :
      ( mem(X0,X1,labels(X0,X3))
      | mem(X0,X1,labels(X0,X2))
      | ~ mem(X0,X1,labels(X0,node(X0,X2,X3))) ),
    inference(cnf_transformation,[],[f197]) ).

tff(f285,plain,
    ! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni,X5: uni] :
      ( same_shape(X1,X0,node(X0,X2,X3),node(X1,X4,X5))
      | ~ same_shape(X1,X0,X3,X5)
      | ~ same_shape(X1,X0,X2,X4) ),
    inference(cnf_transformation,[],[f168]) ).

tff(f313,plain,
    ! [X0: uni] : ( t2tb3(tb2t3(X0)) = X0 ),
    inference(cnf_transformation,[],[f145]) ).

tff(f314,plain,
    same_shape(int,a1,t2tb2(sK16),t2tb(sK18)),
    inference(cnf_transformation,[],[f209]) ).

tff(f315,plain,
    distinct(int,labels(int,t2tb(sK18))),
    inference(cnf_transformation,[],[f209]) ).

tff(f316,plain,
    ~ $less(sK17,sK14),
    inference(cnf_transformation,[],[f209]) ).

tff(f317,plain,
    ! [X9: $int] :
      ( $less(sK14,X9)
      | ~ mem(int,t2tb3(X9),labels(int,t2tb(sK18))) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f318,plain,
    ! [X9: $int] :
      ( ~ $less(sK17,X9)
      | ~ mem(int,t2tb3(X9),labels(int,t2tb(sK18))) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f319,plain,
    same_shape(int,a1,t2tb2(sK15),t2tb(sK20)),
    inference(cnf_transformation,[],[f209]) ).

tff(f320,plain,
    distinct(int,labels(int,t2tb(sK20))),
    inference(cnf_transformation,[],[f209]) ).

tff(f321,plain,
    ~ $less(sK19,sK17),
    inference(cnf_transformation,[],[f209]) ).

tff(f322,plain,
    ! [X8: $int] :
      ( $less(sK17,X8)
      | ~ mem(int,t2tb3(X8),labels(int,t2tb(sK20))) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f323,plain,
    ! [X8: $int] :
      ( ~ $less(sK19,X8)
      | ~ mem(int,t2tb3(X8),labels(int,t2tb(sK20))) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f324,plain,
    ( mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | $less(sK19,sK14)
    | ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f325,plain,
    ( $less(sK19,sK21)
    | ~ $less(sK14,sK21)
    | $less(sK19,sK14)
    | ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) ),
    inference(cnf_transformation,[],[f209]) ).

cnf(c_60,plain,
    ( ~ $less_int(X0_3,X1_3)
    | ~ $less_int(X1_3,X2_3)
    | $less_int(X0_3,X2_3) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_117,plain,
    ( ~ distinct(X0_14,X0_13)
    | ~ distinct(X0_14,X1_13)
    | mem(X0_14,sK7(X0_14,X1_13,X0_13),X0_13)
    | distinct(X0_14,infix_plpl(X0_14,X1_13,X0_13)) ),
    inference(cnf_transformation,[],[f262]) ).

cnf(c_118,plain,
    ( ~ distinct(X0_14,X0_13)
    | ~ distinct(X0_14,X1_13)
    | mem(X0_14,sK7(X0_14,X1_13,X0_13),X1_13)
    | distinct(X0_14,infix_plpl(X0_14,X1_13,X0_13)) ),
    inference(cnf_transformation,[],[f261]) ).

cnf(c_134,plain,
    infix_plpl(X0_14,labels(X0_14,X0_13),labels(X0_14,X1_13)) = labels(X0_14,node(X0_14,X0_13,X1_13)),
    inference(cnf_transformation,[],[f278]) ).

cnf(c_140,plain,
    ( ~ mem(X0_14,X0_13,labels(X0_14,node(X0_14,X1_13,X2_13)))
    | mem(X0_14,X0_13,labels(X0_14,X1_13))
    | mem(X0_14,X0_13,labels(X0_14,X2_13)) ),
    inference(cnf_transformation,[],[f281]) ).

cnf(c_142,plain,
    ( ~ same_shape(X0_14,X1_14,X0_13,X1_13)
    | ~ same_shape(X0_14,X1_14,X2_13,X3_13)
    | same_shape(X0_14,X1_14,node(X1_14,X0_13,X2_13),node(X0_14,X1_13,X3_13)) ),
    inference(cnf_transformation,[],[f285]) ).

cnf(c_170,plain,
    t2tb3(tb2t3(X0_13)) = X0_13,
    inference(cnf_transformation,[],[f313]) ).

cnf(c_171,negated_conjecture,
    ( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
    | ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | ~ $less_int(sK14,sK21)
    | $less_int(sK19,sK14)
    | $less_int(sK19,sK21) ),
    inference(cnf_transformation,[],[f325]) ).

cnf(c_172,negated_conjecture,
    ( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
    | ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | $less_int(sK19,sK14) ),
    inference(cnf_transformation,[],[f324]) ).

cnf(c_173,negated_conjecture,
    ( ~ mem(int,t2tb3(X0_3),labels(int,t2tb(sK20)))
    | ~ $less_int(sK19,X0_3) ),
    inference(cnf_transformation,[],[f323]) ).

cnf(c_174,negated_conjecture,
    ( ~ mem(int,t2tb3(X0_3),labels(int,t2tb(sK20)))
    | $less_int(sK17,X0_3) ),
    inference(cnf_transformation,[],[f322]) ).

cnf(c_175,negated_conjecture,
    ~ $less_int(sK19,sK17),
    inference(cnf_transformation,[],[f321]) ).

cnf(c_176,negated_conjecture,
    distinct(int,labels(int,t2tb(sK20))),
    inference(cnf_transformation,[],[f320]) ).

cnf(c_177,negated_conjecture,
    same_shape(int,a1,t2tb2(sK15),t2tb(sK20)),
    inference(cnf_transformation,[],[f319]) ).

cnf(c_178,negated_conjecture,
    ( ~ mem(int,t2tb3(X0_3),labels(int,t2tb(sK18)))
    | ~ $less_int(sK17,X0_3) ),
    inference(cnf_transformation,[],[f318]) ).

cnf(c_179,negated_conjecture,
    ( ~ mem(int,t2tb3(X0_3),labels(int,t2tb(sK18)))
    | $less_int(sK14,X0_3) ),
    inference(cnf_transformation,[],[f317]) ).

cnf(c_180,negated_conjecture,
    ~ $less_int(sK17,sK14),
    inference(cnf_transformation,[],[f316]) ).

cnf(c_181,negated_conjecture,
    distinct(int,labels(int,t2tb(sK18))),
    inference(cnf_transformation,[],[f315]) ).

cnf(c_182,negated_conjecture,
    same_shape(int,a1,t2tb2(sK16),t2tb(sK18)),
    inference(cnf_transformation,[],[f314]) ).

cnf(c_969,plain,
    ( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
    | ~ distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | ~ $less_int(sK14,sK21)
    | $less_int(sK19,sK21) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_171,c_60]) ).

cnf(c_6378,plain,
    ( ~ mem(int,X0_13,labels(int,t2tb(sK18)))
    | ~ $less_int(sK17,tb2t3(X0_13)) ),
    inference(superposition,[status(thm)],[c_170,c_178]) ).

cnf(c_6382,plain,
    ( ~ mem(int,X0_13,labels(int,t2tb(sK20)))
    | $less_int(sK17,tb2t3(X0_13)) ),
    inference(superposition,[status(thm)],[c_170,c_174]) ).

cnf(c_8394,plain,
    ( ~ same_shape(int,a1,t2tb2(sK16),t2tb(sK18))
    | ~ same_shape(int,a1,X0_13,X1_13)
    | same_shape(int,a1,node(a1,X0_13,t2tb2(sK16)),node(int,X1_13,t2tb(sK18))) ),
    inference(instantiation,[status(thm)],[c_142]) ).

cnf(c_12227,plain,
    ( ~ same_shape(int,a1,t2tb2(sK15),t2tb(sK20))
    | ~ same_shape(int,a1,t2tb2(sK16),t2tb(sK18))
    | same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18))) ),
    inference(instantiation,[status(thm)],[c_8394]) ).

cnf(c_13275,plain,
    ( ~ $less_int(sK17,tb2t3(sK7(int,X0_13,labels(int,t2tb(sK18)))))
    | ~ distinct(int,labels(int,t2tb(sK18)))
    | ~ distinct(int,X0_13)
    | distinct(int,infix_plpl(int,X0_13,labels(int,t2tb(sK18)))) ),
    inference(superposition,[status(thm)],[c_117,c_6378]) ).

cnf(c_13292,plain,
    ( ~ $less_int(sK17,tb2t3(sK7(int,X0_13,labels(int,t2tb(sK18)))))
    | ~ distinct(int,X0_13)
    | distinct(int,infix_plpl(int,X0_13,labels(int,t2tb(sK18)))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13275,c_181]) ).

cnf(c_13354,plain,
    ( ~ distinct(int,labels(int,t2tb(sK20)))
    | ~ distinct(int,X0_13)
    | $less_int(sK17,tb2t3(sK7(int,labels(int,t2tb(sK20)),X0_13)))
    | distinct(int,infix_plpl(int,labels(int,t2tb(sK20)),X0_13)) ),
    inference(superposition,[status(thm)],[c_118,c_6382]) ).

cnf(c_13356,plain,
    ( ~ distinct(int,X0_13)
    | $less_int(sK17,tb2t3(sK7(int,labels(int,t2tb(sK20)),X0_13)))
    | distinct(int,infix_plpl(int,labels(int,t2tb(sK20)),X0_13)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13354,c_176]) ).

cnf(c_13747,plain,
    ( ~ distinct(int,labels(int,t2tb(sK18)))
    | ~ distinct(int,labels(int,t2tb(sK20)))
    | distinct(int,infix_plpl(int,labels(int,t2tb(sK20)),labels(int,t2tb(sK18)))) ),
    inference(superposition,[status(thm)],[c_13356,c_13292]) ).

cnf(c_13748,plain,
    distinct(int,infix_plpl(int,labels(int,t2tb(sK20)),labels(int,t2tb(sK18)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_13747,c_176,c_181]) ).

cnf(c_13861,plain,
    distinct(int,labels(int,node(int,t2tb(sK20),t2tb(sK18)))),
    inference(demodulation,[status(thm)],[c_13748,c_134]) ).

cnf(c_13862,plain,
    ( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
    | ~ $less_int(sK14,sK21)
    | $less_int(sK19,sK21) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_969,c_13861]) ).

cnf(c_13863,plain,
    ( ~ same_shape(int,a1,node(a1,t2tb2(sK15),t2tb2(sK16)),node(int,t2tb(sK20),t2tb(sK18)))
    | mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | $less_int(sK19,sK14) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_172,c_13861]) ).

cnf(c_14341,plain,
    ( mem(int,t2tb3(sK21),labels(int,node(int,t2tb(sK20),t2tb(sK18))))
    | $less_int(sK19,sK14) ),
    inference(global_subsumption_just,[status(thm)],[c_13863,c_182,c_177,c_12227,c_13863]) ).

cnf(c_14350,plain,
    ( ~ $less_int(sK14,sK21)
    | $less_int(sK19,sK21) ),
    inference(global_subsumption_just,[status(thm)],[c_13862,c_182,c_177,c_12227,c_13862]) ).

cnf(c_14644,plain,
    ( mem(int,t2tb3(sK21),labels(int,t2tb(sK18)))
    | mem(int,t2tb3(sK21),labels(int,t2tb(sK20)))
    | $less_int(sK19,sK14) ),
    inference(superposition,[status(thm)],[c_14341,c_140]) ).

cnf(c_14885,plain,
    ( ~ $less_int(sK19,sK21)
    | mem(int,t2tb3(sK21),labels(int,t2tb(sK18)))
    | $less_int(sK19,sK14) ),
    inference(superposition,[status(thm)],[c_14644,c_173]) ).

cnf(c_14886,plain,
    ( mem(int,t2tb3(sK21),labels(int,t2tb(sK18)))
    | $less_int(sK17,sK21)
    | $less_int(sK19,sK14) ),
    inference(superposition,[status(thm)],[c_14644,c_174]) ).

cnf(c_14912,plain,
    ( $less_int(sK14,sK21)
    | $less_int(sK17,sK21)
    | $less_int(sK19,sK14) ),
    inference(superposition,[status(thm)],[c_14886,c_179]) ).

cnf(c_15022,plain,
    ( ~ $less_int(sK17,sK21)
    | ~ $less_int(sK19,sK21)
    | $less_int(sK19,sK14) ),
    inference(superposition,[status(thm)],[c_14885,c_178]) ).

cnf(c_20435,plain,
    $false,
    inference(smt_impl_just,[status(thm)],[c_15022,c_14912,c_14350,c_180,c_175]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SWW637_2 : TPTP v8.1.2. Released v6.1.0.
% 0.05/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.31  % Computer : n004.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu May  2 22:13:33 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.16/0.42  Running TFA theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.91/2.09  % SZS status Started for theBenchmark.p
% 11.91/2.09  % SZS status Theorem for theBenchmark.p
% 11.91/2.09  
% 11.91/2.09  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 11.91/2.09  
% 11.91/2.09  ------  iProver source info
% 11.91/2.09  
% 11.91/2.09  git: date: 2024-05-02 19:28:25 +0000
% 11.91/2.09  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 11.91/2.09  git: non_committed_changes: false
% 11.91/2.09  
% 11.91/2.09  ------ Parsing...
% 11.91/2.09  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 11.91/2.09  
% 11.91/2.09  ------ Preprocessing... sup_sim: 3  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 
% 11.91/2.09  
% 11.91/2.09  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 11.91/2.09  
% 11.91/2.09  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 11.91/2.09  ------ Proving...
% 11.91/2.09  ------ Problem Properties 
% 11.91/2.09  
% 11.91/2.09  
% 11.91/2.09  clauses                                 132
% 11.91/2.09  conjectures                             11
% 11.91/2.09  EPR                                     8
% 11.91/2.09  Horn                                    111
% 11.91/2.09  unary                                   67
% 11.91/2.09  binary                                  43
% 11.91/2.09  lits                                    230
% 11.91/2.09  lits eq                                 67
% 11.91/2.09  fd_pure                                 1
% 11.91/2.09  fd_pseudo                               0
% 11.91/2.09  fd_cond                                 0
% 11.91/2.09  fd_pseudo_cond                          6
% 11.91/2.09  AC symbols                              2
% 11.91/2.09  
% 11.91/2.09  ------ Input Options Time Limit: Unbounded
% 11.91/2.09  
% 11.91/2.09  
% 11.91/2.09  ------ 
% 11.91/2.09  Current options:
% 11.91/2.09  ------ 
% 11.91/2.09  
% 11.91/2.09  
% 11.91/2.09  
% 11.91/2.09  
% 11.91/2.09  ------ Proving...
% 11.91/2.09  
% 11.91/2.09  
% 11.91/2.09  % SZS status Theorem for theBenchmark.p
% 11.91/2.09  
% 11.91/2.09  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.91/2.10  
% 11.91/2.10  
%------------------------------------------------------------------------------