TSTP Solution File: SET787-2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET787-2 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n022.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 05:08:01 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   75
% Syntax   : Number of formulae    :  156 (  31 unt;  11 typ;   0 def)
%            Number of atoms       :  672 (  82 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  913 ( 411   ~; 437   |;   0   &)
%                                         (  65 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :   25 (  25 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  421 ( 387   !;   0   ?; 421   :)

% Comments : 
%------------------------------------------------------------------------------
tff(unionE_sk1_type,type,
    unionE_sk1: ( $i * $i ) > $i ).

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

tff(eptset_type,type,
    eptset: $i ).

tff(b_type,type,
    b: $i ).

tff(a_type,type,
    a: $i ).

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

tff(member_type,type,
    member: ( $i * $i ) > $o ).

tff(pow_type,type,
    pow: $i > $i ).

tff(un_type,type,
    un: ( $i * $i ) > $i ).

tff(union_type,type,
    union: $i > $i ).

tff(subset_type,type,
    subset: ( $i * $i ) > $o ).

tff(1,plain,
    ( member(sk2,union(cons(a,cons(b,eptset))))
  <=> member(sk2,union(cons(a,cons(b,eptset)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    member(sk2,union(cons(a,cons(b,eptset)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).

tff(3,plain,
    member(sk2,union(cons(a,cons(b,eptset)))),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [V: $i,U: $i] :
      refl(
        ( ( ~ member(U,union(V))
          | member(U,unionE_sk1(U,V)) )
      <=> ( ~ member(U,union(V))
          | member(U,unionE_sk1(U,V)) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V: $i,U: $i] :
        ( ~ member(U,union(V))
        | member(U,unionE_sk1(U,V)) )
  <=> ! [V: $i,U: $i] :
        ( ~ member(U,union(V))
        | member(U,unionE_sk1(U,V)) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [V: $i,U: $i] :
        ( ~ member(U,union(V))
        | member(U,unionE_sk1(U,V)) )
  <=> ! [V: $i,U: $i] :
        ( ~ member(U,union(V))
        | member(U,unionE_sk1(U,V)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [V: $i,U: $i] :
      ( ~ member(U,union(V))
      | member(U,unionE_sk1(U,V)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).

tff(8,plain,
    ! [V: $i,U: $i] :
      ( ~ member(U,union(V))
      | member(U,unionE_sk1(U,V)) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [V: $i,U: $i] :
      ( ~ member(U,union(V))
      | member(U,unionE_sk1(U,V)) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V: $i,U: $i] :
      ( ~ member(U,union(V))
      | member(U,unionE_sk1(U,V)) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [V: $i,U: $i] :
            ( ~ member(U,union(V))
            | member(U,unionE_sk1(U,V)) )
      | ~ member(sk2,union(cons(a,cons(b,eptset))))
      | member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) )
  <=> ( ~ ! [V: $i,U: $i] :
            ( ~ member(U,union(V))
            | member(U,unionE_sk1(U,V)) )
      | ~ member(sk2,union(cons(a,cons(b,eptset))))
      | member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [V: $i,U: $i] :
          ( ~ member(U,union(V))
          | member(U,unionE_sk1(U,V)) )
    | ~ member(sk2,union(cons(a,cons(b,eptset))))
    | member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [V: $i,U: $i] :
          ( ~ member(U,union(V))
          | member(U,unionE_sk1(U,V)) )
    | ~ member(sk2,union(cons(a,cons(b,eptset))))
    | member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))),
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    ( ~ member(sk2,un(a,b))
  <=> ~ member(sk2,un(a,b)) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    ~ member(sk2,un(a,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).

tff(17,plain,
    ~ member(sk2,un(a,b)),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ^ [W: $i,V: $i,U: $i] :
      refl(
        ( ( member(W,V)
          | ~ member(W,U)
          | ~ member(U,pow(V)) )
      <=> ( member(W,V)
          | ~ member(W,U)
          | ~ member(U,pow(V)) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( member(W,V)
        | ~ member(W,U)
        | ~ member(U,pow(V)) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( member(W,V)
        | ~ member(W,U)
        | ~ member(U,pow(V)) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( member(W,V)
        | ~ member(W,U)
        | ~ member(U,pow(V)) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( member(W,V)
        | ~ member(W,U)
        | ~ member(U,pow(V)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ^ [W: $i,V: $i,U: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ member(U,pow(V))
              | ~ member(W,U) )
          <=> ( ~ member(W,U)
              | ~ member(U,pow(V)) ) )),
          ( ( ~ member(U,pow(V))
            | ~ member(W,U)
            | member(W,V) )
        <=> ( ~ member(W,U)
            | ~ member(U,pow(V))
            | member(W,V) ) )),
        rewrite(
          ( ( ~ member(W,U)
            | ~ member(U,pow(V))
            | member(W,V) )
        <=> ( member(W,V)
            | ~ member(W,U)
            | ~ member(U,pow(V)) ) )),
        ( ( ~ member(U,pow(V))
          | ~ member(W,U)
          | member(W,V) )
      <=> ( member(W,V)
          | ~ member(W,U)
          | ~ member(U,pow(V)) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( ~ member(U,pow(V))
        | ~ member(W,U)
        | member(W,V) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( member(W,V)
        | ~ member(W,U)
        | ~ member(U,pow(V)) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,axiom,
    ! [W: $i,V: $i,U: $i] :
      ( ~ member(U,pow(V))
      | ~ member(W,U)
      | member(W,V) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).

tff(24,plain,
    ! [W: $i,V: $i,U: $i] :
      ( member(W,V)
      | ~ member(W,U)
      | ~ member(U,pow(V)) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    ! [W: $i,V: $i,U: $i] :
      ( member(W,V)
      | ~ member(W,U)
      | ~ member(U,pow(V)) ),
    inference(modus_ponens,[status(thm)],[24,20]) ).

tff(26,plain,
    ! [W: $i,V: $i,U: $i] :
      ( member(W,V)
      | ~ member(W,U)
      | ~ member(U,pow(V)) ),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [W: $i,V: $i,U: $i] :
      ( member(W,V)
      | ~ member(W,U)
      | ~ member(U,pow(V)) ),
    inference(modus_ponens,[status(thm)],[26,19]) ).

tff(28,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( member(W,V)
            | ~ member(W,U)
            | ~ member(U,pow(V)) )
      | member(sk2,un(a,b))
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( member(W,V)
            | ~ member(W,U)
            | ~ member(U,pow(V)) )
      | member(sk2,un(a,b))
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( member(W,V)
          | ~ member(W,U)
          | ~ member(U,pow(V)) )
    | member(sk2,un(a,b))
    | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
    | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(30,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( member(W,V)
          | ~ member(W,U)
          | ~ member(U,pow(V)) )
    | member(sk2,un(a,b))
    | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
    | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))),
    inference(unit_resolution,[status(thm)],[30,27,17,14]) ).

tff(32,plain,
    ^ [A: $i,X: $i] :
      refl(
        ( ( ~ member(X,eptset)
          | member(X,A) )
      <=> ( ~ member(X,eptset)
          | member(X,A) ) )),
    inference(bind,[status(th)],]) ).

tff(33,plain,
    ( ! [A: $i,X: $i] :
        ( ~ member(X,eptset)
        | member(X,A) )
  <=> ! [A: $i,X: $i] :
        ( ~ member(X,eptset)
        | member(X,A) ) ),
    inference(quant_intro,[status(thm)],[32]) ).

tff(34,plain,
    ( ! [A: $i,X: $i] :
        ( ~ member(X,eptset)
        | member(X,A) )
  <=> ! [A: $i,X: $i] :
        ( ~ member(X,eptset)
        | member(X,A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,axiom,
    ! [A: $i,X: $i] :
      ( ~ member(X,eptset)
      | member(X,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).

tff(36,plain,
    ! [A: $i,X: $i] :
      ( ~ member(X,eptset)
      | member(X,A) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ! [A: $i,X: $i] :
      ( ~ member(X,eptset)
      | member(X,A) ),
    inference(skolemize,[status(sab)],[36]) ).

tff(38,plain,
    ! [A: $i,X: $i] :
      ( ~ member(X,eptset)
      | member(X,A) ),
    inference(modus_ponens,[status(thm)],[37,33]) ).

tff(39,plain,
    ( ( ~ ! [A: $i,X: $i] :
            ( ~ member(X,eptset)
            | member(X,A) )
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) )
  <=> ( ~ ! [A: $i,X: $i] :
            ( ~ member(X,eptset)
            | member(X,A) )
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,plain,
    ( ~ ! [A: $i,X: $i] :
          ( ~ member(X,eptset)
          | member(X,A) )
    | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(41,plain,
    ( ~ ! [A: $i,X: $i] :
          ( ~ member(X,eptset)
          | member(X,A) )
    | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),pow(un(a,b))) ),
    inference(modus_ponens,[status(thm)],[40,39]) ).

tff(42,plain,
    ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset),
    inference(unit_resolution,[status(thm)],[41,38,31]) ).

tff(43,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ member(C,A)
          | member(C,un(A,B)) )
      <=> ( ~ member(C,A)
          | member(C,un(A,B)) ) )),
    inference(bind,[status(th)],]) ).

tff(44,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,un(A,B)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,un(A,B)) ) ),
    inference(quant_intro,[status(thm)],[43]) ).

tff(45,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,un(A,B)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,un(A,B)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,A)
      | member(C,un(A,B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI1) ).

tff(47,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,A)
      | member(C,un(A,B)) ),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,A)
      | member(C,un(A,B)) ),
    inference(skolemize,[status(sab)],[47]) ).

tff(49,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,A)
      | member(C,un(A,B)) ),
    inference(modus_ponens,[status(thm)],[48,44]) ).

tff(50,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,un(A,B)) )
      | ~ member(sk2,a)
      | member(sk2,un(a,b)) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,un(A,B)) )
      | ~ member(sk2,a)
      | member(sk2,un(a,b)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ member(C,A)
          | member(C,un(A,B)) )
    | ~ member(sk2,a)
    | member(sk2,un(a,b)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(52,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ member(C,A)
          | member(C,un(A,B)) )
    | ~ member(sk2,a)
    | member(sk2,un(a,b)) ),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    ~ member(sk2,a),
    inference(unit_resolution,[status(thm)],[52,49,17]) ).

tff(54,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ member(C,A)
          | member(C,B)
          | ~ subset(A,B) )
      <=> ( ~ member(C,A)
          | member(C,B)
          | ~ subset(A,B) ) )),
    inference(bind,[status(th)],]) ).

tff(55,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,B)
        | ~ subset(A,B) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,B)
        | ~ subset(A,B) ) ),
    inference(quant_intro,[status(thm)],[54]) ).

tff(56,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,B)
        | ~ subset(A,B) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,B)
        | ~ subset(A,B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(57,plain,
    ^ [B: $i,A: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ subset(A,B)
              | ~ member(C,A) )
          <=> ( ~ member(C,A)
              | ~ subset(A,B) ) )),
          ( ( ~ subset(A,B)
            | ~ member(C,A)
            | member(C,B) )
        <=> ( ~ member(C,A)
            | ~ subset(A,B)
            | member(C,B) ) )),
        rewrite(
          ( ( ~ member(C,A)
            | ~ subset(A,B)
            | member(C,B) )
        <=> ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) ) )),
        ( ( ~ subset(A,B)
          | ~ member(C,A)
          | member(C,B) )
      <=> ( ~ member(C,A)
          | member(C,B)
          | ~ subset(A,B) ) )),
    inference(bind,[status(th)],]) ).

tff(58,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ subset(A,B)
        | ~ member(C,A)
        | member(C,B) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,A)
        | member(C,B)
        | ~ subset(A,B) ) ),
    inference(quant_intro,[status(thm)],[57]) ).

tff(59,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ subset(A,B)
      | ~ member(C,A)
      | member(C,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetD) ).

tff(60,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,A)
      | member(C,B)
      | ~ subset(A,B) ),
    inference(modus_ponens,[status(thm)],[59,58]) ).

tff(61,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,A)
      | member(C,B)
      | ~ subset(A,B) ),
    inference(modus_ponens,[status(thm)],[60,56]) ).

tff(62,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,A)
      | member(C,B)
      | ~ subset(A,B) ),
    inference(skolemize,[status(sab)],[61]) ).

tff(63,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,A)
      | member(C,B)
      | ~ subset(A,B) ),
    inference(modus_ponens,[status(thm)],[62,55]) ).

tff(64,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | member(sk2,a)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | member(sk2,a)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,plain,
    ( ( ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | member(sk2,a)
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
  <=> ( member(sk2,a)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(66,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | member(sk2,a)
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | member(sk2,a)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
    inference(monotonicity,[status(thm)],[65]) ).

tff(67,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | member(sk2,a)
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | member(sk2,a)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
    inference(transitivity,[status(thm)],[66,64]) ).

tff(68,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ member(C,A)
          | member(C,B)
          | ~ subset(A,B) )
    | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
    | member(sk2,a)
    | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(69,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ member(C,A)
          | member(C,B)
          | ~ subset(A,B) )
    | member(sk2,a)
    | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
    | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
    inference(modus_ponens,[status(thm)],[68,67]) ).

tff(70,plain,
    ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a),
    inference(unit_resolution,[status(thm)],[69,63,14,53]) ).

tff(71,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( ( A != B )
          | subset(A,B) )
      <=> ( ( A != B )
          | subset(A,B) ) )),
    inference(bind,[status(th)],]) ).

tff(72,plain,
    ( ! [B: $i,A: $i] :
        ( ( A != B )
        | subset(A,B) )
  <=> ! [B: $i,A: $i] :
        ( ( A != B )
        | subset(A,B) ) ),
    inference(quant_intro,[status(thm)],[71]) ).

tff(73,plain,
    ( ! [B: $i,A: $i] :
        ( ( A != B )
        | subset(A,B) )
  <=> ! [B: $i,A: $i] :
        ( ( A != B )
        | subset(A,B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(74,axiom,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).

tff(75,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | subset(A,B) ),
    inference(modus_ponens,[status(thm)],[74,73]) ).

tff(76,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | subset(A,B) ),
    inference(skolemize,[status(sab)],[75]) ).

tff(77,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | subset(A,B) ),
    inference(modus_ponens,[status(thm)],[76,72]) ).

tff(78,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ( A != B )
            | subset(A,B) )
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a )
      | subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ( A != B )
            | subset(A,B) )
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a )
      | subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(79,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ( A != B )
          | subset(A,B) )
    | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a )
    | subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(80,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ( A != B )
          | subset(A,B) )
    | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a )
    | subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
    inference(modus_ponens,[status(thm)],[79,78]) ).

tff(81,plain,
    unionE_sk1(sk2,cons(a,cons(b,eptset))) != a,
    inference(unit_resolution,[status(thm)],[80,77,70]) ).

tff(82,plain,
    ^ [V: $i,U: $i] :
      refl(
        ( ( ~ member(U,union(V))
          | member(unionE_sk1(U,V),V) )
      <=> ( ~ member(U,union(V))
          | member(unionE_sk1(U,V),V) ) )),
    inference(bind,[status(th)],]) ).

tff(83,plain,
    ( ! [V: $i,U: $i] :
        ( ~ member(U,union(V))
        | member(unionE_sk1(U,V),V) )
  <=> ! [V: $i,U: $i] :
        ( ~ member(U,union(V))
        | member(unionE_sk1(U,V),V) ) ),
    inference(quant_intro,[status(thm)],[82]) ).

tff(84,plain,
    ( ! [V: $i,U: $i] :
        ( ~ member(U,union(V))
        | member(unionE_sk1(U,V),V) )
  <=> ! [V: $i,U: $i] :
        ( ~ member(U,union(V))
        | member(unionE_sk1(U,V),V) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(85,axiom,
    ! [V: $i,U: $i] :
      ( ~ member(U,union(V))
      | member(unionE_sk1(U,V),V) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).

tff(86,plain,
    ! [V: $i,U: $i] :
      ( ~ member(U,union(V))
      | member(unionE_sk1(U,V),V) ),
    inference(modus_ponens,[status(thm)],[85,84]) ).

tff(87,plain,
    ! [V: $i,U: $i] :
      ( ~ member(U,union(V))
      | member(unionE_sk1(U,V),V) ),
    inference(skolemize,[status(sab)],[86]) ).

tff(88,plain,
    ! [V: $i,U: $i] :
      ( ~ member(U,union(V))
      | member(unionE_sk1(U,V),V) ),
    inference(modus_ponens,[status(thm)],[87,83]) ).

tff(89,plain,
    ( ( ~ ! [V: $i,U: $i] :
            ( ~ member(U,union(V))
            | member(unionE_sk1(U,V),V) )
      | ~ member(sk2,union(cons(a,cons(b,eptset))))
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) )
  <=> ( ~ ! [V: $i,U: $i] :
            ( ~ member(U,union(V))
            | member(unionE_sk1(U,V),V) )
      | ~ member(sk2,union(cons(a,cons(b,eptset))))
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(90,plain,
    ( ~ ! [V: $i,U: $i] :
          ( ~ member(U,union(V))
          | member(unionE_sk1(U,V),V) )
    | ~ member(sk2,union(cons(a,cons(b,eptset))))
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(91,plain,
    ( ~ ! [V: $i,U: $i] :
          ( ~ member(U,union(V))
          | member(unionE_sk1(U,V),V) )
    | ~ member(sk2,union(cons(a,cons(b,eptset))))
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
    inference(modus_ponens,[status(thm)],[90,89]) ).

tff(92,plain,
    member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
    inference(unit_resolution,[status(thm)],[91,88,3]) ).

tff(93,plain,
    ^ [W: $i,V: $i,U: $i] :
      refl(
        ( ( ( U = V )
          | member(U,W)
          | ~ member(U,cons(V,W)) )
      <=> ( ( U = V )
          | member(U,W)
          | ~ member(U,cons(V,W)) ) )),
    inference(bind,[status(th)],]) ).

tff(94,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( ( U = V )
        | member(U,W)
        | ~ member(U,cons(V,W)) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( ( U = V )
        | member(U,W)
        | ~ member(U,cons(V,W)) ) ),
    inference(quant_intro,[status(thm)],[93]) ).

tff(95,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( ( U = V )
        | member(U,W)
        | ~ member(U,cons(V,W)) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( ( U = V )
        | member(U,W)
        | ~ member(U,cons(V,W)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(96,plain,
    ^ [W: $i,V: $i,U: $i] :
      rewrite(
        ( ( ~ member(U,cons(V,W))
          | ( U = V )
          | member(U,W) )
      <=> ( ( U = V )
          | member(U,W)
          | ~ member(U,cons(V,W)) ) )),
    inference(bind,[status(th)],]) ).

tff(97,plain,
    ( ! [W: $i,V: $i,U: $i] :
        ( ~ member(U,cons(V,W))
        | ( U = V )
        | member(U,W) )
  <=> ! [W: $i,V: $i,U: $i] :
        ( ( U = V )
        | member(U,W)
        | ~ member(U,cons(V,W)) ) ),
    inference(quant_intro,[status(thm)],[96]) ).

tff(98,axiom,
    ! [W: $i,V: $i,U: $i] :
      ( ~ member(U,cons(V,W))
      | ( U = V )
      | member(U,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).

tff(99,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ( U = V )
      | member(U,W)
      | ~ member(U,cons(V,W)) ),
    inference(modus_ponens,[status(thm)],[98,97]) ).

tff(100,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ( U = V )
      | member(U,W)
      | ~ member(U,cons(V,W)) ),
    inference(modus_ponens,[status(thm)],[99,95]) ).

tff(101,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ( U = V )
      | member(U,W)
      | ~ member(U,cons(V,W)) ),
    inference(skolemize,[status(sab)],[100]) ).

tff(102,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ( U = V )
      | member(U,W)
      | ~ member(U,cons(V,W)) ),
    inference(modus_ponens,[status(thm)],[101,94]) ).

tff(103,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ( U = V )
            | member(U,W)
            | ~ member(U,cons(V,W)) )
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ( U = V )
            | member(U,W)
            | ~ member(U,cons(V,W)) )
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(104,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ( U = V )
          | member(U,W)
          | ~ member(U,cons(V,W)) )
    | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
    | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(105,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ( U = V )
          | member(U,W)
          | ~ member(U,cons(V,W)) )
    | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
    | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
    inference(modus_ponens,[status(thm)],[104,103]) ).

tff(106,plain,
    ( ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a )
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
    inference(unit_resolution,[status(thm)],[105,102,92]) ).

tff(107,plain,
    member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)),
    inference(unit_resolution,[status(thm)],[106,81]) ).

tff(108,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ( U = V )
            | member(U,W)
            | ~ member(U,cons(V,W)) )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ( U = V )
            | member(U,W)
            | ~ member(U,cons(V,W)) )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(109,plain,
    ( ( ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) )
  <=> ( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(110,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ( U = V )
            | member(U,W)
            | ~ member(U,cons(V,W)) )
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ( U = V )
            | member(U,W)
            | ~ member(U,cons(V,W)) )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ) ),
    inference(monotonicity,[status(thm)],[109]) ).

tff(111,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ( U = V )
            | member(U,W)
            | ~ member(U,cons(V,W)) )
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ( U = V )
            | member(U,W)
            | ~ member(U,cons(V,W)) )
      | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
      | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
      | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ) ),
    inference(transitivity,[status(thm)],[110,108]) ).

tff(112,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ( U = V )
          | member(U,W)
          | ~ member(U,cons(V,W)) )
    | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b )
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
    | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(113,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ( U = V )
          | member(U,W)
          | ~ member(U,cons(V,W)) )
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
    | ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
    | ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ) ),
    inference(modus_ponens,[status(thm)],[112,111]) ).

tff(114,plain,
    unionE_sk1(sk2,cons(a,cons(b,eptset))) = b,
    inference(unit_resolution,[status(thm)],[113,102,107,42]) ).

tff(115,plain,
    b = unionE_sk1(sk2,cons(a,cons(b,eptset))),
    inference(symmetry,[status(thm)],[114]) ).

tff(116,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ member(C,B)
          | member(C,un(A,B)) )
      <=> ( ~ member(C,B)
          | member(C,un(A,B)) ) )),
    inference(bind,[status(th)],]) ).

tff(117,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,B)
        | member(C,un(A,B)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,B)
        | member(C,un(A,B)) ) ),
    inference(quant_intro,[status(thm)],[116]) ).

tff(118,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,B)
        | member(C,un(A,B)) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ member(C,B)
        | member(C,un(A,B)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(119,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,B)
      | member(C,un(A,B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI2) ).

tff(120,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,B)
      | member(C,un(A,B)) ),
    inference(modus_ponens,[status(thm)],[119,118]) ).

tff(121,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,B)
      | member(C,un(A,B)) ),
    inference(skolemize,[status(sab)],[120]) ).

tff(122,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ member(C,B)
      | member(C,un(A,B)) ),
    inference(modus_ponens,[status(thm)],[121,117]) ).

tff(123,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,B)
            | member(C,un(A,B)) )
      | ~ member(sk2,b)
      | member(sk2,un(a,b)) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,B)
            | member(C,un(A,B)) )
      | ~ member(sk2,b)
      | member(sk2,un(a,b)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(124,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ member(C,B)
          | member(C,un(A,B)) )
    | ~ member(sk2,b)
    | member(sk2,un(a,b)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(125,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ member(C,B)
          | member(C,un(A,B)) )
    | ~ member(sk2,b)
    | member(sk2,un(a,b)) ),
    inference(modus_ponens,[status(thm)],[124,123]) ).

tff(126,plain,
    ~ member(sk2,b),
    inference(unit_resolution,[status(thm)],[125,122,17]) ).

tff(127,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | member(sk2,b)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | member(sk2,b)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(128,plain,
    ( ( ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | member(sk2,b)
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
  <=> ( member(sk2,b)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(129,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | member(sk2,b)
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | member(sk2,b)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
    inference(monotonicity,[status(thm)],[128]) ).

tff(130,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | member(sk2,b)
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ member(C,A)
            | member(C,B)
            | ~ subset(A,B) )
      | member(sk2,b)
      | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
      | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
    inference(transitivity,[status(thm)],[129,127]) ).

tff(131,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ member(C,A)
          | member(C,B)
          | ~ subset(A,B) )
    | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
    | member(sk2,b)
    | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(132,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ member(C,A)
          | member(C,B)
          | ~ subset(A,B) )
    | member(sk2,b)
    | ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
    | ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
    inference(modus_ponens,[status(thm)],[131,130]) ).

tff(133,plain,
    ~ subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b),
    inference(unit_resolution,[status(thm)],[132,63,14,126]) ).

tff(134,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( ( A != B )
          | subset(B,A) )
      <=> ( ( A != B )
          | subset(B,A) ) )),
    inference(bind,[status(th)],]) ).

tff(135,plain,
    ( ! [B: $i,A: $i] :
        ( ( A != B )
        | subset(B,A) )
  <=> ! [B: $i,A: $i] :
        ( ( A != B )
        | subset(B,A) ) ),
    inference(quant_intro,[status(thm)],[134]) ).

tff(136,plain,
    ( ! [B: $i,A: $i] :
        ( ( A != B )
        | subset(B,A) )
  <=> ! [B: $i,A: $i] :
        ( ( A != B )
        | subset(B,A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(137,axiom,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | subset(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).

tff(138,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | subset(B,A) ),
    inference(modus_ponens,[status(thm)],[137,136]) ).

tff(139,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | subset(B,A) ),
    inference(skolemize,[status(sab)],[138]) ).

tff(140,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | subset(B,A) ),
    inference(modus_ponens,[status(thm)],[139,135]) ).

tff(141,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ( A != B )
            | subset(B,A) )
      | ( b != unionE_sk1(sk2,cons(a,cons(b,eptset))) )
      | subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ( A != B )
            | subset(B,A) )
      | ( b != unionE_sk1(sk2,cons(a,cons(b,eptset))) )
      | subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(142,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ( A != B )
          | subset(B,A) )
    | ( b != unionE_sk1(sk2,cons(a,cons(b,eptset))) )
    | subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(143,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ( A != B )
          | subset(B,A) )
    | ( b != unionE_sk1(sk2,cons(a,cons(b,eptset))) )
    | subset(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
    inference(modus_ponens,[status(thm)],[142,141]) ).

tff(144,plain,
    b != unionE_sk1(sk2,cons(a,cons(b,eptset))),
    inference(unit_resolution,[status(thm)],[143,140,133]) ).

tff(145,plain,
    $false,
    inference(unit_resolution,[status(thm)],[144,115]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET787-2 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.32  % Computer : n022.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Sat Sep  3 08:00:09 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33  Usage: tptp [options] [-file:]file
% 0.13/0.33    -h, -?       prints this message.
% 0.13/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.33    -m, -model   generate model.
% 0.13/0.33    -p, -proof   generate proof.
% 0.13/0.33    -c, -core    generate unsat core of named formulas.
% 0.13/0.33    -st, -statistics display statistics.
% 0.13/0.33    -t:timeout   set timeout (in second).
% 0.13/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33    -<param>:<value> configuration parameter and value.
% 0.13/0.33    -o:<output-file> file to place output in.
% 0.19/0.42  % SZS status Unsatisfiable
% 0.19/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------