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

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%------------------------------------------------------------------------------
% File     : Leo-III---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 : n013.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 23:18:39 EDT 2024

% Result   : Theorem 5.78s 3.43s
% Output   : Refutation 6.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   38 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :  111 (   0 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  378 (  34   ~;  11   |;  36   &; 263   @)
%                                         (   6 <=>;  26  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   14 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   8 usr;   1 con; 0-3 aty)
%            Number of variables   :  112 (   0   ^  58   !;  54   ?; 112   :)

% 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(mighta_type,type,
    mighta: $i > $i > $o ).

thf(model_type,type,
    model: $i > $i > $o ).

thf(not_type,type,
    not: $i > $i ).

thf(14,axiom,
    ? [A: $i,B: $i] :
      ( ? [C: $i] : ( model @ C @ A )
      & ! [C: $i] :
          ( ( model @ C @ A )
         => ( model @ C @ B ) )
      & ? [C: $i] :
          ( ~ ( model @ C @ A )
          & ( model @ C @ B ) )
      & ? [C: $i] :
          ~ ( model @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mixed_pair) ).

thf(84,plain,
    ? [A: $i,B: $i] :
      ( ? [C: $i] : ( model @ C @ A )
      & ! [C: $i] :
          ( ( model @ C @ A )
         => ( model @ C @ B ) )
      & ? [C: $i] :
          ( ~ ( model @ C @ A )
          & ( model @ C @ B ) )
      & ? [C: $i] :
          ~ ( model @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( model @ A @ B )
    <=> ~ ( model @ A @ ( not @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not) ).

thf(65,plain,
    ! [A: $i,B: $i] :
      ( ( ( model @ A @ B )
       => ~ ( model @ A @ ( not @ B ) ) )
      & ( ~ ( model @ A @ ( not @ B ) )
       => ( model @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

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/sandbox/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(5,axiom,
    ! [A: $i,B: $i] :
      ( ? [C: $i,D: $i] :
          ( ( status @ C @ D @ A )
          & ~ ( status @ C @ D @ B ) )
    <=> ( nota @ A @ B ) ),
    file('/export/starexec/sandbox/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(8,axiom,
    ! [A: $i,B: $i] :
      ( ( model @ A @ B )
    <~> ( model @ A @ ( not @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',completeness) ).

thf(59,plain,
    ! [A: $i,B: $i] :
      ~ ( ( ( model @ A @ B )
         => ( model @ A @ ( not @ B ) ) )
        & ( ( model @ A @ B )
          | ~ ( model @ A @ ( not @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(12,axiom,
    ? [A: $i] :
    ! [B: $i] :
      ~ ( model @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',contradiction) ).

thf(76,plain,
    ? [A: $i] :
    ! [B: $i] :
      ~ ( model @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(15,axiom,
    ? [A: $i,B: $i,C: $i] :
      ( ( model @ A @ B )
      & ~ ( model @ A @ C )
      & ? [D: $i] : ( model @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_thm_spt) ).

thf(91,plain,
    ? [A: $i,B: $i,C: $i] :
      ( ( model @ A @ B )
      & ~ ( model @ A @ C )
      & ? [D: $i] : ( model @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

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/sandbox/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(11,axiom,
    ? [A: $i] :
      ( ? [B: $i] : ( model @ B @ A )
      & ? [B: $i] :
          ~ ( model @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satisfiable) ).

thf(72,plain,
    ? [A: $i] :
      ( ? [B: $i] : ( model @ B @ A )
      & ? [B: $i] :
          ~ ( model @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(13,axiom,
    ? [A: $i,B: $i] :
      ( ? [C: $i] :
          ( ( model @ C @ A )
          & ( model @ C @ B ) )
      & ? [C: $i] :
          ( ~ ( model @ C @ A )
          | ~ ( model @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sat_non_taut_pair) ).

thf(79,plain,
    ? [A: $i,B: $i] :
      ( ? [C: $i] :
          ( ( model @ C @ A )
          & ( model @ C @ B ) )
      & ? [C: $i] :
          ( ~ ( model @ C @ A )
          | ~ ( model @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

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/sandbox/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(4,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( status @ C @ D @ A )
         => ( status @ C @ D @ B ) )
    <=> ( isa @ A @ B ) ),
    file('/export/starexec/sandbox/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(10,axiom,
    ? [A: $i] :
    ! [B: $i] : ( model @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tautology) ).

thf(70,plain,
    ? [A: $i] :
    ! [B: $i] : ( model @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ? [C: $i,D: $i] :
          ( ( status @ C @ D @ A )
          & ( status @ C @ D @ B ) )
    <=> ( mighta @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta) ).

thf(21,plain,
    ! [A: $i,B: $i] :
      ( ( ? [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
            & ( status @ C @ D @ B ) )
       => ( mighta @ A @ B ) )
      & ( ( mighta @ A @ B )
       => ? [C: $i,D: $i] :
            ( ( status @ C @ D @ A )
            & ( status @ C @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(96,plain,
    $false,
    inference(e,[status(thm)],[84,65,41,34,59,76,91,16,72,79,47,28,70,21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15  % Problem  : KRS180+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.17/0.18  % Command  : run_Leo-III %s %d
% 0.18/0.40  % Computer : n013.cluster.edu
% 0.18/0.40  % Model    : x86_64 x86_64
% 0.18/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40  % Memory   : 8042.1875MB
% 0.18/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40  % CPULimit : 300
% 0.18/0.40  % WCLimit  : 300
% 0.18/0.40  % DateTime : Sat May 18 22:12:39 EDT 2024
% 0.18/0.41  % CPUTime  : 
% 1.41/1.32  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.98/1.54  % [INFO] 	 Parsing done (218ms). 
% 1.98/1.56  % [INFO] 	 Running in sequential loop mode. 
% 2.84/2.08  % [INFO] 	 eprover registered as external prover. 
% 2.84/2.09  % [INFO] 	 cvc4 registered as external prover. 
% 2.84/2.10  % [INFO] 	 Scanning for conjecture ... 
% 3.05/2.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ... 
% 3.16/2.29  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 3.28/2.35  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.47/2.36  % [INFO] 	 Type checking passed. 
% 3.47/2.36  % [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 ... 
% 5.78/3.42  % External prover 'e' found a proof!
% 5.78/3.42  % [INFO] 	 Killing All external provers ... 
% 5.78/3.42  % Time passed: 2817ms (effective reasoning time: 1856ms)
% 5.78/3.42  % 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)>
% 5.78/3.43  % Axioms used in derivation (13): completeness, nevera, contradiction, nota, mighta, isa, sat_non_taut_pair, satisfiable, mixed_pair, tautology, non_thm_spt, xora, not
% 5.78/3.43  % No. of inferences in proof: 30
% 5.78/3.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2817 ms resp. 1856 ms w/o parsing
% 6.29/3.52  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.29/3.52  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------