TSTP Solution File: SYN247-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN247-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n018.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 23:54:22 EDT 2022

% Result   : Unsatisfiable 0.20s 0.49s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   33 (  11 unt;   4 typ;   0 def)
%            Number of atoms       :  133 (   0 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  186 (  91   ~;  79   |;   0   &)
%                                         (  16 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 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  :    5 (   2   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   83 (  75   !;   0   ?;  83   :)

% Comments : 
%------------------------------------------------------------------------------
tff(m1_type,type,
    m1: ( $i * $i * $i ) > $o ).

tff(d_type,type,
    d: $i ).

tff(q0_type,type,
    q0: ( $i * $i ) > $o ).

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

tff(1,plain,
    ^ [D: $i,E: $i,C: $i] :
      refl(
        ( ( m1(C,C,C)
          | ~ q0(D,C)
          | ~ q0(D,E) )
      <=> ( m1(C,C,C)
          | ~ q0(D,C)
          | ~ q0(D,E) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [D: $i,E: $i,C: $i] :
        ( m1(C,C,C)
        | ~ q0(D,C)
        | ~ q0(D,E) )
  <=> ! [D: $i,E: $i,C: $i] :
        ( m1(C,C,C)
        | ~ q0(D,C)
        | ~ q0(D,E) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [D: $i,E: $i,C: $i] :
        ( m1(C,C,C)
        | ~ q0(D,C)
        | ~ q0(D,E) )
  <=> ! [D: $i,E: $i,C: $i] :
        ( m1(C,C,C)
        | ~ q0(D,C)
        | ~ q0(D,E) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [D: $i,E: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( m1(C,C,C)
              | ~ q0(D,E) )
          <=> ( m1(C,C,C)
              | ~ q0(D,E) ) )),
          ( ( m1(C,C,C)
            | ~ q0(D,E)
            | ~ q0(D,C) )
        <=> ( m1(C,C,C)
            | ~ q0(D,E)
            | ~ q0(D,C) ) )),
        rewrite(
          ( ( m1(C,C,C)
            | ~ q0(D,E)
            | ~ q0(D,C) )
        <=> ( m1(C,C,C)
            | ~ q0(D,C)
            | ~ q0(D,E) ) )),
        ( ( m1(C,C,C)
          | ~ q0(D,E)
          | ~ q0(D,C) )
      <=> ( m1(C,C,C)
          | ~ q0(D,C)
          | ~ q0(D,E) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [D: $i,E: $i,C: $i] :
        ( m1(C,C,C)
        | ~ q0(D,E)
        | ~ q0(D,C) )
  <=> ! [D: $i,E: $i,C: $i] :
        ( m1(C,C,C)
        | ~ q0(D,C)
        | ~ q0(D,E) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [D: $i,E: $i,C: $i] :
      ( m1(C,C,C)
      | ~ q0(D,E)
      | ~ q0(D,C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_018) ).

tff(7,plain,
    ! [D: $i,E: $i,C: $i] :
      ( m1(C,C,C)
      | ~ q0(D,C)
      | ~ q0(D,E) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [D: $i,E: $i,C: $i] :
      ( m1(C,C,C)
      | ~ q0(D,C)
      | ~ q0(D,E) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [D: $i,E: $i,C: $i] :
      ( m1(C,C,C)
      | ~ q0(D,C)
      | ~ q0(D,E) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [D: $i,E: $i,C: $i] :
      ( m1(C,C,C)
      | ~ q0(D,C)
      | ~ q0(D,E) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( q0(e,d)
  <=> q0(e,d) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    q0(e,d),
    file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_2) ).

tff(13,plain,
    q0(e,d),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ( ~ ! [D: $i,E: $i,C: $i] :
            ( m1(C,C,C)
            | ~ q0(D,C)
            | ~ q0(D,E) )
      | ~ q0(e,d)
      | m1(d,d,d) )
  <=> ( ~ ! [D: $i,E: $i,C: $i] :
            ( m1(C,C,C)
            | ~ q0(D,C)
            | ~ q0(D,E) )
      | ~ q0(e,d)
      | m1(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ( m1(d,d,d)
      | ~ q0(e,d)
      | ~ q0(e,d) )
  <=> ( ~ q0(e,d)
      | m1(d,d,d) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,plain,
    ( ( ~ ! [D: $i,E: $i,C: $i] :
            ( m1(C,C,C)
            | ~ q0(D,C)
            | ~ q0(D,E) )
      | m1(d,d,d)
      | ~ q0(e,d)
      | ~ q0(e,d) )
  <=> ( ~ ! [D: $i,E: $i,C: $i] :
            ( m1(C,C,C)
            | ~ q0(D,C)
            | ~ q0(D,E) )
      | ~ q0(e,d)
      | m1(d,d,d) ) ),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    ( ( ~ ! [D: $i,E: $i,C: $i] :
            ( m1(C,C,C)
            | ~ q0(D,C)
            | ~ q0(D,E) )
      | m1(d,d,d)
      | ~ q0(e,d)
      | ~ q0(e,d) )
  <=> ( ~ ! [D: $i,E: $i,C: $i] :
            ( m1(C,C,C)
            | ~ q0(D,C)
            | ~ q0(D,E) )
      | ~ q0(e,d)
      | m1(d,d,d) ) ),
    inference(transitivity,[status(thm)],[16,14]) ).

tff(18,plain,
    ( ~ ! [D: $i,E: $i,C: $i] :
          ( m1(C,C,C)
          | ~ q0(D,C)
          | ~ q0(D,E) )
    | m1(d,d,d)
    | ~ q0(e,d)
    | ~ q0(e,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [D: $i,E: $i,C: $i] :
          ( m1(C,C,C)
          | ~ q0(D,C)
          | ~ q0(D,E) )
    | ~ q0(e,d)
    | m1(d,d,d) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    m1(d,d,d),
    inference(unit_resolution,[status(thm)],[19,13,10]) ).

tff(21,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ~ m1(d,X,Y)
      <=> ~ m1(d,X,Y) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [Y: $i,X: $i] : ~ m1(d,X,Y)
  <=> ! [Y: $i,X: $i] : ~ m1(d,X,Y) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [Y: $i,X: $i] : ~ m1(d,X,Y)
  <=> ! [Y: $i,X: $i] : ~ m1(d,X,Y) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ! [Y: $i,X: $i] : ~ m1(d,X,Y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

tff(25,plain,
    ! [Y: $i,X: $i] : ~ m1(d,X,Y),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [Y: $i,X: $i] : ~ m1(d,X,Y),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [Y: $i,X: $i] : ~ m1(d,X,Y),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ( ~ ! [Y: $i,X: $i] : ~ m1(d,X,Y)
    | ~ m1(d,d,d) ),
    inference(quant_inst,[status(thm)],]) ).

tff(29,plain,
    $false,
    inference(unit_resolution,[status(thm)],[28,27,20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYN247-1 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n018.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 : Mon Sep  5 02:20:31 EDT 2022
% 0.13/0.34  % 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.
% 0.20/0.49  % SZS status Unsatisfiable
% 0.20/0.49  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------