TSTP Solution File: LCL170-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL170-1 : 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 : Sun Sep 18 04:55:10 EDT 2022

% Result   : Unsatisfiable 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   29 (  10 unt;   6 typ;   0 def)
%            Number of atoms       :   56 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   58 (  27   ~;  23   |;   0   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   4   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   33 (  30   !;   0   ?;  33   :)

% Comments : 
%------------------------------------------------------------------------------
tff(axiom_type,type,
    axiom: $i > $o ).

tff(or_type,type,
    or: ( $i * $i ) > $i ).

tff(q_type,type,
    q: $i ).

tff(not_type,type,
    not: $i > $i ).

tff(p_type,type,
    p: $i ).

tff(theorem_type,type,
    theorem: $i > $o ).

tff(1,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( axiom(or(not(A),or(B,A)))
      <=> axiom(or(not(A),or(B,A))) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [B: $i,A: $i] : axiom(or(not(A),or(B,A)))
  <=> ! [B: $i,A: $i] : axiom(or(not(A),or(B,A))) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [B: $i,A: $i] : axiom(or(not(A),or(B,A)))
  <=> ! [B: $i,A: $i] : axiom(or(not(A),or(B,A))) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [B: $i,A: $i] : axiom(or(not(A),or(B,A))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',axiom_1_3) ).

tff(5,plain,
    ! [B: $i,A: $i] : axiom(or(not(A),or(B,A))),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [B: $i,A: $i] : axiom(or(not(A),or(B,A))),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [B: $i,A: $i] : axiom(or(not(A),or(B,A))),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [B: $i,A: $i] : axiom(or(not(A),or(B,A)))
    | axiom(or(not(q),or(not(p),q))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    axiom(or(not(q),or(not(p),q))),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ( ~ theorem(or(not(q),or(not(p),q)))
  <=> ~ theorem(or(not(q),or(not(p),q))) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ~ theorem(or(not(q),or(not(p),q))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

tff(12,plain,
    ~ theorem(or(not(q),or(not(p),q))),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ^ [X: $i] :
      refl(
        ( ( theorem(X)
          | ~ axiom(X) )
      <=> ( theorem(X)
          | ~ axiom(X) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) )
  <=> ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,plain,
    ( ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) )
  <=> ! [X: $i] :
        ( theorem(X)
        | ~ axiom(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',rule_1) ).

tff(17,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [X: $i] :
      ( theorem(X)
      | ~ axiom(X) ),
    inference(modus_ponens,[status(thm)],[18,14]) ).

tff(20,plain,
    ( ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(or(not(q),or(not(p),q)))
      | ~ axiom(or(not(q),or(not(p),q))) )
  <=> ( ~ ! [X: $i] :
            ( theorem(X)
            | ~ axiom(X) )
      | theorem(or(not(q),or(not(p),q)))
      | ~ axiom(or(not(q),or(not(p),q))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(or(not(q),or(not(p),q)))
    | ~ axiom(or(not(q),or(not(p),q))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(22,plain,
    ( ~ ! [X: $i] :
          ( theorem(X)
          | ~ axiom(X) )
    | theorem(or(not(q),or(not(p),q)))
    | ~ axiom(or(not(q),or(not(p),q))) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    $false,
    inference(unit_resolution,[status(thm)],[22,19,12,9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LCL170-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Sep  1 18:31:12 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33  Usage: tptp [options] [-file:]file
% 0.12/0.33    -h, -?       prints this message.
% 0.12/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.33    -m, -model   generate model.
% 0.12/0.33    -p, -proof   generate proof.
% 0.12/0.33    -c, -core    generate unsat core of named formulas.
% 0.12/0.33    -st, -statistics display statistics.
% 0.12/0.33    -t:timeout   set timeout (in second).
% 0.12/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33    -<param>:<value> configuration parameter and value.
% 0.12/0.33    -o:<output-file> file to place output in.
% 0.19/0.39  % SZS status Unsatisfiable
% 0.19/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------