TSTP Solution File: SWC411-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWC411-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n004.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 : Tue Sep 20 11:57:48 EDT 2022

% Result   : Unsatisfiable 0.19s 0.44s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   34 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :   90 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  118 (  57   ~;  50   |;   0   &)
%                                         (  11 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   17 (  15   !;   0   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
tff(memberP_type,type,
    memberP: ( $i * $i ) > $o ).

tff(sk5_type,type,
    sk5: $i ).

tff(sk3_type,type,
    sk3: $i ).

tff(sk1_type,type,
    sk1: $i ).

tff(sk4_type,type,
    sk4: $i ).

tff(sk2_type,type,
    sk2: $i ).

tff(ssItem_type,type,
    ssItem: $i > $o ).

tff(1,plain,
    ( ~ memberP(sk1,sk5)
  <=> ~ memberP(sk3,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ memberP(sk1,sk5)
  <=> ~ memberP(sk1,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ~ memberP(sk1,sk5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).

tff(4,plain,
    ~ memberP(sk1,sk5),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    ~ memberP(sk3,sk5),
    inference(modus_ponens,[status(thm)],[4,1]) ).

tff(6,plain,
    ( memberP(sk2,sk5)
  <=> memberP(sk4,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,plain,
    ( memberP(sk2,sk5)
  <=> memberP(sk2,sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,axiom,
    memberP(sk2,sk5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).

tff(9,plain,
    memberP(sk2,sk5),
    inference(modus_ponens,[status(thm)],[8,7]) ).

tff(10,plain,
    memberP(sk4,sk5),
    inference(modus_ponens,[status(thm)],[9,6]) ).

tff(11,plain,
    ( ssItem(sk5)
  <=> ssItem(sk5) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    ssItem(sk5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).

tff(13,plain,
    ssItem(sk5),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ^ [A: $i] :
      refl(
        ( ( ~ ssItem(A)
          | ~ memberP(sk4,A)
          | memberP(sk3,A) )
      <=> ( ~ ssItem(A)
          | ~ memberP(sk4,A)
          | memberP(sk3,A) ) )),
    inference(bind,[status(th)],]) ).

tff(15,plain,
    ( ! [A: $i] :
        ( ~ ssItem(A)
        | ~ memberP(sk4,A)
        | memberP(sk3,A) )
  <=> ! [A: $i] :
        ( ~ ssItem(A)
        | ~ memberP(sk4,A)
        | memberP(sk3,A) ) ),
    inference(quant_intro,[status(thm)],[14]) ).

tff(16,plain,
    ( ! [A: $i] :
        ( ~ ssItem(A)
        | ~ memberP(sk4,A)
        | memberP(sk3,A) )
  <=> ! [A: $i] :
        ( ~ ssItem(A)
        | ~ memberP(sk4,A)
        | memberP(sk3,A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(17,plain,
    ^ [A: $i] :
      rewrite(
        ( ( ~ ssItem(A)
          | memberP(sk3,A)
          | ~ memberP(sk4,A) )
      <=> ( ~ ssItem(A)
          | ~ memberP(sk4,A)
          | memberP(sk3,A) ) )),
    inference(bind,[status(th)],]) ).

tff(18,plain,
    ( ! [A: $i] :
        ( ~ ssItem(A)
        | memberP(sk3,A)
        | ~ memberP(sk4,A) )
  <=> ! [A: $i] :
        ( ~ ssItem(A)
        | ~ memberP(sk4,A)
        | memberP(sk3,A) ) ),
    inference(quant_intro,[status(thm)],[17]) ).

tff(19,axiom,
    ! [A: $i] :
      ( ~ ssItem(A)
      | memberP(sk3,A)
      | ~ memberP(sk4,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

tff(20,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ~ memberP(sk4,A)
      | memberP(sk3,A) ),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ~ memberP(sk4,A)
      | memberP(sk3,A) ),
    inference(modus_ponens,[status(thm)],[20,16]) ).

tff(22,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ~ memberP(sk4,A)
      | memberP(sk3,A) ),
    inference(skolemize,[status(sab)],[21]) ).

tff(23,plain,
    ! [A: $i] :
      ( ~ ssItem(A)
      | ~ memberP(sk4,A)
      | memberP(sk3,A) ),
    inference(modus_ponens,[status(thm)],[22,15]) ).

tff(24,plain,
    ( ( ~ ! [A: $i] :
            ( ~ ssItem(A)
            | ~ memberP(sk4,A)
            | memberP(sk3,A) )
      | ~ ssItem(sk5)
      | ~ memberP(sk4,sk5)
      | memberP(sk3,sk5) )
  <=> ( ~ ! [A: $i] :
            ( ~ ssItem(A)
            | ~ memberP(sk4,A)
            | memberP(sk3,A) )
      | ~ ssItem(sk5)
      | ~ memberP(sk4,sk5)
      | memberP(sk3,sk5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ( ~ ! [A: $i] :
          ( ~ ssItem(A)
          | ~ memberP(sk4,A)
          | memberP(sk3,A) )
    | ~ ssItem(sk5)
    | ~ memberP(sk4,sk5)
    | memberP(sk3,sk5) ),
    inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [A: $i] :
          ( ~ ssItem(A)
          | ~ memberP(sk4,A)
          | memberP(sk3,A) )
    | ~ ssItem(sk5)
    | ~ memberP(sk4,sk5)
    | memberP(sk3,sk5) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    $false,
    inference(unit_resolution,[status(thm)],[26,23,13,10,5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SWC411-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n004.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 : Sun Sep  4 00:44:04 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.
% 0.19/0.44  % SZS status Unsatisfiable
% 0.19/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------