TSTP Solution File: KRS152+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : KRS152+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n005.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 : Sat Sep 17 17:44:59 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   71 (  13 unt;  12 typ;   0 def)
%            Number of atoms       :  267 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  353 ( 149   ~;  50   |;  82   &)
%                                         (  72 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   48 (  44   !;   0   ?;  48   :)

% Comments : 
%------------------------------------------------------------------------------
tff(cC12_type,type,
    cC12: $i > $o ).

tff(iV21080_type,type,
    iV21080: $i ).

tff(cC8_type,type,
    cC8: $i > $o ).

tff(cTEST_type,type,
    cTEST: $i > $o ).

tff(cC10_type,type,
    cC10: $i > $o ).

tff(iV21081_type,type,
    iV21081: $i ).

tff(cC4_type,type,
    cC4: $i > $o ).

tff(cC2_type,type,
    cC2: $i > $o ).

tff(cowlThing_type,type,
    cowlThing: $i > $o ).

tff(xsd_integer_type,type,
    xsd_integer: $i > $o ).

tff(xsd_string_type,type,
    xsd_string: $i > $o ).

tff(cowlNothing_type,type,
    cowlNothing: $i > $o ).

tff(1,plain,
    ^ [X: $i] :
      refl(
        ( ( cTEST(X)
        <=> ~ ( cC8(X)
              | ~ cC12(X) ) )
      <=> ( cTEST(X)
        <=> ~ ( cC8(X)
              | ~ cC12(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] :
        ( cTEST(X)
      <=> ~ ( cC8(X)
            | ~ cC12(X) ) )
  <=> ! [X: $i] :
        ( cTEST(X)
      <=> ~ ( cC8(X)
            | ~ cC12(X) ) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cTEST(X)
        <=> ( cC12(X)
            & ~ cC8(X) ) )
      <=> ( cTEST(X)
        <=> ~ ( cC8(X)
              | ~ cC12(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [X: $i] :
        ( cTEST(X)
      <=> ( cC12(X)
          & ~ cC8(X) ) )
  <=> ! [X: $i] :
        ( cTEST(X)
      <=> ~ ( cC8(X)
            | ~ cC12(X) ) ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ( ! [X: $i] :
        ( cTEST(X)
      <=> ( cC12(X)
          & ~ cC8(X) ) )
  <=> ! [X: $i] :
        ( cTEST(X)
      <=> ( cC12(X)
          & ~ cC8(X) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    ! [X: $i] :
      ( cTEST(X)
    <=> ( cC12(X)
        & ~ cC8(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

tff(7,plain,
    ! [X: $i] :
      ( cTEST(X)
    <=> ( cC12(X)
        & ~ cC8(X) ) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [X: $i] :
      ( cTEST(X)
    <=> ( cC12(X)
        & ~ cC8(X) ) ),
    inference(skolemize,[status(sab)],[7]) ).

tff(9,plain,
    ! [X: $i] :
      ( cTEST(X)
    <=> ~ ( cC8(X)
          | ~ cC12(X) ) ),
    inference(modus_ponens,[status(thm)],[8,4]) ).

tff(10,plain,
    ! [X: $i] :
      ( cTEST(X)
    <=> ~ ( cC8(X)
          | ~ cC12(X) ) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ~ ! [X: $i] :
          ( cTEST(X)
        <=> ~ ( cC8(X)
              | ~ cC12(X) ) )
    | ( cTEST(iV21080)
    <=> ~ ( cC8(iV21080)
          | ~ cC12(iV21080) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    ( cTEST(iV21080)
  <=> ~ ( cC8(iV21080)
        | ~ cC12(iV21080) ) ),
    inference(unit_resolution,[status(thm)],[11,10]) ).

tff(13,plain,
    ( cTEST(iV21080)
  <=> cTEST(iV21080) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,axiom,
    cTEST(iV21080),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).

tff(15,plain,
    cTEST(iV21080),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ( ~ ( cTEST(iV21080)
      <=> ~ ( cC8(iV21080)
            | ~ cC12(iV21080) ) )
    | ~ cTEST(iV21080)
    | ~ ( cC8(iV21080)
        | ~ cC12(iV21080) ) ),
    inference(tautology,[status(thm)],]) ).

tff(17,plain,
    ( ~ ( cTEST(iV21080)
      <=> ~ ( cC8(iV21080)
            | ~ cC12(iV21080) ) )
    | ~ ( cC8(iV21080)
        | ~ cC12(iV21080) ) ),
    inference(unit_resolution,[status(thm)],[16,15]) ).

tff(18,plain,
    ~ ( cC8(iV21080)
      | ~ cC12(iV21080) ),
    inference(unit_resolution,[status(thm)],[17,12]) ).

tff(19,plain,
    ^ [X: $i] :
      refl(
        ( ( cC10(X)
        <=> ~ ( ~ cC2(X)
              | ~ cC4(X) ) )
      <=> ( cC10(X)
        <=> ~ ( ~ cC2(X)
              | ~ cC4(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(20,plain,
    ( ! [X: $i] :
        ( cC10(X)
      <=> ~ ( ~ cC2(X)
            | ~ cC4(X) ) )
  <=> ! [X: $i] :
        ( cC10(X)
      <=> ~ ( ~ cC2(X)
            | ~ cC4(X) ) ) ),
    inference(quant_intro,[status(thm)],[19]) ).

tff(21,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cC10(X)
        <=> ( cC2(X)
            & cC4(X) ) )
      <=> ( cC10(X)
        <=> ~ ( ~ cC2(X)
              | ~ cC4(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [X: $i] :
        ( cC10(X)
      <=> ( cC2(X)
          & cC4(X) ) )
  <=> ! [X: $i] :
        ( cC10(X)
      <=> ~ ( ~ cC2(X)
            | ~ cC4(X) ) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [X: $i] :
        ( cC10(X)
      <=> ( cC2(X)
          & cC4(X) ) )
  <=> ! [X: $i] :
        ( cC10(X)
      <=> ( cC2(X)
          & cC4(X) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ! [X: $i] :
      ( cC10(X)
    <=> ( cC2(X)
        & cC4(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

tff(25,plain,
    ! [X: $i] :
      ( cC10(X)
    <=> ( cC2(X)
        & cC4(X) ) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [X: $i] :
      ( cC10(X)
    <=> ( cC2(X)
        & cC4(X) ) ),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [X: $i] :
      ( cC10(X)
    <=> ~ ( ~ cC2(X)
          | ~ cC4(X) ) ),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ! [X: $i] :
      ( cC10(X)
    <=> ~ ( ~ cC2(X)
          | ~ cC4(X) ) ),
    inference(modus_ponens,[status(thm)],[27,20]) ).

tff(29,plain,
    ( ~ ! [X: $i] :
          ( cC10(X)
        <=> ~ ( ~ cC2(X)
              | ~ cC4(X) ) )
    | ( cC10(iV21081)
    <=> ~ ( ~ cC2(iV21081)
          | ~ cC4(iV21081) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(30,plain,
    ( cC10(iV21081)
  <=> ~ ( ~ cC2(iV21081)
        | ~ cC4(iV21081) ) ),
    inference(unit_resolution,[status(thm)],[29,28]) ).

tff(31,plain,
    ( cC4(iV21081)
  <=> cC4(iV21081) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    cC4(iV21081),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).

tff(33,plain,
    cC4(iV21081),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ( cC2(iV21081)
  <=> cC2(iV21081) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,axiom,
    cC2(iV21081),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).

tff(36,plain,
    cC2(iV21081),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ( ~ ( ~ cC2(iV21081)
        | ~ cC4(iV21081) )
    | ~ cC2(iV21081)
    | ~ cC4(iV21081) ),
    inference(tautology,[status(thm)],]) ).

tff(38,plain,
    ~ ( ~ cC2(iV21081)
      | ~ cC4(iV21081) ),
    inference(unit_resolution,[status(thm)],[37,36,33]) ).

tff(39,plain,
    ( ~ ( cC10(iV21081)
      <=> ~ ( ~ cC2(iV21081)
            | ~ cC4(iV21081) ) )
    | cC10(iV21081)
    | ~ cC2(iV21081)
    | ~ cC4(iV21081) ),
    inference(tautology,[status(thm)],]) ).

tff(40,plain,
    ( ~ ( cC10(iV21081)
      <=> ~ ( ~ cC2(iV21081)
            | ~ cC4(iV21081) ) )
    | cC10(iV21081) ),
    inference(unit_resolution,[status(thm)],[39,38]) ).

tff(41,plain,
    cC10(iV21081),
    inference(unit_resolution,[status(thm)],[40,30]) ).

tff(42,plain,
    ( ~ ~ ( ~ cC12(iV21080)
          | ~ cC10(iV21081) )
  <=> ( ~ cC12(iV21080)
      | ~ cC10(iV21081) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(43,plain,
    ( ( cC12(iV21080)
      & cC10(iV21081) )
  <=> ~ ( ~ cC12(iV21080)
        | ~ cC10(iV21081) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ~ ( cC12(iV21080)
        & cC10(iV21081) )
  <=> ~ ~ ( ~ cC12(iV21080)
          | ~ cC10(iV21081) ) ),
    inference(monotonicity,[status(thm)],[43]) ).

tff(45,plain,
    ( ~ ( cC12(iV21080)
        & cC10(iV21081) )
  <=> ( ~ cC12(iV21080)
      | ~ cC10(iV21081) ) ),
    inference(transitivity,[status(thm)],[44,42]) ).

tff(46,plain,
    ( ~ ( cC12(iV21080)
        & cC10(iV21081) )
  <=> ~ ( cC12(iV21080)
        & cC10(iV21081) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iV21080)
        & cC12(iV21080)
        & cC10(iV21081)
        & cowlThing(iV21081) )
  <=> ~ ( cC12(iV21080)
        & cC10(iV21081) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(48,plain,
    ( ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iV21080)
      & cC12(iV21080)
      & cC10(iV21081)
      & cowlThing(iV21081) )
  <=> ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iV21080)
      & cC12(iV21080)
      & cC10(iV21081)
      & cowlThing(iV21081) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iV21080)
        & cC12(iV21080)
        & cC10(iV21081)
        & cowlThing(iV21081) )
  <=> ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iV21080)
        & cC12(iV21080)
        & cC10(iV21081)
        & cowlThing(iV21081) ) ),
    inference(monotonicity,[status(thm)],[48]) ).

tff(50,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iV21080)
        & cC12(iV21080)
        & cC10(iV21081)
        & cowlThing(iV21081) )
  <=> ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iV21080)
        & cC12(iV21080)
        & cC10(iV21081)
        & cowlThing(iV21081) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,axiom,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iV21080)
      & cC12(iV21080)
      & cC10(iV21081)
      & cowlThing(iV21081) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).

tff(52,plain,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iV21080)
      & cC12(iV21080)
      & cC10(iV21081)
      & cowlThing(iV21081) ),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iV21080)
      & cC12(iV21080)
      & cC10(iV21081)
      & cowlThing(iV21081) ),
    inference(modus_ponens,[status(thm)],[52,49]) ).

tff(54,plain,
    ~ ( cC12(iV21080)
      & cC10(iV21081) ),
    inference(modus_ponens,[status(thm)],[53,47]) ).

tff(55,plain,
    ~ ( cC12(iV21080)
      & cC10(iV21081) ),
    inference(modus_ponens,[status(thm)],[54,46]) ).

tff(56,plain,
    ( ~ cC12(iV21080)
    | ~ cC10(iV21081) ),
    inference(modus_ponens,[status(thm)],[55,45]) ).

tff(57,plain,
    ~ cC12(iV21080),
    inference(unit_resolution,[status(thm)],[56,41]) ).

tff(58,plain,
    ( cC8(iV21080)
    | ~ cC12(iV21080)
    | cC12(iV21080) ),
    inference(tautology,[status(thm)],]) ).

tff(59,plain,
    $false,
    inference(unit_resolution,[status(thm)],[58,57,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KRS152+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Sep  1 09:38:03 EDT 2022
% 0.12/0.34  % 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.
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------