TSTP Solution File: GEO147-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO147-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n013.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 20:35:06 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   64 (  12 unt;   9 typ;   0 def)
%            Number of atoms       :  182 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  231 ( 108   ~; 104   |;   0   &)
%                                         (  19 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  125 ( 116   !;   0   ?; 125   :)

% Comments : 
%------------------------------------------------------------------------------
tff(incident_o_type,type,
    incident_o: ( $i * $i ) > $o ).

tff(trajectory_of_type,type,
    trajectory_of: $i > $i ).

tff(sk29_type,type,
    sk29: $i ).

tff(sk27_type,type,
    sk27: $i ).

tff(once_type,type,
    once: $i > $o ).

tff(at_type,type,
    at: ( $i * $i ) > $i ).

tff(at_the_same_time_type,type,
    at_the_same_time: ( $i * $i ) > $i ).

tff(sk28_type,type,
    sk28: $i ).

tff(connect_type,type,
    connect: ( $i * $i * $i ) > $o ).

tff(1,plain,
    ( connect(sk28,sk29,sk27)
  <=> connect(sk28,sk29,sk27) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    connect(sk28,sk29,sk27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_156) ).

tff(3,plain,
    connect(sk28,sk29,sk27),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( ~ connect(A,B,C)
          | once(at_the_same_time(at(A,C),at(B,C))) )
      <=> ( ~ connect(A,B,C)
          | once(at_the_same_time(at(A,C),at(B,C))) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ connect(A,B,C)
        | once(at_the_same_time(at(A,C),at(B,C))) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ connect(A,B,C)
        | once(at_the_same_time(at(A,C),at(B,C))) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [B: $i,A: $i,C: $i] :
        ( ~ connect(A,B,C)
        | once(at_the_same_time(at(A,C),at(B,C))) )
  <=> ! [B: $i,A: $i,C: $i] :
        ( ~ connect(A,B,C)
        | once(at_the_same_time(at(A,C),at(B,C))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [B: $i,A: $i,C: $i] :
      ( ~ connect(A,B,C)
      | once(at_the_same_time(at(A,C),at(B,C))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-3.ax',connect_defn_1) ).

tff(8,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ connect(A,B,C)
      | once(at_the_same_time(at(A,C),at(B,C))) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ connect(A,B,C)
      | once(at_the_same_time(at(A,C),at(B,C))) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [B: $i,A: $i,C: $i] :
      ( ~ connect(A,B,C)
      | once(at_the_same_time(at(A,C),at(B,C))) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ connect(A,B,C)
            | once(at_the_same_time(at(A,C),at(B,C))) )
      | ~ connect(sk28,sk29,sk27)
      | once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) )
  <=> ( ~ ! [B: $i,A: $i,C: $i] :
            ( ~ connect(A,B,C)
            | once(at_the_same_time(at(A,C),at(B,C))) )
      | ~ connect(sk28,sk29,sk27)
      | once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ connect(A,B,C)
          | once(at_the_same_time(at(A,C),at(B,C))) )
    | ~ connect(sk28,sk29,sk27)
    | once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [B: $i,A: $i,C: $i] :
          ( ~ connect(A,B,C)
          | once(at_the_same_time(at(A,C),at(B,C))) )
    | ~ connect(sk28,sk29,sk27)
    | once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    once(at_the_same_time(at(sk28,sk27),at(sk29,sk27))),
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( ~ once(at_the_same_time(A,B))
          | once(B) )
      <=> ( ~ once(at_the_same_time(A,B))
          | once(B) ) )),
    inference(bind,[status(th)],]) ).

tff(16,plain,
    ( ! [B: $i,A: $i] :
        ( ~ once(at_the_same_time(A,B))
        | once(B) )
  <=> ! [B: $i,A: $i] :
        ( ~ once(at_the_same_time(A,B))
        | once(B) ) ),
    inference(quant_intro,[status(thm)],[15]) ).

tff(17,plain,
    ( ! [B: $i,A: $i] :
        ( ~ once(at_the_same_time(A,B))
        | once(B) )
  <=> ! [B: $i,A: $i] :
        ( ~ once(at_the_same_time(A,B))
        | once(B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,axiom,
    ! [B: $i,A: $i] :
      ( ~ once(at_the_same_time(A,B))
      | once(B) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-3.ax',conjunction_at_the_same_time_9) ).

tff(19,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at_the_same_time(A,B))
      | once(B) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at_the_same_time(A,B))
      | once(B) ),
    inference(skolemize,[status(sab)],[19]) ).

tff(21,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at_the_same_time(A,B))
      | once(B) ),
    inference(modus_ponens,[status(thm)],[20,16]) ).

tff(22,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ~ once(at_the_same_time(A,B))
            | once(B) )
      | ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
      | once(at(sk29,sk27)) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ~ once(at_the_same_time(A,B))
            | once(B) )
      | ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
      | once(at(sk29,sk27)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ once(at_the_same_time(A,B))
          | once(B) )
    | ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
    | once(at(sk29,sk27)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(24,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ once(at_the_same_time(A,B))
          | once(B) )
    | ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
    | once(at(sk29,sk27)) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    once(at(sk29,sk27)),
    inference(unit_resolution,[status(thm)],[24,21,14]) ).

tff(26,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( ~ once(at(A,B))
          | incident_o(B,trajectory_of(A)) )
      <=> ( ~ once(at(A,B))
          | incident_o(B,trajectory_of(A)) ) )),
    inference(bind,[status(th)],]) ).

tff(27,plain,
    ( ! [B: $i,A: $i] :
        ( ~ once(at(A,B))
        | incident_o(B,trajectory_of(A)) )
  <=> ! [B: $i,A: $i] :
        ( ~ once(at(A,B))
        | incident_o(B,trajectory_of(A)) ) ),
    inference(quant_intro,[status(thm)],[26]) ).

tff(28,plain,
    ( ! [B: $i,A: $i] :
        ( ~ once(at(A,B))
        | incident_o(B,trajectory_of(A)) )
  <=> ! [B: $i,A: $i] :
        ( ~ once(at(A,B))
        | incident_o(B,trajectory_of(A)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,axiom,
    ! [B: $i,A: $i] :
      ( ~ once(at(A,B))
      | incident_o(B,trajectory_of(A)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-3.ax',at_on_trajectory_10) ).

tff(30,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at(A,B))
      | incident_o(B,trajectory_of(A)) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at(A,B))
      | incident_o(B,trajectory_of(A)) ),
    inference(skolemize,[status(sab)],[30]) ).

tff(32,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at(A,B))
      | incident_o(B,trajectory_of(A)) ),
    inference(modus_ponens,[status(thm)],[31,27]) ).

tff(33,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ~ once(at(A,B))
            | incident_o(B,trajectory_of(A)) )
      | ~ once(at(sk29,sk27))
      | incident_o(sk27,trajectory_of(sk29)) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ~ once(at(A,B))
            | incident_o(B,trajectory_of(A)) )
      | ~ once(at(sk29,sk27))
      | incident_o(sk27,trajectory_of(sk29)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ once(at(A,B))
          | incident_o(B,trajectory_of(A)) )
    | ~ once(at(sk29,sk27))
    | incident_o(sk27,trajectory_of(sk29)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(35,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ once(at(A,B))
          | incident_o(B,trajectory_of(A)) )
    | ~ once(at(sk29,sk27))
    | incident_o(sk27,trajectory_of(sk29)) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    incident_o(sk27,trajectory_of(sk29)),
    inference(unit_resolution,[status(thm)],[35,32,25]) ).

tff(37,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( ~ once(at_the_same_time(A,B))
          | once(A) )
      <=> ( ~ once(at_the_same_time(A,B))
          | once(A) ) )),
    inference(bind,[status(th)],]) ).

tff(38,plain,
    ( ! [B: $i,A: $i] :
        ( ~ once(at_the_same_time(A,B))
        | once(A) )
  <=> ! [B: $i,A: $i] :
        ( ~ once(at_the_same_time(A,B))
        | once(A) ) ),
    inference(quant_intro,[status(thm)],[37]) ).

tff(39,plain,
    ( ! [B: $i,A: $i] :
        ( ~ once(at_the_same_time(A,B))
        | once(A) )
  <=> ! [B: $i,A: $i] :
        ( ~ once(at_the_same_time(A,B))
        | once(A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,axiom,
    ! [B: $i,A: $i] :
      ( ~ once(at_the_same_time(A,B))
      | once(A) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-3.ax',conjunction_at_the_same_time_8) ).

tff(41,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at_the_same_time(A,B))
      | once(A) ),
    inference(modus_ponens,[status(thm)],[40,39]) ).

tff(42,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at_the_same_time(A,B))
      | once(A) ),
    inference(skolemize,[status(sab)],[41]) ).

tff(43,plain,
    ! [B: $i,A: $i] :
      ( ~ once(at_the_same_time(A,B))
      | once(A) ),
    inference(modus_ponens,[status(thm)],[42,38]) ).

tff(44,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ~ once(at_the_same_time(A,B))
            | once(A) )
      | ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
      | once(at(sk28,sk27)) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ~ once(at_the_same_time(A,B))
            | once(A) )
      | ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
      | once(at(sk28,sk27)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ once(at_the_same_time(A,B))
          | once(A) )
    | ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
    | once(at(sk28,sk27)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(46,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ once(at_the_same_time(A,B))
          | once(A) )
    | ~ once(at_the_same_time(at(sk28,sk27),at(sk29,sk27)))
    | once(at(sk28,sk27)) ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    once(at(sk28,sk27)),
    inference(unit_resolution,[status(thm)],[46,43,14]) ).

tff(48,plain,
    ( ( ~ ! [B: $i,A: $i] :
            ( ~ once(at(A,B))
            | incident_o(B,trajectory_of(A)) )
      | ~ once(at(sk28,sk27))
      | incident_o(sk27,trajectory_of(sk28)) )
  <=> ( ~ ! [B: $i,A: $i] :
            ( ~ once(at(A,B))
            | incident_o(B,trajectory_of(A)) )
      | ~ once(at(sk28,sk27))
      | incident_o(sk27,trajectory_of(sk28)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ once(at(A,B))
          | incident_o(B,trajectory_of(A)) )
    | ~ once(at(sk28,sk27))
    | incident_o(sk27,trajectory_of(sk28)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(50,plain,
    ( ~ ! [B: $i,A: $i] :
          ( ~ once(at(A,B))
          | incident_o(B,trajectory_of(A)) )
    | ~ once(at(sk28,sk27))
    | incident_o(sk27,trajectory_of(sk28)) ),
    inference(modus_ponens,[status(thm)],[49,48]) ).

tff(51,plain,
    incident_o(sk27,trajectory_of(sk28)),
    inference(unit_resolution,[status(thm)],[50,32,47]) ).

tff(52,plain,
    ( ( ~ incident_o(sk27,trajectory_of(sk28))
      | ~ incident_o(sk27,trajectory_of(sk29)) )
  <=> ( ~ incident_o(sk27,trajectory_of(sk28))
      | ~ incident_o(sk27,trajectory_of(sk29)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,axiom,
    ( ~ incident_o(sk27,trajectory_of(sk28))
    | ~ incident_o(sk27,trajectory_of(sk29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_157) ).

tff(54,plain,
    ( ~ incident_o(sk27,trajectory_of(sk28))
    | ~ incident_o(sk27,trajectory_of(sk29)) ),
    inference(modus_ponens,[status(thm)],[53,52]) ).

tff(55,plain,
    $false,
    inference(unit_resolution,[status(thm)],[54,51,36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO147-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33  % Computer : n013.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Aug 31 06:19:46 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.20/0.42  % SZS status Unsatisfiable
% 0.20/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------