TSTP Solution File: SYN149-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN149-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n029.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 23:53:57 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   37 (  13 unt;   5 typ;   0 def)
%            Number of atoms       :  143 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  199 (  97   ~;  85   |;   0   &)
%                                         (  17 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    9 (   9 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   2   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   94 (  85   !;   0   ?;  94   :)

% Comments : 
%------------------------------------------------------------------------------
tff(n1_type,type,
    n1: ( $i * $i * $i ) > $o ).

tff(b_type,type,
    b: $i ).

tff(e_type,type,
    e: $i ).

tff(m0_type,type,
    m0: ( $i * $i * $i ) > $o ).

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

tff(1,plain,
    ^ [I: $i,A: $i,J: $i,H: $i] :
      refl(
        ( ( ~ m0(I,J,H)
          | ~ m0(J,A,A)
          | n1(H,H,I) )
      <=> ( ~ m0(I,J,H)
          | ~ m0(J,A,A)
          | n1(H,H,I) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [I: $i,A: $i,J: $i,H: $i] :
        ( ~ m0(I,J,H)
        | ~ m0(J,A,A)
        | n1(H,H,I) )
  <=> ! [I: $i,A: $i,J: $i,H: $i] :
        ( ~ m0(I,J,H)
        | ~ m0(J,A,A)
        | n1(H,H,I) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [I: $i,A: $i,J: $i,H: $i] :
        ( ~ m0(I,J,H)
        | ~ m0(J,A,A)
        | n1(H,H,I) )
  <=> ! [I: $i,A: $i,J: $i,H: $i] :
        ( ~ m0(I,J,H)
        | ~ m0(J,A,A)
        | n1(H,H,I) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [I: $i,A: $i,J: $i,H: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( n1(H,H,I)
              | ~ m0(J,A,A) )
          <=> ( ~ m0(J,A,A)
              | n1(H,H,I) ) )),
          ( ( n1(H,H,I)
            | ~ m0(J,A,A)
            | ~ m0(I,J,H) )
        <=> ( ~ m0(J,A,A)
            | n1(H,H,I)
            | ~ m0(I,J,H) ) )),
        rewrite(
          ( ( ~ m0(J,A,A)
            | n1(H,H,I)
            | ~ m0(I,J,H) )
        <=> ( ~ m0(I,J,H)
            | ~ m0(J,A,A)
            | n1(H,H,I) ) )),
        ( ( n1(H,H,I)
          | ~ m0(J,A,A)
          | ~ m0(I,J,H) )
      <=> ( ~ m0(I,J,H)
          | ~ m0(J,A,A)
          | n1(H,H,I) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [I: $i,A: $i,J: $i,H: $i] :
        ( n1(H,H,I)
        | ~ m0(J,A,A)
        | ~ m0(I,J,H) )
  <=> ! [I: $i,A: $i,J: $i,H: $i] :
        ( ~ m0(I,J,H)
        | ~ m0(J,A,A)
        | n1(H,H,I) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [I: $i,A: $i,J: $i,H: $i] :
      ( n1(H,H,I)
      | ~ m0(J,A,A)
      | ~ m0(I,J,H) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_059) ).

tff(7,plain,
    ! [I: $i,A: $i,J: $i,H: $i] :
      ( ~ m0(I,J,H)
      | ~ m0(J,A,A)
      | n1(H,H,I) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [I: $i,A: $i,J: $i,H: $i] :
      ( ~ m0(I,J,H)
      | ~ m0(J,A,A)
      | n1(H,H,I) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [I: $i,A: $i,J: $i,H: $i] :
      ( ~ m0(I,J,H)
      | ~ m0(J,A,A)
      | n1(H,H,I) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [I: $i,A: $i,J: $i,H: $i] :
      ( ~ m0(I,J,H)
      | ~ m0(J,A,A)
      | n1(H,H,I) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( m0(b,a,a)
  <=> m0(b,a,a) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    m0(b,a,a),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_38) ).

tff(13,plain,
    m0(b,a,a),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( m0(b,b,e)
  <=> m0(b,b,e) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    m0(b,b,e),
    file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_31) ).

tff(16,plain,
    m0(b,b,e),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
            ( ~ m0(I,J,H)
            | ~ m0(J,A,A)
            | n1(H,H,I) )
      | ~ m0(b,a,a)
      | ~ m0(b,b,e)
      | n1(e,e,b) )
  <=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
            ( ~ m0(I,J,H)
            | ~ m0(J,A,A)
            | n1(H,H,I) )
      | ~ m0(b,a,a)
      | ~ m0(b,b,e)
      | n1(e,e,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ( ~ m0(b,b,e)
      | ~ m0(b,a,a)
      | n1(e,e,b) )
  <=> ( ~ m0(b,a,a)
      | ~ m0(b,b,e)
      | n1(e,e,b) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
            ( ~ m0(I,J,H)
            | ~ m0(J,A,A)
            | n1(H,H,I) )
      | ~ m0(b,b,e)
      | ~ m0(b,a,a)
      | n1(e,e,b) )
  <=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
            ( ~ m0(I,J,H)
            | ~ m0(J,A,A)
            | n1(H,H,I) )
      | ~ m0(b,a,a)
      | ~ m0(b,b,e)
      | n1(e,e,b) ) ),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    ( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
            ( ~ m0(I,J,H)
            | ~ m0(J,A,A)
            | n1(H,H,I) )
      | ~ m0(b,b,e)
      | ~ m0(b,a,a)
      | n1(e,e,b) )
  <=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
            ( ~ m0(I,J,H)
            | ~ m0(J,A,A)
            | n1(H,H,I) )
      | ~ m0(b,a,a)
      | ~ m0(b,b,e)
      | n1(e,e,b) ) ),
    inference(transitivity,[status(thm)],[19,17]) ).

tff(21,plain,
    ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
          ( ~ m0(I,J,H)
          | ~ m0(J,A,A)
          | n1(H,H,I) )
    | ~ m0(b,b,e)
    | ~ m0(b,a,a)
    | n1(e,e,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(22,plain,
    ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
          ( ~ m0(I,J,H)
          | ~ m0(J,A,A)
          | n1(H,H,I) )
    | ~ m0(b,a,a)
    | ~ m0(b,b,e)
    | n1(e,e,b) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    n1(e,e,b),
    inference(unit_resolution,[status(thm)],[22,16,13,10]) ).

tff(24,plain,
    ^ [X: $i] :
      refl(
        ( ~ n1(e,e,X)
      <=> ~ n1(e,e,X) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [X: $i] : ~ n1(e,e,X)
  <=> ! [X: $i] : ~ n1(e,e,X) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,plain,
    ( ! [X: $i] : ~ n1(e,e,X)
  <=> ! [X: $i] : ~ n1(e,e,X) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,axiom,
    ! [X: $i] : ~ n1(e,e,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

tff(28,plain,
    ! [X: $i] : ~ n1(e,e,X),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ! [X: $i] : ~ n1(e,e,X),
    inference(skolemize,[status(sab)],[28]) ).

tff(30,plain,
    ! [X: $i] : ~ n1(e,e,X),
    inference(modus_ponens,[status(thm)],[29,25]) ).

tff(31,plain,
    ( ~ ! [X: $i] : ~ n1(e,e,X)
    | ~ n1(e,e,b) ),
    inference(quant_inst,[status(thm)],]) ).

tff(32,plain,
    $false,
    inference(unit_resolution,[status(thm)],[31,30,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN149-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Sep  5 02:07:46 EDT 2022
% 0.13/0.33  % 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.
% 0.19/0.48  % SZS status Unsatisfiable
% 0.19/0.48  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------