TSTP Solution File: SWC358-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWC358-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n012.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 11:57:22 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   55 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :  177 (  51 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  221 ( 100   ~;  93   |;   0   &)
%                                         (  28 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    8 (   8 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   21 (  19   !;   0   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
tff(ssList_type,type,
    ssList: $i > $o ).

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

tff(nil_type,type,
    nil: $i ).

tff(segmentP_type,type,
    segmentP: ( $i * $i ) > $o ).

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

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

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

tff(1,plain,
    ( ( ( nil = sk4 )
      | $false )
  <=> ( nil = sk4 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ segmentP(sk2,sk1)
  <=> ~ segmentP(sk4,sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ~ segmentP(sk2,sk1)
  <=> ~ segmentP(sk2,sk1) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ~ segmentP(sk2,sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

tff(5,plain,
    ~ segmentP(sk2,sk1),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ~ segmentP(sk4,sk3),
    inference(modus_ponens,[status(thm)],[5,2]) ).

tff(7,plain,
    ( segmentP(sk4,sk3)
  <=> $false ),
    inference(iff_false,[status(thm)],[6]) ).

tff(8,plain,
    ( ( ( nil = sk4 )
      | segmentP(sk4,sk3) )
  <=> ( ( nil = sk4 )
      | $false ) ),
    inference(monotonicity,[status(thm)],[7]) ).

tff(9,plain,
    ( ( ( nil = sk4 )
      | segmentP(sk4,sk3) )
  <=> ( nil = sk4 ) ),
    inference(transitivity,[status(thm)],[8,1]) ).

tff(10,plain,
    ( ( ( nil = sk4 )
      | segmentP(sk4,sk3) )
  <=> ( ( nil = sk4 )
      | segmentP(sk4,sk3) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ( ( nil = sk4 )
    | segmentP(sk4,sk3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

tff(12,plain,
    ( ( nil = sk4 )
    | segmentP(sk4,sk3) ),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    nil = sk4,
    inference(modus_ponens,[status(thm)],[12,9]) ).

tff(14,plain,
    sk4 = nil,
    inference(symmetry,[status(thm)],[13]) ).

tff(15,plain,
    ( ssList(sk4)
  <=> ssList(nil) ),
    inference(monotonicity,[status(thm)],[14]) ).

tff(16,plain,
    ( ssList(nil)
  <=> ssList(sk4) ),
    inference(symmetry,[status(thm)],[15]) ).

tff(17,plain,
    ( ssList(sk3)
  <=> ssList(nil) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ssList(sk1)
  <=> ssList(sk3) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( ssList(sk1)
  <=> ssList(sk1) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,axiom,
    ssList(sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).

tff(21,plain,
    ssList(sk1),
    inference(modus_ponens,[status(thm)],[20,19]) ).

tff(22,plain,
    ssList(sk3),
    inference(modus_ponens,[status(thm)],[21,18]) ).

tff(23,plain,
    ssList(nil),
    inference(modus_ponens,[status(thm)],[22,17]) ).

tff(24,plain,
    ssList(sk4),
    inference(modus_ponens,[status(thm)],[23,16]) ).

tff(25,plain,
    ( segmentP(nil,sk4)
  <=> segmentP(nil,nil) ),
    inference(monotonicity,[status(thm)],[14]) ).

tff(26,plain,
    ( segmentP(nil,nil)
  <=> segmentP(nil,sk4) ),
    inference(symmetry,[status(thm)],[25]) ).

tff(27,plain,
    ( ~ segmentP(nil,nil)
  <=> ~ segmentP(nil,sk4) ),
    inference(monotonicity,[status(thm)],[26]) ).

tff(28,plain,
    ( ~ segmentP(sk4,sk3)
  <=> ~ segmentP(nil,nil) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,plain,
    ~ segmentP(nil,nil),
    inference(modus_ponens,[status(thm)],[6,28]) ).

tff(30,plain,
    ~ segmentP(nil,sk4),
    inference(modus_ponens,[status(thm)],[29,27]) ).

tff(31,plain,
    ^ [U: $i] :
      refl(
        ( ( ~ ssList(U)
          | segmentP(nil,U)
          | ( nil != U ) )
      <=> ( ~ ssList(U)
          | segmentP(nil,U)
          | ( nil != U ) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [U: $i] :
        ( ~ ssList(U)
        | segmentP(nil,U)
        | ( nil != U ) )
  <=> ! [U: $i] :
        ( ~ ssList(U)
        | segmentP(nil,U)
        | ( nil != U ) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,plain,
    ( ! [U: $i] :
        ( ~ ssList(U)
        | segmentP(nil,U)
        | ( nil != U ) )
  <=> ! [U: $i] :
        ( ~ ssList(U)
        | segmentP(nil,U)
        | ( nil != U ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,plain,
    ^ [U: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ( nil != U )
              | ~ ssList(U) )
          <=> ( ~ ssList(U)
              | ( nil != U ) ) )),
          ( ( ( nil != U )
            | ~ ssList(U)
            | segmentP(nil,U) )
        <=> ( ~ ssList(U)
            | ( nil != U )
            | segmentP(nil,U) ) )),
        rewrite(
          ( ( ~ ssList(U)
            | ( nil != U )
            | segmentP(nil,U) )
        <=> ( ~ ssList(U)
            | segmentP(nil,U)
            | ( nil != U ) ) )),
        ( ( ( nil != U )
          | ~ ssList(U)
          | segmentP(nil,U) )
      <=> ( ~ ssList(U)
          | segmentP(nil,U)
          | ( nil != U ) ) )),
    inference(bind,[status(th)],]) ).

tff(35,plain,
    ( ! [U: $i] :
        ( ( nil != U )
        | ~ ssList(U)
        | segmentP(nil,U) )
  <=> ! [U: $i] :
        ( ~ ssList(U)
        | segmentP(nil,U)
        | ( nil != U ) ) ),
    inference(quant_intro,[status(thm)],[34]) ).

tff(36,axiom,
    ! [U: $i] :
      ( ( nil != U )
      | ~ ssList(U)
      | segmentP(nil,U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).

tff(37,plain,
    ! [U: $i] :
      ( ~ ssList(U)
      | segmentP(nil,U)
      | ( nil != U ) ),
    inference(modus_ponens,[status(thm)],[36,35]) ).

tff(38,plain,
    ! [U: $i] :
      ( ~ ssList(U)
      | segmentP(nil,U)
      | ( nil != U ) ),
    inference(modus_ponens,[status(thm)],[37,33]) ).

tff(39,plain,
    ! [U: $i] :
      ( ~ ssList(U)
      | segmentP(nil,U)
      | ( nil != U ) ),
    inference(skolemize,[status(sab)],[38]) ).

tff(40,plain,
    ! [U: $i] :
      ( ~ ssList(U)
      | segmentP(nil,U)
      | ( nil != U ) ),
    inference(modus_ponens,[status(thm)],[39,32]) ).

tff(41,plain,
    ( ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | segmentP(nil,U)
            | ( nil != U ) )
      | ~ ssList(sk4)
      | ( nil != sk4 )
      | segmentP(nil,sk4) )
  <=> ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | segmentP(nil,U)
            | ( nil != U ) )
      | ~ ssList(sk4)
      | ( nil != sk4 )
      | segmentP(nil,sk4) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,plain,
    ( ( ~ ssList(sk4)
      | segmentP(nil,sk4)
      | ( nil != sk4 ) )
  <=> ( ~ ssList(sk4)
      | ( nil != sk4 )
      | segmentP(nil,sk4) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(43,plain,
    ( ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | segmentP(nil,U)
            | ( nil != U ) )
      | ~ ssList(sk4)
      | segmentP(nil,sk4)
      | ( nil != sk4 ) )
  <=> ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | segmentP(nil,U)
            | ( nil != U ) )
      | ~ ssList(sk4)
      | ( nil != sk4 )
      | segmentP(nil,sk4) ) ),
    inference(monotonicity,[status(thm)],[42]) ).

tff(44,plain,
    ( ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | segmentP(nil,U)
            | ( nil != U ) )
      | ~ ssList(sk4)
      | segmentP(nil,sk4)
      | ( nil != sk4 ) )
  <=> ( ~ ! [U: $i] :
            ( ~ ssList(U)
            | segmentP(nil,U)
            | ( nil != U ) )
      | ~ ssList(sk4)
      | ( nil != sk4 )
      | segmentP(nil,sk4) ) ),
    inference(transitivity,[status(thm)],[43,41]) ).

tff(45,plain,
    ( ~ ! [U: $i] :
          ( ~ ssList(U)
          | segmentP(nil,U)
          | ( nil != U ) )
    | ~ ssList(sk4)
    | segmentP(nil,sk4)
    | ( nil != sk4 ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(46,plain,
    ( ~ ! [U: $i] :
          ( ~ ssList(U)
          | segmentP(nil,U)
          | ( nil != U ) )
    | ~ ssList(sk4)
    | ( nil != sk4 )
    | segmentP(nil,sk4) ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ( ~ ssList(sk4)
    | segmentP(nil,sk4) ),
    inference(unit_resolution,[status(thm)],[46,40,13]) ).

tff(48,plain,
    $false,
    inference(unit_resolution,[status(thm)],[47,30,24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC358-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n012.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 00:20:18 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.20/0.44  % SZS status Unsatisfiable
% 0.20/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------