TSTP Solution File: MGT041-2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : MGT041-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n012.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 05:22:09 EDT 2022

% Result   : Unsatisfiable 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   78 (  20 unt;  10 typ;   0 def)
%            Number of atoms       :  434 (   0 equ)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives :  632 ( 304   ~; 285   |;   0   &)
%                                         (  43 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   38 (  38 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :  136 ( 120   !;   0   ?; 136   :)

% Comments : 
%------------------------------------------------------------------------------
tff(first_mover_type,type,
    first_mover: $i > $o ).

tff(sk1_type,type,
    sk1: $i ).

tff(number_of_routines_type,type,
    number_of_routines: ( $i * $i * $i ) > $o ).

tff(low_type,type,
    low: $i ).

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

tff(high_type,type,
    high: $i ).

tff(founding_time_type,type,
    founding_time: ( $i * $i ) > $o ).

tff(organisation_at_time_type,type,
    organisation_at_time: ( $i * $i ) > $o ).

tff(efficient_producer_type,type,
    efficient_producer: $i > $o ).

tff(has_elaborated_routines_type,type,
    has_elaborated_routines: ( $i * $i ) > $o ).

tff(1,plain,
    ( number_of_routines(sk1,sk2,high)
  <=> number_of_routines(sk1,sk2,high) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    number_of_routines(sk1,sk2,high),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a16_6) ).

tff(3,plain,
    number_of_routines(sk1,sk2,high),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( ~ number_of_routines(A,B,high)
          | ~ number_of_routines(A,B,low) )
      <=> ( ~ number_of_routines(A,B,high)
          | ~ number_of_routines(A,B,low) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [B: $i,A: $i] :
        ( ~ number_of_routines(A,B,high)
        | ~ number_of_routines(A,B,low) )
  <=> ! [B: $i,A: $i] :
        ( ~ number_of_routines(A,B,high)
        | ~ number_of_routines(A,B,low) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [B: $i,A: $i] :
        ( ~ number_of_routines(A,B,high)
        | ~ number_of_routines(A,B,low) )
  <=> ! [B: $i,A: $i] :
        ( ~ number_of_routines(A,B,high)
        | ~ number_of_routines(A,B,low) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,plain,
    ^ [B: $i,A: $i] :
      rewrite(
        ( ( ~ number_of_routines(A,B,low)
          | ~ number_of_routines(A,B,high) )
      <=> ( ~ number_of_routines(A,B,high)
          | ~ number_of_routines(A,B,low) ) )),
    inference(bind,[status(th)],]) ).

tff(8,plain,
    ( ! [B: $i,A: $i] :
        ( ~ number_of_routines(A,B,low)
        | ~ number_of_routines(A,B,high) )
  <=> ! [B: $i,A: $i] :
        ( ~ number_of_routines(A,B,high)
        | ~ number_of_routines(A,B,low) ) ),
    inference(quant_intro,[status(thm)],[7]) ).

tff(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ number_of_routines(A,B,low)
      | ~ number_of_routines(A,B,high) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_not_high_and_low_1) ).

tff(10,plain,
    ! [B: $i,A: $i] :
      ( ~ number_of_routines(A,B,high)
      | ~ number_of_routines(A,B,low) ),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ! [B: $i,A: $i] :
      ( ~ number_of_routines(A,B,high)
      | ~ number_of_routines(A,B,low) ),
    inference(modus_ponens,[status(thm)],[10,6]) ).

tff(12,plain,
    ! [B: $i,A: $i] :
      ( ~ number_of_routines(A,B,high)
      | ~ number_of_routines(A,B,low) ),
    inference(skolemize,[status(sab)],[11]) ).

tff(13,plain,
    ! [B: $i,A: $i] :
      ( ~ number_of_routines(A,B,high)
      | ~ number_of_routines(A,B,low) ),
    inference(modus_ponens,[status(thm)],[12,5]) ).

tff(14,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ~ number_of_routines(A,B,high)
            | ~ number_of_routines(A,B,low) )
      | ~ number_of_routines(sk1,sk2,high)
      | ~ number_of_routines(sk1,sk2,low) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ~ number_of_routines(A,B,high)
            | ~ number_of_routines(A,B,low) )
      | ~ number_of_routines(sk1,sk2,high)
      | ~ number_of_routines(sk1,sk2,low) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ number_of_routines(A,B,high)
          | ~ number_of_routines(A,B,low) )
    | ~ number_of_routines(sk1,sk2,high)
    | ~ number_of_routines(sk1,sk2,low) ),
    inference(quant_inst,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ number_of_routines(A,B,high)
          | ~ number_of_routines(A,B,low) )
    | ~ number_of_routines(sk1,sk2,high)
    | ~ number_of_routines(sk1,sk2,low) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ~ number_of_routines(sk1,sk2,low),
    inference(unit_resolution,[status(thm)],[16,13,3]) ).

tff(18,plain,
    ( founding_time(sk1,sk2)
  <=> founding_time(sk1,sk2) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    founding_time(sk1,sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a16_5) ).

tff(20,plain,
    founding_time(sk1,sk2),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ( organisation_at_time(sk1,sk2)
  <=> organisation_at_time(sk1,sk2) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,axiom,
    organisation_at_time(sk1,sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a16_4) ).

tff(23,plain,
    organisation_at_time(sk1,sk2),
    inference(modus_ponens,[status(thm)],[22,21]) ).

tff(24,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( number_of_routines(A,B,low)
          | ~ founding_time(A,B)
          | ~ organisation_at_time(A,B)
          | ~ first_mover(A) )
      <=> ( number_of_routines(A,B,low)
          | ~ founding_time(A,B)
          | ~ organisation_at_time(A,B)
          | ~ first_mover(A) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [B: $i,A: $i] :
        ( number_of_routines(A,B,low)
        | ~ founding_time(A,B)
        | ~ organisation_at_time(A,B)
        | ~ first_mover(A) )
  <=> ! [B: $i,A: $i] :
        ( number_of_routines(A,B,low)
        | ~ founding_time(A,B)
        | ~ organisation_at_time(A,B)
        | ~ first_mover(A) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,plain,
    ( ! [B: $i,A: $i] :
        ( number_of_routines(A,B,low)
        | ~ founding_time(A,B)
        | ~ organisation_at_time(A,B)
        | ~ first_mover(A) )
  <=> ! [B: $i,A: $i] :
        ( number_of_routines(A,B,low)
        | ~ founding_time(A,B)
        | ~ organisation_at_time(A,B)
        | ~ first_mover(A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ^ [B: $i,A: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ organisation_at_time(A,B)
                  | ~ first_mover(A) )
              <=> ( ~ organisation_at_time(A,B)
                  | ~ first_mover(A) ) )),
              ( ( ~ organisation_at_time(A,B)
                | ~ first_mover(A)
                | ~ founding_time(A,B) )
            <=> ( ~ organisation_at_time(A,B)
                | ~ first_mover(A)
                | ~ founding_time(A,B) ) )),
            rewrite(
              ( ( ~ organisation_at_time(A,B)
                | ~ first_mover(A)
                | ~ founding_time(A,B) )
            <=> ( ~ founding_time(A,B)
                | ~ organisation_at_time(A,B)
                | ~ first_mover(A) ) )),
            ( ( ~ organisation_at_time(A,B)
              | ~ first_mover(A)
              | ~ founding_time(A,B) )
          <=> ( ~ founding_time(A,B)
              | ~ organisation_at_time(A,B)
              | ~ first_mover(A) ) )),
          ( ( ~ organisation_at_time(A,B)
            | ~ first_mover(A)
            | ~ founding_time(A,B)
            | number_of_routines(A,B,low) )
        <=> ( ~ founding_time(A,B)
            | ~ organisation_at_time(A,B)
            | ~ first_mover(A)
            | number_of_routines(A,B,low) ) )),
        rewrite(
          ( ( ~ founding_time(A,B)
            | ~ organisation_at_time(A,B)
            | ~ first_mover(A)
            | number_of_routines(A,B,low) )
        <=> ( number_of_routines(A,B,low)
            | ~ founding_time(A,B)
            | ~ organisation_at_time(A,B)
            | ~ first_mover(A) ) )),
        ( ( ~ organisation_at_time(A,B)
          | ~ first_mover(A)
          | ~ founding_time(A,B)
          | number_of_routines(A,B,low) )
      <=> ( number_of_routines(A,B,low)
          | ~ founding_time(A,B)
          | ~ organisation_at_time(A,B)
          | ~ first_mover(A) ) )),
    inference(bind,[status(th)],]) ).

tff(28,plain,
    ( ! [B: $i,A: $i] :
        ( ~ organisation_at_time(A,B)
        | ~ first_mover(A)
        | ~ founding_time(A,B)
        | number_of_routines(A,B,low) )
  <=> ! [B: $i,A: $i] :
        ( number_of_routines(A,B,low)
        | ~ founding_time(A,B)
        | ~ organisation_at_time(A,B)
        | ~ first_mover(A) ) ),
    inference(quant_intro,[status(thm)],[27]) ).

tff(29,axiom,
    ! [B: $i,A: $i] :
      ( ~ organisation_at_time(A,B)
      | ~ first_mover(A)
      | ~ founding_time(A,B)
      | number_of_routines(A,B,low) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a15_3) ).

tff(30,plain,
    ! [B: $i,A: $i] :
      ( number_of_routines(A,B,low)
      | ~ founding_time(A,B)
      | ~ organisation_at_time(A,B)
      | ~ first_mover(A) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ! [B: $i,A: $i] :
      ( number_of_routines(A,B,low)
      | ~ founding_time(A,B)
      | ~ organisation_at_time(A,B)
      | ~ first_mover(A) ),
    inference(modus_ponens,[status(thm)],[30,26]) ).

tff(32,plain,
    ! [B: $i,A: $i] :
      ( number_of_routines(A,B,low)
      | ~ founding_time(A,B)
      | ~ organisation_at_time(A,B)
      | ~ first_mover(A) ),
    inference(skolemize,[status(sab)],[31]) ).

tff(33,plain,
    ! [B: $i,A: $i] :
      ( number_of_routines(A,B,low)
      | ~ founding_time(A,B)
      | ~ organisation_at_time(A,B)
      | ~ first_mover(A) ),
    inference(modus_ponens,[status(thm)],[32,25]) ).

tff(34,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( number_of_routines(A,B,low)
            | ~ founding_time(A,B)
            | ~ organisation_at_time(A,B)
            | ~ first_mover(A) )
      | number_of_routines(sk1,sk2,low)
      | ~ founding_time(sk1,sk2)
      | ~ organisation_at_time(sk1,sk2)
      | ~ first_mover(sk1) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( number_of_routines(A,B,low)
            | ~ founding_time(A,B)
            | ~ organisation_at_time(A,B)
            | ~ first_mover(A) )
      | number_of_routines(sk1,sk2,low)
      | ~ founding_time(sk1,sk2)
      | ~ organisation_at_time(sk1,sk2)
      | ~ first_mover(sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ~ ! [B: $i,A: $i] :
          ( number_of_routines(A,B,low)
          | ~ founding_time(A,B)
          | ~ organisation_at_time(A,B)
          | ~ first_mover(A) )
    | number_of_routines(sk1,sk2,low)
    | ~ founding_time(sk1,sk2)
    | ~ organisation_at_time(sk1,sk2)
    | ~ first_mover(sk1) ),
    inference(quant_inst,[status(thm)],]) ).

tff(36,plain,
    ( ~ ! [B: $i,A: $i] :
          ( number_of_routines(A,B,low)
          | ~ founding_time(A,B)
          | ~ organisation_at_time(A,B)
          | ~ first_mover(A) )
    | number_of_routines(sk1,sk2,low)
    | ~ founding_time(sk1,sk2)
    | ~ organisation_at_time(sk1,sk2)
    | ~ first_mover(sk1) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ~ first_mover(sk1),
    inference(unit_resolution,[status(thm)],[36,33,23,20,17]) ).

tff(38,plain,
    ( ~ has_elaborated_routines(sk1,sk2)
  <=> ~ has_elaborated_routines(sk1,sk2) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,axiom,
    ~ has_elaborated_routines(sk1,sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a16_7) ).

tff(40,plain,
    ~ has_elaborated_routines(sk1,sk2),
    inference(modus_ponens,[status(thm)],[39,38]) ).

tff(41,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( has_elaborated_routines(A,B)
          | ~ founding_time(A,B)
          | ~ efficient_producer(A)
          | ~ organisation_at_time(A,B) )
      <=> ( has_elaborated_routines(A,B)
          | ~ founding_time(A,B)
          | ~ efficient_producer(A)
          | ~ organisation_at_time(A,B) ) )),
    inference(bind,[status(th)],]) ).

tff(42,plain,
    ( ! [B: $i,A: $i] :
        ( has_elaborated_routines(A,B)
        | ~ founding_time(A,B)
        | ~ efficient_producer(A)
        | ~ organisation_at_time(A,B) )
  <=> ! [B: $i,A: $i] :
        ( has_elaborated_routines(A,B)
        | ~ founding_time(A,B)
        | ~ efficient_producer(A)
        | ~ organisation_at_time(A,B) ) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,plain,
    ( ! [B: $i,A: $i] :
        ( has_elaborated_routines(A,B)
        | ~ founding_time(A,B)
        | ~ efficient_producer(A)
        | ~ organisation_at_time(A,B) )
  <=> ! [B: $i,A: $i] :
        ( has_elaborated_routines(A,B)
        | ~ founding_time(A,B)
        | ~ efficient_producer(A)
        | ~ organisation_at_time(A,B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ^ [B: $i,A: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ organisation_at_time(A,B)
                  | ~ efficient_producer(A) )
              <=> ( ~ efficient_producer(A)
                  | ~ organisation_at_time(A,B) ) )),
              ( ( ~ organisation_at_time(A,B)
                | ~ efficient_producer(A)
                | ~ founding_time(A,B) )
            <=> ( ~ efficient_producer(A)
                | ~ organisation_at_time(A,B)
                | ~ founding_time(A,B) ) )),
            rewrite(
              ( ( ~ efficient_producer(A)
                | ~ organisation_at_time(A,B)
                | ~ founding_time(A,B) )
            <=> ( ~ founding_time(A,B)
                | ~ efficient_producer(A)
                | ~ organisation_at_time(A,B) ) )),
            ( ( ~ organisation_at_time(A,B)
              | ~ efficient_producer(A)
              | ~ founding_time(A,B) )
          <=> ( ~ founding_time(A,B)
              | ~ efficient_producer(A)
              | ~ organisation_at_time(A,B) ) )),
          ( ( ~ organisation_at_time(A,B)
            | ~ efficient_producer(A)
            | ~ founding_time(A,B)
            | has_elaborated_routines(A,B) )
        <=> ( ~ founding_time(A,B)
            | ~ efficient_producer(A)
            | ~ organisation_at_time(A,B)
            | has_elaborated_routines(A,B) ) )),
        rewrite(
          ( ( ~ founding_time(A,B)
            | ~ efficient_producer(A)
            | ~ organisation_at_time(A,B)
            | has_elaborated_routines(A,B) )
        <=> ( has_elaborated_routines(A,B)
            | ~ founding_time(A,B)
            | ~ efficient_producer(A)
            | ~ organisation_at_time(A,B) ) )),
        ( ( ~ organisation_at_time(A,B)
          | ~ efficient_producer(A)
          | ~ founding_time(A,B)
          | has_elaborated_routines(A,B) )
      <=> ( has_elaborated_routines(A,B)
          | ~ founding_time(A,B)
          | ~ efficient_producer(A)
          | ~ organisation_at_time(A,B) ) )),
    inference(bind,[status(th)],]) ).

tff(45,plain,
    ( ! [B: $i,A: $i] :
        ( ~ organisation_at_time(A,B)
        | ~ efficient_producer(A)
        | ~ founding_time(A,B)
        | has_elaborated_routines(A,B) )
  <=> ! [B: $i,A: $i] :
        ( has_elaborated_routines(A,B)
        | ~ founding_time(A,B)
        | ~ efficient_producer(A)
        | ~ organisation_at_time(A,B) ) ),
    inference(quant_intro,[status(thm)],[44]) ).

tff(46,axiom,
    ! [B: $i,A: $i] :
      ( ~ organisation_at_time(A,B)
      | ~ efficient_producer(A)
      | ~ founding_time(A,B)
      | has_elaborated_routines(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a14_2) ).

tff(47,plain,
    ! [B: $i,A: $i] :
      ( has_elaborated_routines(A,B)
      | ~ founding_time(A,B)
      | ~ efficient_producer(A)
      | ~ organisation_at_time(A,B) ),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    ! [B: $i,A: $i] :
      ( has_elaborated_routines(A,B)
      | ~ founding_time(A,B)
      | ~ efficient_producer(A)
      | ~ organisation_at_time(A,B) ),
    inference(modus_ponens,[status(thm)],[47,43]) ).

tff(49,plain,
    ! [B: $i,A: $i] :
      ( has_elaborated_routines(A,B)
      | ~ founding_time(A,B)
      | ~ efficient_producer(A)
      | ~ organisation_at_time(A,B) ),
    inference(skolemize,[status(sab)],[48]) ).

tff(50,plain,
    ! [B: $i,A: $i] :
      ( has_elaborated_routines(A,B)
      | ~ founding_time(A,B)
      | ~ efficient_producer(A)
      | ~ organisation_at_time(A,B) ),
    inference(modus_ponens,[status(thm)],[49,42]) ).

tff(51,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( has_elaborated_routines(A,B)
            | ~ founding_time(A,B)
            | ~ efficient_producer(A)
            | ~ organisation_at_time(A,B) )
      | has_elaborated_routines(sk1,sk2)
      | ~ founding_time(sk1,sk2)
      | ~ efficient_producer(sk1)
      | ~ organisation_at_time(sk1,sk2) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( has_elaborated_routines(A,B)
            | ~ founding_time(A,B)
            | ~ efficient_producer(A)
            | ~ organisation_at_time(A,B) )
      | has_elaborated_routines(sk1,sk2)
      | ~ founding_time(sk1,sk2)
      | ~ efficient_producer(sk1)
      | ~ organisation_at_time(sk1,sk2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,plain,
    ( ~ ! [B: $i,A: $i] :
          ( has_elaborated_routines(A,B)
          | ~ founding_time(A,B)
          | ~ efficient_producer(A)
          | ~ organisation_at_time(A,B) )
    | has_elaborated_routines(sk1,sk2)
    | ~ founding_time(sk1,sk2)
    | ~ efficient_producer(sk1)
    | ~ organisation_at_time(sk1,sk2) ),
    inference(quant_inst,[status(thm)],]) ).

tff(53,plain,
    ( ~ ! [B: $i,A: $i] :
          ( has_elaborated_routines(A,B)
          | ~ founding_time(A,B)
          | ~ efficient_producer(A)
          | ~ organisation_at_time(A,B) )
    | has_elaborated_routines(sk1,sk2)
    | ~ founding_time(sk1,sk2)
    | ~ efficient_producer(sk1)
    | ~ organisation_at_time(sk1,sk2) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ~ efficient_producer(sk1),
    inference(unit_resolution,[status(thm)],[53,50,23,20,40]) ).

tff(55,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( efficient_producer(A)
          | ~ organisation_at_time(A,B)
          | first_mover(A) )
      <=> ( efficient_producer(A)
          | ~ organisation_at_time(A,B)
          | first_mover(A) ) )),
    inference(bind,[status(th)],]) ).

tff(56,plain,
    ( ! [B: $i,A: $i] :
        ( efficient_producer(A)
        | ~ organisation_at_time(A,B)
        | first_mover(A) )
  <=> ! [B: $i,A: $i] :
        ( efficient_producer(A)
        | ~ organisation_at_time(A,B)
        | first_mover(A) ) ),
    inference(quant_intro,[status(thm)],[55]) ).

tff(57,plain,
    ( ! [B: $i,A: $i] :
        ( efficient_producer(A)
        | ~ organisation_at_time(A,B)
        | first_mover(A) )
  <=> ! [B: $i,A: $i] :
        ( efficient_producer(A)
        | ~ organisation_at_time(A,B)
        | first_mover(A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(58,plain,
    ^ [B: $i,A: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ organisation_at_time(A,B)
              | first_mover(A) )
          <=> ( ~ organisation_at_time(A,B)
              | first_mover(A) ) )),
          ( ( ~ organisation_at_time(A,B)
            | first_mover(A)
            | efficient_producer(A) )
        <=> ( ~ organisation_at_time(A,B)
            | first_mover(A)
            | efficient_producer(A) ) )),
        rewrite(
          ( ( ~ organisation_at_time(A,B)
            | first_mover(A)
            | efficient_producer(A) )
        <=> ( efficient_producer(A)
            | ~ organisation_at_time(A,B)
            | first_mover(A) ) )),
        ( ( ~ organisation_at_time(A,B)
          | first_mover(A)
          | efficient_producer(A) )
      <=> ( efficient_producer(A)
          | ~ organisation_at_time(A,B)
          | first_mover(A) ) )),
    inference(bind,[status(th)],]) ).

tff(59,plain,
    ( ! [B: $i,A: $i] :
        ( ~ organisation_at_time(A,B)
        | first_mover(A)
        | efficient_producer(A) )
  <=> ! [B: $i,A: $i] :
        ( efficient_producer(A)
        | ~ organisation_at_time(A,B)
        | first_mover(A) ) ),
    inference(quant_intro,[status(thm)],[58]) ).

tff(60,axiom,
    ! [B: $i,A: $i] :
      ( ~ organisation_at_time(A,B)
      | first_mover(A)
      | efficient_producer(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t10_8) ).

tff(61,plain,
    ! [B: $i,A: $i] :
      ( efficient_producer(A)
      | ~ organisation_at_time(A,B)
      | first_mover(A) ),
    inference(modus_ponens,[status(thm)],[60,59]) ).

tff(62,plain,
    ! [B: $i,A: $i] :
      ( efficient_producer(A)
      | ~ organisation_at_time(A,B)
      | first_mover(A) ),
    inference(modus_ponens,[status(thm)],[61,57]) ).

tff(63,plain,
    ! [B: $i,A: $i] :
      ( efficient_producer(A)
      | ~ organisation_at_time(A,B)
      | first_mover(A) ),
    inference(skolemize,[status(sab)],[62]) ).

tff(64,plain,
    ! [B: $i,A: $i] :
      ( efficient_producer(A)
      | ~ organisation_at_time(A,B)
      | first_mover(A) ),
    inference(modus_ponens,[status(thm)],[63,56]) ).

tff(65,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( efficient_producer(A)
            | ~ organisation_at_time(A,B)
            | first_mover(A) )
      | efficient_producer(sk1)
      | ~ organisation_at_time(sk1,sk2)
      | first_mover(sk1) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( efficient_producer(A)
            | ~ organisation_at_time(A,B)
            | first_mover(A) )
      | efficient_producer(sk1)
      | ~ organisation_at_time(sk1,sk2)
      | first_mover(sk1) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(66,plain,
    ( ~ ! [B: $i,A: $i] :
          ( efficient_producer(A)
          | ~ organisation_at_time(A,B)
          | first_mover(A) )
    | efficient_producer(sk1)
    | ~ organisation_at_time(sk1,sk2)
    | first_mover(sk1) ),
    inference(quant_inst,[status(thm)],]) ).

tff(67,plain,
    ( ~ ! [B: $i,A: $i] :
          ( efficient_producer(A)
          | ~ organisation_at_time(A,B)
          | first_mover(A) )
    | efficient_producer(sk1)
    | ~ organisation_at_time(sk1,sk2)
    | first_mover(sk1) ),
    inference(modus_ponens,[status(thm)],[66,65]) ).

tff(68,plain,
    $false,
    inference(unit_resolution,[status(thm)],[67,23,64,54,37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : MGT041-2 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri Sep  2 02:50:19 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.39  % SZS status Unsatisfiable
% 0.20/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------