TSTP Solution File: SYN060-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN060-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.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 23:53:26 EDT 2022

% Result   : Unsatisfiable 0.12s 0.39s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   46 (  10 unt;   4 typ;   0 def)
%            Number of atoms       :  140 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  145 (  52   ~;  76   |;   0   &)
%                                         (  17 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    5 (   5 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   47 (  42   !;   0   ?;  47   :)

% Comments : 
%------------------------------------------------------------------------------
tff(big_h_type,type,
    big_h: $i > $o ).

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

tff(big_i_type,type,
    big_i: $i > $o ).

tff(big_f_type,type,
    big_f: $i > $o ).

tff(1,plain,
    ( ~ big_i(a)
  <=> ~ big_i(a) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ big_i(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).

tff(3,plain,
    ~ big_i(a),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [X: $i] :
      refl(
        ( ( big_h(X)
          | big_i(X) )
      <=> ( big_h(X)
          | big_i(X) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [X: $i] :
        ( big_h(X)
        | big_i(X) )
  <=> ! [X: $i] :
        ( big_h(X)
        | big_i(X) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [X: $i] :
        ( big_h(X)
        | big_i(X) )
  <=> ! [X: $i] :
        ( big_h(X)
        | big_i(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,plain,
    ^ [X: $i] :
      rewrite(
        ( ( big_i(X)
          | big_h(X) )
      <=> ( big_h(X)
          | big_i(X) ) )),
    inference(bind,[status(th)],]) ).

tff(8,plain,
    ( ! [X: $i] :
        ( big_i(X)
        | big_h(X) )
  <=> ! [X: $i] :
        ( big_h(X)
        | big_i(X) ) ),
    inference(quant_intro,[status(thm)],[7]) ).

tff(9,axiom,
    ! [X: $i] :
      ( big_i(X)
      | big_h(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).

tff(10,plain,
    ! [X: $i] :
      ( big_h(X)
      | big_i(X) ),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ! [X: $i] :
      ( big_h(X)
      | big_i(X) ),
    inference(modus_ponens,[status(thm)],[10,6]) ).

tff(12,plain,
    ! [X: $i] :
      ( big_h(X)
      | big_i(X) ),
    inference(skolemize,[status(sab)],[11]) ).

tff(13,plain,
    ! [X: $i] :
      ( big_h(X)
      | big_i(X) ),
    inference(modus_ponens,[status(thm)],[12,5]) ).

tff(14,plain,
    ( ( ~ ! [X: $i] :
            ( big_h(X)
            | big_i(X) )
      | big_h(a)
      | big_i(a) )
  <=> ( ~ ! [X: $i] :
            ( big_h(X)
            | big_i(X) )
      | big_h(a)
      | big_i(a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ~ ! [X: $i] :
          ( big_h(X)
          | big_i(X) )
    | big_h(a)
    | big_i(a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [X: $i] :
          ( big_h(X)
          | big_i(X) )
    | big_h(a)
    | big_i(a) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    big_h(a),
    inference(unit_resolution,[status(thm)],[16,13,3]) ).

tff(18,plain,
    ^ [X: $i] :
      refl(
        ( ( big_f(X)
          | big_i(X) )
      <=> ( big_f(X)
          | big_i(X) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [X: $i] :
        ( big_f(X)
        | big_i(X) )
  <=> ! [X: $i] :
        ( big_f(X)
        | big_i(X) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [X: $i] :
        ( big_f(X)
        | big_i(X) )
  <=> ! [X: $i] :
        ( big_f(X)
        | big_i(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ^ [X: $i] :
      rewrite(
        ( ( big_i(X)
          | big_f(X) )
      <=> ( big_f(X)
          | big_i(X) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [X: $i] :
        ( big_i(X)
        | big_f(X) )
  <=> ! [X: $i] :
        ( big_f(X)
        | big_i(X) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,axiom,
    ! [X: $i] :
      ( big_i(X)
      | big_f(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).

tff(24,plain,
    ! [X: $i] :
      ( big_f(X)
      | big_i(X) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    ! [X: $i] :
      ( big_f(X)
      | big_i(X) ),
    inference(modus_ponens,[status(thm)],[24,20]) ).

tff(26,plain,
    ! [X: $i] :
      ( big_f(X)
      | big_i(X) ),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [X: $i] :
      ( big_f(X)
      | big_i(X) ),
    inference(modus_ponens,[status(thm)],[26,19]) ).

tff(28,plain,
    ( ( ~ ! [X: $i] :
            ( big_f(X)
            | big_i(X) )
      | big_f(a)
      | big_i(a) )
  <=> ( ~ ! [X: $i] :
            ( big_f(X)
            | big_i(X) )
      | big_f(a)
      | big_i(a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,plain,
    ( ~ ! [X: $i] :
          ( big_f(X)
          | big_i(X) )
    | big_f(a)
    | big_i(a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(30,plain,
    ( ~ ! [X: $i] :
          ( big_f(X)
          | big_i(X) )
    | big_f(a)
    | big_i(a) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    big_f(a),
    inference(unit_resolution,[status(thm)],[30,27,3]) ).

tff(32,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ big_f(X)
          | ~ big_h(X) )
      <=> ( ~ big_f(X)
          | ~ big_h(X) ) )),
    inference(bind,[status(th)],]) ).

tff(33,plain,
    ( ! [X: $i] :
        ( ~ big_f(X)
        | ~ big_h(X) )
  <=> ! [X: $i] :
        ( ~ big_f(X)
        | ~ big_h(X) ) ),
    inference(quant_intro,[status(thm)],[32]) ).

tff(34,plain,
    ( ! [X: $i] :
        ( ~ big_f(X)
        | ~ big_h(X) )
  <=> ! [X: $i] :
        ( ~ big_f(X)
        | ~ big_h(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,axiom,
    ! [X: $i] :
      ( ~ big_f(X)
      | ~ big_h(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).

tff(36,plain,
    ! [X: $i] :
      ( ~ big_f(X)
      | ~ big_h(X) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ! [X: $i] :
      ( ~ big_f(X)
      | ~ big_h(X) ),
    inference(skolemize,[status(sab)],[36]) ).

tff(38,plain,
    ! [X: $i] :
      ( ~ big_f(X)
      | ~ big_h(X) ),
    inference(modus_ponens,[status(thm)],[37,33]) ).

tff(39,plain,
    ( ( ~ ! [X: $i] :
            ( ~ big_f(X)
            | ~ big_h(X) )
      | ~ big_f(a)
      | ~ big_h(a) )
  <=> ( ~ ! [X: $i] :
            ( ~ big_f(X)
            | ~ big_h(X) )
      | ~ big_f(a)
      | ~ big_h(a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,plain,
    ( ~ ! [X: $i] :
          ( ~ big_f(X)
          | ~ big_h(X) )
    | ~ big_f(a)
    | ~ big_h(a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(41,plain,
    ( ~ ! [X: $i] :
          ( ~ big_f(X)
          | ~ big_h(X) )
    | ~ big_f(a)
    | ~ big_h(a) ),
    inference(modus_ponens,[status(thm)],[40,39]) ).

tff(42,plain,
    $false,
    inference(unit_resolution,[status(thm)],[41,38,31,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN060-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Sep  5 01:28:56 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35  Usage: tptp [options] [-file:]file
% 0.12/0.35    -h, -?       prints this message.
% 0.12/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.35    -m, -model   generate model.
% 0.12/0.35    -p, -proof   generate proof.
% 0.12/0.35    -c, -core    generate unsat core of named formulas.
% 0.12/0.35    -st, -statistics display statistics.
% 0.12/0.35    -t:timeout   set timeout (in second).
% 0.12/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35    -<param>:<value> configuration parameter and value.
% 0.12/0.35    -o:<output-file> file to place output in.
% 0.12/0.39  % SZS status Unsatisfiable
% 0.12/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------