TSTP Solution File: KRS163+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : KRS163+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 : Mon May 20 23:18:36 EDT 2024

% Result   : Theorem 4.04s 2.53s
% Output   : Refutation 4.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   38 (   9 unt;   8 typ;   0 def)
%            Number of atoms       :   82 (  15 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  137 (  19   ~;   0   |;  33   &;  66   @)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (   0   ^  36   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cowlThing_type,type,
    cowlThing: $i > $o ).

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

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

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

thf(ia_type,type,
    ia: $i ).

thf(ib_type,type,
    ib: $i ).

thf(cA_type,type,
    cA: $i > $o ).

thf(cB_type,type,
    cB: $i > $o ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_integer @ A ) )
     => ( xsd_integer @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).

thf(42,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_integer @ A ) )
     => ( xsd_integer @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_string @ A ) )
     => ( xsd_string @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xsd_string_substitution_1) ).

thf(46,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_string @ A ) )
     => ( xsd_string @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(12,axiom,
    cowlThing @ ia,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

thf(61,plain,
    cowlThing @ ia,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(11,axiom,
    cA @ ia,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

thf(60,plain,
    cA @ ia,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlThing @ A ) )
     => ( cowlThing @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).

thf(38,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlThing @ A ) )
     => ( cowlThing @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(14,axiom,
    cowlThing @ ib,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

thf(63,plain,
    cowlThing @ ib,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cB @ A ) )
     => ( cB @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cB_substitution_1) ).

thf(30,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cB @ A ) )
     => ( cB @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,axiom,
    cB @ ib,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

thf(62,plain,
    cB @ ib,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlNothing @ A ) )
     => ( cowlNothing @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).

thf(34,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlNothing @ A ) )
     => ( cowlNothing @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(15,axiom,
    ! [A: $i] :
      ~ ( ( cB @ A )
        & ( cA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

thf(64,plain,
    ! [A: $i] :
      ~ ( ( cB @ A )
        & ( cA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).

thf(50,plain,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1,conjecture,
    ( ! [A: $i] :
        ( ( cowlThing @ A )
        & ~ ( cowlNothing @ A ) )
    & ! [A: $i] :
        ( ( xsd_string @ A )
      <=> ~ ( xsd_integer @ A ) )
    & ( cowlThing @ ia )
    & ( cowlThing @ ib )
    & ( ia != ib ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( xsd_string @ A )
        <=> ~ ( xsd_integer @ A ) )
      & ( cowlThing @ ia )
      & ( cowlThing @ ib )
      & ( ia != ib ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(16,plain,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( ( xsd_string @ A )
           => ~ ( xsd_integer @ A ) )
          & ( ~ ( xsd_integer @ A )
           => ( xsd_string @ A ) ) )
      & ( cowlThing @ ia )
      & ( cowlThing @ ib )
      & ( ia != ib ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cA @ A ) )
     => ( cA @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cA_substitution_1) ).

thf(26,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cA @ A ) )
     => ( cA @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( xsd_string @ A )
    <=> ~ ( xsd_integer @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

thf(55,plain,
    ! [A: $i] :
      ( ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
      & ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(67,plain,
    $false,
    inference(e,[status(thm)],[42,46,61,60,38,63,30,62,34,64,50,16,26,55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : KRS163+1 : TPTP v8.2.0. Released v3.1.0.
% 0.03/0.16  % Command  : run_Leo-III %s %d
% 0.13/0.37  % Computer : n002.cluster.edu
% 0.13/0.37  % Model    : x86_64 x86_64
% 0.13/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37  % Memory   : 8042.1875MB
% 0.13/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit : 300
% 0.13/0.37  % WCLimit  : 300
% 0.13/0.37  % DateTime : Sat May 18 22:25:09 EDT 2024
% 0.13/0.37  % CPUTime  : 
% 1.11/1.08  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.48/1.26  % [INFO] 	 Parsing done (176ms). 
% 1.57/1.27  % [INFO] 	 Running in sequential loop mode. 
% 2.17/1.68  % [INFO] 	 eprover registered as external prover. 
% 2.17/1.68  % [INFO] 	 cvc4 registered as external prover. 
% 2.17/1.69  % [INFO] 	 Scanning for conjecture ... 
% 2.35/1.79  % [INFO] 	 Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ... 
% 2.44/1.84  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 2.50/1.86  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.50/1.87  % [INFO] 	 Type checking passed. 
% 2.50/1.87  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 4.04/2.52  % External prover 'e' found a proof!
% 4.04/2.52  % [INFO] 	 Killing All external provers ... 
% 4.04/2.52  % Time passed: 1985ms (effective reasoning time: 1244ms)
% 4.04/2.52  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.04/2.53  % Axioms used in derivation (13): cA_substitution_1, axiom_2, xsd_string_substitution_1, axiom_6, cowlThing_substitution_1, axiom_3, axiom_5, axiom_0, axiom_4, cowlNothing_substitution_1, cB_substitution_1, axiom_1, xsd_integer_substitution_1
% 4.04/2.53  % No. of inferences in proof: 30
% 4.04/2.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1985 ms resp. 1244 ms w/o parsing
% 4.17/2.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.17/2.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------