TSTP Solution File: SWV002-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n025.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 : Thu Sep 29 15:09:35 EDT 2022

% Result   : Unsatisfiable 0.14s 0.34s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   84 (  22 unt;   6 typ;   0 def)
%            Number of atoms       :  373 (  37 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  477 ( 200   ~; 238   |;   0   &)
%                                         (  39 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   18 (  18 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :  137 ( 126   !;   0   ?; 137   :)

% Comments : 
%------------------------------------------------------------------------------
tff(less_than_type,type,
    less_than: ( $i * $i ) > $o ).

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

tff(q_type,type,
    q: $i ).

tff(j_type,type,
    j: $i ).

tff(k_type,type,
    k: $i ).

tff(i_type,type,
    i: $i ).

tff(1,plain,
    ( less_than(a(q),a(j))
  <=> less_than(a(q),a(j)) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    less_than(a(q),a(j)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).

tff(3,plain,
    less_than(a(q),a(j)),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ( less_than(a(j),a(k))
  <=> less_than(a(j),a(k)) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    less_than(a(j),a(k)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).

tff(6,plain,
    less_than(a(j),a(k)),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ( ! [Z: $i,Y: $i,X: $i] :
        ( ~ less_than(Y,Z)
        | ~ less_than(X,Y)
        | less_than(X,Z) )
  <=> ! [Z: $i,Y: $i,X: $i] :
        ( ~ less_than(Y,Z)
        | ~ less_than(X,Y)
        | less_than(X,Z) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,plain,
    ( ! [Z: $i,Y: $i,X: $i] :
        ( ~ less_than(Y,Z)
        | ~ less_than(X,Y)
        | less_than(X,Z) )
  <=> ! [Z: $i,Y: $i,X: $i] :
        ( ~ less_than(Y,Z)
        | ~ less_than(X,Y)
        | less_than(X,Z) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,plain,
    ^ [Z: $i,Y: $i,X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( less_than(X,Z)
              | ~ less_than(X,Y) )
          <=> ( ~ less_than(X,Y)
              | less_than(X,Z) ) )),
          ( ( less_than(X,Z)
            | ~ less_than(X,Y)
            | ~ less_than(Y,Z) )
        <=> ( ~ less_than(X,Y)
            | less_than(X,Z)
            | ~ less_than(Y,Z) ) )),
        rewrite(
          ( ( ~ less_than(X,Y)
            | less_than(X,Z)
            | ~ less_than(Y,Z) )
        <=> ( ~ less_than(Y,Z)
            | ~ less_than(X,Y)
            | less_than(X,Z) ) )),
        ( ( less_than(X,Z)
          | ~ less_than(X,Y)
          | ~ less_than(Y,Z) )
      <=> ( ~ less_than(Y,Z)
          | ~ less_than(X,Y)
          | less_than(X,Z) ) )),
    inference(bind,[status(th)],]) ).

tff(10,plain,
    ( ! [Z: $i,Y: $i,X: $i] :
        ( less_than(X,Z)
        | ~ less_than(X,Y)
        | ~ less_than(Y,Z) )
  <=> ! [Z: $i,Y: $i,X: $i] :
        ( ~ less_than(Y,Z)
        | ~ less_than(X,Y)
        | less_than(X,Z) ) ),
    inference(quant_intro,[status(thm)],[9]) ).

tff(11,axiom,
    ! [Z: $i,Y: $i,X: $i] :
      ( less_than(X,Z)
      | ~ less_than(X,Y)
      | ~ less_than(Y,Z) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax',transitivity_of_less_than) ).

tff(12,plain,
    ! [Z: $i,Y: $i,X: $i] :
      ( ~ less_than(Y,Z)
      | ~ less_than(X,Y)
      | less_than(X,Z) ),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ! [Z: $i,Y: $i,X: $i] :
      ( ~ less_than(Y,Z)
      | ~ less_than(X,Y)
      | less_than(X,Z) ),
    inference(modus_ponens,[status(thm)],[12,8]) ).

tff(14,plain,
    ! [Z: $i,Y: $i,X: $i] :
      ( ~ less_than(Y,Z)
      | ~ less_than(X,Y)
      | less_than(X,Z) ),
    inference(skolemize,[status(sab)],[13]) ).

tff(15,plain,
    ! [Z: $i,Y: $i,X: $i] :
      ( ~ less_than(Y,Z)
      | ~ less_than(X,Y)
      | less_than(X,Z) ),
    inference(modus_ponens,[status(thm)],[14,7]) ).

tff(16,plain,
    ( ( ~ ! [Z: $i,Y: $i,X: $i] :
            ( ~ less_than(Y,Z)
            | ~ less_than(X,Y)
            | less_than(X,Z) )
      | ~ less_than(a(j),a(k))
      | ~ less_than(a(q),a(j))
      | less_than(a(q),a(k)) )
  <=> ( ~ ! [Z: $i,Y: $i,X: $i] :
            ( ~ less_than(Y,Z)
            | ~ less_than(X,Y)
            | less_than(X,Z) )
      | ~ less_than(a(j),a(k))
      | ~ less_than(a(q),a(j))
      | less_than(a(q),a(k)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(17,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] :
          ( ~ less_than(Y,Z)
          | ~ less_than(X,Y)
          | less_than(X,Z) )
    | ~ less_than(a(j),a(k))
    | ~ less_than(a(q),a(j))
    | less_than(a(q),a(k)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] :
          ( ~ less_than(Y,Z)
          | ~ less_than(X,Y)
          | less_than(X,Z) )
    | ~ less_than(a(j),a(k))
    | ~ less_than(a(q),a(j))
    | less_than(a(q),a(k)) ),
    inference(modus_ponens,[status(thm)],[17,16]) ).

tff(19,plain,
    less_than(a(q),a(k)),
    inference(unit_resolution,[status(thm)],[18,15,6,3]) ).

tff(20,plain,
    ( ~ less_than(q,i)
  <=> ~ less_than(q,i) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    ~ less_than(q,i),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).

tff(22,plain,
    ~ less_than(q,i),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ less_than(a(X),a(k))
          | ~ less_than(X,j)
          | less_than(X,i) )
      <=> ( ~ less_than(a(X),a(k))
          | ~ less_than(X,j)
          | less_than(X,i) ) )),
    inference(bind,[status(th)],]) ).

tff(24,plain,
    ( ! [X: $i] :
        ( ~ less_than(a(X),a(k))
        | ~ less_than(X,j)
        | less_than(X,i) )
  <=> ! [X: $i] :
        ( ~ less_than(a(X),a(k))
        | ~ less_than(X,j)
        | less_than(X,i) ) ),
    inference(quant_intro,[status(thm)],[23]) ).

tff(25,plain,
    ( ! [X: $i] :
        ( ~ less_than(a(X),a(k))
        | ~ less_than(X,j)
        | less_than(X,i) )
  <=> ! [X: $i] :
        ( ~ less_than(a(X),a(k))
        | ~ less_than(X,j)
        | less_than(X,i) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,plain,
    ^ [X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( less_than(X,i)
              | ~ less_than(X,j) )
          <=> ( ~ less_than(X,j)
              | less_than(X,i) ) )),
          ( ( less_than(X,i)
            | ~ less_than(X,j)
            | ~ less_than(a(X),a(k)) )
        <=> ( ~ less_than(X,j)
            | less_than(X,i)
            | ~ less_than(a(X),a(k)) ) )),
        rewrite(
          ( ( ~ less_than(X,j)
            | less_than(X,i)
            | ~ less_than(a(X),a(k)) )
        <=> ( ~ less_than(a(X),a(k))
            | ~ less_than(X,j)
            | less_than(X,i) ) )),
        ( ( less_than(X,i)
          | ~ less_than(X,j)
          | ~ less_than(a(X),a(k)) )
      <=> ( ~ less_than(a(X),a(k))
          | ~ less_than(X,j)
          | less_than(X,i) ) )),
    inference(bind,[status(th)],]) ).

tff(27,plain,
    ( ! [X: $i] :
        ( less_than(X,i)
        | ~ less_than(X,j)
        | ~ less_than(a(X),a(k)) )
  <=> ! [X: $i] :
        ( ~ less_than(a(X),a(k))
        | ~ less_than(X,j)
        | less_than(X,i) ) ),
    inference(quant_intro,[status(thm)],[26]) ).

tff(28,axiom,
    ! [X: $i] :
      ( less_than(X,i)
      | ~ less_than(X,j)
      | ~ less_than(a(X),a(k)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).

tff(29,plain,
    ! [X: $i] :
      ( ~ less_than(a(X),a(k))
      | ~ less_than(X,j)
      | less_than(X,i) ),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    ! [X: $i] :
      ( ~ less_than(a(X),a(k))
      | ~ less_than(X,j)
      | less_than(X,i) ),
    inference(modus_ponens,[status(thm)],[29,25]) ).

tff(31,plain,
    ! [X: $i] :
      ( ~ less_than(a(X),a(k))
      | ~ less_than(X,j)
      | less_than(X,i) ),
    inference(skolemize,[status(sab)],[30]) ).

tff(32,plain,
    ! [X: $i] :
      ( ~ less_than(a(X),a(k))
      | ~ less_than(X,j)
      | less_than(X,i) ),
    inference(modus_ponens,[status(thm)],[31,24]) ).

tff(33,plain,
    ( ( ~ ! [X: $i] :
            ( ~ less_than(a(X),a(k))
            | ~ less_than(X,j)
            | less_than(X,i) )
      | less_than(q,i)
      | ~ less_than(a(q),a(k))
      | ~ less_than(q,j) )
  <=> ( ~ ! [X: $i] :
            ( ~ less_than(a(X),a(k))
            | ~ less_than(X,j)
            | less_than(X,i) )
      | less_than(q,i)
      | ~ less_than(a(q),a(k))
      | ~ less_than(q,j) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,plain,
    ( ( ~ less_than(a(q),a(k))
      | ~ less_than(q,j)
      | less_than(q,i) )
  <=> ( less_than(q,i)
      | ~ less_than(a(q),a(k))
      | ~ less_than(q,j) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ( ~ ! [X: $i] :
            ( ~ less_than(a(X),a(k))
            | ~ less_than(X,j)
            | less_than(X,i) )
      | ~ less_than(a(q),a(k))
      | ~ less_than(q,j)
      | less_than(q,i) )
  <=> ( ~ ! [X: $i] :
            ( ~ less_than(a(X),a(k))
            | ~ less_than(X,j)
            | less_than(X,i) )
      | less_than(q,i)
      | ~ less_than(a(q),a(k))
      | ~ less_than(q,j) ) ),
    inference(monotonicity,[status(thm)],[34]) ).

tff(36,plain,
    ( ( ~ ! [X: $i] :
            ( ~ less_than(a(X),a(k))
            | ~ less_than(X,j)
            | less_than(X,i) )
      | ~ less_than(a(q),a(k))
      | ~ less_than(q,j)
      | less_than(q,i) )
  <=> ( ~ ! [X: $i] :
            ( ~ less_than(a(X),a(k))
            | ~ less_than(X,j)
            | less_than(X,i) )
      | less_than(q,i)
      | ~ less_than(a(q),a(k))
      | ~ less_than(q,j) ) ),
    inference(transitivity,[status(thm)],[35,33]) ).

tff(37,plain,
    ( ~ ! [X: $i] :
          ( ~ less_than(a(X),a(k))
          | ~ less_than(X,j)
          | less_than(X,i) )
    | ~ less_than(a(q),a(k))
    | ~ less_than(q,j)
    | less_than(q,i) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [X: $i] :
          ( ~ less_than(a(X),a(k))
          | ~ less_than(X,j)
          | less_than(X,i) )
    | less_than(q,i)
    | ~ less_than(a(q),a(k))
    | ~ less_than(q,j) ),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    ( ~ less_than(a(q),a(k))
    | ~ less_than(q,j) ),
    inference(unit_resolution,[status(thm)],[38,32,22]) ).

tff(40,plain,
    ~ less_than(q,j),
    inference(unit_resolution,[status(thm)],[39,19]) ).

tff(41,plain,
    ( ~ less_than(j,q)
  <=> ~ less_than(j,q) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,axiom,
    ~ less_than(j,q),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).

tff(43,plain,
    ~ less_than(j,q),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( ( X = Y )
          | less_than(Y,X)
          | less_than(X,Y) )
      <=> ( ( X = Y )
          | less_than(Y,X)
          | less_than(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(45,plain,
    ( ! [Y: $i,X: $i] :
        ( ( X = Y )
        | less_than(Y,X)
        | less_than(X,Y) )
  <=> ! [Y: $i,X: $i] :
        ( ( X = Y )
        | less_than(Y,X)
        | less_than(X,Y) ) ),
    inference(quant_intro,[status(thm)],[44]) ).

tff(46,plain,
    ( ! [Y: $i,X: $i] :
        ( ( X = Y )
        | less_than(Y,X)
        | less_than(X,Y) )
  <=> ! [Y: $i,X: $i] :
        ( ( X = Y )
        | less_than(Y,X)
        | less_than(X,Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,plain,
    ^ [Y: $i,X: $i] :
      rewrite(
        ( ( less_than(X,Y)
          | less_than(Y,X)
          | ( X = Y ) )
      <=> ( ( X = Y )
          | less_than(Y,X)
          | less_than(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(48,plain,
    ( ! [Y: $i,X: $i] :
        ( less_than(X,Y)
        | less_than(Y,X)
        | ( X = Y ) )
  <=> ! [Y: $i,X: $i] :
        ( ( X = Y )
        | less_than(Y,X)
        | less_than(X,Y) ) ),
    inference(quant_intro,[status(thm)],[47]) ).

tff(49,axiom,
    ! [Y: $i,X: $i] :
      ( less_than(X,Y)
      | less_than(Y,X)
      | ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax',all_related) ).

tff(50,plain,
    ! [Y: $i,X: $i] :
      ( ( X = Y )
      | less_than(Y,X)
      | less_than(X,Y) ),
    inference(modus_ponens,[status(thm)],[49,48]) ).

tff(51,plain,
    ! [Y: $i,X: $i] :
      ( ( X = Y )
      | less_than(Y,X)
      | less_than(X,Y) ),
    inference(modus_ponens,[status(thm)],[50,46]) ).

tff(52,plain,
    ! [Y: $i,X: $i] :
      ( ( X = Y )
      | less_than(Y,X)
      | less_than(X,Y) ),
    inference(skolemize,[status(sab)],[51]) ).

tff(53,plain,
    ! [Y: $i,X: $i] :
      ( ( X = Y )
      | less_than(Y,X)
      | less_than(X,Y) ),
    inference(modus_ponens,[status(thm)],[52,45]) ).

tff(54,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( ( X = Y )
            | less_than(Y,X)
            | less_than(X,Y) )
      | less_than(j,q)
      | less_than(q,j)
      | ( j = q ) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( ( X = Y )
            | less_than(Y,X)
            | less_than(X,Y) )
      | less_than(j,q)
      | less_than(q,j)
      | ( j = q ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ( ( j = q )
      | less_than(q,j)
      | less_than(j,q) )
  <=> ( less_than(j,q)
      | less_than(q,j)
      | ( j = q ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(56,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( ( X = Y )
            | less_than(Y,X)
            | less_than(X,Y) )
      | ( j = q )
      | less_than(q,j)
      | less_than(j,q) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( ( X = Y )
            | less_than(Y,X)
            | less_than(X,Y) )
      | less_than(j,q)
      | less_than(q,j)
      | ( j = q ) ) ),
    inference(monotonicity,[status(thm)],[55]) ).

tff(57,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( ( X = Y )
            | less_than(Y,X)
            | less_than(X,Y) )
      | ( j = q )
      | less_than(q,j)
      | less_than(j,q) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( ( X = Y )
            | less_than(Y,X)
            | less_than(X,Y) )
      | less_than(j,q)
      | less_than(q,j)
      | ( j = q ) ) ),
    inference(transitivity,[status(thm)],[56,54]) ).

tff(58,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( ( X = Y )
          | less_than(Y,X)
          | less_than(X,Y) )
    | ( j = q )
    | less_than(q,j)
    | less_than(j,q) ),
    inference(quant_inst,[status(thm)],]) ).

tff(59,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( ( X = Y )
          | less_than(Y,X)
          | less_than(X,Y) )
    | less_than(j,q)
    | less_than(q,j)
    | ( j = q ) ),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ( less_than(q,j)
    | ( j = q ) ),
    inference(unit_resolution,[status(thm)],[59,53,43]) ).

tff(61,plain,
    j = q,
    inference(unit_resolution,[status(thm)],[60,40]) ).

tff(62,plain,
    a(j) = a(q),
    inference(monotonicity,[status(thm)],[61]) ).

tff(63,plain,
    a(q) = a(j),
    inference(symmetry,[status(thm)],[62]) ).

tff(64,plain,
    ( less_than(a(j),a(q))
  <=> less_than(a(q),a(j)) ),
    inference(monotonicity,[status(thm)],[62,63]) ).

tff(65,plain,
    ( less_than(a(q),a(j))
  <=> less_than(a(j),a(q)) ),
    inference(symmetry,[status(thm)],[64]) ).

tff(66,plain,
    less_than(a(j),a(q)),
    inference(modus_ponens,[status(thm)],[3,65]) ).

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

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

tff(69,plain,
    ( ! [Y: $i,X: $i] :
        ( ~ less_than(X,Y)
        | ~ less_than(Y,X) )
  <=> ! [Y: $i,X: $i] :
        ( ~ less_than(X,Y)
        | ~ less_than(Y,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,axiom,
    ! [Y: $i,X: $i] :
      ( ~ less_than(X,Y)
      | ~ less_than(Y,X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV001-0.ax',anti_symmetry_of_less_than) ).

tff(71,plain,
    ! [Y: $i,X: $i] :
      ( ~ less_than(X,Y)
      | ~ less_than(Y,X) ),
    inference(modus_ponens,[status(thm)],[70,69]) ).

tff(72,plain,
    ! [Y: $i,X: $i] :
      ( ~ less_than(X,Y)
      | ~ less_than(Y,X) ),
    inference(skolemize,[status(sab)],[71]) ).

tff(73,plain,
    ! [Y: $i,X: $i] :
      ( ~ less_than(X,Y)
      | ~ less_than(Y,X) ),
    inference(modus_ponens,[status(thm)],[72,68]) ).

tff(74,plain,
    ( ( ~ ! [Y: $i,X: $i] :
            ( ~ less_than(X,Y)
            | ~ less_than(Y,X) )
      | ~ less_than(a(j),a(q))
      | ~ less_than(a(q),a(j)) )
  <=> ( ~ ! [Y: $i,X: $i] :
            ( ~ less_than(X,Y)
            | ~ less_than(Y,X) )
      | ~ less_than(a(j),a(q))
      | ~ less_than(a(q),a(j)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(75,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( ~ less_than(X,Y)
          | ~ less_than(Y,X) )
    | ~ less_than(a(j),a(q))
    | ~ less_than(a(q),a(j)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(76,plain,
    ( ~ ! [Y: $i,X: $i] :
          ( ~ less_than(X,Y)
          | ~ less_than(Y,X) )
    | ~ less_than(a(j),a(q))
    | ~ less_than(a(q),a(j)) ),
    inference(modus_ponens,[status(thm)],[75,74]) ).

tff(77,plain,
    ~ less_than(a(j),a(q)),
    inference(unit_resolution,[status(thm)],[76,73,3]) ).

tff(78,plain,
    $false,
    inference(unit_resolution,[status(thm)],[77,66]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SWV002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30  % Computer : n025.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Sun Sep  4 01:04:48 EDT 2022
% 0.09/0.30  % CPUTime  : 
% 0.14/0.30  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.30  Usage: tptp [options] [-file:]file
% 0.14/0.30    -h, -?       prints this message.
% 0.14/0.30    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.30    -m, -model   generate model.
% 0.14/0.30    -p, -proof   generate proof.
% 0.14/0.30    -c, -core    generate unsat core of named formulas.
% 0.14/0.30    -st, -statistics display statistics.
% 0.14/0.30    -t:timeout   set timeout (in second).
% 0.14/0.30    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.30    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.30    -<param>:<value> configuration parameter and value.
% 0.14/0.30    -o:<output-file> file to place output in.
% 0.14/0.34  % SZS status Unsatisfiable
% 0.14/0.34  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------