TSTP Solution File: SWC220-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWC220-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n025.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 : Tue Sep 20 11:56:14 EDT 2022

% Result   : Unsatisfiable 0.77s 0.96s
% Output   : Proof 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   77
% Syntax   : Number of formulae    :  179 (  31 unt;  13 typ;   0 def)
%            Number of atoms       : 1843 ( 370 equ)
%            Maximal formula atoms :   20 (  11 avg)
%            Number of connectives : 2940 (1411   ~;1381   |;   0   &)
%                                         ( 148 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :  148 ( 148 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   7   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :  400 ( 352   !;   0   ?; 400   :)

% Comments : 
%------------------------------------------------------------------------------
tff(memberP_type,type,
    memberP: ( $i * $i ) > $o ).

tff(sk5_type,type,
    sk5: ( $i * $i * $i ) > $i ).

tff(sk6_type,type,
    sk6: $i ).

tff(sk7_type,type,
    sk7: $i ).

tff(sk8_type,type,
    sk8: $i ).

tff(sk3_type,type,
    sk3: $i ).

tff(app_type,type,
    app: ( $i * $i ) > $i ).

tff(cons_type,type,
    cons: ( $i * $i ) > $i ).

tff(nil_type,type,
    nil: $i ).

tff(sk1_type,type,
    sk1: $i ).

tff(ssList_type,type,
    ssList: $i > $o ).

tff(ssItem_type,type,
    ssItem: $i > $o ).

tff(leq_type,type,
    leq: ( $i * $i ) > $o ).

tff(1,plain,
    ( ( $false
      | ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
  <=> ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( nil != sk1 )
  <=> ( nil != sk3 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ( nil != sk1 )
  <=> ( nil != sk1 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    nil != sk1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

tff(5,plain,
    nil != sk1,
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    nil != sk3,
    inference(modus_ponens,[status(thm)],[5,2]) ).

tff(7,plain,
    ( ( nil = sk3 )
  <=> $false ),
    inference(iff_false,[status(thm)],[6]) ).

tff(8,plain,
    ( ( ( nil = sk3 )
      | ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
  <=> ( $false
      | ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ) ),
    inference(monotonicity,[status(thm)],[7]) ).

tff(9,plain,
    ( ( ( nil = sk3 )
      | ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
  <=> ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
    inference(transitivity,[status(thm)],[8,1]) ).

tff(10,plain,
    ( ( ( nil = sk3 )
      | ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
  <=> ( ( nil = sk3 )
      | ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ( ( nil = sk3 )
    | ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).

tff(12,plain,
    ( ( nil = sk3 )
    | ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    app(app(sk7,cons(sk6,nil)),sk8) = sk3,
    inference(modus_ponens,[status(thm)],[12,9]) ).

tff(14,plain,
    ( ( $false
      | ssList(sk8) )
  <=> ssList(sk8) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ( ( nil = sk3 )
      | ssList(sk8) )
  <=> ( $false
      | ssList(sk8) ) ),
    inference(monotonicity,[status(thm)],[7]) ).

tff(16,plain,
    ( ( ( nil = sk3 )
      | ssList(sk8) )
  <=> ssList(sk8) ),
    inference(transitivity,[status(thm)],[15,14]) ).

tff(17,plain,
    ( ( ( nil = sk3 )
      | ssList(sk8) )
  <=> ( ( nil = sk3 )
      | ssList(sk8) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,axiom,
    ( ( nil = sk3 )
    | ssList(sk8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).

tff(19,plain,
    ( ( nil = sk3 )
    | ssList(sk8) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ( ( nil = sk3 )
    | ssList(sk8) ),
    inference(modus_ponens,[status(thm)],[19,17]) ).

tff(21,plain,
    ( ( nil = sk3 )
    | ssList(sk8) ),
    inference(modus_ponens,[status(thm)],[20,17]) ).

tff(22,plain,
    ( ( nil = sk3 )
    | ssList(sk8) ),
    inference(modus_ponens,[status(thm)],[21,17]) ).

tff(23,plain,
    ( ( nil = sk3 )
    | ssList(sk8) ),
    inference(modus_ponens,[status(thm)],[22,17]) ).

tff(24,plain,
    ( ( nil = sk3 )
    | ssList(sk8) ),
    inference(modus_ponens,[status(thm)],[23,17]) ).

tff(25,plain,
    ssList(sk8),
    inference(modus_ponens,[status(thm)],[24,16]) ).

tff(26,plain,
    ( ( ssList(sk7)
      | $false )
  <=> ssList(sk7) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ( ( ssList(sk7)
      | ( nil = sk3 ) )
  <=> ( ssList(sk7)
      | $false ) ),
    inference(monotonicity,[status(thm)],[7]) ).

tff(28,plain,
    ( ( ssList(sk7)
      | ( nil = sk3 ) )
  <=> ssList(sk7) ),
    inference(transitivity,[status(thm)],[27,26]) ).

tff(29,plain,
    ( ( ssList(sk7)
      | ( nil = sk3 ) )
  <=> ( ssList(sk7)
      | ( nil = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ( ( nil = sk3 )
      | ssList(sk7) )
  <=> ( ssList(sk7)
      | ( nil = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,axiom,
    ( ( nil = sk3 )
    | ssList(sk7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).

tff(32,plain,
    ( ssList(sk7)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[31,30]) ).

tff(33,plain,
    ( ssList(sk7)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[32,29]) ).

tff(34,plain,
    ssList(sk7),
    inference(modus_ponens,[status(thm)],[33,28]) ).

tff(35,plain,
    ( ( $false
      | ssItem(sk6) )
  <=> ssItem(sk6) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ( ( ( nil = sk3 )
      | ssItem(sk6) )
  <=> ( $false
      | ssItem(sk6) ) ),
    inference(monotonicity,[status(thm)],[7]) ).

tff(37,plain,
    ( ( ( nil = sk3 )
      | ssItem(sk6) )
  <=> ssItem(sk6) ),
    inference(transitivity,[status(thm)],[36,35]) ).

tff(38,plain,
    ( ( ( nil = sk3 )
      | ssItem(sk6) )
  <=> ( ( nil = sk3 )
      | ssItem(sk6) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,axiom,
    ( ( nil = sk3 )
    | ssItem(sk6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).

tff(40,plain,
    ( ( nil = sk3 )
    | ssItem(sk6) ),
    inference(modus_ponens,[status(thm)],[39,38]) ).

tff(41,plain,
    ( ( nil = sk3 )
    | ssItem(sk6) ),
    inference(modus_ponens,[status(thm)],[40,38]) ).

tff(42,plain,
    ( ( nil = sk3 )
    | ssItem(sk6) ),
    inference(modus_ponens,[status(thm)],[41,38]) ).

tff(43,plain,
    ( ( nil = sk3 )
    | ssItem(sk6) ),
    inference(modus_ponens,[status(thm)],[42,38]) ).

tff(44,plain,
    ( ( nil = sk3 )
    | ssItem(sk6) ),
    inference(modus_ponens,[status(thm)],[43,38]) ).

tff(45,plain,
    ( ( nil = sk3 )
    | ssItem(sk6) ),
    inference(modus_ponens,[status(thm)],[44,38]) ).

tff(46,plain,
    ssItem(sk6),
    inference(modus_ponens,[status(thm)],[45,37]) ).

tff(47,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(B,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(B,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(48,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | memberP(B,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | memberP(B,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[47]) ).

tff(49,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( app(app(B,cons(A,nil)),C) != sk1 )
          <=> ( app(app(B,cons(A,nil)),C) != sk3 ) )),
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(B,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk3 )
            | memberP(B,sk5(C,B,A)) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk3 )
            | memberP(B,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(B,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | memberP(B,sk5(C,B,A)) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(B,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(50,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(B,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | memberP(B,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[49]) ).

tff(51,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(B,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(B,sk5(C,B,A)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ ssItem(A)
                  | ~ ssList(B)
                  | ~ ssList(C) )
              <=> ( ~ ssList(C)
                  | ~ ssItem(A)
                  | ~ ssList(B) ) )),
              ( ( ~ ssItem(A)
                | ~ ssList(B)
                | ~ ssList(C)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            rewrite(
              ( ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            ( ( ~ ssItem(A)
              | ~ ssList(B)
              | ~ ssList(C)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) )
          <=> ( ~ ssList(C)
              | ~ ssItem(A)
              | ~ ssList(B)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
          ( ( ~ ssItem(A)
            | ~ ssList(B)
            | ~ ssList(C)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(B,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(B,sk5(C,B,A)) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(B,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(B,sk5(C,B,A)) ) )),
        ( ( ~ ssItem(A)
          | ~ ssList(B)
          | ~ ssList(C)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | memberP(B,sk5(C,B,A)) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | memberP(B,sk5(C,B,A)) ) )),
    inference(bind,[status(th)],]) ).

tff(53,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssItem(A)
        | ~ ssList(B)
        | ~ ssList(C)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(B,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(B,sk5(C,B,A)) ) ),
    inference(quant_intro,[status(thm)],[52]) ).

tff(54,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | memberP(B,sk5(C,B,A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

tff(55,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | memberP(B,sk5(C,B,A)) ),
    inference(modus_ponens,[status(thm)],[54,53]) ).

tff(56,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | memberP(B,sk5(C,B,A)) ),
    inference(modus_ponens,[status(thm)],[55,51]) ).

tff(57,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | memberP(B,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[56,50]) ).

tff(58,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | memberP(B,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(skolemize,[status(sab)],[57]) ).

tff(59,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | memberP(B,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[58,48]) ).

tff(60,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(B,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk7,sk5(sk8,sk7,sk6)) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(B,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,plain,
    ( ( ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | memberP(sk7,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(B,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | memberP(sk7,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(B,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
    inference(monotonicity,[status(thm)],[61]) ).

tff(63,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(B,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | memberP(sk7,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(B,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
    inference(transitivity,[status(thm)],[62,60]) ).

tff(64,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(B,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ~ ssList(sk7)
    | memberP(sk7,sk5(sk8,sk7,sk6))
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(65,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(B,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk7)
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
    | memberP(sk7,sk5(sk8,sk7,sk6)) ),
    inference(modus_ponens,[status(thm)],[64,63]) ).

tff(66,plain,
    memberP(sk7,sk5(sk8,sk7,sk6)),
    inference(unit_resolution,[status(thm)],[65,59,46,34,25,13]) ).

tff(67,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ssItem(sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ssItem(sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(68,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ssItem(sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ssItem(sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( app(app(B,cons(A,nil)),C) != sk1 )
          <=> ( app(app(B,cons(A,nil)),C) != sk3 ) )),
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk1 ) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ssItem(sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk1 ) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ssItem(sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(70,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ssItem(sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk1 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ssItem(sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[69]) ).

tff(71,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ssItem(sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk1 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ssItem(sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(72,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ ssItem(A)
                  | ~ ssList(B)
                  | ~ ssList(C) )
              <=> ( ~ ssList(C)
                  | ~ ssItem(A)
                  | ~ ssList(B) ) )),
              ( ( ~ ssItem(A)
                | ~ ssList(B)
                | ~ ssList(C)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            rewrite(
              ( ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            ( ( ~ ssItem(A)
              | ~ ssList(B)
              | ~ ssList(C)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) )
          <=> ( ~ ssList(C)
              | ~ ssItem(A)
              | ~ ssList(B)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
          ( ( ~ ssItem(A)
            | ~ ssList(B)
            | ~ ssList(C)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | ssItem(sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | ssItem(sk5(C,B,A)) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | ssItem(sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
        ( ( ~ ssItem(A)
          | ~ ssList(B)
          | ~ ssList(C)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | ssItem(sk5(C,B,A)) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ssItem(sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
    inference(bind,[status(th)],]) ).

tff(73,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssItem(A)
        | ~ ssList(B)
        | ~ ssList(C)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | ssItem(sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ssItem(sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
    inference(quant_intro,[status(thm)],[72]) ).

tff(74,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | ssItem(sk5(C,B,A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

tff(75,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ssItem(sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk1 ) ),
    inference(modus_ponens,[status(thm)],[74,73]) ).

tff(76,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ssItem(sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk1 ) ),
    inference(modus_ponens,[status(thm)],[75,71]) ).

tff(77,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ssItem(sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[76,70]) ).

tff(78,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ssItem(sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(skolemize,[status(sab)],[77]) ).

tff(79,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ssItem(sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[78,68]) ).

tff(80,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | ssItem(sk5(sk8,sk7,sk6)) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | ssItem(sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(81,plain,
    ( ( ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | ssItem(sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | ssItem(sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(82,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | ssItem(sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | ssItem(sk5(sk8,sk7,sk6)) ) ),
    inference(monotonicity,[status(thm)],[81]) ).

tff(83,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | ssItem(sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ssItem(sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | ssItem(sk5(sk8,sk7,sk6)) ) ),
    inference(transitivity,[status(thm)],[82,80]) ).

tff(84,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ssItem(sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ~ ssList(sk7)
    | ssItem(sk5(sk8,sk7,sk6))
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(85,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ssItem(sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk7)
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
    | ssItem(sk5(sk8,sk7,sk6)) ),
    inference(modus_ponens,[status(thm)],[84,83]) ).

tff(86,plain,
    ssItem(sk5(sk8,sk7,sk6)),
    inference(unit_resolution,[status(thm)],[85,79,46,34,25,13]) ).

tff(87,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(C,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(C,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(88,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | memberP(C,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | memberP(C,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[87]) ).

tff(89,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( app(app(B,cons(A,nil)),C) != sk1 )
          <=> ( app(app(B,cons(A,nil)),C) != sk3 ) )),
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(C,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk3 )
            | memberP(C,sk5(C,B,A)) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk3 )
            | memberP(C,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(C,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | memberP(C,sk5(C,B,A)) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(C,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(90,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(C,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | memberP(C,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[89]) ).

tff(91,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(C,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(C,sk5(C,B,A)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(92,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ ssItem(A)
                  | ~ ssList(B)
                  | ~ ssList(C) )
              <=> ( ~ ssList(C)
                  | ~ ssItem(A)
                  | ~ ssList(B) ) )),
              ( ( ~ ssItem(A)
                | ~ ssList(B)
                | ~ ssList(C)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            rewrite(
              ( ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            ( ( ~ ssItem(A)
              | ~ ssList(B)
              | ~ ssList(C)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) )
          <=> ( ~ ssList(C)
              | ~ ssItem(A)
              | ~ ssList(B)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
          ( ( ~ ssItem(A)
            | ~ ssList(B)
            | ~ ssList(C)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(C,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(C,sk5(C,B,A)) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(C,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | memberP(C,sk5(C,B,A)) ) )),
        ( ( ~ ssItem(A)
          | ~ ssList(B)
          | ~ ssList(C)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | memberP(C,sk5(C,B,A)) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | memberP(C,sk5(C,B,A)) ) )),
    inference(bind,[status(th)],]) ).

tff(93,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssItem(A)
        | ~ ssList(B)
        | ~ ssList(C)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(C,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | memberP(C,sk5(C,B,A)) ) ),
    inference(quant_intro,[status(thm)],[92]) ).

tff(94,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | memberP(C,sk5(C,B,A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

tff(95,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | memberP(C,sk5(C,B,A)) ),
    inference(modus_ponens,[status(thm)],[94,93]) ).

tff(96,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | memberP(C,sk5(C,B,A)) ),
    inference(modus_ponens,[status(thm)],[95,91]) ).

tff(97,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | memberP(C,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[96,90]) ).

tff(98,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | memberP(C,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(skolemize,[status(sab)],[97]) ).

tff(99,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | memberP(C,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[98,88]) ).

tff(100,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(C,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk8,sk5(sk8,sk7,sk6)) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(C,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk8,sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(101,plain,
    ( ( ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | memberP(sk8,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk8,sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(102,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(C,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | memberP(sk8,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(C,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk8,sk5(sk8,sk7,sk6)) ) ),
    inference(monotonicity,[status(thm)],[101]) ).

tff(103,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(C,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | memberP(sk8,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | memberP(C,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | memberP(sk8,sk5(sk8,sk7,sk6)) ) ),
    inference(transitivity,[status(thm)],[102,100]) ).

tff(104,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(C,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ~ ssList(sk7)
    | memberP(sk8,sk5(sk8,sk7,sk6))
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(105,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | memberP(C,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk7)
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
    | memberP(sk8,sk5(sk8,sk7,sk6)) ),
    inference(modus_ponens,[status(thm)],[104,103]) ).

tff(106,plain,
    memberP(sk8,sk5(sk8,sk7,sk6)),
    inference(unit_resolution,[status(thm)],[105,99,46,34,25,13]) ).

tff(107,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | leq(A,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | leq(A,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(108,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | leq(A,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | leq(A,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[107]) ).

tff(109,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( app(app(B,cons(A,nil)),C) != sk1 )
          <=> ( app(app(B,cons(A,nil)),C) != sk3 ) )),
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | leq(A,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk3 )
            | leq(A,sk5(C,B,A)) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk3 )
            | leq(A,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | leq(A,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | leq(A,sk5(C,B,A)) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | leq(A,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(110,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | leq(A,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | leq(A,sk5(C,B,A))
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[109]) ).

tff(111,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | leq(A,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | leq(A,sk5(C,B,A)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(112,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ ssItem(A)
                  | ~ ssList(B)
                  | ~ ssList(C) )
              <=> ( ~ ssList(C)
                  | ~ ssItem(A)
                  | ~ ssList(B) ) )),
              ( ( ~ ssItem(A)
                | ~ ssList(B)
                | ~ ssList(C)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            rewrite(
              ( ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            ( ( ~ ssItem(A)
              | ~ ssList(B)
              | ~ ssList(C)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) )
          <=> ( ~ ssList(C)
              | ~ ssItem(A)
              | ~ ssList(B)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
          ( ( ~ ssItem(A)
            | ~ ssList(B)
            | ~ ssList(C)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | leq(A,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | leq(A,sk5(C,B,A)) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | leq(A,sk5(C,B,A)) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | leq(A,sk5(C,B,A)) ) )),
        ( ( ~ ssItem(A)
          | ~ ssList(B)
          | ~ ssList(C)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | leq(A,sk5(C,B,A)) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | leq(A,sk5(C,B,A)) ) )),
    inference(bind,[status(th)],]) ).

tff(113,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssItem(A)
        | ~ ssList(B)
        | ~ ssList(C)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | leq(A,sk5(C,B,A)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | leq(A,sk5(C,B,A)) ) ),
    inference(quant_intro,[status(thm)],[112]) ).

tff(114,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | leq(A,sk5(C,B,A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).

tff(115,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | leq(A,sk5(C,B,A)) ),
    inference(modus_ponens,[status(thm)],[114,113]) ).

tff(116,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | leq(A,sk5(C,B,A)) ),
    inference(modus_ponens,[status(thm)],[115,111]) ).

tff(117,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | leq(A,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[116,110]) ).

tff(118,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | leq(A,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(skolemize,[status(sab)],[117]) ).

tff(119,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | leq(A,sk5(C,B,A))
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[118,108]) ).

tff(120,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | leq(A,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | leq(sk6,sk5(sk8,sk7,sk6)) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | leq(A,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | leq(sk6,sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(121,plain,
    ( ( ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | leq(sk6,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | leq(sk6,sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(122,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | leq(A,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | leq(sk6,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | leq(A,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | leq(sk6,sk5(sk8,sk7,sk6)) ) ),
    inference(monotonicity,[status(thm)],[121]) ).

tff(123,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | leq(A,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | leq(sk6,sk5(sk8,sk7,sk6))
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | leq(A,sk5(C,B,A))
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
      | leq(sk6,sk5(sk8,sk7,sk6)) ) ),
    inference(transitivity,[status(thm)],[122,120]) ).

tff(124,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | leq(A,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ~ ssList(sk7)
    | leq(sk6,sk5(sk8,sk7,sk6))
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(125,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | leq(A,sk5(C,B,A))
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk7)
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 )
    | leq(sk6,sk5(sk8,sk7,sk6)) ),
    inference(modus_ponens,[status(thm)],[124,123]) ).

tff(126,plain,
    leq(sk6,sk5(sk8,sk7,sk6)),
    inference(unit_resolution,[status(thm)],[125,119,46,34,25,13]) ).

tff(127,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ~ leq(sk5(C,B,A),A)
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ~ leq(sk5(C,B,A),A)
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(128,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ~ leq(sk5(C,B,A),A)
        | ( app(app(B,cons(A,nil)),C) != sk3 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ~ leq(sk5(C,B,A),A)
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[127]) ).

tff(129,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( app(app(B,cons(A,nil)),C) != sk1 )
          <=> ( app(app(B,cons(A,nil)),C) != sk3 ) )),
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | ~ leq(sk5(C,B,A),A) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk3 )
            | ~ leq(sk5(C,B,A),A) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk3 )
            | ~ leq(sk5(C,B,A),A) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ~ leq(sk5(C,B,A),A)
            | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | ~ leq(sk5(C,B,A),A) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ~ leq(sk5(C,B,A),A)
          | ( app(app(B,cons(A,nil)),C) != sk3 ) ) )),
    inference(bind,[status(th)],]) ).

tff(130,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | ~ leq(sk5(C,B,A),A) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ~ leq(sk5(C,B,A),A)
        | ( app(app(B,cons(A,nil)),C) != sk3 ) ) ),
    inference(quant_intro,[status(thm)],[129]) ).

tff(131,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | ~ leq(sk5(C,B,A),A) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | ~ leq(sk5(C,B,A),A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(132,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ ssItem(A)
                  | ~ ssList(B)
                  | ~ ssList(C) )
              <=> ( ~ ssList(C)
                  | ~ ssItem(A)
                  | ~ ssList(B) ) )),
              ( ( ~ ssItem(A)
                | ~ ssList(B)
                | ~ ssList(C)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            rewrite(
              ( ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
            ( ( ~ ssItem(A)
              | ~ ssList(B)
              | ~ ssList(C)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) )
          <=> ( ~ ssList(C)
              | ~ ssItem(A)
              | ~ ssList(B)
              | ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
          ( ( ~ ssItem(A)
            | ~ ssList(B)
            | ~ ssList(C)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | ~ leq(sk5(C,B,A),A) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | ~ leq(sk5(C,B,A),A) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | ~ leq(sk5(C,B,A),A) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(app(B,cons(A,nil)),C) != sk1 )
            | ~ leq(sk5(C,B,A),A) ) )),
        ( ( ~ ssItem(A)
          | ~ ssList(B)
          | ~ ssList(C)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | ~ leq(sk5(C,B,A),A) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(app(B,cons(A,nil)),C) != sk1 )
          | ~ leq(sk5(C,B,A),A) ) )),
    inference(bind,[status(th)],]) ).

tff(133,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssItem(A)
        | ~ ssList(B)
        | ~ ssList(C)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | ~ leq(sk5(C,B,A),A) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(app(B,cons(A,nil)),C) != sk1 )
        | ~ leq(sk5(C,B,A),A) ) ),
    inference(quant_intro,[status(thm)],[132]) ).

tff(134,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | ~ leq(sk5(C,B,A),A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).

tff(135,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | ~ leq(sk5(C,B,A),A) ),
    inference(modus_ponens,[status(thm)],[134,133]) ).

tff(136,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(app(B,cons(A,nil)),C) != sk1 )
      | ~ leq(sk5(C,B,A),A) ),
    inference(modus_ponens,[status(thm)],[135,131]) ).

tff(137,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ~ leq(sk5(C,B,A),A)
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[136,130]) ).

tff(138,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ~ leq(sk5(C,B,A),A)
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(skolemize,[status(sab)],[137]) ).

tff(139,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ~ leq(sk5(C,B,A),A)
      | ( app(app(B,cons(A,nil)),C) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[138,128]) ).

tff(140,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ~ leq(sk5(C,B,A),A)
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ leq(sk5(sk8,sk7,sk6),sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ~ leq(sk5(C,B,A),A)
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ leq(sk5(sk8,sk7,sk6),sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(141,plain,
    ( ( ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | ~ leq(sk5(sk8,sk7,sk6),sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ leq(sk5(sk8,sk7,sk6),sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(142,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ~ leq(sk5(C,B,A),A)
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | ~ leq(sk5(sk8,sk7,sk6),sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ~ leq(sk5(C,B,A),A)
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ leq(sk5(sk8,sk7,sk6),sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ) ),
    inference(monotonicity,[status(thm)],[141]) ).

tff(143,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ~ leq(sk5(C,B,A),A)
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | ~ leq(sk5(sk8,sk7,sk6),sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ~ leq(sk5(C,B,A),A)
            | ( app(app(B,cons(A,nil)),C) != sk3 ) )
      | ~ ssList(sk7)
      | ~ ssList(sk8)
      | ~ ssItem(sk6)
      | ~ leq(sk5(sk8,sk7,sk6),sk6)
      | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ) ),
    inference(transitivity,[status(thm)],[142,140]) ).

tff(144,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ~ leq(sk5(C,B,A),A)
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ~ ssList(sk7)
    | ~ leq(sk5(sk8,sk7,sk6),sk6)
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(145,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ~ leq(sk5(C,B,A),A)
          | ( app(app(B,cons(A,nil)),C) != sk3 ) )
    | ~ ssList(sk7)
    | ~ ssList(sk8)
    | ~ ssItem(sk6)
    | ~ leq(sk5(sk8,sk7,sk6),sk6)
    | ( app(app(sk7,cons(sk6,nil)),sk8) != sk3 ) ),
    inference(modus_ponens,[status(thm)],[144,143]) ).

tff(146,plain,
    ~ leq(sk5(sk8,sk7,sk6),sk6),
    inference(unit_resolution,[status(thm)],[145,139,46,34,25,13]) ).

tff(147,plain,
    ^ [A: $i] :
      refl(
        ( ( ~ ssItem(A)
          | ~ leq(sk6,A)
          | ~ memberP(sk8,A)
          | ~ memberP(sk7,A)
          | leq(A,sk6) )
      <=> ( ~ ssItem(A)
          | ~ leq(sk6,A)
          | ~ memberP(sk8,A)
          | ~ memberP(sk7,A)
          | leq(A,sk6) ) )),
    inference(bind,[status(th)],]) ).

tff(148,plain,
    ( ! [A: $i] :
        ( ~ ssItem(A)
        | ~ leq(sk6,A)
        | ~ memberP(sk8,A)
        | ~ memberP(sk7,A)
        | leq(A,sk6) )
  <=> ! [A: $i] :
        ( ~ ssItem(A)
        | ~ leq(sk6,A)
        | ~ memberP(sk8,A)
        | ~ memberP(sk7,A)
        | leq(A,sk6) ) ),
    inference(quant_intro,[status(thm)],[147]) ).

tff(149,plain,
    ^ [A: $i] :
      trans(
        monotonicity(
          iff_false(
            mp(
              mp(asserted(nil != sk1),
                rewrite(
                  ( ( nil != sk1 )
                <=> ( nil != sk1 ) )),
                nil != sk1),
              rewrite(
                ( ( nil != sk1 )
              <=> ( nil != sk3 ) )),
              nil != sk3),
            ( ( nil = sk3 )
          <=> $false )),
          ( ( ~ ssItem(A)
            | ( nil = sk3 )
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) )
        <=> ( ~ ssItem(A)
            | $false
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) ) )),
        rewrite(
          ( ( ~ ssItem(A)
            | $false
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) )
        <=> ( ~ ssItem(A)
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) ) )),
        ( ( ~ ssItem(A)
          | ( nil = sk3 )
          | ~ leq(sk6,A)
          | ~ memberP(sk8,A)
          | ~ memberP(sk7,A)
          | leq(A,sk6) )
      <=> ( ~ ssItem(A)
          | ~ leq(sk6,A)
          | ~ memberP(sk8,A)
          | ~ memberP(sk7,A)
          | leq(A,sk6) ) )),
    inference(bind,[status(th)],]) ).

tff(150,plain,
    ( ! [A: $i] :
        ( ~ ssItem(A)
        | ( nil = sk3 )
        | ~ leq(sk6,A)
        | ~ memberP(sk8,A)
        | ~ memberP(sk7,A)
        | leq(A,sk6) )
  <=> ! [A: $i] :
        ( ~ ssItem(A)
        | ~ leq(sk6,A)
        | ~ memberP(sk8,A)
        | ~ memberP(sk7,A)
        | leq(A,sk6) ) ),
    inference(quant_intro,[status(thm)],[149]) ).

tff(151,plain,
    ( ! [A: $i] :
        ( ~ ssItem(A)
        | ( nil = sk3 )
        | ~ leq(sk6,A)
        | ~ memberP(sk8,A)
        | ~ memberP(sk7,A)
        | leq(A,sk6) )
  <=> ! [A: $i] :
        ( ~ ssItem(A)
        | ( nil = sk3 )
        | ~ leq(sk6,A)
        | ~ memberP(sk8,A)
        | ~ memberP(sk7,A)
        | leq(A,sk6) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(152,plain,
    ^ [A: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              trans(
                monotonicity(
                  trans(
                    monotonicity(
                      rewrite(
                        ( ( ( nil = sk3 )
                          | ~ ssItem(A) )
                      <=> ( ~ ssItem(A)
                          | ( nil = sk3 ) ) )),
                      ( ( ( nil = sk3 )
                        | ~ ssItem(A)
                        | leq(A,sk6) )
                    <=> ( ~ ssItem(A)
                        | ( nil = sk3 )
                        | leq(A,sk6) ) )),
                    rewrite(
                      ( ( ~ ssItem(A)
                        | ( nil = sk3 )
                        | leq(A,sk6) )
                    <=> ( ~ ssItem(A)
                        | ( nil = sk3 )
                        | leq(A,sk6) ) )),
                    ( ( ( nil = sk3 )
                      | ~ ssItem(A)
                      | leq(A,sk6) )
                  <=> ( ~ ssItem(A)
                      | ( nil = sk3 )
                      | leq(A,sk6) ) )),
                  ( ( ( nil = sk3 )
                    | ~ ssItem(A)
                    | leq(A,sk6)
                    | ~ memberP(sk7,A) )
                <=> ( ~ ssItem(A)
                    | ( nil = sk3 )
                    | leq(A,sk6)
                    | ~ memberP(sk7,A) ) )),
                rewrite(
                  ( ( ~ ssItem(A)
                    | ( nil = sk3 )
                    | leq(A,sk6)
                    | ~ memberP(sk7,A) )
                <=> ( ~ ssItem(A)
                    | ( nil = sk3 )
                    | ~ memberP(sk7,A)
                    | leq(A,sk6) ) )),
                ( ( ( nil = sk3 )
                  | ~ ssItem(A)
                  | leq(A,sk6)
                  | ~ memberP(sk7,A) )
              <=> ( ~ ssItem(A)
                  | ( nil = sk3 )
                  | ~ memberP(sk7,A)
                  | leq(A,sk6) ) )),
              ( ( ( nil = sk3 )
                | ~ ssItem(A)
                | leq(A,sk6)
                | ~ memberP(sk7,A)
                | ~ memberP(sk8,A) )
            <=> ( ~ ssItem(A)
                | ( nil = sk3 )
                | ~ memberP(sk7,A)
                | leq(A,sk6)
                | ~ memberP(sk8,A) ) )),
            rewrite(
              ( ( ~ ssItem(A)
                | ( nil = sk3 )
                | ~ memberP(sk7,A)
                | leq(A,sk6)
                | ~ memberP(sk8,A) )
            <=> ( ~ ssItem(A)
                | ( nil = sk3 )
                | ~ memberP(sk8,A)
                | ~ memberP(sk7,A)
                | leq(A,sk6) ) )),
            ( ( ( nil = sk3 )
              | ~ ssItem(A)
              | leq(A,sk6)
              | ~ memberP(sk7,A)
              | ~ memberP(sk8,A) )
          <=> ( ~ ssItem(A)
              | ( nil = sk3 )
              | ~ memberP(sk8,A)
              | ~ memberP(sk7,A)
              | leq(A,sk6) ) )),
          ( ( ( nil = sk3 )
            | ~ ssItem(A)
            | leq(A,sk6)
            | ~ memberP(sk7,A)
            | ~ memberP(sk8,A)
            | ~ leq(sk6,A) )
        <=> ( ~ ssItem(A)
            | ( nil = sk3 )
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6)
            | ~ leq(sk6,A) ) )),
        rewrite(
          ( ( ~ ssItem(A)
            | ( nil = sk3 )
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6)
            | ~ leq(sk6,A) )
        <=> ( ~ ssItem(A)
            | ( nil = sk3 )
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) ) )),
        ( ( ( nil = sk3 )
          | ~ ssItem(A)
          | leq(A,sk6)
          | ~ memberP(sk7,A)
          | ~ memberP(sk8,A)
          | ~ leq(sk6,A) )
      <=> ( ~ ssItem(A)
          | ( nil = sk3 )
          | ~ leq(sk6,A)
          | ~ memberP(sk8,A)
          | ~ memberP(sk7,A)
          | leq(A,sk6) ) )),
    inference(bind,[status(th)],]) ).

tff(153,plain,
    ( ! [A: $i] :
        ( ( nil = sk3 )
        | ~ ssItem(A)
        | leq(A,sk6)
        | ~ memberP(sk7,A)
        | ~ memberP(sk8,A)
        | ~ leq(sk6,A) )
  <=> ! [A: $i] :
        ( ~ ssItem(A)
        | ( nil = sk3 )
        | ~ leq(sk6,A)
        | ~ memberP(sk8,A)
        | ~ memberP(sk7,A)
        | leq(A,sk6) ) ),
    inference(quant_intro,[status(thm)],[152]) ).

tff(154,axiom,
    ! [A: $i] :
      ( ( nil = sk3 )
      | ~ ssItem(A)
      | leq(A,sk6)
      | ~ memberP(sk7,A)
      | ~ memberP(sk8,A)
      | ~ leq(sk6,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).

tff(155,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ( nil = sk3 )
      | ~ leq(sk6,A)
      | ~ memberP(sk8,A)
      | ~ memberP(sk7,A)
      | leq(A,sk6) ),
    inference(modus_ponens,[status(thm)],[154,153]) ).

tff(156,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ( nil = sk3 )
      | ~ leq(sk6,A)
      | ~ memberP(sk8,A)
      | ~ memberP(sk7,A)
      | leq(A,sk6) ),
    inference(modus_ponens,[status(thm)],[155,151]) ).

tff(157,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ~ leq(sk6,A)
      | ~ memberP(sk8,A)
      | ~ memberP(sk7,A)
      | leq(A,sk6) ),
    inference(modus_ponens,[status(thm)],[156,150]) ).

tff(158,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ~ leq(sk6,A)
      | ~ memberP(sk8,A)
      | ~ memberP(sk7,A)
      | leq(A,sk6) ),
    inference(skolemize,[status(sab)],[157]) ).

tff(159,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ~ leq(sk6,A)
      | ~ memberP(sk8,A)
      | ~ memberP(sk7,A)
      | leq(A,sk6) ),
    inference(modus_ponens,[status(thm)],[158,148]) ).

tff(160,plain,
    ( ( ~ ! [A: $i] :
            ( ~ ssItem(A)
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) )
      | leq(sk5(sk8,sk7,sk6),sk6)
      | ~ ssItem(sk5(sk8,sk7,sk6))
      | ~ leq(sk6,sk5(sk8,sk7,sk6))
      | ~ memberP(sk8,sk5(sk8,sk7,sk6))
      | ~ memberP(sk7,sk5(sk8,sk7,sk6)) )
  <=> ( ~ ! [A: $i] :
            ( ~ ssItem(A)
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) )
      | leq(sk5(sk8,sk7,sk6),sk6)
      | ~ ssItem(sk5(sk8,sk7,sk6))
      | ~ leq(sk6,sk5(sk8,sk7,sk6))
      | ~ memberP(sk8,sk5(sk8,sk7,sk6))
      | ~ memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(161,plain,
    ( ( ~ ssItem(sk5(sk8,sk7,sk6))
      | ~ leq(sk6,sk5(sk8,sk7,sk6))
      | ~ memberP(sk8,sk5(sk8,sk7,sk6))
      | ~ memberP(sk7,sk5(sk8,sk7,sk6))
      | leq(sk5(sk8,sk7,sk6),sk6) )
  <=> ( leq(sk5(sk8,sk7,sk6),sk6)
      | ~ ssItem(sk5(sk8,sk7,sk6))
      | ~ leq(sk6,sk5(sk8,sk7,sk6))
      | ~ memberP(sk8,sk5(sk8,sk7,sk6))
      | ~ memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(162,plain,
    ( ( ~ ! [A: $i] :
            ( ~ ssItem(A)
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) )
      | ~ ssItem(sk5(sk8,sk7,sk6))
      | ~ leq(sk6,sk5(sk8,sk7,sk6))
      | ~ memberP(sk8,sk5(sk8,sk7,sk6))
      | ~ memberP(sk7,sk5(sk8,sk7,sk6))
      | leq(sk5(sk8,sk7,sk6),sk6) )
  <=> ( ~ ! [A: $i] :
            ( ~ ssItem(A)
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) )
      | leq(sk5(sk8,sk7,sk6),sk6)
      | ~ ssItem(sk5(sk8,sk7,sk6))
      | ~ leq(sk6,sk5(sk8,sk7,sk6))
      | ~ memberP(sk8,sk5(sk8,sk7,sk6))
      | ~ memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
    inference(monotonicity,[status(thm)],[161]) ).

tff(163,plain,
    ( ( ~ ! [A: $i] :
            ( ~ ssItem(A)
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) )
      | ~ ssItem(sk5(sk8,sk7,sk6))
      | ~ leq(sk6,sk5(sk8,sk7,sk6))
      | ~ memberP(sk8,sk5(sk8,sk7,sk6))
      | ~ memberP(sk7,sk5(sk8,sk7,sk6))
      | leq(sk5(sk8,sk7,sk6),sk6) )
  <=> ( ~ ! [A: $i] :
            ( ~ ssItem(A)
            | ~ leq(sk6,A)
            | ~ memberP(sk8,A)
            | ~ memberP(sk7,A)
            | leq(A,sk6) )
      | leq(sk5(sk8,sk7,sk6),sk6)
      | ~ ssItem(sk5(sk8,sk7,sk6))
      | ~ leq(sk6,sk5(sk8,sk7,sk6))
      | ~ memberP(sk8,sk5(sk8,sk7,sk6))
      | ~ memberP(sk7,sk5(sk8,sk7,sk6)) ) ),
    inference(transitivity,[status(thm)],[162,160]) ).

tff(164,plain,
    ( ~ ! [A: $i] :
          ( ~ ssItem(A)
          | ~ leq(sk6,A)
          | ~ memberP(sk8,A)
          | ~ memberP(sk7,A)
          | leq(A,sk6) )
    | ~ ssItem(sk5(sk8,sk7,sk6))
    | ~ leq(sk6,sk5(sk8,sk7,sk6))
    | ~ memberP(sk8,sk5(sk8,sk7,sk6))
    | ~ memberP(sk7,sk5(sk8,sk7,sk6))
    | leq(sk5(sk8,sk7,sk6),sk6) ),
    inference(quant_inst,[status(thm)],]) ).

tff(165,plain,
    ( ~ ! [A: $i] :
          ( ~ ssItem(A)
          | ~ leq(sk6,A)
          | ~ memberP(sk8,A)
          | ~ memberP(sk7,A)
          | leq(A,sk6) )
    | leq(sk5(sk8,sk7,sk6),sk6)
    | ~ ssItem(sk5(sk8,sk7,sk6))
    | ~ leq(sk6,sk5(sk8,sk7,sk6))
    | ~ memberP(sk8,sk5(sk8,sk7,sk6))
    | ~ memberP(sk7,sk5(sk8,sk7,sk6)) ),
    inference(modus_ponens,[status(thm)],[164,163]) ).

tff(166,plain,
    $false,
    inference(unit_resolution,[status(thm)],[165,159,146,126,106,86,66]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC220-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Sep  3 22:53:48 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.77/0.96  % SZS status Unsatisfiable
% 0.77/0.96  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------