TSTP Solution File: PUZ001-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : PUZ001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n020.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 : Sun Sep 18 14:10:45 EDT 2022

% Result   : Unsatisfiable 0.19s 0.38s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   49
% Syntax   : Number of formulae    :   97 (  22 unt;   7 typ;   0 def)
%            Number of atoms       :  336 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  477 ( 239   ~; 205   |;   0   &)
%                                         (  33 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    8 (   8 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :  116 ( 106   !;   0   ?; 116   :)

% Comments : 
%------------------------------------------------------------------------------
tff(richer_type,type,
    richer: ( $i * $i ) > $o ).

tff(agatha_type,type,
    agatha: $i ).

tff(butler_type,type,
    butler: $i ).

tff(hates_type,type,
    hates: ( $i * $i ) > $o ).

tff(charles_type,type,
    charles: $i ).

tff(lives_type,type,
    lives: $i > $o ).

tff(killed_type,type,
    killed: ( $i * $i ) > $o ).

tff(1,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ hates(agatha,X)
          | hates(butler,X) )
      <=> ( ~ hates(agatha,X)
          | hates(butler,X) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] :
        ( ~ hates(agatha,X)
        | hates(butler,X) )
  <=> ! [X: $i] :
        ( ~ hates(agatha,X)
        | hates(butler,X) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X: $i] :
        ( ~ hates(agatha,X)
        | hates(butler,X) )
  <=> ! [X: $i] :
        ( ~ hates(agatha,X)
        | hates(butler,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X: $i] :
      ( ~ hates(agatha,X)
      | hates(butler,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',same_hates) ).

tff(5,plain,
    ! [X: $i] :
      ( ~ hates(agatha,X)
      | hates(butler,X) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X: $i] :
      ( ~ hates(agatha,X)
      | hates(butler,X) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X: $i] :
      ( ~ hates(agatha,X)
      | hates(butler,X) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( hates(agatha,charles)
  <=> hates(agatha,charles) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,axiom,
    hates(agatha,charles),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',agatha_hates_charles) ).

tff(10,plain,
    hates(agatha,charles),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ( ( ~ ! [X: $i] :
            ( ~ hates(agatha,X)
            | hates(butler,X) )
      | ~ hates(agatha,charles)
      | hates(butler,charles) )
  <=> ( ~ ! [X: $i] :
            ( ~ hates(agatha,X)
            | hates(butler,X) )
      | ~ hates(agatha,charles)
      | hates(butler,charles) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [X: $i] :
          ( ~ hates(agatha,X)
          | hates(butler,X) )
    | ~ hates(agatha,charles)
    | hates(butler,charles) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [X: $i] :
          ( ~ hates(agatha,X)
          | hates(butler,X) )
    | ~ hates(agatha,charles)
    | hates(butler,charles) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    hates(butler,charles),
    inference(unit_resolution,[status(thm)],[13,10,7]) ).

tff(15,plain,
    ( hates(agatha,agatha)
  <=> hates(agatha,agatha) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    hates(agatha,agatha),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',agatha_hates_agatha) ).

tff(17,plain,
    hates(agatha,agatha),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ( ( ~ ! [X: $i] :
            ( ~ hates(agatha,X)
            | hates(butler,X) )
      | ~ hates(agatha,agatha)
      | hates(butler,agatha) )
  <=> ( ~ ! [X: $i] :
            ( ~ hates(agatha,X)
            | hates(butler,X) )
      | ~ hates(agatha,agatha)
      | hates(butler,agatha) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [X: $i] :
          ( ~ hates(agatha,X)
          | hates(butler,X) )
    | ~ hates(agatha,agatha)
    | hates(butler,agatha) ),
    inference(quant_inst,[status(thm)],]) ).

tff(20,plain,
    ( ~ ! [X: $i] :
          ( ~ hates(agatha,X)
          | hates(butler,X) )
    | ~ hates(agatha,agatha)
    | hates(butler,agatha) ),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    hates(butler,agatha),
    inference(unit_resolution,[status(thm)],[20,17,7]) ).

tff(22,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ hates(X,charles)
          | ~ hates(X,butler)
          | ~ hates(X,agatha) )
      <=> ( ~ hates(X,charles)
          | ~ hates(X,butler)
          | ~ hates(X,agatha) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [X: $i] :
        ( ~ hates(X,charles)
        | ~ hates(X,butler)
        | ~ hates(X,agatha) )
  <=> ! [X: $i] :
        ( ~ hates(X,charles)
        | ~ hates(X,butler)
        | ~ hates(X,agatha) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,plain,
    ( ! [X: $i] :
        ( ~ hates(X,charles)
        | ~ hates(X,butler)
        | ~ hates(X,agatha) )
  <=> ! [X: $i] :
        ( ~ hates(X,charles)
        | ~ hates(X,butler)
        | ~ hates(X,agatha) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ~ hates(X,agatha)
          | ~ hates(X,butler)
          | ~ hates(X,charles) )
      <=> ( ~ hates(X,charles)
          | ~ hates(X,butler)
          | ~ hates(X,agatha) ) )),
    inference(bind,[status(th)],]) ).

tff(26,plain,
    ( ! [X: $i] :
        ( ~ hates(X,agatha)
        | ~ hates(X,butler)
        | ~ hates(X,charles) )
  <=> ! [X: $i] :
        ( ~ hates(X,charles)
        | ~ hates(X,butler)
        | ~ hates(X,agatha) ) ),
    inference(quant_intro,[status(thm)],[25]) ).

tff(27,axiom,
    ! [X: $i] :
      ( ~ hates(X,agatha)
      | ~ hates(X,butler)
      | ~ hates(X,charles) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_one_hates_everyone) ).

tff(28,plain,
    ! [X: $i] :
      ( ~ hates(X,charles)
      | ~ hates(X,butler)
      | ~ hates(X,agatha) ),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ! [X: $i] :
      ( ~ hates(X,charles)
      | ~ hates(X,butler)
      | ~ hates(X,agatha) ),
    inference(modus_ponens,[status(thm)],[28,24]) ).

tff(30,plain,
    ! [X: $i] :
      ( ~ hates(X,charles)
      | ~ hates(X,butler)
      | ~ hates(X,agatha) ),
    inference(skolemize,[status(sab)],[29]) ).

tff(31,plain,
    ! [X: $i] :
      ( ~ hates(X,charles)
      | ~ hates(X,butler)
      | ~ hates(X,agatha) ),
    inference(modus_ponens,[status(thm)],[30,23]) ).

tff(32,plain,
    ( ( ~ ! [X: $i] :
            ( ~ hates(X,charles)
            | ~ hates(X,butler)
            | ~ hates(X,agatha) )
      | ~ hates(butler,charles)
      | ~ hates(butler,butler)
      | ~ hates(butler,agatha) )
  <=> ( ~ ! [X: $i] :
            ( ~ hates(X,charles)
            | ~ hates(X,butler)
            | ~ hates(X,agatha) )
      | ~ hates(butler,charles)
      | ~ hates(butler,butler)
      | ~ hates(butler,agatha) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [X: $i] :
          ( ~ hates(X,charles)
          | ~ hates(X,butler)
          | ~ hates(X,agatha) )
    | ~ hates(butler,charles)
    | ~ hates(butler,butler)
    | ~ hates(butler,agatha) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [X: $i] :
          ( ~ hates(X,charles)
          | ~ hates(X,butler)
          | ~ hates(X,agatha) )
    | ~ hates(butler,charles)
    | ~ hates(butler,butler)
    | ~ hates(butler,agatha) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    ~ hates(butler,butler),
    inference(unit_resolution,[status(thm)],[34,31,21,14]) ).

tff(36,plain,
    ^ [X: $i] :
      refl(
        ( ( hates(butler,X)
          | richer(X,agatha)
          | ~ lives(X) )
      <=> ( hates(butler,X)
          | richer(X,agatha)
          | ~ lives(X) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [X: $i] :
        ( hates(butler,X)
        | richer(X,agatha)
        | ~ lives(X) )
  <=> ! [X: $i] :
        ( hates(butler,X)
        | richer(X,agatha)
        | ~ lives(X) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,plain,
    ( ! [X: $i] :
        ( hates(butler,X)
        | richer(X,agatha)
        | ~ lives(X) )
  <=> ! [X: $i] :
        ( hates(butler,X)
        | richer(X,agatha)
        | ~ lives(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ~ lives(X)
          | richer(X,agatha)
          | hates(butler,X) )
      <=> ( hates(butler,X)
          | richer(X,agatha)
          | ~ lives(X) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [X: $i] :
        ( ~ lives(X)
        | richer(X,agatha)
        | hates(butler,X) )
  <=> ! [X: $i] :
        ( hates(butler,X)
        | richer(X,agatha)
        | ~ lives(X) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,axiom,
    ! [X: $i] :
      ( ~ lives(X)
      | richer(X,agatha)
      | hates(butler,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',butler_hates_poor) ).

tff(42,plain,
    ! [X: $i] :
      ( hates(butler,X)
      | richer(X,agatha)
      | ~ lives(X) ),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ! [X: $i] :
      ( hates(butler,X)
      | richer(X,agatha)
      | ~ lives(X) ),
    inference(modus_ponens,[status(thm)],[42,38]) ).

tff(44,plain,
    ! [X: $i] :
      ( hates(butler,X)
      | richer(X,agatha)
      | ~ lives(X) ),
    inference(skolemize,[status(sab)],[43]) ).

tff(45,plain,
    ! [X: $i] :
      ( hates(butler,X)
      | richer(X,agatha)
      | ~ lives(X) ),
    inference(modus_ponens,[status(thm)],[44,37]) ).

tff(46,plain,
    ( lives(butler)
  <=> lives(butler) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,axiom,
    lives(butler),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',butler) ).

tff(48,plain,
    lives(butler),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    ( ( ~ ! [X: $i] :
            ( hates(butler,X)
            | richer(X,agatha)
            | ~ lives(X) )
      | hates(butler,butler)
      | richer(butler,agatha)
      | ~ lives(butler) )
  <=> ( ~ ! [X: $i] :
            ( hates(butler,X)
            | richer(X,agatha)
            | ~ lives(X) )
      | hates(butler,butler)
      | richer(butler,agatha)
      | ~ lives(butler) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,plain,
    ( ~ ! [X: $i] :
          ( hates(butler,X)
          | richer(X,agatha)
          | ~ lives(X) )
    | hates(butler,butler)
    | richer(butler,agatha)
    | ~ lives(butler) ),
    inference(quant_inst,[status(thm)],]) ).

tff(51,plain,
    ( ~ ! [X: $i] :
          ( hates(butler,X)
          | richer(X,agatha)
          | ~ lives(X) )
    | hates(butler,butler)
    | richer(butler,agatha)
    | ~ lives(butler) ),
    inference(modus_ponens,[status(thm)],[50,49]) ).

tff(52,plain,
    ( hates(butler,butler)
    | richer(butler,agatha) ),
    inference(unit_resolution,[status(thm)],[51,48,45]) ).

tff(53,plain,
    richer(butler,agatha),
    inference(unit_resolution,[status(thm)],[52,35]) ).

tff(54,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ hates(agatha,X)
          | ~ hates(charles,X) )
      <=> ( ~ hates(agatha,X)
          | ~ hates(charles,X) ) )),
    inference(bind,[status(th)],]) ).

tff(55,plain,
    ( ! [X: $i] :
        ( ~ hates(agatha,X)
        | ~ hates(charles,X) )
  <=> ! [X: $i] :
        ( ~ hates(agatha,X)
        | ~ hates(charles,X) ) ),
    inference(quant_intro,[status(thm)],[54]) ).

tff(56,plain,
    ( ! [X: $i] :
        ( ~ hates(agatha,X)
        | ~ hates(charles,X) )
  <=> ! [X: $i] :
        ( ~ hates(agatha,X)
        | ~ hates(charles,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(57,axiom,
    ! [X: $i] :
      ( ~ hates(agatha,X)
      | ~ hates(charles,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_hates) ).

tff(58,plain,
    ! [X: $i] :
      ( ~ hates(agatha,X)
      | ~ hates(charles,X) ),
    inference(modus_ponens,[status(thm)],[57,56]) ).

tff(59,plain,
    ! [X: $i] :
      ( ~ hates(agatha,X)
      | ~ hates(charles,X) ),
    inference(skolemize,[status(sab)],[58]) ).

tff(60,plain,
    ! [X: $i] :
      ( ~ hates(agatha,X)
      | ~ hates(charles,X) ),
    inference(modus_ponens,[status(thm)],[59,55]) ).

tff(61,plain,
    ( ( ~ ! [X: $i] :
            ( ~ hates(agatha,X)
            | ~ hates(charles,X) )
      | ~ hates(agatha,agatha)
      | ~ hates(charles,agatha) )
  <=> ( ~ ! [X: $i] :
            ( ~ hates(agatha,X)
            | ~ hates(charles,X) )
      | ~ hates(agatha,agatha)
      | ~ hates(charles,agatha) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,plain,
    ( ~ ! [X: $i] :
          ( ~ hates(agatha,X)
          | ~ hates(charles,X) )
    | ~ hates(agatha,agatha)
    | ~ hates(charles,agatha) ),
    inference(quant_inst,[status(thm)],]) ).

tff(63,plain,
    ( ~ ! [X: $i] :
          ( ~ hates(agatha,X)
          | ~ hates(charles,X) )
    | ~ hates(agatha,agatha)
    | ~ hates(charles,agatha) ),
    inference(modus_ponens,[status(thm)],[62,61]) ).

tff(64,plain,
    ~ hates(charles,agatha),
    inference(unit_resolution,[status(thm)],[63,60,17]) ).

tff(65,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( ~ killed(X,Y)
          | hates(X,Y) )
      <=> ( ~ killed(X,Y)
          | hates(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(66,plain,
    ( ! [Y: $i,X: $i] :
        ( ~ killed(X,Y)
        | hates(X,Y) )
  <=> ! [Y: $i,X: $i] :
        ( ~ killed(X,Y)
        | hates(X,Y) ) ),
    inference(quant_intro,[status(thm)],[65]) ).

tff(67,plain,
    ( ! [Y: $i,X: $i] :
        ( ~ killed(X,Y)
        | hates(X,Y) )
  <=> ! [Y: $i,X: $i] :
        ( ~ killed(X,Y)
        | hates(X,Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(68,axiom,
    ! [Y: $i,X: $i] :
      ( ~ killed(X,Y)
      | hates(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',killer_hates_victim) ).

tff(69,plain,
    ! [Y: $i,X: $i] :
      ( ~ killed(X,Y)
      | hates(X,Y) ),
    inference(modus_ponens,[status(thm)],[68,67]) ).

tff(70,plain,
    ! [Y: $i,X: $i] :
      ( ~ killed(X,Y)
      | hates(X,Y) ),
    inference(skolemize,[status(sab)],[69]) ).

tff(71,plain,
    ! [Y: $i,X: $i] :
      ( ~ killed(X,Y)
      | hates(X,Y) ),
    inference(modus_ponens,[status(thm)],[70,66]) ).

tff(72,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( ~ killed(X,Y)
            | hates(X,Y) )
      | ~ killed(charles,agatha)
      | hates(charles,agatha) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( ~ killed(X,Y)
            | hates(X,Y) )
      | ~ killed(charles,agatha)
      | hates(charles,agatha) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( ~ killed(X,Y)
          | hates(X,Y) )
    | ~ killed(charles,agatha)
    | hates(charles,agatha) ),
    inference(quant_inst,[status(thm)],]) ).

tff(74,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( ~ killed(X,Y)
          | hates(X,Y) )
    | ~ killed(charles,agatha)
    | hates(charles,agatha) ),
    inference(modus_ponens,[status(thm)],[73,72]) ).

tff(75,plain,
    ~ killed(charles,agatha),
    inference(unit_resolution,[status(thm)],[74,71,64]) ).

tff(76,plain,
    ( ( killed(butler,agatha)
      | killed(charles,agatha) )
  <=> ( killed(butler,agatha)
      | killed(charles,agatha) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(77,axiom,
    ( killed(butler,agatha)
    | killed(charles,agatha) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_neither_charles_nor_butler_did_it) ).

tff(78,plain,
    ( killed(butler,agatha)
    | killed(charles,agatha) ),
    inference(modus_ponens,[status(thm)],[77,76]) ).

tff(79,plain,
    killed(butler,agatha),
    inference(unit_resolution,[status(thm)],[78,75]) ).

tff(80,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( ~ killed(X,Y)
          | ~ richer(X,Y) )
      <=> ( ~ killed(X,Y)
          | ~ richer(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(81,plain,
    ( ! [Y: $i,X: $i] :
        ( ~ killed(X,Y)
        | ~ richer(X,Y) )
  <=> ! [Y: $i,X: $i] :
        ( ~ killed(X,Y)
        | ~ richer(X,Y) ) ),
    inference(quant_intro,[status(thm)],[80]) ).

tff(82,plain,
    ( ! [Y: $i,X: $i] :
        ( ~ killed(X,Y)
        | ~ richer(X,Y) )
  <=> ! [Y: $i,X: $i] :
        ( ~ killed(X,Y)
        | ~ richer(X,Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(83,axiom,
    ! [Y: $i,X: $i] :
      ( ~ killed(X,Y)
      | ~ richer(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',poorer_killer) ).

tff(84,plain,
    ! [Y: $i,X: $i] :
      ( ~ killed(X,Y)
      | ~ richer(X,Y) ),
    inference(modus_ponens,[status(thm)],[83,82]) ).

tff(85,plain,
    ! [Y: $i,X: $i] :
      ( ~ killed(X,Y)
      | ~ richer(X,Y) ),
    inference(skolemize,[status(sab)],[84]) ).

tff(86,plain,
    ! [Y: $i,X: $i] :
      ( ~ killed(X,Y)
      | ~ richer(X,Y) ),
    inference(modus_ponens,[status(thm)],[85,81]) ).

tff(87,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( ~ killed(X,Y)
            | ~ richer(X,Y) )
      | ~ killed(butler,agatha)
      | ~ richer(butler,agatha) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( ~ killed(X,Y)
            | ~ richer(X,Y) )
      | ~ killed(butler,agatha)
      | ~ richer(butler,agatha) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(88,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( ~ killed(X,Y)
          | ~ richer(X,Y) )
    | ~ killed(butler,agatha)
    | ~ richer(butler,agatha) ),
    inference(quant_inst,[status(thm)],]) ).

tff(89,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( ~ killed(X,Y)
          | ~ richer(X,Y) )
    | ~ killed(butler,agatha)
    | ~ richer(butler,agatha) ),
    inference(modus_ponens,[status(thm)],[88,87]) ).

tff(90,plain,
    $false,
    inference(unit_resolution,[status(thm)],[89,86,79,53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : PUZ001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n020.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 : Fri Sep  2 18:16:44 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.
% 0.19/0.38  % SZS status Unsatisfiable
% 0.19/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------