TSTP Solution File: KRS180+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : KRS180+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 23:19:28 EDT 2024

% Result   : Timeout 290.30s 53.71s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   60 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :  173 (   7 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  609 (  75   ~;  48   |;  21   &; 426   @)
%                                         (   4 <=>;  34  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   14 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  175 (   0   ^ 154   !;  21   ?; 175   :)

% Comments : 
%------------------------------------------------------------------------------
thf(status_type,type,
    status: $i > $i > $i > $o ).

thf(isa_type,type,
    isa: $i > $i > $o ).

thf(nota_type,type,
    nota: $i > $i > $o ).

thf(nevera_type,type,
    nevera: $i > $i > $o ).

thf(xora_type,type,
    xora: $i > $i > $o ).

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

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

thf(sk7_type,type,
    sk7: $i > $i > $i ).

thf(sk8_type,type,
    sk8: $i > $i > $i ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
    ? [C: $i,D: $i] :
      ( ( status @ C @ D @ A )
     => ~ ( ( isa @ A @ B )
          & ( ( nota @ A @ B )
            | ( nevera @ A @ B )
            | ( xora @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa_exclusive) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
      ? [C: $i,D: $i] :
        ( ( status @ C @ D @ A )
       => ~ ( ( isa @ A @ B )
            & ( ( nota @ A @ B )
              | ( nevera @ A @ B )
              | ( xora @ A @ B ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(16,plain,
    ~ ! [A: $i,B: $i] :
      ? [C: $i,D: $i] :
        ( ( status @ C @ D @ A )
       => ~ ( ( isa @ A @ B )
            & ( ( nota @ A @ B )
              | ( nevera @ A @ B )
              | ( xora @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(17,plain,
    ~ ! [A: $i] :
        ( ! [B: $i,C: $i] : ( status @ B @ C @ A )
       => ~ ? [B: $i] :
              ( ( isa @ A @ B )
              & ( ( nota @ A @ B )
                | ( nevera @ A @ B )
                | ( xora @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[16]) ).

thf(19,plain,
    isa @ sk1 @ sk2,
    inference(cnf,[status(esa)],[17]) ).

thf(20,plain,
    ! [B: $i,A: $i] : ( status @ A @ B @ sk1 ),
    inference(cnf,[status(esa)],[17]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( status @ C @ D @ A )
         => ( status @ C @ D @ B ) )
    <=> ( isa @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isa) ).

thf(28,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
           => ( status @ C @ D @ B ) )
       => ( isa @ A @ B ) )
      & ( ( isa @ A @ B )
       => ! [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
           => ( status @ C @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(29,plain,
    ( ! [A: $i,B: $i] :
        ( ! [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
           => ( status @ C @ D @ B ) )
       => ( isa @ A @ B ) )
    & ! [A: $i,B: $i] :
        ( ( isa @ A @ B )
       => ! [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
           => ( status @ C @ D @ B ) ) ) ),
    inference(miniscope,[status(thm)],[28]) ).

thf(30,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( isa @ A @ B )
      | ~ ( status @ C @ D @ A )
      | ( status @ C @ D @ B ) ),
    inference(cnf,[status(esa)],[29]) ).

thf(33,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( isa @ A @ B )
      | ~ ( status @ C @ D @ A )
      | ( status @ C @ D @ B ) ),
    inference(simp,[status(thm)],[30]) ).

thf(317,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( isa @ C @ D )
      | ( status @ E @ F @ D )
      | ( ( status @ A @ B @ sk1 )
       != ( status @ E @ F @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[20,33]) ).

thf(318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( isa @ sk1 @ C )
      | ( status @ A @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).

thf(347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( isa @ sk1 @ C )
      | ( status @ A @ B @ C ) ),
    inference(simp,[status(thm)],[318]) ).

thf(1826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( status @ A @ B @ C )
      | ( ( isa @ sk1 @ sk2 )
       != ( isa @ sk1 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[19,347]) ).

thf(1827,plain,
    ! [B: $i,A: $i] : ( status @ A @ B @ sk2 ),
    inference(pattern_uni,[status(thm)],[1826:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( status @ C @ D @ A )
        <~> ( status @ C @ D @ B ) )
    <=> ( xora @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xora) ).

thf(47,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ~ ( ( ( status @ C @ D @ A )
               => ( status @ C @ D @ B ) )
              & ( ( status @ C @ D @ A )
                | ~ ( status @ C @ D @ B ) ) )
       => ( xora @ A @ B ) )
      & ( ( xora @ A @ B )
       => ! [C: $i,D: $i] :
            ~ ( ( ( status @ C @ D @ A )
               => ( status @ C @ D @ B ) )
              & ( ( status @ C @ D @ A )
                | ~ ( status @ C @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(48,plain,
    ( ! [A: $i,B: $i] :
        ( ~ ? [C: $i,D: $i] :
              ( ( ( status @ C @ D @ A )
               => ( status @ C @ D @ B ) )
              & ( ( status @ C @ D @ A )
                | ~ ( status @ C @ D @ B ) ) )
       => ( xora @ A @ B ) )
    & ! [A: $i,B: $i] :
        ( ( xora @ A @ B )
       => ~ ? [C: $i,D: $i] :
              ( ( ( status @ C @ D @ A )
               => ( status @ C @ D @ B ) )
              & ( ( status @ C @ D @ A )
                | ~ ( status @ C @ D @ B ) ) ) ) ),
    inference(miniscope,[status(thm)],[47]) ).

thf(49,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( xora @ A @ B )
      | ~ ( status @ C @ D @ B )
      | ~ ( status @ C @ D @ A ) ),
    inference(cnf,[status(esa)],[48]) ).

thf(58,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( xora @ A @ B )
      | ~ ( status @ C @ D @ B )
      | ~ ( status @ C @ D @ A ) ),
    inference(simp,[status(thm)],[49]) ).

thf(1499,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( xora @ C @ D )
      | ~ ( status @ E @ F @ D )
      | ( ( status @ A @ B @ sk1 )
       != ( status @ E @ F @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[20,58]) ).

thf(1500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( xora @ sk1 @ C )
      | ~ ( status @ A @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[1499:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( xora @ sk1 @ C )
      | ~ ( status @ A @ B @ C ) ),
    inference(simp,[status(thm)],[1500]) ).

thf(85343,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( xora @ sk1 @ E )
      | ( ( status @ A @ B @ sk2 )
       != ( status @ C @ D @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[1827,1556]) ).

thf(85344,plain,
    ~ ( xora @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[85343:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( sk2 ))]]) ).

thf(18,plain,
    ( ( nota @ sk1 @ sk2 )
    | ( nevera @ sk1 @ sk2 )
    | ( xora @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ? [C: $i,D: $i] :
          ( ( status @ C @ D @ A )
          & ~ ( status @ C @ D @ B ) )
    <=> ( nota @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nota) ).

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

thf(35,plain,
    ( ! [A: $i,B: $i] :
        ( ? [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
            & ~ ( status @ C @ D @ B ) )
       => ( nota @ A @ B ) )
    & ! [A: $i,B: $i] :
        ( ( nota @ A @ B )
       => ? [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
            & ~ ( status @ C @ D @ B ) ) ) ),
    inference(miniscope,[status(thm)],[34]) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ~ ( nota @ A @ B )
      | ~ ( status @ ( sk7 @ B @ A ) @ ( sk8 @ B @ A ) @ B ) ),
    inference(cnf,[status(esa)],[35]) ).

thf(40,plain,
    ! [B: $i,A: $i] :
      ( ~ ( nota @ A @ B )
      | ~ ( status @ ( sk7 @ B @ A ) @ ( sk8 @ B @ A ) @ B ) ),
    inference(simp,[status(thm)],[37]) ).

thf(1935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( nota @ C @ D )
      | ( ( status @ A @ B @ sk2 )
       != ( status @ ( sk7 @ D @ C ) @ ( sk8 @ D @ C ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1827,40]) ).

thf(1936,plain,
    ! [A: $i] :
      ~ ( nota @ A @ sk2 ),
    inference(pattern_uni,[status(thm)],[1935:[bind(A,$thf( sk7 @ sk2 @ H )),bind(B,$thf( sk8 @ sk2 @ H )),bind(C,$thf( H )),bind(D,$thf( sk2 ))]]) ).

thf(1948,plain,
    ! [A: $i] :
      ~ ( nota @ A @ sk2 ),
    inference(simp,[status(thm)],[1936]) ).

thf(2071,plain,
    ( $false
    | ( nevera @ sk1 @ sk2 )
    | ( xora @ sk1 @ sk2 ) ),
    inference(rewrite,[status(thm)],[18,1948]) ).

thf(2072,plain,
    ( ( nevera @ sk1 @ sk2 )
    | ( xora @ sk1 @ sk2 ) ),
    inference(simp,[status(thm)],[2071]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( status @ C @ D @ A )
         => ~ ( status @ C @ D @ B ) )
    <=> ( nevera @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nevera) ).

thf(41,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
           => ~ ( status @ C @ D @ B ) )
       => ( nevera @ A @ B ) )
      & ( ( nevera @ A @ B )
       => ! [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
           => ~ ( status @ C @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(42,plain,
    ( ! [A: $i,B: $i] :
        ( ! [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
           => ~ ( status @ C @ D @ B ) )
       => ( nevera @ A @ B ) )
    & ! [A: $i,B: $i] :
        ( ( nevera @ A @ B )
       => ! [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
           => ~ ( status @ C @ D @ B ) ) ) ),
    inference(miniscope,[status(thm)],[41]) ).

thf(43,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( nevera @ A @ B )
      | ~ ( status @ C @ D @ A )
      | ~ ( status @ C @ D @ B ) ),
    inference(cnf,[status(esa)],[42]) ).

thf(46,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( nevera @ A @ B )
      | ~ ( status @ C @ D @ A )
      | ~ ( status @ C @ D @ B ) ),
    inference(simp,[status(thm)],[43]) ).

thf(965,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( nevera @ C @ D )
      | ~ ( status @ E @ F @ D )
      | ( ( status @ A @ B @ sk1 )
       != ( status @ E @ F @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[20,46]) ).

thf(966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( nevera @ sk1 @ C )
      | ~ ( status @ A @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[965:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).

thf(1008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( nevera @ sk1 @ C )
      | ~ ( status @ A @ B @ C ) ),
    inference(simp,[status(thm)],[966]) ).

thf(32958,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( nevera @ sk1 @ E )
      | ( ( status @ A @ B @ sk2 )
       != ( status @ C @ D @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[1827,1008]) ).

thf(32959,plain,
    ~ ( nevera @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[32958:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( sk2 ))]]) ).

thf(33002,plain,
    ( $false
    | ( xora @ sk1 @ sk2 ) ),
    inference(rewrite,[status(thm)],[2072,32959]) ).

thf(33003,plain,
    xora @ sk1 @ sk2,
    inference(simp,[status(thm)],[33002]) ).

thf(85440,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[85344,33003]) ).

thf(85441,plain,
    $false,
    inference(simp,[status(thm)],[85440]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : KRS180+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n017.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Sat May 18 22:12:39 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.96/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.22/1.07  % [INFO] 	 Parsing done (159ms). 
% 1.22/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.90/1.43  % [INFO] 	 nitpick registered as external prover. 
% 1.90/1.43  % [INFO] 	 Scanning for conjecture ... 
% 2.02/1.53  % [INFO] 	 Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ... 
% 2.17/1.57  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 2.17/1.61  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.33/1.61  % [INFO] 	 Type checking passed. 
% 2.33/1.62  % [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 ... 
% 290.30/53.71  % [INFO] 	 Killing All external provers ... 
% 290.30/53.72  % Time passed: 53255ms (effective reasoning time: 52632ms)
% 290.30/53.72  % 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)>
% 290.30/53.72  % Axioms used in derivation (4): isa, xora, nota, nevera
% 290.30/53.72  % No. of inferences in proof: 51
% 290.30/53.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 53255 ms resp. 52632 ms w/o parsing
% 290.30/53.76  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 290.30/53.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------