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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n027.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 23:19:25 EDT 2024

% Result   : Theorem 4.27s 2.12s
% Output   : Refutation 4.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   70 (  16 unt;  12 typ;   0 def)
%            Number of atoms       :  206 (  29 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  393 ( 100   ~;  95   |;  30   &; 157   @)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :   32 (   0   ^  29   !;   3   ?;  32   :)

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

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

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

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

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/sandbox2/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(17,plain,
    ~ ( ! [A: $i] : ( cowlThing @ A )
      & ~ ? [A: $i] : ( cowlNothing @ A )
      & ! [A: $i] :
          ( ( xsd_string @ A )
         => ~ ( xsd_integer @ A ) )
      & ! [A: $i] :
          ( ~ ( xsd_integer @ A )
         => ( xsd_string @ A ) )
      & ( cowlThing @ ia )
      & ( cowlThing @ ib )
      & ( ia != ib ) ),
    inference(miniscope,[status(thm)],[16]) ).

thf(21,plain,
    ( ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ ( cowlThing @ ia )
    | ~ ( cowlThing @ ib )
    | ( ia = ib ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(25,plain,
    ( ( ib = ia )
    | ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ ( cowlThing @ ia )
    | ~ ( cowlThing @ ib ) ),
    inference(lifteq,[status(thm)],[21]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

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

thf(51,plain,
    ( ! [A: $i] : ( cowlThing @ A )
    & ~ ? [A: $i] : ( cowlNothing @ A ) ),
    inference(miniscope,[status(thm)],[50]) ).

thf(53,plain,
    ! [A: $i] : ( cowlThing @ A ),
    inference(cnf,[status(esa)],[51]) ).

thf(52,plain,
    ! [A: $i] :
      ~ ( cowlNothing @ A ),
    inference(cnf,[status(esa)],[51]) ).

thf(54,plain,
    ! [A: $i] :
      ~ ( cowlNothing @ A ),
    inference(simp,[status(thm)],[52]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( xsd_string @ A )
    <=> ~ ( xsd_integer @ A ) ),
    file('/export/starexec/sandbox2/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(56,plain,
    ( ! [A: $i] :
        ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
    & ! [A: $i] :
        ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(miniscope,[status(thm)],[55]) ).

thf(57,plain,
    ! [A: $i] :
      ( ( xsd_integer @ A )
      | ( xsd_string @ A ) ),
    inference(cnf,[status(esa)],[56]) ).

thf(59,plain,
    ! [A: $i] :
      ( ( xsd_integer @ A )
      | ( xsd_string @ A ) ),
    inference(simp,[status(thm)],[57]) ).

thf(18,plain,
    ( ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ ( cowlThing @ ia )
    | ~ ( cowlThing @ ib )
    | ( ia = ib ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(22,plain,
    ( ( ib = ia )
    | ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ ( cowlThing @ ia )
    | ~ ( cowlThing @ ib ) ),
    inference(lifteq,[status(thm)],[18]) ).

thf(69,plain,
    ( ( ib = ia )
    | ~ $true
    | $false
    | ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[22,53,54]) ).

thf(70,plain,
    ( ( ib = ia )
    | ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 ) ),
    inference(simp,[status(thm)],[69]) ).

thf(81,plain,
    ! [A: $i] :
      ( ( xsd_string @ A )
      | ( ib = ia )
      | ( xsd_string @ sk3 )
      | ( ( xsd_integer @ A )
       != ( xsd_integer @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[59,70]) ).

thf(82,plain,
    ( ( xsd_string @ sk4 )
    | ( ib = ia )
    | ( xsd_string @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( sk4 ))]]) ).

thf(13,axiom,
    cB @ ib,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

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

thf(11,axiom,
    cA @ ia,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

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

thf(15,axiom,
    ! [A: $i] :
      ~ ( ( cB @ A )
        & ( cA @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

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

thf(65,plain,
    ~ ? [A: $i] :
        ( ( cB @ A )
        & ( cA @ A ) ),
    inference(miniscope,[status(thm)],[64]) ).

thf(66,plain,
    ! [A: $i] :
      ( ~ ( cB @ A )
      | ~ ( cA @ A ) ),
    inference(cnf,[status(esa)],[65]) ).

thf(87,plain,
    ! [A: $i] :
      ( ~ ( cB @ A )
      | ( ( cA @ ia )
       != ( cA @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[60,66]) ).

thf(88,plain,
    ~ ( cB @ ia ),
    inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( ia ))]]) ).

thf(95,plain,
    ( ( cB @ ib )
   != ( cB @ ia ) ),
    inference(paramod_ordered,[status(thm)],[62,88]) ).

thf(96,plain,
    ib != ia,
    inference(simp,[status(thm)],[95]) ).

thf(105,plain,
    ( ( xsd_string @ sk4 )
    | ( xsd_string @ sk3 ) ),
    inference(simplifyReflect,[status(thm)],[82,96]) ).

thf(19,plain,
    ( ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ ( cowlThing @ ia )
    | ~ ( cowlThing @ ib )
    | ( ia = ib ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(23,plain,
    ( ( ib = ia )
    | ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ ( cowlThing @ ia )
    | ~ ( cowlThing @ ib ) ),
    inference(lifteq,[status(thm)],[19]) ).

thf(73,plain,
    ( ( ib = ia )
    | ~ $true
    | $false
    | ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[23,53,54]) ).

thf(74,plain,
    ( ( ib = ia )
    | ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 ) ),
    inference(simp,[status(thm)],[73]) ).

thf(103,plain,
    ( ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 ) ),
    inference(simplifyReflect,[status(thm)],[74,96]) ).

thf(113,plain,
    ( ( xsd_string @ sk3 )
    | ( ( xsd_string @ sk4 )
     != ( xsd_string @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[105,103]) ).

thf(114,plain,
    xsd_string @ sk3,
    inference(pattern_uni,[status(thm)],[113:[]]) ).

thf(58,plain,
    ! [A: $i] :
      ( ~ ( xsd_string @ A )
      | ~ ( xsd_integer @ A ) ),
    inference(cnf,[status(esa)],[56]) ).

thf(120,plain,
    ! [A: $i] :
      ( ~ ( xsd_integer @ A )
      | ( ( xsd_string @ sk3 )
       != ( xsd_string @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[114,58]) ).

thf(121,plain,
    ~ ( xsd_integer @ sk3 ),
    inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( sk3 ))]]) ).

thf(20,plain,
    ( ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ ( cowlThing @ ia )
    | ~ ( cowlThing @ ib )
    | ( ia = ib ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(24,plain,
    ( ( ib = ia )
    | ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ ( cowlThing @ ia )
    | ~ ( cowlThing @ ib ) ),
    inference(lifteq,[status(thm)],[20]) ).

thf(115,plain,
    ( ( ib = ia )
    | ~ $true
    | $false
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[24,53,54]) ).

thf(116,plain,
    ( ( ib = ia )
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_integer @ sk4 ) ),
    inference(simp,[status(thm)],[115]) ).

thf(117,plain,
    ( ( xsd_integer @ sk3 )
    | ~ ( xsd_integer @ sk4 ) ),
    inference(simplifyReflect,[status(thm)],[116,96]) ).

thf(122,plain,
    ( $false
    | ~ ( xsd_integer @ sk4 ) ),
    inference(rewrite,[status(thm)],[117,121]) ).

thf(123,plain,
    ~ ( xsd_integer @ sk4 ),
    inference(simp,[status(thm)],[122]) ).

thf(126,plain,
    ! [A: $i] :
      ( ( xsd_string @ A )
      | ( ( xsd_integer @ A )
       != ( xsd_integer @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[59,123]) ).

thf(127,plain,
    xsd_string @ sk4,
    inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( sk4 ))]]) ).

thf(138,plain,
    ( ( ib = ia )
    | ~ $true
    | $false
    | $false
    | ~ $true
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[25,53,54,121,127]) ).

thf(139,plain,
    ib = ia,
    inference(simp,[status(thm)],[138]) ).

thf(140,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[139,96]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : KRS163+1 : TPTP v8.2.0. Released v3.1.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat May 18 22:25:09 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.84/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.12/0.97  % [INFO] 	 Parsing done (118ms). 
% 1.12/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.57/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ... 
% 1.79/1.31  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 1.92/1.33  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.92/1.33  % [INFO] 	 Type checking passed. 
% 1.92/1.34  % [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 ... 
% 4.27/2.11  % [INFO] 	 Killing All external provers ... 
% 4.27/2.11  % Time passed: 1634ms (effective reasoning time: 1131ms)
% 4.27/2.11  % 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)>
% 4.27/2.12  % Axioms used in derivation (5): axiom_2, axiom_6, axiom_1, axiom_0, axiom_4
% 4.27/2.12  % No. of inferences in proof: 58
% 4.27/2.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1634 ms resp. 1131 ms w/o parsing
% 4.27/2.18  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.27/2.18  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------