TSTP Solution File: KRS169+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : KRS169+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n019.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 17:45:03 EDT 2022

% Result   : Theorem 0.21s 0.39s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   32 (   6 unt;   8 typ;   0 def)
%            Number of atoms       :  111 (   0 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  123 (  37   ~;   3   |;  50   &)
%                                         (  33 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   6   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   40 (  38   !;   0   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
tff(rhasHead_type,type,
    rhasHead: ( $i * $i ) > $o ).

tff(iY_type,type,
    iY: $i ).

tff(iX_type,type,
    iX: $i ).

tff(rhasLeader_type,type,
    rhasLeader: ( $i * $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,
    ( ~ rhasHead(iX,iY)
  <=> ~ rhasHead(iX,iY) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iX)
        & rhasHead(iX,iY)
        & cowlThing(iY) )
  <=> ~ rhasHead(iX,iY) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iX)
      & rhasHead(iX,iY)
      & cowlThing(iY) )
  <=> ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iX)
      & rhasHead(iX,iY)
      & cowlThing(iY) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iX)
        & rhasHead(iX,iY)
        & cowlThing(iY) )
  <=> ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iX)
        & rhasHead(iX,iY)
        & cowlThing(iY) ) ),
    inference(monotonicity,[status(thm)],[3]) ).

tff(5,plain,
    ( ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iX)
        & rhasHead(iX,iY)
        & cowlThing(iY) )
  <=> ~ ( ! [X: $i] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X: $i] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) )
        & cowlThing(iX)
        & rhasHead(iX,iY)
        & cowlThing(iY) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iX)
      & rhasHead(iX,iY)
      & cowlThing(iY) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).

tff(7,plain,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iX)
      & rhasHead(iX,iY)
      & cowlThing(iY) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ~ ( ! [X: $i] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X: $i] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & cowlThing(iX)
      & rhasHead(iX,iY)
      & cowlThing(iY) ),
    inference(modus_ponens,[status(thm)],[7,4]) ).

tff(9,plain,
    ~ rhasHead(iX,iY),
    inference(modus_ponens,[status(thm)],[8,2]) ).

tff(10,plain,
    ~ rhasHead(iX,iY),
    inference(modus_ponens,[status(thm)],[9,1]) ).

tff(11,plain,
    ( rhasLeader(iX,iY)
  <=> rhasLeader(iX,iY) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    rhasLeader(iX,iY),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

tff(13,plain,
    rhasLeader(iX,iY),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ~ ( rhasLeader(iX,iY)
      <=> rhasHead(iX,iY) )
    | ~ rhasLeader(iX,iY)
    | rhasHead(iX,iY) ),
    inference(tautology,[status(thm)],]) ).

tff(15,plain,
    ~ ( rhasLeader(iX,iY)
    <=> rhasHead(iX,iY) ),
    inference(unit_resolution,[status(thm)],[14,13,10]) ).

tff(16,plain,
    ^ [X: $i,Y: $i] :
      refl(
        ( ( rhasLeader(X,Y)
        <=> rhasHead(X,Y) )
      <=> ( rhasLeader(X,Y)
        <=> rhasHead(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(17,plain,
    ( ! [X: $i,Y: $i] :
        ( rhasLeader(X,Y)
      <=> rhasHead(X,Y) )
  <=> ! [X: $i,Y: $i] :
        ( rhasLeader(X,Y)
      <=> rhasHead(X,Y) ) ),
    inference(quant_intro,[status(thm)],[16]) ).

tff(18,plain,
    ( ! [X: $i,Y: $i] :
        ( rhasLeader(X,Y)
      <=> rhasHead(X,Y) )
  <=> ! [X: $i,Y: $i] :
        ( rhasLeader(X,Y)
      <=> rhasHead(X,Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    ! [X: $i,Y: $i] :
      ( rhasLeader(X,Y)
    <=> rhasHead(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

tff(20,plain,
    ! [X: $i,Y: $i] :
      ( rhasLeader(X,Y)
    <=> rhasHead(X,Y) ),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ! [X: $i,Y: $i] :
      ( rhasLeader(X,Y)
    <=> rhasHead(X,Y) ),
    inference(skolemize,[status(sab)],[20]) ).

tff(22,plain,
    ! [X: $i,Y: $i] :
      ( rhasLeader(X,Y)
    <=> rhasHead(X,Y) ),
    inference(modus_ponens,[status(thm)],[21,17]) ).

tff(23,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( rhasLeader(X,Y)
        <=> rhasHead(X,Y) )
    | ( rhasLeader(iX,iY)
    <=> rhasHead(iX,iY) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(24,plain,
    $false,
    inference(unit_resolution,[status(thm)],[23,22,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KRS169+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n019.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 : Thu Sep  1 09:43:35 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.21/0.39  % SZS status Theorem
% 0.21/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------