TSTP Solution File: SWC012-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWC012-1 : 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 11:54:38 EDT 2022

% Result   : Unsatisfiable 0.21s 0.46s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   47
% Syntax   : Number of formulae    :   92 (  24 unt;  11 typ;   0 def)
%            Number of atoms       :  557 ( 177 equ)
%            Maximal formula atoms :   20 (   6 avg)
%            Number of connectives :  849 ( 430   ~; 358   |;   0   &)
%                                         (  61 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :   57 (  57 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  11 usr;   2 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  104 (  91   !;   0   ?; 104   :)

% Comments : 
%------------------------------------------------------------------------------
tff(sk4_type,type,
    sk4: $i ).

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

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

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

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

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

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

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

tff(neq_type,type,
    neq: ( $i * $i ) > $o ).

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

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

tff(1,plain,
    ( ssList(sk2)
  <=> ssList(sk4) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ssList(sk2)
  <=> ssList(sk2) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ssList(sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).

tff(4,plain,
    ssList(sk2),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    ssList(sk4),
    inference(modus_ponens,[status(thm)],[4,1]) ).

tff(6,plain,
    ^ [U: $i] :
      refl(
        ( ( ~ ssList(U)
          | ( app(U,nil) = U ) )
      <=> ( ~ ssList(U)
          | ( app(U,nil) = U ) ) )),
    inference(bind,[status(th)],]) ).

tff(7,plain,
    ( ! [U: $i] :
        ( ~ ssList(U)
        | ( app(U,nil) = U ) )
  <=> ! [U: $i] :
        ( ~ ssList(U)
        | ( app(U,nil) = U ) ) ),
    inference(quant_intro,[status(thm)],[6]) ).

tff(8,plain,
    ( ! [U: $i] :
        ( ~ ssList(U)
        | ( app(U,nil) = U ) )
  <=> ! [U: $i] :
        ( ~ ssList(U)
        | ( app(U,nil) = U ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,axiom,
    ! [U: $i] :
      ( ~ ssList(U)
      | ( app(U,nil) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).

tff(10,plain,
    ! [U: $i] :
      ( ~ ssList(U)
      | ( app(U,nil) = U ) ),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ! [U: $i] :
      ( ~ ssList(U)
      | ( app(U,nil) = U ) ),
    inference(skolemize,[status(sab)],[10]) ).

tff(12,plain,
    ! [U: $i] :
      ( ~ ssList(U)
      | ( app(U,nil) = U ) ),
    inference(modus_ponens,[status(thm)],[11,7]) ).

tff(13,plain,
    ( ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | ( app(U,nil) = U ) )
      | ~ ssList(sk4)
      | ( app(sk4,nil) = sk4 ) )
  <=> ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | ( app(U,nil) = U ) )
      | ~ ssList(sk4)
      | ( app(sk4,nil) = sk4 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ( ~ ! [U: $i] :
          ( ~ ssList(U)
          | ( app(U,nil) = U ) )
    | ~ ssList(sk4)
    | ( app(sk4,nil) = sk4 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(15,plain,
    ( ~ ! [U: $i] :
          ( ~ ssList(U)
          | ( app(U,nil) = U ) )
    | ~ ssList(sk4)
    | ( app(sk4,nil) = sk4 ) ),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    app(sk4,nil) = sk4,
    inference(unit_resolution,[status(thm)],[15,12,5]) ).

tff(17,plain,
    ( ( $false
      | ( app(sk3,cons(sk5,nil)) = sk4 ) )
  <=> ( app(sk3,cons(sk5,nil)) = sk4 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( neq(sk2,nil)
  <=> neq(sk4,nil) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,plain,
    ( neq(sk2,nil)
  <=> neq(sk2,nil) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ( neq(sk2,nil)
      | neq(sk2,nil) )
  <=> neq(sk2,nil) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,axiom,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

tff(23,plain,
    neq(sk2,nil),
    inference(modus_ponens,[status(thm)],[22,21]) ).

tff(24,plain,
    neq(sk2,nil),
    inference(modus_ponens,[status(thm)],[23,20]) ).

tff(25,plain,
    neq(sk4,nil),
    inference(modus_ponens,[status(thm)],[24,19]) ).

tff(26,plain,
    ( neq(sk4,nil)
  <=> $true ),
    inference(iff_true,[status(thm)],[25]) ).

tff(27,plain,
    ( ~ neq(sk4,nil)
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[26]) ).

tff(28,plain,
    ( ~ neq(sk4,nil)
  <=> $false ),
    inference(transitivity,[status(thm)],[27,18]) ).

tff(29,plain,
    ( ( ~ neq(sk4,nil)
      | ( app(sk3,cons(sk5,nil)) = sk4 ) )
  <=> ( $false
      | ( app(sk3,cons(sk5,nil)) = sk4 ) ) ),
    inference(monotonicity,[status(thm)],[28]) ).

tff(30,plain,
    ( ( ~ neq(sk4,nil)
      | ( app(sk3,cons(sk5,nil)) = sk4 ) )
  <=> ( app(sk3,cons(sk5,nil)) = sk4 ) ),
    inference(transitivity,[status(thm)],[29,17]) ).

tff(31,plain,
    ( ( ~ neq(sk4,nil)
      | ( app(sk3,cons(sk5,nil)) = sk4 ) )
  <=> ( ~ neq(sk4,nil)
      | ( app(sk3,cons(sk5,nil)) = sk4 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ( ( app(sk3,cons(sk5,nil)) = sk4 )
      | ~ neq(sk4,nil) )
  <=> ( ~ neq(sk4,nil)
      | ( app(sk3,cons(sk5,nil)) = sk4 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,axiom,
    ( ( app(sk3,cons(sk5,nil)) = sk4 )
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).

tff(34,plain,
    ( ~ neq(sk4,nil)
    | ( app(sk3,cons(sk5,nil)) = sk4 ) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    ( ~ neq(sk4,nil)
    | ( app(sk3,cons(sk5,nil)) = sk4 ) ),
    inference(modus_ponens,[status(thm)],[34,31]) ).

tff(36,plain,
    app(sk3,cons(sk5,nil)) = sk4,
    inference(modus_ponens,[status(thm)],[35,30]) ).

tff(37,plain,
    app(app(sk3,cons(sk5,nil)),nil) = app(sk4,nil),
    inference(monotonicity,[status(thm)],[36]) ).

tff(38,plain,
    app(app(sk3,cons(sk5,nil)),nil) = sk4,
    inference(transitivity,[status(thm)],[37,16]) ).

tff(39,plain,
    ( ssList(sk1)
  <=> ssList(sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,plain,
    ( ssList(sk1)
  <=> ssList(sk1) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,axiom,
    ssList(sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).

tff(42,plain,
    ssList(sk1),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ssList(sk3),
    inference(modus_ponens,[status(thm)],[42,39]) ).

tff(44,plain,
    ( ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | ( app(U,nil) = U ) )
      | ~ ssList(sk3)
      | ( app(sk3,nil) = sk3 ) )
  <=> ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | ( app(U,nil) = U ) )
      | ~ ssList(sk3)
      | ( app(sk3,nil) = sk3 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ~ ! [U: $i] :
          ( ~ ssList(U)
          | ( app(U,nil) = U ) )
    | ~ ssList(sk3)
    | ( app(sk3,nil) = sk3 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(46,plain,
    ( ~ ! [U: $i] :
          ( ~ ssList(U)
          | ( app(U,nil) = U ) )
    | ~ ssList(sk3)
    | ( app(sk3,nil) = sk3 ) ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    app(sk3,nil) = sk3,
    inference(unit_resolution,[status(thm)],[46,12,43]) ).

tff(48,plain,
    ( ( ssItem(sk5)
      | $false )
  <=> ssItem(sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,plain,
    ( ( ssItem(sk5)
      | ~ neq(sk4,nil) )
  <=> ( ssItem(sk5)
      | $false ) ),
    inference(monotonicity,[status(thm)],[28]) ).

tff(50,plain,
    ( ( ssItem(sk5)
      | ~ neq(sk4,nil) )
  <=> ssItem(sk5) ),
    inference(transitivity,[status(thm)],[49,48]) ).

tff(51,plain,
    ( ( ssItem(sk5)
      | ~ neq(sk4,nil) )
  <=> ( ssItem(sk5)
      | ~ neq(sk4,nil) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,axiom,
    ( ssItem(sk5)
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).

tff(53,plain,
    ( ssItem(sk5)
    | ~ neq(sk4,nil) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ssItem(sk5),
    inference(modus_ponens,[status(thm)],[53,50]) ).

tff(55,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk3 )
          | ( app(app(B,cons(A,nil)),C) != sk4 ) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk3 )
          | ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
    inference(bind,[status(th)],]) ).

tff(56,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk3 )
        | ( app(app(B,cons(A,nil)),C) != sk4 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk3 )
        | ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
    inference(quant_intro,[status(thm)],[55]) ).

tff(57,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              iff_true(
                mp(
                  mp(
                    mp(
                      asserted(
                        ( neq(sk2,nil)
                        | neq(sk2,nil) )),
                      rewrite(
                        ( ( neq(sk2,nil)
                          | neq(sk2,nil) )
                      <=> neq(sk2,nil) )),
                      neq(sk2,nil)),
                    rewrite(
                      ( neq(sk2,nil)
                    <=> neq(sk2,nil) )),
                    neq(sk2,nil)),
                  rewrite(
                    ( neq(sk2,nil)
                  <=> neq(sk4,nil) )),
                  neq(sk4,nil)),
                ( neq(sk4,nil)
              <=> $true )),
              ( ~ neq(sk4,nil)
            <=> ~ $true )),
            rewrite(
              ( ~ $true
            <=> $false )),
            ( ~ neq(sk4,nil)
          <=> $false )),
          ( ( ~ ssList(C)
            | ~ neq(sk4,nil)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
        <=> ( ~ ssList(C)
            | $false
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | $false
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
        ( ( ~ ssList(C)
          | ~ neq(sk4,nil)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk3 )
          | ( app(app(B,cons(A,nil)),C) != sk4 ) )
      <=> ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk3 )
          | ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
    inference(bind,[status(th)],]) ).

tff(58,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ neq(sk4,nil)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk3 )
        | ( app(app(B,cons(A,nil)),C) != sk4 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk3 )
        | ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
    inference(quant_intro,[status(thm)],[57]) ).

tff(59,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( app(B,C) != sk1 )
          <=> ( app(B,C) != sk3 ) )),
          rewrite(
            ( ( app(app(B,cons(A,nil)),C) != sk2 )
          <=> ( app(app(B,cons(A,nil)),C) != sk4 ) )),
          ( ( ~ ssList(C)
            | ~ neq(sk4,nil)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk1 )
            | ( app(app(B,cons(A,nil)),C) != sk2 ) )
        <=> ( ~ ssList(C)
            | ~ neq(sk4,nil)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ neq(sk4,nil)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
        <=> ( ~ ssList(C)
            | ~ neq(sk4,nil)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
        ( ( ~ ssList(C)
          | ~ neq(sk4,nil)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk1 )
          | ( app(app(B,cons(A,nil)),C) != sk2 ) )
      <=> ( ~ ssList(C)
          | ~ neq(sk4,nil)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk3 )
          | ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
    inference(bind,[status(th)],]) ).

tff(60,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ neq(sk4,nil)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk1 )
        | ( app(app(B,cons(A,nil)),C) != sk2 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ neq(sk4,nil)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk3 )
        | ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
    inference(quant_intro,[status(thm)],[59]) ).

tff(61,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ neq(sk4,nil)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk1 )
        | ( app(app(B,cons(A,nil)),C) != sk2 ) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ neq(sk4,nil)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk1 )
        | ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          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) != sk2 ) )
                <=> ( ~ ssList(C)
                    | ~ ssItem(A)
                    | ~ ssList(B)
                    | ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
                rewrite(
                  ( ( ~ ssList(C)
                    | ~ ssItem(A)
                    | ~ ssList(B)
                    | ( app(app(B,cons(A,nil)),C) != sk2 ) )
                <=> ( ~ ssList(C)
                    | ~ ssItem(A)
                    | ~ ssList(B)
                    | ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
                ( ( ~ ssItem(A)
                  | ~ ssList(B)
                  | ~ ssList(C)
                  | ( app(app(B,cons(A,nil)),C) != sk2 ) )
              <=> ( ~ ssList(C)
                  | ~ ssItem(A)
                  | ~ ssList(B)
                  | ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
              ( ( ~ ssItem(A)
                | ~ ssList(B)
                | ~ ssList(C)
                | ( app(app(B,cons(A,nil)),C) != sk2 )
                | ( app(B,C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk2 )
                | ( app(B,C) != sk1 ) ) )),
            rewrite(
              ( ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(app(B,cons(A,nil)),C) != sk2 )
                | ( app(B,C) != sk1 ) )
            <=> ( ~ ssList(C)
                | ~ ssItem(A)
                | ~ ssList(B)
                | ( app(B,C) != sk1 )
                | ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
            ( ( ~ ssItem(A)
              | ~ ssList(B)
              | ~ ssList(C)
              | ( app(app(B,cons(A,nil)),C) != sk2 )
              | ( app(B,C) != sk1 ) )
          <=> ( ~ ssList(C)
              | ~ ssItem(A)
              | ~ ssList(B)
              | ( app(B,C) != sk1 )
              | ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
          ( ( ~ ssItem(A)
            | ~ ssList(B)
            | ~ ssList(C)
            | ( app(app(B,cons(A,nil)),C) != sk2 )
            | ( app(B,C) != sk1 )
            | ~ neq(sk4,nil) )
        <=> ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk1 )
            | ( app(app(B,cons(A,nil)),C) != sk2 )
            | ~ neq(sk4,nil) ) )),
        rewrite(
          ( ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk1 )
            | ( app(app(B,cons(A,nil)),C) != sk2 )
            | ~ neq(sk4,nil) )
        <=> ( ~ ssList(C)
            | ~ neq(sk4,nil)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk1 )
            | ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
        ( ( ~ ssItem(A)
          | ~ ssList(B)
          | ~ ssList(C)
          | ( app(app(B,cons(A,nil)),C) != sk2 )
          | ( app(B,C) != sk1 )
          | ~ neq(sk4,nil) )
      <=> ( ~ ssList(C)
          | ~ neq(sk4,nil)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk1 )
          | ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
    inference(bind,[status(th)],]) ).

tff(63,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ ssItem(A)
        | ~ ssList(B)
        | ~ ssList(C)
        | ( app(app(B,cons(A,nil)),C) != sk2 )
        | ( app(B,C) != sk1 )
        | ~ neq(sk4,nil) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ ssList(C)
        | ~ neq(sk4,nil)
        | ~ ssItem(A)
        | ~ ssList(B)
        | ( app(B,C) != sk1 )
        | ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
    inference(quant_intro,[status(thm)],[62]) ).

tff(64,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(B,cons(A,nil)),C) != sk2 )
      | ( app(B,C) != sk1 )
      | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).

tff(65,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ neq(sk4,nil)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(B,C) != sk1 )
      | ( app(app(B,cons(A,nil)),C) != sk2 ) ),
    inference(modus_ponens,[status(thm)],[64,63]) ).

tff(66,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ neq(sk4,nil)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(B,C) != sk1 )
      | ( app(app(B,cons(A,nil)),C) != sk2 ) ),
    inference(modus_ponens,[status(thm)],[65,61]) ).

tff(67,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ neq(sk4,nil)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(B,C) != sk3 )
      | ( app(app(B,cons(A,nil)),C) != sk4 ) ),
    inference(modus_ponens,[status(thm)],[66,60]) ).

tff(68,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(B,C) != sk3 )
      | ( app(app(B,cons(A,nil)),C) != sk4 ) ),
    inference(modus_ponens,[status(thm)],[67,58]) ).

tff(69,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(B,C) != sk3 )
      | ( app(app(B,cons(A,nil)),C) != sk4 ) ),
    inference(skolemize,[status(sab)],[68]) ).

tff(70,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ ssList(C)
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(B,C) != sk3 )
      | ( app(app(B,cons(A,nil)),C) != sk4 ) ),
    inference(modus_ponens,[status(thm)],[69,56]) ).

tff(71,plain,
    ( ssList(nil)
  <=> ssList(nil) ),
    inference(rewrite,[status(thm)],]) ).

tff(72,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).

tff(73,plain,
    ssList(nil),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(sk5)
      | ( app(sk3,nil) != sk3 )
      | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(sk5)
      | ( app(sk3,nil) != sk3 )
      | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(75,plain,
    ( ( ~ ssList(nil)
      | ~ ssItem(sk5)
      | ~ ssList(sk3)
      | ( app(sk3,nil) != sk3 )
      | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) )
  <=> ( ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(sk5)
      | ( app(sk3,nil) != sk3 )
      | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(76,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | ~ ssList(sk3)
      | ( app(sk3,nil) != sk3 )
      | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(sk5)
      | ( app(sk3,nil) != sk3 )
      | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) ) ),
    inference(monotonicity,[status(thm)],[75]) ).

tff(77,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
      | ~ ssList(nil)
      | ~ ssItem(sk5)
      | ~ ssList(sk3)
      | ( app(sk3,nil) != sk3 )
      | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ ssList(C)
            | ~ ssItem(A)
            | ~ ssList(B)
            | ( app(B,C) != sk3 )
            | ( app(app(B,cons(A,nil)),C) != sk4 ) )
      | ~ ssList(nil)
      | ~ ssList(sk3)
      | ~ ssItem(sk5)
      | ( app(sk3,nil) != sk3 )
      | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) ) ),
    inference(transitivity,[status(thm)],[76,74]) ).

tff(78,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk3 )
          | ( app(app(B,cons(A,nil)),C) != sk4 ) )
    | ~ ssList(nil)
    | ~ ssItem(sk5)
    | ~ ssList(sk3)
    | ( app(sk3,nil) != sk3 )
    | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(79,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ ssList(C)
          | ~ ssItem(A)
          | ~ ssList(B)
          | ( app(B,C) != sk3 )
          | ( app(app(B,cons(A,nil)),C) != sk4 ) )
    | ~ ssList(nil)
    | ~ ssList(sk3)
    | ~ ssItem(sk5)
    | ( app(sk3,nil) != sk3 )
    | ( app(app(sk3,cons(sk5,nil)),nil) != sk4 ) ),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    app(app(sk3,cons(sk5,nil)),nil) != sk4,
    inference(unit_resolution,[status(thm)],[79,73,43,70,54,47]) ).

tff(81,plain,
    $false,
    inference(unit_resolution,[status(thm)],[80,38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SWC012-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n007.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 20:24:49 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.
% 0.21/0.46  % SZS status Unsatisfiable
% 0.21/0.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------