TSTP Solution File: COM004-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : COM004-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n018.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  6 18:05:43 EDT 2022

% Result   : Unsatisfiable 0.17s 0.37s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   67 (  27 unt;  13 typ;   0 def)
%            Number of atoms       :  299 (   0 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  425 ( 203   ~; 191   |;   0   &)
%                                         (  31 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   23 (  23 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   8   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  156 ( 141   !;   0   ?; 156   :)

% Comments : 
%------------------------------------------------------------------------------
tff(failure_node_type,type,
    failure_node: ( $i * $i ) > $o ).

tff(or_type,type,
    or: ( $i * $i ) > $i ).

tff(empty_type,type,
    empty: $i ).

tff(parent_of_type,type,
    parent_of: ( $i * $i ) > $i ).

tff(right_child_of_type,type,
    right_child_of: $i > $i ).

tff(n_type,type,
    n: $i ).

tff(left_child_of_type,type,
    left_child_of: $i > $i ).

tff(siblings_type,type,
    siblings: ( $i * $i ) > $o ).

tff(contradictory_type,type,
    contradictory: ( $i * $i ) > $o ).

tff(negate_type,type,
    negate: $i > $i ).

tff(atom_type,type,
    atom: $i ).

tff(n_right_type,type,
    n_right: $i ).

tff(n_left_type,type,
    n_left: $i ).

tff(1,plain,
    ^ [X: $i] :
      refl(
        ( siblings(left_child_of(X),right_child_of(X))
      <=> siblings(left_child_of(X),right_child_of(X)) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] : siblings(left_child_of(X),right_child_of(X))
  <=> ! [X: $i] : siblings(left_child_of(X),right_child_of(X)) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X: $i] : siblings(left_child_of(X),right_child_of(X))
  <=> ! [X: $i] : siblings(left_child_of(X),right_child_of(X)) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X: $i] : siblings(left_child_of(X),right_child_of(X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_left_and_n_right_are_siblings) ).

tff(5,plain,
    ! [X: $i] : siblings(left_child_of(X),right_child_of(X)),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X: $i] : siblings(left_child_of(X),right_child_of(X)),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X: $i] : siblings(left_child_of(X),right_child_of(X)),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X: $i] : siblings(left_child_of(X),right_child_of(X))
    | siblings(left_child_of(n),right_child_of(n)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    siblings(left_child_of(n),right_child_of(n)),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X: $i] :
      refl(
        ( contradictory(X,negate(X))
      <=> contradictory(X,negate(X)) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X: $i] : contradictory(X,negate(X))
  <=> ! [X: $i] : contradictory(X,negate(X)) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X: $i] : contradictory(X,negate(X))
  <=> ! [X: $i] : contradictory(X,negate(X)) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,axiom,
    ! [X: $i] : contradictory(X,negate(X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_contradicts_not_x) ).

tff(14,plain,
    ! [X: $i] : contradictory(X,negate(X)),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [X: $i] : contradictory(X,negate(X)),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [X: $i] : contradictory(X,negate(X)),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [X: $i] : contradictory(X,negate(X))
    | contradictory(atom,negate(atom)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    contradictory(atom,negate(atom)),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    ( failure_node(n_right,or(empty,negate(atom)))
  <=> failure_node(right_child_of(n),or(empty,negate(atom))) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,plain,
    ( failure_node(n_right,or(empty,negate(atom)))
  <=> failure_node(n_right,or(empty,negate(atom))) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    failure_node(n_right,or(empty,negate(atom))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_right_is_not_atom) ).

tff(22,plain,
    failure_node(n_right,or(empty,negate(atom))),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    failure_node(right_child_of(n),or(empty,negate(atom))),
    inference(modus_ponens,[status(thm)],[22,19]) ).

tff(24,plain,
    ( failure_node(n_left,or(empty,atom))
  <=> failure_node(left_child_of(n),or(empty,atom)) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ( failure_node(n_left,or(empty,atom))
  <=> failure_node(n_left,or(empty,atom)) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,axiom,
    failure_node(n_left,or(empty,atom)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_left_is_atom) ).

tff(27,plain,
    failure_node(n_left,or(empty,atom)),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    failure_node(left_child_of(n),or(empty,atom)),
    inference(modus_ponens,[status(thm)],[27,24]) ).

tff(29,plain,
    ^ [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
      refl(
        ( ( ~ siblings(X,Y)
          | ~ contradictory(P,Q)
          | ~ failure_node(Y,or(D,Q))
          | ~ failure_node(X,or(C,P))
          | failure_node(parent_of(X,Y),or(C,D)) )
      <=> ( ~ siblings(X,Y)
          | ~ contradictory(P,Q)
          | ~ failure_node(Y,or(D,Q))
          | ~ failure_node(X,or(C,P))
          | failure_node(parent_of(X,Y),or(C,D)) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
        ( ~ siblings(X,Y)
        | ~ contradictory(P,Q)
        | ~ failure_node(Y,or(D,Q))
        | ~ failure_node(X,or(C,P))
        | failure_node(parent_of(X,Y),or(C,D)) )
  <=> ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
        ( ~ siblings(X,Y)
        | ~ contradictory(P,Q)
        | ~ failure_node(Y,or(D,Q))
        | ~ failure_node(X,or(C,P))
        | failure_node(parent_of(X,Y),or(C,D)) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ( ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
        ( ~ siblings(X,Y)
        | ~ contradictory(P,Q)
        | ~ failure_node(Y,or(D,Q))
        | ~ failure_node(X,or(C,P))
        | failure_node(parent_of(X,Y),or(C,D)) )
  <=> ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
        ( ~ siblings(X,Y)
        | ~ contradictory(P,Q)
        | ~ failure_node(Y,or(D,Q))
        | ~ failure_node(X,or(C,P))
        | failure_node(parent_of(X,Y),or(C,D)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ^ [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              trans(
                monotonicity(
                  rewrite(
                    ( ( failure_node(parent_of(X,Y),or(C,D))
                      | ~ failure_node(X,or(C,P)) )
                  <=> ( ~ failure_node(X,or(C,P))
                      | failure_node(parent_of(X,Y),or(C,D)) ) )),
                  ( ( failure_node(parent_of(X,Y),or(C,D))
                    | ~ failure_node(X,or(C,P))
                    | ~ failure_node(Y,or(D,Q)) )
                <=> ( ~ failure_node(X,or(C,P))
                    | failure_node(parent_of(X,Y),or(C,D))
                    | ~ failure_node(Y,or(D,Q)) ) )),
                rewrite(
                  ( ( ~ failure_node(X,or(C,P))
                    | failure_node(parent_of(X,Y),or(C,D))
                    | ~ failure_node(Y,or(D,Q)) )
                <=> ( ~ failure_node(Y,or(D,Q))
                    | ~ failure_node(X,or(C,P))
                    | failure_node(parent_of(X,Y),or(C,D)) ) )),
                ( ( failure_node(parent_of(X,Y),or(C,D))
                  | ~ failure_node(X,or(C,P))
                  | ~ failure_node(Y,or(D,Q)) )
              <=> ( ~ failure_node(Y,or(D,Q))
                  | ~ failure_node(X,or(C,P))
                  | failure_node(parent_of(X,Y),or(C,D)) ) )),
              ( ( failure_node(parent_of(X,Y),or(C,D))
                | ~ failure_node(X,or(C,P))
                | ~ failure_node(Y,or(D,Q))
                | ~ contradictory(P,Q) )
            <=> ( ~ failure_node(Y,or(D,Q))
                | ~ failure_node(X,or(C,P))
                | failure_node(parent_of(X,Y),or(C,D))
                | ~ contradictory(P,Q) ) )),
            rewrite(
              ( ( ~ failure_node(Y,or(D,Q))
                | ~ failure_node(X,or(C,P))
                | failure_node(parent_of(X,Y),or(C,D))
                | ~ contradictory(P,Q) )
            <=> ( ~ contradictory(P,Q)
                | ~ failure_node(Y,or(D,Q))
                | ~ failure_node(X,or(C,P))
                | failure_node(parent_of(X,Y),or(C,D)) ) )),
            ( ( failure_node(parent_of(X,Y),or(C,D))
              | ~ failure_node(X,or(C,P))
              | ~ failure_node(Y,or(D,Q))
              | ~ contradictory(P,Q) )
          <=> ( ~ contradictory(P,Q)
              | ~ failure_node(Y,or(D,Q))
              | ~ failure_node(X,or(C,P))
              | failure_node(parent_of(X,Y),or(C,D)) ) )),
          ( ( failure_node(parent_of(X,Y),or(C,D))
            | ~ failure_node(X,or(C,P))
            | ~ failure_node(Y,or(D,Q))
            | ~ contradictory(P,Q)
            | ~ siblings(X,Y) )
        <=> ( ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D))
            | ~ siblings(X,Y) ) )),
        rewrite(
          ( ( ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D))
            | ~ siblings(X,Y) )
        <=> ( ~ siblings(X,Y)
            | ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D)) ) )),
        ( ( failure_node(parent_of(X,Y),or(C,D))
          | ~ failure_node(X,or(C,P))
          | ~ failure_node(Y,or(D,Q))
          | ~ contradictory(P,Q)
          | ~ siblings(X,Y) )
      <=> ( ~ siblings(X,Y)
          | ~ contradictory(P,Q)
          | ~ failure_node(Y,or(D,Q))
          | ~ failure_node(X,or(C,P))
          | failure_node(parent_of(X,Y),or(C,D)) ) )),
    inference(bind,[status(th)],]) ).

tff(33,plain,
    ( ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
        ( failure_node(parent_of(X,Y),or(C,D))
        | ~ failure_node(X,or(C,P))
        | ~ failure_node(Y,or(D,Q))
        | ~ contradictory(P,Q)
        | ~ siblings(X,Y) )
  <=> ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
        ( ~ siblings(X,Y)
        | ~ contradictory(P,Q)
        | ~ failure_node(Y,or(D,Q))
        | ~ failure_node(X,or(C,P))
        | failure_node(parent_of(X,Y),or(C,D)) ) ),
    inference(quant_intro,[status(thm)],[32]) ).

tff(34,axiom,
    ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
      ( failure_node(parent_of(X,Y),or(C,D))
      | ~ failure_node(X,or(C,P))
      | ~ failure_node(Y,or(D,Q))
      | ~ contradictory(P,Q)
      | ~ siblings(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',make_node) ).

tff(35,plain,
    ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
      ( ~ siblings(X,Y)
      | ~ contradictory(P,Q)
      | ~ failure_node(Y,or(D,Q))
      | ~ failure_node(X,or(C,P))
      | failure_node(parent_of(X,Y),or(C,D)) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
      ( ~ siblings(X,Y)
      | ~ contradictory(P,Q)
      | ~ failure_node(Y,or(D,Q))
      | ~ failure_node(X,or(C,P))
      | failure_node(parent_of(X,Y),or(C,D)) ),
    inference(modus_ponens,[status(thm)],[35,31]) ).

tff(37,plain,
    ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
      ( ~ siblings(X,Y)
      | ~ contradictory(P,Q)
      | ~ failure_node(Y,or(D,Q))
      | ~ failure_node(X,or(C,P))
      | failure_node(parent_of(X,Y),or(C,D)) ),
    inference(skolemize,[status(sab)],[36]) ).

tff(38,plain,
    ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
      ( ~ siblings(X,Y)
      | ~ contradictory(P,Q)
      | ~ failure_node(Y,or(D,Q))
      | ~ failure_node(X,or(C,P))
      | failure_node(parent_of(X,Y),or(C,D)) ),
    inference(modus_ponens,[status(thm)],[37,30]) ).

tff(39,plain,
    ( ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
            ( ~ siblings(X,Y)
            | ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D)) )
      | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
      | ~ siblings(left_child_of(n),right_child_of(n))
      | ~ contradictory(atom,negate(atom))
      | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
      | ~ failure_node(left_child_of(n),or(empty,atom)) )
  <=> ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
            ( ~ siblings(X,Y)
            | ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D)) )
      | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
      | ~ siblings(left_child_of(n),right_child_of(n))
      | ~ contradictory(atom,negate(atom))
      | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
      | ~ failure_node(left_child_of(n),or(empty,atom)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,plain,
    ( ( ~ siblings(left_child_of(n),right_child_of(n))
      | ~ contradictory(atom,negate(atom))
      | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
      | ~ failure_node(left_child_of(n),or(empty,atom))
      | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) )
  <=> ( failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
      | ~ siblings(left_child_of(n),right_child_of(n))
      | ~ contradictory(atom,negate(atom))
      | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
      | ~ failure_node(left_child_of(n),or(empty,atom)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,plain,
    ( ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
            ( ~ siblings(X,Y)
            | ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D)) )
      | ~ siblings(left_child_of(n),right_child_of(n))
      | ~ contradictory(atom,negate(atom))
      | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
      | ~ failure_node(left_child_of(n),or(empty,atom))
      | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) )
  <=> ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
            ( ~ siblings(X,Y)
            | ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D)) )
      | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
      | ~ siblings(left_child_of(n),right_child_of(n))
      | ~ contradictory(atom,negate(atom))
      | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
      | ~ failure_node(left_child_of(n),or(empty,atom)) ) ),
    inference(monotonicity,[status(thm)],[40]) ).

tff(42,plain,
    ( ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
            ( ~ siblings(X,Y)
            | ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D)) )
      | ~ siblings(left_child_of(n),right_child_of(n))
      | ~ contradictory(atom,negate(atom))
      | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
      | ~ failure_node(left_child_of(n),or(empty,atom))
      | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) )
  <=> ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
            ( ~ siblings(X,Y)
            | ~ contradictory(P,Q)
            | ~ failure_node(Y,or(D,Q))
            | ~ failure_node(X,or(C,P))
            | failure_node(parent_of(X,Y),or(C,D)) )
      | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
      | ~ siblings(left_child_of(n),right_child_of(n))
      | ~ contradictory(atom,negate(atom))
      | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
      | ~ failure_node(left_child_of(n),or(empty,atom)) ) ),
    inference(transitivity,[status(thm)],[41,39]) ).

tff(43,plain,
    ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
          ( ~ siblings(X,Y)
          | ~ contradictory(P,Q)
          | ~ failure_node(Y,or(D,Q))
          | ~ failure_node(X,or(C,P))
          | failure_node(parent_of(X,Y),or(C,D)) )
    | ~ siblings(left_child_of(n),right_child_of(n))
    | ~ contradictory(atom,negate(atom))
    | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
    | ~ failure_node(left_child_of(n),or(empty,atom))
    | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(44,plain,
    ( ~ ! [D: $i,Y: $i,Q: $i,P: $i,X: $i,C: $i] :
          ( ~ siblings(X,Y)
          | ~ contradictory(P,Q)
          | ~ failure_node(Y,or(D,Q))
          | ~ failure_node(X,or(C,P))
          | failure_node(parent_of(X,Y),or(C,D)) )
    | failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty))
    | ~ siblings(left_child_of(n),right_child_of(n))
    | ~ contradictory(atom,negate(atom))
    | ~ failure_node(right_child_of(n),or(empty,negate(atom)))
    | ~ failure_node(left_child_of(n),or(empty,atom)) ),
    inference(modus_ponens,[status(thm)],[43,42]) ).

tff(45,plain,
    failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)),
    inference(unit_resolution,[status(thm)],[44,38,28,23,18,9]) ).

tff(46,plain,
    ^ [Z: $i] :
      refl(
        ( ~ failure_node(Z,or(empty,empty))
      <=> ~ failure_node(Z,or(empty,empty)) )),
    inference(bind,[status(th)],]) ).

tff(47,plain,
    ( ! [Z: $i] : ~ failure_node(Z,or(empty,empty))
  <=> ! [Z: $i] : ~ failure_node(Z,or(empty,empty)) ),
    inference(quant_intro,[status(thm)],[46]) ).

tff(48,plain,
    ( ! [Z: $i] : ~ failure_node(Z,or(empty,empty))
  <=> ! [Z: $i] : ~ failure_node(Z,or(empty,empty)) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,axiom,
    ! [Z: $i] : ~ failure_node(Z,or(empty,empty)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_is_there_an_empty_node) ).

tff(50,plain,
    ! [Z: $i] : ~ failure_node(Z,or(empty,empty)),
    inference(modus_ponens,[status(thm)],[49,48]) ).

tff(51,plain,
    ! [Z: $i] : ~ failure_node(Z,or(empty,empty)),
    inference(skolemize,[status(sab)],[50]) ).

tff(52,plain,
    ! [Z: $i] : ~ failure_node(Z,or(empty,empty)),
    inference(modus_ponens,[status(thm)],[51,47]) ).

tff(53,plain,
    ( ~ ! [Z: $i] : ~ failure_node(Z,or(empty,empty))
    | ~ failure_node(parent_of(left_child_of(n),right_child_of(n)),or(empty,empty)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(54,plain,
    $false,
    inference(unit_resolution,[status(thm)],[53,52,45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : COM004-1 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32  % Computer : n018.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Tue Aug 30 13:28:40 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.17/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.17/0.33  Usage: tptp [options] [-file:]file
% 0.17/0.33    -h, -?       prints this message.
% 0.17/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.17/0.33    -m, -model   generate model.
% 0.17/0.33    -p, -proof   generate proof.
% 0.17/0.33    -c, -core    generate unsat core of named formulas.
% 0.17/0.33    -st, -statistics display statistics.
% 0.17/0.33    -t:timeout   set timeout (in second).
% 0.17/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.17/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.17/0.33    -<param>:<value> configuration parameter and value.
% 0.17/0.33    -o:<output-file> file to place output in.
% 0.17/0.37  % SZS status Unsatisfiable
% 0.17/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------