TSTP Solution File: SWC407-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWC407-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 11:57:46 EDT 2022

% Result   : Unsatisfiable 0.74s 0.73s
% Output   : Proof 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   69
% Syntax   : Number of formulae    :  153 (  45 unt;  14 typ;   0 def)
%            Number of atoms       :  948 ( 167 equ)
%            Maximal formula atoms :   24 (   6 avg)
%            Number of connectives : 1412 ( 673   ~; 652   |;   0   &)
%                                         (  87 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :   70 (  70 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  238 ( 214   !;   0   ?; 238   :)

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

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

tff(sk4_type,type,
    sk4: $i ).

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

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

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

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

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

tff(skaf43_type,type,
    skaf43: ( $i * $i ) > $i ).

tff(skaf42_type,type,
    skaf42: ( $i * $i ) > $i ).

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

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

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

tff(sk2_type,type,
    sk2: $i ).

tff(1,plain,
    ( ( sk3 = nil )
  <=> ( nil = sk3 ) ),
    inference(commutativity,[status(thm)],]) ).

tff(2,plain,
    ( memberP(sk1,sk5)
  <=> memberP(sk3,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( memberP(sk1,sk5)
  <=> memberP(sk1,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    memberP(sk1,sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

tff(5,plain,
    memberP(sk1,sk5),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    memberP(sk3,sk5),
    inference(modus_ponens,[status(thm)],[5,2]) ).

tff(7,plain,
    ( ssItem(sk5)
  <=> ssItem(sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,axiom,
    ssItem(sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

tff(9,plain,
    ssItem(sk5),
    inference(modus_ponens,[status(thm)],[8,7]) ).

tff(10,plain,
    ( ssList(sk1)
  <=> ssList(sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,plain,
    ( ssList(sk1)
  <=> ssList(sk1) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    ssList(sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).

tff(13,plain,
    ssList(sk1),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ssList(sk3),
    inference(modus_ponens,[status(thm)],[13,10]) ).

tff(15,plain,
    ^ [V: $i,U: $i] :
      refl(
        ( ( ~ ssList(U)
          | ~ ssItem(V)
          | ~ memberP(U,V)
          | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
      <=> ( ~ ssList(U)
          | ~ ssItem(V)
          | ~ memberP(U,V)
          | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
    inference(bind,[status(th)],]) ).

tff(16,plain,
    ( ! [V: $i,U: $i] :
        ( ~ ssList(U)
        | ~ ssItem(V)
        | ~ memberP(U,V)
        | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
  <=> ! [V: $i,U: $i] :
        ( ~ ssList(U)
        | ~ ssItem(V)
        | ~ memberP(U,V)
        | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
    inference(quant_intro,[status(thm)],[15]) ).

tff(17,plain,
    ( ! [V: $i,U: $i] :
        ( ~ ssList(U)
        | ~ ssItem(V)
        | ~ memberP(U,V)
        | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
  <=> ! [V: $i,U: $i] :
        ( ~ ssList(U)
        | ~ ssItem(V)
        | ~ memberP(U,V)
        | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ^ [V: $i,U: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ memberP(U,V)
                  | ~ ssItem(V) )
              <=> ( ~ ssItem(V)
                  | ~ memberP(U,V) ) )),
              ( ( ~ memberP(U,V)
                | ~ ssItem(V)
                | ~ ssList(U) )
            <=> ( ~ ssItem(V)
                | ~ memberP(U,V)
                | ~ ssList(U) ) )),
            rewrite(
              ( ( ~ ssItem(V)
                | ~ memberP(U,V)
                | ~ ssList(U) )
            <=> ( ~ ssList(U)
                | ~ ssItem(V)
                | ~ memberP(U,V) ) )),
            ( ( ~ memberP(U,V)
              | ~ ssItem(V)
              | ~ ssList(U) )
          <=> ( ~ ssList(U)
              | ~ ssItem(V)
              | ~ memberP(U,V) ) )),
          ( ( ~ memberP(U,V)
            | ~ ssItem(V)
            | ~ ssList(U)
            | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
        <=> ( ~ ssList(U)
            | ~ ssItem(V)
            | ~ memberP(U,V)
            | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
        rewrite(
          ( ( ~ ssList(U)
            | ~ ssItem(V)
            | ~ memberP(U,V)
            | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
        <=> ( ~ ssList(U)
            | ~ ssItem(V)
            | ~ memberP(U,V)
            | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
        ( ( ~ memberP(U,V)
          | ~ ssItem(V)
          | ~ ssList(U)
          | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
      <=> ( ~ ssList(U)
          | ~ ssItem(V)
          | ~ memberP(U,V)
          | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [V: $i,U: $i] :
        ( ~ memberP(U,V)
        | ~ ssItem(V)
        | ~ ssList(U)
        | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
  <=> ! [V: $i,U: $i] :
        ( ~ ssList(U)
        | ~ ssItem(V)
        | ~ memberP(U,V)
        | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,axiom,
    ! [V: $i,U: $i] :
      ( ~ memberP(U,V)
      | ~ ssItem(V)
      | ~ ssList(U)
      | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).

tff(21,plain,
    ! [V: $i,U: $i] :
      ( ~ ssList(U)
      | ~ ssItem(V)
      | ~ memberP(U,V)
      | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
    inference(modus_ponens,[status(thm)],[20,19]) ).

tff(22,plain,
    ! [V: $i,U: $i] :
      ( ~ ssList(U)
      | ~ ssItem(V)
      | ~ memberP(U,V)
      | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
    inference(modus_ponens,[status(thm)],[21,17]) ).

tff(23,plain,
    ! [V: $i,U: $i] :
      ( ~ ssList(U)
      | ~ ssItem(V)
      | ~ memberP(U,V)
      | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [V: $i,U: $i] :
      ( ~ ssList(U)
      | ~ ssItem(V)
      | ~ memberP(U,V)
      | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
    inference(modus_ponens,[status(thm)],[23,16]) ).

tff(25,plain,
    ( ( ~ ! [V: $i,U: $i] :
            ( ~ ssList(U)
            | ~ ssItem(V)
            | ~ memberP(U,V)
            | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
      | ~ ssList(sk3)
      | ~ ssItem(sk5)
      | ~ memberP(sk3,sk5)
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) )
  <=> ( ~ ! [V: $i,U: $i] :
            ( ~ ssList(U)
            | ~ ssItem(V)
            | ~ memberP(U,V)
            | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
      | ~ ssList(sk3)
      | ~ ssItem(sk5)
      | ~ memberP(sk3,sk5)
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [V: $i,U: $i] :
          ( ~ ssList(U)
          | ~ ssItem(V)
          | ~ memberP(U,V)
          | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
    | ~ ssList(sk3)
    | ~ ssItem(sk5)
    | ~ memberP(sk3,sk5)
    | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [V: $i,U: $i] :
          ( ~ ssList(U)
          | ~ ssItem(V)
          | ~ memberP(U,V)
          | ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
    | ~ ssList(sk3)
    | ~ ssItem(sk5)
    | ~ memberP(sk3,sk5)
    | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3,
    inference(unit_resolution,[status(thm)],[27,24,14,9,6]) ).

tff(29,plain,
    ( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = nil )
  <=> ( sk3 = nil ) ),
    inference(monotonicity,[status(thm)],[28]) ).

tff(30,plain,
    ( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = nil )
  <=> ( nil = sk3 ) ),
    inference(transitivity,[status(thm)],[29,1]) ).

tff(31,plain,
    ( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil )
  <=> ( nil != sk3 ) ),
    inference(monotonicity,[status(thm)],[30]) ).

tff(32,plain,
    ^ [V: $i,U: $i] :
      refl(
        ( ssList(skaf42(U,V))
      <=> ssList(skaf42(U,V)) )),
    inference(bind,[status(th)],]) ).

tff(33,plain,
    ( ! [V: $i,U: $i] : ssList(skaf42(U,V))
  <=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
    inference(quant_intro,[status(thm)],[32]) ).

tff(34,plain,
    ( ! [V: $i,U: $i] : ssList(skaf42(U,V))
  <=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,axiom,
    ! [V: $i,U: $i] : ssList(skaf42(U,V)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).

tff(36,plain,
    ! [V: $i,U: $i] : ssList(skaf42(U,V)),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ! [V: $i,U: $i] : ssList(skaf42(U,V)),
    inference(skolemize,[status(sab)],[36]) ).

tff(38,plain,
    ! [V: $i,U: $i] : ssList(skaf42(U,V)),
    inference(modus_ponens,[status(thm)],[37,33]) ).

tff(39,plain,
    ( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
    | ssList(skaf42(sk3,sk5)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(40,plain,
    ssList(skaf42(sk3,sk5)),
    inference(unit_resolution,[status(thm)],[39,38]) ).

tff(41,plain,
    ^ [V: $i,U: $i] :
      refl(
        ( ssList(skaf43(U,V))
      <=> ssList(skaf43(U,V)) )),
    inference(bind,[status(th)],]) ).

tff(42,plain,
    ( ! [V: $i,U: $i] : ssList(skaf43(U,V))
  <=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,plain,
    ( ! [V: $i,U: $i] : ssList(skaf43(U,V))
  <=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,axiom,
    ! [V: $i,U: $i] : ssList(skaf43(U,V)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).

tff(45,plain,
    ! [V: $i,U: $i] : ssList(skaf43(U,V)),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ! [V: $i,U: $i] : ssList(skaf43(U,V)),
    inference(skolemize,[status(sab)],[45]) ).

tff(47,plain,
    ! [V: $i,U: $i] : ssList(skaf43(U,V)),
    inference(modus_ponens,[status(thm)],[46,42]) ).

tff(48,plain,
    ( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
    | ssList(skaf43(sk5,sk3)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(49,plain,
    ssList(skaf43(sk5,sk3)),
    inference(unit_resolution,[status(thm)],[48,47]) ).

tff(50,plain,
    ^ [U: $i] :
      refl(
        ( ( ~ ssItem(U)
          | ~ memberP(nil,U) )
      <=> ( ~ ssItem(U)
          | ~ memberP(nil,U) ) )),
    inference(bind,[status(th)],]) ).

tff(51,plain,
    ( ! [U: $i] :
        ( ~ ssItem(U)
        | ~ memberP(nil,U) )
  <=> ! [U: $i] :
        ( ~ ssItem(U)
        | ~ memberP(nil,U) ) ),
    inference(quant_intro,[status(thm)],[50]) ).

tff(52,plain,
    ( ! [U: $i] :
        ( ~ ssItem(U)
        | ~ memberP(nil,U) )
  <=> ! [U: $i] :
        ( ~ ssItem(U)
        | ~ memberP(nil,U) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,plain,
    ^ [U: $i] :
      rewrite(
        ( ( ~ memberP(nil,U)
          | ~ ssItem(U) )
      <=> ( ~ ssItem(U)
          | ~ memberP(nil,U) ) )),
    inference(bind,[status(th)],]) ).

tff(54,plain,
    ( ! [U: $i] :
        ( ~ memberP(nil,U)
        | ~ ssItem(U) )
  <=> ! [U: $i] :
        ( ~ ssItem(U)
        | ~ memberP(nil,U) ) ),
    inference(quant_intro,[status(thm)],[53]) ).

tff(55,axiom,
    ! [U: $i] :
      ( ~ memberP(nil,U)
      | ~ ssItem(U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).

tff(56,plain,
    ! [U: $i] :
      ( ~ ssItem(U)
      | ~ memberP(nil,U) ),
    inference(modus_ponens,[status(thm)],[55,54]) ).

tff(57,plain,
    ! [U: $i] :
      ( ~ ssItem(U)
      | ~ memberP(nil,U) ),
    inference(modus_ponens,[status(thm)],[56,52]) ).

tff(58,plain,
    ! [U: $i] :
      ( ~ ssItem(U)
      | ~ memberP(nil,U) ),
    inference(skolemize,[status(sab)],[57]) ).

tff(59,plain,
    ! [U: $i] :
      ( ~ ssItem(U)
      | ~ memberP(nil,U) ),
    inference(modus_ponens,[status(thm)],[58,51]) ).

tff(60,plain,
    ( ( ~ ! [U: $i] :
            ( ~ ssItem(U)
            | ~ memberP(nil,U) )
      | ~ ssItem(sk5)
      | ~ memberP(nil,sk5) )
  <=> ( ~ ! [U: $i] :
            ( ~ ssItem(U)
            | ~ memberP(nil,U) )
      | ~ ssItem(sk5)
      | ~ memberP(nil,sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,plain,
    ( ~ ! [U: $i] :
          ( ~ ssItem(U)
          | ~ memberP(nil,U) )
    | ~ ssItem(sk5)
    | ~ memberP(nil,sk5) ),
    inference(quant_inst,[status(thm)],]) ).

tff(62,plain,
    ( ~ ! [U: $i] :
          ( ~ ssItem(U)
          | ~ memberP(nil,U) )
    | ~ ssItem(sk5)
    | ~ memberP(nil,sk5) ),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    ~ memberP(nil,sk5),
    inference(unit_resolution,[status(thm)],[62,59,9]) ).

tff(64,plain,
    ^ [W: $i,V: $i,U: $i,X: $i] :
      refl(
        ( ( ~ ssList(X)
          | ~ ssList(U)
          | ~ ssItem(V)
          | memberP(X,V)
          | ~ ssList(W)
          | ( app(U,cons(V,W)) != X ) )
      <=> ( ~ ssList(X)
          | ~ ssList(U)
          | ~ ssItem(V)
          | memberP(X,V)
          | ~ ssList(W)
          | ( app(U,cons(V,W)) != X ) ) )),
    inference(bind,[status(th)],]) ).

tff(65,plain,
    ( ! [W: $i,V: $i,U: $i,X: $i] :
        ( ~ ssList(X)
        | ~ ssList(U)
        | ~ ssItem(V)
        | memberP(X,V)
        | ~ ssList(W)
        | ( app(U,cons(V,W)) != X ) )
  <=> ! [W: $i,V: $i,U: $i,X: $i] :
        ( ~ ssList(X)
        | ~ ssList(U)
        | ~ ssItem(V)
        | memberP(X,V)
        | ~ ssList(W)
        | ( app(U,cons(V,W)) != X ) ) ),
    inference(quant_intro,[status(thm)],[64]) ).

tff(66,plain,
    ( ! [W: $i,V: $i,U: $i,X: $i] :
        ( ~ ssList(X)
        | ~ ssList(U)
        | ~ ssItem(V)
        | memberP(X,V)
        | ~ ssList(W)
        | ( app(U,cons(V,W)) != X ) )
  <=> ! [W: $i,V: $i,U: $i,X: $i] :
        ( ~ ssList(X)
        | ~ ssList(U)
        | ~ ssItem(V)
        | memberP(X,V)
        | ~ ssList(W)
        | ( app(U,cons(V,W)) != X ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,plain,
    ^ [W: $i,V: $i,U: $i,X: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              trans(
                monotonicity(
                  trans(
                    monotonicity(
                      rewrite(
                        ( ( ( app(U,cons(V,W)) != X )
                          | ~ ssList(W) )
                      <=> ( ~ ssList(W)
                          | ( app(U,cons(V,W)) != X ) ) )),
                      ( ( ( app(U,cons(V,W)) != X )
                        | ~ ssList(W)
                        | ~ ssList(U) )
                    <=> ( ~ ssList(W)
                        | ( app(U,cons(V,W)) != X )
                        | ~ ssList(U) ) )),
                    rewrite(
                      ( ( ~ ssList(W)
                        | ( app(U,cons(V,W)) != X )
                        | ~ ssList(U) )
                    <=> ( ~ ssList(U)
                        | ~ ssList(W)
                        | ( app(U,cons(V,W)) != X ) ) )),
                    ( ( ( app(U,cons(V,W)) != X )
                      | ~ ssList(W)
                      | ~ ssList(U) )
                  <=> ( ~ ssList(U)
                      | ~ ssList(W)
                      | ( app(U,cons(V,W)) != X ) ) )),
                  ( ( ( app(U,cons(V,W)) != X )
                    | ~ ssList(W)
                    | ~ ssList(U)
                    | ~ ssItem(V) )
                <=> ( ~ ssList(U)
                    | ~ ssList(W)
                    | ( app(U,cons(V,W)) != X )
                    | ~ ssItem(V) ) )),
                rewrite(
                  ( ( ~ ssList(U)
                    | ~ ssList(W)
                    | ( app(U,cons(V,W)) != X )
                    | ~ ssItem(V) )
                <=> ( ~ ssList(U)
                    | ~ ssItem(V)
                    | ~ ssList(W)
                    | ( app(U,cons(V,W)) != X ) ) )),
                ( ( ( app(U,cons(V,W)) != X )
                  | ~ ssList(W)
                  | ~ ssList(U)
                  | ~ ssItem(V) )
              <=> ( ~ ssList(U)
                  | ~ ssItem(V)
                  | ~ ssList(W)
                  | ( app(U,cons(V,W)) != X ) ) )),
              ( ( ( app(U,cons(V,W)) != X )
                | ~ ssList(W)
                | ~ ssList(U)
                | ~ ssItem(V)
                | ~ ssList(X) )
            <=> ( ~ ssList(U)
                | ~ ssItem(V)
                | ~ ssList(W)
                | ( app(U,cons(V,W)) != X )
                | ~ ssList(X) ) )),
            rewrite(
              ( ( ~ ssList(U)
                | ~ ssItem(V)
                | ~ ssList(W)
                | ( app(U,cons(V,W)) != X )
                | ~ ssList(X) )
            <=> ( ~ ssList(X)
                | ~ ssList(U)
                | ~ ssItem(V)
                | ~ ssList(W)
                | ( app(U,cons(V,W)) != X ) ) )),
            ( ( ( app(U,cons(V,W)) != X )
              | ~ ssList(W)
              | ~ ssList(U)
              | ~ ssItem(V)
              | ~ ssList(X) )
          <=> ( ~ ssList(X)
              | ~ ssList(U)
              | ~ ssItem(V)
              | ~ ssList(W)
              | ( app(U,cons(V,W)) != X ) ) )),
          ( ( ( app(U,cons(V,W)) != X )
            | ~ ssList(W)
            | ~ ssList(U)
            | ~ ssItem(V)
            | ~ ssList(X)
            | memberP(X,V) )
        <=> ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X )
            | memberP(X,V) ) )),
        rewrite(
          ( ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X )
            | memberP(X,V) )
        <=> ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | memberP(X,V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X ) ) )),
        ( ( ( app(U,cons(V,W)) != X )
          | ~ ssList(W)
          | ~ ssList(U)
          | ~ ssItem(V)
          | ~ ssList(X)
          | memberP(X,V) )
      <=> ( ~ ssList(X)
          | ~ ssList(U)
          | ~ ssItem(V)
          | memberP(X,V)
          | ~ ssList(W)
          | ( app(U,cons(V,W)) != X ) ) )),
    inference(bind,[status(th)],]) ).

tff(68,plain,
    ( ! [W: $i,V: $i,U: $i,X: $i] :
        ( ( app(U,cons(V,W)) != X )
        | ~ ssList(W)
        | ~ ssList(U)
        | ~ ssItem(V)
        | ~ ssList(X)
        | memberP(X,V) )
  <=> ! [W: $i,V: $i,U: $i,X: $i] :
        ( ~ ssList(X)
        | ~ ssList(U)
        | ~ ssItem(V)
        | memberP(X,V)
        | ~ ssList(W)
        | ( app(U,cons(V,W)) != X ) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,axiom,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( ( app(U,cons(V,W)) != X )
      | ~ ssList(W)
      | ~ ssList(U)
      | ~ ssItem(V)
      | ~ ssList(X)
      | memberP(X,V) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause175) ).

tff(70,plain,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( ~ ssList(X)
      | ~ ssList(U)
      | ~ ssItem(V)
      | memberP(X,V)
      | ~ ssList(W)
      | ( app(U,cons(V,W)) != X ) ),
    inference(modus_ponens,[status(thm)],[69,68]) ).

tff(71,plain,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( ~ ssList(X)
      | ~ ssList(U)
      | ~ ssItem(V)
      | memberP(X,V)
      | ~ ssList(W)
      | ( app(U,cons(V,W)) != X ) ),
    inference(modus_ponens,[status(thm)],[70,66]) ).

tff(72,plain,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( ~ ssList(X)
      | ~ ssList(U)
      | ~ ssItem(V)
      | memberP(X,V)
      | ~ ssList(W)
      | ( app(U,cons(V,W)) != X ) ),
    inference(skolemize,[status(sab)],[71]) ).

tff(73,plain,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( ~ ssList(X)
      | ~ ssList(U)
      | ~ ssItem(V)
      | memberP(X,V)
      | ~ ssList(W)
      | ( app(U,cons(V,W)) != X ) ),
    inference(modus_ponens,[status(thm)],[72,65]) ).

tff(74,plain,
    ( ssList(nil)
  <=> ssList(nil) ),
    inference(rewrite,[status(thm)],]) ).

tff(75,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).

tff(76,plain,
    ssList(nil),
    inference(modus_ponens,[status(thm)],[75,74]) ).

tff(77,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
            ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | memberP(X,V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X ) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssList(skaf43(sk5,sk3))
      | ~ ssList(skaf42(sk3,sk5))
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) )
  <=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
            ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | memberP(X,V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X ) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssList(skaf43(sk5,sk3))
      | ~ ssList(skaf42(sk3,sk5))
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,plain,
    ( ( ~ ssList(nil)
      | ~ ssList(skaf42(sk3,sk5))
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssList(skaf43(sk5,sk3))
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) )
  <=> ( ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssList(skaf43(sk5,sk3))
      | ~ ssList(skaf42(sk3,sk5))
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(79,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
            ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | memberP(X,V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X ) )
      | ~ ssList(nil)
      | ~ ssList(skaf42(sk3,sk5))
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssList(skaf43(sk5,sk3))
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) )
  <=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
            ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | memberP(X,V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X ) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssList(skaf43(sk5,sk3))
      | ~ ssList(skaf42(sk3,sk5))
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ) ),
    inference(monotonicity,[status(thm)],[78]) ).

tff(80,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
            ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | memberP(X,V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X ) )
      | ~ ssList(nil)
      | ~ ssList(skaf42(sk3,sk5))
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssList(skaf43(sk5,sk3))
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) )
  <=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
            ( ~ ssList(X)
            | ~ ssList(U)
            | ~ ssItem(V)
            | memberP(X,V)
            | ~ ssList(W)
            | ( app(U,cons(V,W)) != X ) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssList(skaf43(sk5,sk3))
      | ~ ssList(skaf42(sk3,sk5))
      | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ) ),
    inference(transitivity,[status(thm)],[79,77]) ).

tff(81,plain,
    ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
          ( ~ ssList(X)
          | ~ ssList(U)
          | ~ ssItem(V)
          | memberP(X,V)
          | ~ ssList(W)
          | ( app(U,cons(V,W)) != X ) )
    | ~ ssList(nil)
    | ~ ssList(skaf42(sk3,sk5))
    | ~ ssItem(sk5)
    | memberP(nil,sk5)
    | ~ ssList(skaf43(sk5,sk3))
    | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(82,plain,
    ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
          ( ~ ssList(X)
          | ~ ssList(U)
          | ~ ssItem(V)
          | memberP(X,V)
          | ~ ssList(W)
          | ( app(U,cons(V,W)) != X ) )
    | ~ ssList(nil)
    | ~ ssItem(sk5)
    | memberP(nil,sk5)
    | ~ ssList(skaf43(sk5,sk3))
    | ~ ssList(skaf42(sk3,sk5))
    | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ),
    inference(modus_ponens,[status(thm)],[81,80]) ).

tff(83,plain,
    ( ~ ssList(skaf43(sk5,sk3))
    | ~ ssList(skaf42(sk3,sk5))
    | ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ),
    inference(unit_resolution,[status(thm)],[82,76,73,9,63]) ).

tff(84,plain,
    app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil,
    inference(unit_resolution,[status(thm)],[83,49,40]) ).

tff(85,plain,
    nil != sk3,
    inference(modus_ponens,[status(thm)],[84,31]) ).

tff(86,plain,
    ( ( ( nil = sk3 )
      | ( cons(sk6,nil) = sk3 ) )
  <=> ( ( nil = sk3 )
      | ( cons(sk6,nil) = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(87,plain,
    ( ( ( cons(sk6,nil) = sk3 )
      | ( nil = sk3 ) )
  <=> ( ( nil = sk3 )
      | ( cons(sk6,nil) = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(88,axiom,
    ( ( cons(sk6,nil) = sk3 )
    | ( nil = sk3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).

tff(89,plain,
    ( ( nil = sk3 )
    | ( cons(sk6,nil) = sk3 ) ),
    inference(modus_ponens,[status(thm)],[88,87]) ).

tff(90,plain,
    ( ( nil = sk3 )
    | ( cons(sk6,nil) = sk3 ) ),
    inference(modus_ponens,[status(thm)],[89,86]) ).

tff(91,plain,
    cons(sk6,nil) = sk3,
    inference(unit_resolution,[status(thm)],[90,85]) ).

tff(92,plain,
    ( memberP(cons(sk6,nil),sk5)
  <=> memberP(sk3,sk5) ),
    inference(monotonicity,[status(thm)],[91]) ).

tff(93,plain,
    ( memberP(sk3,sk5)
  <=> memberP(cons(sk6,nil),sk5) ),
    inference(symmetry,[status(thm)],[92]) ).

tff(94,plain,
    memberP(cons(sk6,nil),sk5),
    inference(modus_ponens,[status(thm)],[6,93]) ).

tff(95,plain,
    ( ( ssItem(sk6)
      | ( nil = sk3 ) )
  <=> ( ssItem(sk6)
      | ( nil = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(96,axiom,
    ( ssItem(sk6)
    | ( nil = sk3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).

tff(97,plain,
    ( ssItem(sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[96,95]) ).

tff(98,plain,
    ssItem(sk6),
    inference(unit_resolution,[status(thm)],[97,85]) ).

tff(99,plain,
    ^ [W: $i,V: $i,U: $i] :
      refl(
        ( ( ~ ssItem(U)
          | ~ ssList(V)
          | ~ ssItem(W)
          | memberP(V,W)
          | ( W = U )
          | ~ memberP(cons(U,V),W) )
      <=> ( ~ ssItem(U)
          | ~ ssList(V)
          | ~ ssItem(W)
          | memberP(V,W)
          | ( W = U )
          | ~ memberP(cons(U,V),W) ) )),
    inference(bind,[status(th)],]) ).

tff(100,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( ~ ssItem(U)
        | ~ ssList(V)
        | ~ ssItem(W)
        | memberP(V,W)
        | ( W = U )
        | ~ memberP(cons(U,V),W) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( ~ ssItem(U)
        | ~ ssList(V)
        | ~ ssItem(W)
        | memberP(V,W)
        | ( W = U )
        | ~ memberP(cons(U,V),W) ) ),
    inference(quant_intro,[status(thm)],[99]) ).

tff(101,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( ~ ssItem(U)
        | ~ ssList(V)
        | ~ ssItem(W)
        | memberP(V,W)
        | ( W = U )
        | ~ memberP(cons(U,V),W) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( ~ ssItem(U)
        | ~ ssList(V)
        | ~ ssItem(W)
        | memberP(V,W)
        | ( W = U )
        | ~ memberP(cons(U,V),W) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(102,plain,
    ^ [W: $i,V: $i,U: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              trans(
                monotonicity(
                  trans(
                    monotonicity(
                      rewrite(
                        ( ( ~ memberP(cons(U,V),W)
                          | ~ ssList(V) )
                      <=> ( ~ ssList(V)
                          | ~ memberP(cons(U,V),W) ) )),
                      ( ( ~ memberP(cons(U,V),W)
                        | ~ ssList(V)
                        | ~ ssItem(U) )
                    <=> ( ~ ssList(V)
                        | ~ memberP(cons(U,V),W)
                        | ~ ssItem(U) ) )),
                    rewrite(
                      ( ( ~ ssList(V)
                        | ~ memberP(cons(U,V),W)
                        | ~ ssItem(U) )
                    <=> ( ~ ssItem(U)
                        | ~ ssList(V)
                        | ~ memberP(cons(U,V),W) ) )),
                    ( ( ~ memberP(cons(U,V),W)
                      | ~ ssList(V)
                      | ~ ssItem(U) )
                  <=> ( ~ ssItem(U)
                      | ~ ssList(V)
                      | ~ memberP(cons(U,V),W) ) )),
                  ( ( ~ memberP(cons(U,V),W)
                    | ~ ssList(V)
                    | ~ ssItem(U)
                    | ~ ssItem(W) )
                <=> ( ~ ssItem(U)
                    | ~ ssList(V)
                    | ~ memberP(cons(U,V),W)
                    | ~ ssItem(W) ) )),
                rewrite(
                  ( ( ~ ssItem(U)
                    | ~ ssList(V)
                    | ~ memberP(cons(U,V),W)
                    | ~ ssItem(W) )
                <=> ( ~ ssItem(U)
                    | ~ ssList(V)
                    | ~ ssItem(W)
                    | ~ memberP(cons(U,V),W) ) )),
                ( ( ~ memberP(cons(U,V),W)
                  | ~ ssList(V)
                  | ~ ssItem(U)
                  | ~ ssItem(W) )
              <=> ( ~ ssItem(U)
                  | ~ ssList(V)
                  | ~ ssItem(W)
                  | ~ memberP(cons(U,V),W) ) )),
              ( ( ~ memberP(cons(U,V),W)
                | ~ ssList(V)
                | ~ ssItem(U)
                | ~ ssItem(W)
                | memberP(V,W) )
            <=> ( ~ ssItem(U)
                | ~ ssList(V)
                | ~ ssItem(W)
                | ~ memberP(cons(U,V),W)
                | memberP(V,W) ) )),
            rewrite(
              ( ( ~ ssItem(U)
                | ~ ssList(V)
                | ~ ssItem(W)
                | ~ memberP(cons(U,V),W)
                | memberP(V,W) )
            <=> ( ~ ssItem(U)
                | ~ ssList(V)
                | ~ ssItem(W)
                | memberP(V,W)
                | ~ memberP(cons(U,V),W) ) )),
            ( ( ~ memberP(cons(U,V),W)
              | ~ ssList(V)
              | ~ ssItem(U)
              | ~ ssItem(W)
              | memberP(V,W) )
          <=> ( ~ ssItem(U)
              | ~ ssList(V)
              | ~ ssItem(W)
              | memberP(V,W)
              | ~ memberP(cons(U,V),W) ) )),
          ( ( ~ memberP(cons(U,V),W)
            | ~ ssList(V)
            | ~ ssItem(U)
            | ~ ssItem(W)
            | memberP(V,W)
            | ( W = U ) )
        <=> ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ~ memberP(cons(U,V),W)
            | ( W = U ) ) )),
        rewrite(
          ( ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ~ memberP(cons(U,V),W)
            | ( W = U ) )
        <=> ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ( W = U )
            | ~ memberP(cons(U,V),W) ) )),
        ( ( ~ memberP(cons(U,V),W)
          | ~ ssList(V)
          | ~ ssItem(U)
          | ~ ssItem(W)
          | memberP(V,W)
          | ( W = U ) )
      <=> ( ~ ssItem(U)
          | ~ ssList(V)
          | ~ ssItem(W)
          | memberP(V,W)
          | ( W = U )
          | ~ memberP(cons(U,V),W) ) )),
    inference(bind,[status(th)],]) ).

tff(103,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( ~ memberP(cons(U,V),W)
        | ~ ssList(V)
        | ~ ssItem(U)
        | ~ ssItem(W)
        | memberP(V,W)
        | ( W = U ) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( ~ ssItem(U)
        | ~ ssList(V)
        | ~ ssItem(W)
        | memberP(V,W)
        | ( W = U )
        | ~ memberP(cons(U,V),W) ) ),
    inference(quant_intro,[status(thm)],[102]) ).

tff(104,axiom,
    ! [W: $i,V: $i,U: $i] :
      ( ~ memberP(cons(U,V),W)
      | ~ ssList(V)
      | ~ ssItem(U)
      | ~ ssItem(W)
      | memberP(V,W)
      | ( W = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).

tff(105,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ~ ssItem(W)
      | memberP(V,W)
      | ( W = U )
      | ~ memberP(cons(U,V),W) ),
    inference(modus_ponens,[status(thm)],[104,103]) ).

tff(106,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ~ ssItem(W)
      | memberP(V,W)
      | ( W = U )
      | ~ memberP(cons(U,V),W) ),
    inference(modus_ponens,[status(thm)],[105,101]) ).

tff(107,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ~ ssItem(W)
      | memberP(V,W)
      | ( W = U )
      | ~ memberP(cons(U,V),W) ),
    inference(skolemize,[status(sab)],[106]) ).

tff(108,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ~ ssItem(W)
      | memberP(V,W)
      | ( W = U )
      | ~ memberP(cons(U,V),W) ),
    inference(modus_ponens,[status(thm)],[107,100]) ).

tff(109,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ( W = U )
            | ~ memberP(cons(U,V),W) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssItem(sk6)
      | ( sk5 = sk6 )
      | ~ memberP(cons(sk6,nil),sk5) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ( W = U )
            | ~ memberP(cons(U,V),W) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssItem(sk6)
      | ( sk5 = sk6 )
      | ~ memberP(cons(sk6,nil),sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(110,plain,
    ( ( ~ ssItem(sk6)
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ( sk5 = sk6 )
      | ~ memberP(cons(sk6,nil),sk5) )
  <=> ( ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssItem(sk6)
      | ( sk5 = sk6 )
      | ~ memberP(cons(sk6,nil),sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(111,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ( W = U )
            | ~ memberP(cons(U,V),W) )
      | ~ ssItem(sk6)
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ( sk5 = sk6 )
      | ~ memberP(cons(sk6,nil),sk5) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ( W = U )
            | ~ memberP(cons(U,V),W) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssItem(sk6)
      | ( sk5 = sk6 )
      | ~ memberP(cons(sk6,nil),sk5) ) ),
    inference(monotonicity,[status(thm)],[110]) ).

tff(112,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ( W = U )
            | ~ memberP(cons(U,V),W) )
      | ~ ssItem(sk6)
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ( sk5 = sk6 )
      | ~ memberP(cons(sk6,nil),sk5) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ ssItem(U)
            | ~ ssList(V)
            | ~ ssItem(W)
            | memberP(V,W)
            | ( W = U )
            | ~ memberP(cons(U,V),W) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | memberP(nil,sk5)
      | ~ ssItem(sk6)
      | ( sk5 = sk6 )
      | ~ memberP(cons(sk6,nil),sk5) ) ),
    inference(transitivity,[status(thm)],[111,109]) ).

tff(113,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ ssItem(U)
          | ~ ssList(V)
          | ~ ssItem(W)
          | memberP(V,W)
          | ( W = U )
          | ~ memberP(cons(U,V),W) )
    | ~ ssItem(sk6)
    | ~ ssList(nil)
    | ~ ssItem(sk5)
    | memberP(nil,sk5)
    | ( sk5 = sk6 )
    | ~ memberP(cons(sk6,nil),sk5) ),
    inference(quant_inst,[status(thm)],]) ).

tff(114,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ ssItem(U)
          | ~ ssList(V)
          | ~ ssItem(W)
          | memberP(V,W)
          | ( W = U )
          | ~ memberP(cons(U,V),W) )
    | ~ ssList(nil)
    | ~ ssItem(sk5)
    | memberP(nil,sk5)
    | ~ ssItem(sk6)
    | ( sk5 = sk6 )
    | ~ memberP(cons(sk6,nil),sk5) ),
    inference(modus_ponens,[status(thm)],[113,112]) ).

tff(115,plain,
    ( ( sk5 = sk6 )
    | ~ memberP(cons(sk6,nil),sk5) ),
    inference(unit_resolution,[status(thm)],[114,76,108,9,98,63]) ).

tff(116,plain,
    sk5 = sk6,
    inference(unit_resolution,[status(thm)],[115,94]) ).

tff(117,plain,
    sk6 = sk5,
    inference(symmetry,[status(thm)],[116]) ).

tff(118,plain,
    ( memberP(sk4,sk6)
  <=> memberP(sk4,sk5) ),
    inference(monotonicity,[status(thm)],[117]) ).

tff(119,plain,
    ( memberP(sk4,sk5)
  <=> memberP(sk4,sk6) ),
    inference(symmetry,[status(thm)],[118]) ).

tff(120,plain,
    ( ~ memberP(sk4,sk5)
  <=> ~ memberP(sk4,sk6) ),
    inference(monotonicity,[status(thm)],[119]) ).

tff(121,plain,
    ( ~ memberP(sk2,sk5)
  <=> ~ memberP(sk4,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(122,plain,
    ( ~ memberP(sk2,sk5)
  <=> ~ memberP(sk2,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(123,axiom,
    ~ memberP(sk2,sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

tff(124,plain,
    ~ memberP(sk2,sk5),
    inference(modus_ponens,[status(thm)],[123,122]) ).

tff(125,plain,
    ~ memberP(sk4,sk5),
    inference(modus_ponens,[status(thm)],[124,121]) ).

tff(126,plain,
    ~ memberP(sk4,sk6),
    inference(modus_ponens,[status(thm)],[125,120]) ).

tff(127,plain,
    ( ( memberP(sk4,sk6)
      | ( nil = sk3 ) )
  <=> ( memberP(sk4,sk6)
      | ( nil = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(128,axiom,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).

tff(129,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[128,127]) ).

tff(130,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[129,127]) ).

tff(131,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[130,127]) ).

tff(132,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[131,127]) ).

tff(133,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[132,127]) ).

tff(134,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[133,127]) ).

tff(135,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[134,127]) ).

tff(136,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[135,127]) ).

tff(137,plain,
    ( memberP(sk4,sk6)
    | ( nil = sk3 ) ),
    inference(modus_ponens,[status(thm)],[136,127]) ).

tff(138,plain,
    memberP(sk4,sk6),
    inference(unit_resolution,[status(thm)],[137,85]) ).

tff(139,plain,
    $false,
    inference(unit_resolution,[status(thm)],[138,126]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC407-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Sep  4 00:30:34 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34  Usage: tptp [options] [-file:]file
% 0.19/0.34    -h, -?       prints this message.
% 0.19/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.19/0.34    -m, -model   generate model.
% 0.19/0.34    -p, -proof   generate proof.
% 0.19/0.34    -c, -core    generate unsat core of named formulas.
% 0.19/0.34    -st, -statistics display statistics.
% 0.19/0.34    -t:timeout   set timeout (in second).
% 0.19/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.19/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34    -<param>:<value> configuration parameter and value.
% 0.19/0.34    -o:<output-file> file to place output in.
% 0.74/0.73  % SZS status Unsatisfiable
% 0.74/0.73  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------