TSTP Solution File: HWV011-3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : HWV011-3 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n017.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 : Sat Sep 17 02:10:34 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   34 (  13 unt;   6 typ;   0 def)
%            Number of atoms       :   69 (  38 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   71 (  33   ~;  28   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-1 aty)
%            Number of variables   :   27 (  24   !;   0   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
tff(fwork_DOTfifo_DOTrtl_DOTlevel__type,type,
    fwork_DOTfifo_DOTrtl_DOTlevel_: $i > $i ).

tff(t_206_type,type,
    t_206: $i ).

tff(fwork_DOTfifo_DOTrtl_DOTint__level__type,type,
    fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i ).

tff(p__pred__type,type,
    p__pred_: $i > $o ).

tff(fwork_DOTfifo_DOTrtl_DOTfull__type,type,
    fwork_DOTfifo_DOTrtl_DOTfull_: $i > $i ).

tff(fwork_DOTfifo_DOTrtl_DOTfifo__length__type,type,
    fwork_DOTfifo_DOTrtl_DOTfifo__length_: $i ).

tff(1,plain,
    ^ [T_0: $i] :
      refl(
        ( ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
      <=> ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
  <=> ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
  <=> ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_5) ).

tff(5,plain,
    ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [T_0: $i] : ( fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0) )
    | ( fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ( ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
  <=> ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206)) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).

tff(13,plain,
    ~ p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206)),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ^ [T_1: $i] :
      refl(
        ( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
          | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) )
      <=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
          | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ) )),
    inference(bind,[status(th)],]) ).

tff(15,plain,
    ( ! [T_1: $i] :
        ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
        | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) )
  <=> ! [T_1: $i] :
        ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
        | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ) ),
    inference(quant_intro,[status(thm)],[14]) ).

tff(16,plain,
    ^ [T_1: $i] :
      rewrite(
        ( ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
          | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
      <=> ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
          | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ) )),
    inference(bind,[status(th)],]) ).

tff(17,plain,
    ( ! [T_1: $i] :
        ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
        | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
  <=> ! [T_1: $i] :
        ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
        | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ) ),
    inference(quant_intro,[status(thm)],[16]) ).

tff(18,plain,
    ( ! [T_1: $i] :
        ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
        | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) )
  <=> ! [T_1: $i] :
        ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
        | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    ! [T_1: $i] :
      ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
      | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax',axiom_6) ).

tff(20,plain,
    ! [T_1: $i] :
      ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
      | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTfifo__length_ ) ),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ! [T_1: $i] :
      ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
      | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ),
    inference(modus_ponens,[status(thm)],[20,17]) ).

tff(22,plain,
    ! [T_1: $i] :
      ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
      | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ),
    inference(skolemize,[status(sab)],[21]) ).

tff(23,plain,
    ! [T_1: $i] :
      ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
      | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ),
    inference(modus_ponens,[status(thm)],[22,15]) ).

tff(24,plain,
    ( ( ~ ! [T_1: $i] :
            ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
            | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) )
      | p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
      | ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) )
  <=> ( ~ ! [T_1: $i] :
            ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
            | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) )
      | p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
      | ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ( ~ ! [T_1: $i] :
          ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
          | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) )
    | p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
    | ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [T_1: $i] :
          ( p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_1))
          | ( fwork_DOTfifo_DOTrtl_DOTint__level_(T_1) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) )
    | p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))
    | ( fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) ) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) != fwork_DOTfifo_DOTrtl_DOTlevel_(t_206),
    inference(unit_resolution,[status(thm)],[26,23,13]) ).

tff(28,plain,
    $false,
    inference(unit_resolution,[status(thm)],[27,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : HWV011-3 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 31 21:24:51 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.20/0.44  % SZS status Unsatisfiable
% 0.20/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------