TSTP Solution File: GEO052-3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO052-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n010.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 : Fri Sep 16 20:34:32 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   87 (  25 unt;   6 typ;   0 def)
%            Number of atoms       :  310 (  30 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  391 ( 172   ~; 184   |;   0   &)
%                                         (  35 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   10 (  10 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   2   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-4 aty)
%            Number of variables   :  194 ( 180   !;   0   ?; 194   :)

% Comments : 
%------------------------------------------------------------------------------
tff(between_type,type,
    between: ( $i * $i * $i ) > $o ).

tff(u_type,type,
    u: $i ).

tff(insertion_type,type,
    insertion: ( $i * $i * $i * $i ) > $i ).

tff(w_type,type,
    w: $i ).

tff(x_type,type,
    x: $i ).

tff(v_type,type,
    v: $i ).

tff(1,plain,
    ( between(u,w,x)
  <=> between(u,w,x) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    between(u,w,x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_between_u_and_x) ).

tff(3,plain,
    between(u,w,x),
    inference(modus_ponens,[status(thm)],[2,1]) ).

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

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

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

tff(7,axiom,
    ! [W: $i,V: $i,U: $i] :
      ( ~ between(U,V,W)
      | ( V = insertion(U,W,U,V) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',i3) ).

tff(8,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ between(U,V,W)
      | ( V = insertion(U,W,U,V) ) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ between(U,V,W)
      | ( V = insertion(U,W,U,V) ) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ between(U,V,W)
      | ( V = insertion(U,W,U,V) ) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | ( V = insertion(U,W,U,V) ) )
      | ~ between(u,w,x)
      | ( w = insertion(u,x,u,w) ) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | ( V = insertion(U,W,U,V) ) )
      | ~ between(u,w,x)
      | ( w = insertion(u,x,u,w) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | ( V = insertion(U,W,U,V) ) )
    | ~ between(u,w,x)
    | ( w = insertion(u,x,u,w) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | ( V = insertion(U,W,U,V) ) )
    | ~ between(u,w,x)
    | ( w = insertion(u,x,u,w) ) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    w = insertion(u,x,u,w),
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    insertion(u,x,u,w) = w,
    inference(symmetry,[status(thm)],[14]) ).

tff(16,plain,
    ( between(x,insertion(u,x,u,w),u)
  <=> between(x,w,u) ),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    ( between(x,w,u)
  <=> between(x,insertion(u,x,u,w),u) ),
    inference(symmetry,[status(thm)],[16]) ).

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

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

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

tff(21,axiom,
    ! [W: $i,V: $i,U: $i] :
      ( ~ between(U,V,W)
      | between(W,V,U) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).

tff(22,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ between(U,V,W)
      | between(W,V,U) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ between(U,V,W)
      | between(W,V,U) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [W: $i,V: $i,U: $i] :
      ( ~ between(U,V,W)
      | between(W,V,U) ),
    inference(modus_ponens,[status(thm)],[23,19]) ).

tff(25,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | between(W,V,U) )
      | ~ between(u,w,x)
      | between(x,w,u) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | between(W,V,U) )
      | ~ between(u,w,x)
      | between(x,w,u) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | between(W,V,U) )
    | ~ between(u,w,x)
    | between(x,w,u) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | between(W,V,U) )
    | ~ between(u,w,x)
    | between(x,w,u) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    between(x,w,u),
    inference(unit_resolution,[status(thm)],[27,24,3]) ).

tff(29,plain,
    between(x,insertion(u,x,u,w),u),
    inference(modus_ponens,[status(thm)],[28,17]) ).

tff(30,plain,
    ( between(u,v,x)
  <=> between(u,v,x) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,axiom,
    between(u,v,x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_x) ).

tff(32,plain,
    between(u,v,x),
    inference(modus_ponens,[status(thm)],[31,30]) ).

tff(33,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | ( V = insertion(U,W,U,V) ) )
      | ~ between(u,v,x)
      | ( v = insertion(u,x,u,v) ) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | ( V = insertion(U,W,U,V) ) )
      | ~ between(u,v,x)
      | ( v = insertion(u,x,u,v) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | ( V = insertion(U,W,U,V) ) )
    | ~ between(u,v,x)
    | ( v = insertion(u,x,u,v) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(35,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | ( V = insertion(U,W,U,V) ) )
    | ~ between(u,v,x)
    | ( v = insertion(u,x,u,v) ) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    v = insertion(u,x,u,v),
    inference(unit_resolution,[status(thm)],[35,10,32]) ).

tff(37,plain,
    insertion(u,x,u,v) = v,
    inference(symmetry,[status(thm)],[36]) ).

tff(38,plain,
    ( between(x,insertion(u,x,u,v),insertion(u,x,u,w))
  <=> between(x,v,w) ),
    inference(monotonicity,[status(thm)],[37,15]) ).

tff(39,plain,
    ( between(x,v,w)
  <=> between(x,insertion(u,x,u,v),insertion(u,x,u,w)) ),
    inference(symmetry,[status(thm)],[38]) ).

tff(40,plain,
    ( ~ between(x,v,w)
  <=> ~ between(x,insertion(u,x,u,v),insertion(u,x,u,w)) ),
    inference(monotonicity,[status(thm)],[39]) ).

tff(41,plain,
    ( ~ between(w,v,x)
  <=> ~ between(w,v,x) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    ~ between(w,v,x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_between_w_and_x) ).

tff(43,plain,
    ~ between(w,v,x),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | between(W,V,U) )
      | ~ between(x,v,w)
      | between(w,v,x) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | between(W,V,U) )
      | ~ between(x,v,w)
      | between(w,v,x) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | between(W,V,U) )
    | ~ between(x,v,w)
    | between(w,v,x) ),
    inference(quant_inst,[status(thm)],]) ).

tff(46,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | between(W,V,U) )
    | ~ between(x,v,w)
    | between(w,v,x) ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ~ between(x,v,w),
    inference(unit_resolution,[status(thm)],[46,24,43]) ).

tff(48,plain,
    ~ between(x,insertion(u,x,u,v),insertion(u,x,u,w)),
    inference(modus_ponens,[status(thm)],[47,40]) ).

tff(49,plain,
    ( between(x,insertion(u,x,u,w),insertion(u,x,u,v))
  <=> between(x,w,v) ),
    inference(monotonicity,[status(thm)],[15,37]) ).

tff(50,plain,
    ( between(x,w,v)
  <=> between(x,insertion(u,x,u,w),insertion(u,x,u,v)) ),
    inference(symmetry,[status(thm)],[49]) ).

tff(51,plain,
    ( ~ between(x,w,v)
  <=> ~ between(x,insertion(u,x,u,w),insertion(u,x,u,v)) ),
    inference(monotonicity,[status(thm)],[50]) ).

tff(52,plain,
    ( ~ between(v,w,x)
  <=> ~ between(v,w,x) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,axiom,
    ~ between(v,w,x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_not_between_v_and_x) ).

tff(54,plain,
    ~ between(v,w,x),
    inference(modus_ponens,[status(thm)],[53,52]) ).

tff(55,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | between(W,V,U) )
      | ~ between(x,w,v)
      | between(v,w,x) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | between(W,V,U) )
      | ~ between(x,w,v)
      | between(v,w,x) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(56,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | between(W,V,U) )
    | ~ between(x,w,v)
    | between(v,w,x) ),
    inference(quant_inst,[status(thm)],]) ).

tff(57,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | between(W,V,U) )
    | ~ between(x,w,v)
    | between(v,w,x) ),
    inference(modus_ponens,[status(thm)],[56,55]) ).

tff(58,plain,
    ~ between(x,w,v),
    inference(unit_resolution,[status(thm)],[57,24,54]) ).

tff(59,plain,
    ~ between(x,insertion(u,x,u,w),insertion(u,x,u,v)),
    inference(modus_ponens,[status(thm)],[58,51]) ).

tff(60,plain,
    ( between(x,insertion(u,x,u,v),u)
  <=> between(x,v,u) ),
    inference(monotonicity,[status(thm)],[37]) ).

tff(61,plain,
    ( between(x,v,u)
  <=> between(x,insertion(u,x,u,v),u) ),
    inference(symmetry,[status(thm)],[60]) ).

tff(62,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | between(W,V,U) )
      | ~ between(u,v,x)
      | between(x,v,u) )
  <=> ( ~ ! [W: $i,V: $i,U: $i] :
            ( ~ between(U,V,W)
            | between(W,V,U) )
      | ~ between(u,v,x)
      | between(x,v,u) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(63,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | between(W,V,U) )
    | ~ between(u,v,x)
    | between(x,v,u) ),
    inference(quant_inst,[status(thm)],]) ).

tff(64,plain,
    ( ~ ! [W: $i,V: $i,U: $i] :
          ( ~ between(U,V,W)
          | between(W,V,U) )
    | ~ between(u,v,x)
    | between(x,v,u) ),
    inference(modus_ponens,[status(thm)],[63,62]) ).

tff(65,plain,
    between(x,v,u),
    inference(unit_resolution,[status(thm)],[64,24,32]) ).

tff(66,plain,
    between(x,insertion(u,x,u,v),u),
    inference(modus_ponens,[status(thm)],[65,61]) ).

tff(67,plain,
    ^ [W: $i,V: $i,U: $i,X: $i] :
      refl(
        ( ( between(U,W,V)
          | ~ between(U,V,X)
          | between(U,V,W)
          | ~ between(U,W,X) )
      <=> ( between(U,W,V)
          | ~ between(U,V,X)
          | between(U,V,W)
          | ~ between(U,W,X) ) )),
    inference(bind,[status(th)],]) ).

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

tff(69,plain,
    ( ! [W: $i,V: $i,U: $i,X: $i] :
        ( between(U,W,V)
        | ~ between(U,V,X)
        | between(U,V,W)
        | ~ between(U,W,X) )
  <=> ! [W: $i,V: $i,U: $i,X: $i] :
        ( between(U,W,V)
        | ~ between(U,V,X)
        | between(U,V,W)
        | ~ between(U,W,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ^ [W: $i,V: $i,U: $i,X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ between(U,V,X)
              | ~ between(U,W,X)
              | between(U,V,W) )
          <=> ( ~ between(U,V,X)
              | between(U,V,W)
              | ~ between(U,W,X) ) )),
          ( ( ~ between(U,V,X)
            | ~ between(U,W,X)
            | between(U,V,W)
            | between(U,W,V) )
        <=> ( ~ between(U,V,X)
            | between(U,V,W)
            | ~ between(U,W,X)
            | between(U,W,V) ) )),
        rewrite(
          ( ( ~ between(U,V,X)
            | between(U,V,W)
            | ~ between(U,W,X)
            | between(U,W,V) )
        <=> ( between(U,W,V)
            | ~ between(U,V,X)
            | between(U,V,W)
            | ~ between(U,W,X) ) )),
        ( ( ~ between(U,V,X)
          | ~ between(U,W,X)
          | between(U,V,W)
          | between(U,W,V) )
      <=> ( between(U,W,V)
          | ~ between(U,V,X)
          | between(U,V,W)
          | ~ between(U,W,X) ) )),
    inference(bind,[status(th)],]) ).

tff(71,plain,
    ( ! [W: $i,V: $i,U: $i,X: $i] :
        ( ~ between(U,V,X)
        | ~ between(U,W,X)
        | between(U,V,W)
        | between(U,W,V) )
  <=> ! [W: $i,V: $i,U: $i,X: $i] :
        ( between(U,W,V)
        | ~ between(U,V,X)
        | between(U,V,W)
        | ~ between(U,W,X) ) ),
    inference(quant_intro,[status(thm)],[70]) ).

tff(72,axiom,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( ~ between(U,V,X)
      | ~ between(U,W,X)
      | between(U,V,W)
      | between(U,W,V) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9) ).

tff(73,plain,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( between(U,W,V)
      | ~ between(U,V,X)
      | between(U,V,W)
      | ~ between(U,W,X) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( between(U,W,V)
      | ~ between(U,V,X)
      | between(U,V,W)
      | ~ between(U,W,X) ),
    inference(modus_ponens,[status(thm)],[73,69]) ).

tff(75,plain,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( between(U,W,V)
      | ~ between(U,V,X)
      | between(U,V,W)
      | ~ between(U,W,X) ),
    inference(skolemize,[status(sab)],[74]) ).

tff(76,plain,
    ! [W: $i,V: $i,U: $i,X: $i] :
      ( between(U,W,V)
      | ~ between(U,V,X)
      | between(U,V,W)
      | ~ between(U,W,X) ),
    inference(modus_ponens,[status(thm)],[75,68]) ).

tff(77,plain,
    ( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
            ( between(U,W,V)
            | ~ between(U,V,X)
            | between(U,V,W)
            | ~ between(U,W,X) )
      | between(x,insertion(u,x,u,w),insertion(u,x,u,v))
      | ~ between(x,insertion(u,x,u,v),u)
      | between(x,insertion(u,x,u,v),insertion(u,x,u,w))
      | ~ between(x,insertion(u,x,u,w),u) )
  <=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
            ( between(U,W,V)
            | ~ between(U,V,X)
            | between(U,V,W)
            | ~ between(U,W,X) )
      | between(x,insertion(u,x,u,w),insertion(u,x,u,v))
      | ~ between(x,insertion(u,x,u,v),u)
      | between(x,insertion(u,x,u,v),insertion(u,x,u,w))
      | ~ between(x,insertion(u,x,u,w),u) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,plain,
    ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
          ( between(U,W,V)
          | ~ between(U,V,X)
          | between(U,V,W)
          | ~ between(U,W,X) )
    | between(x,insertion(u,x,u,w),insertion(u,x,u,v))
    | ~ between(x,insertion(u,x,u,v),u)
    | between(x,insertion(u,x,u,v),insertion(u,x,u,w))
    | ~ between(x,insertion(u,x,u,w),u) ),
    inference(quant_inst,[status(thm)],]) ).

tff(79,plain,
    ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
          ( between(U,W,V)
          | ~ between(U,V,X)
          | between(U,V,W)
          | ~ between(U,W,X) )
    | between(x,insertion(u,x,u,w),insertion(u,x,u,v))
    | ~ between(x,insertion(u,x,u,v),u)
    | between(x,insertion(u,x,u,v),insertion(u,x,u,w))
    | ~ between(x,insertion(u,x,u,w),u) ),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    ( between(x,insertion(u,x,u,w),insertion(u,x,u,v))
    | ~ between(x,insertion(u,x,u,v),u)
    | between(x,insertion(u,x,u,v),insertion(u,x,u,w))
    | ~ between(x,insertion(u,x,u,w),u) ),
    inference(unit_resolution,[status(thm)],[79,76]) ).

tff(81,plain,
    $false,
    inference(unit_resolution,[status(thm)],[80,66,59,48,29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO052-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 31 04:53:58 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.41  % SZS status Unsatisfiable
% 0.19/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------