TSTP Solution File: SYO068^4.001 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 : Tue May 21 08:55:41 EDT 2024

% Result   : Theorem 2.77s 1.54s
% Output   : Refutation 2.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   21 (   8 unt;   6 typ;   3 def)
%            Number of atoms       :   46 (   3 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :   62 (   4   ~;   2   |;   2   &;  48   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   18 (   3   ^  15   !;   0   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
thf(irel_type,type,
    irel: $i > $i > $o ).

thf(iatom_type,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(iatom_def,definition,
    ( iatom
    = ( ^ [A: $i > $o] : A ) ) ).

thf(iimplies_type,type,
    iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(iimplies_def,definition,
    ( iimplies
    = ( ^ [A: $i > $o,B: $i > $o] : ( mimplies @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).

thf(ivalid_type,type,
    ivalid: ( $i > $o ) > $o ).

thf(ivalid_def,definition,
    ( ivalid
    = ( '!' @ $i ) ) ).

thf(p0_type,type,
    p0: $i > $o ).

thf(p1_type,type,
    p1: $i > $o ).

thf(3,axiom,
    ! [A: $i] : ( irel @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).

thf(9,plain,
    ! [A: $i] : ( irel @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ivalid @ ( iatom @ p1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).

thf(13,plain,
    ! [A: $i] : ( p1 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1,conjecture,
    ivalid @ ( iatom @ p0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( ivalid @ ( iatom @ p0 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ! [A: $i] : ( p0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(11,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( irel @ A @ B )
        & ( irel @ B @ C ) )
     => ( irel @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).

thf(15,plain,
    ! [A: $i] :
      ( ~ ! [B: $i] :
            ( ( irel @ A @ B )
           => ( p1 @ B ) )
      | ! [B: $i] :
          ( ( irel @ A @ B )
         => ( ~ ! [C: $i] :
                  ( ( irel @ B @ C )
                 => ( p1 @ C ) )
            | ! [C: $i] :
                ( ( irel @ B @ C )
               => ( p0 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(20,plain,
    $false,
    inference(cvc4,[status(thm)],[9,13,7,11,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon May 20 10:41:39 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.94/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.97  % [INFO] 	 Parsing done (121ms). 
% 1.19/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.73/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.73/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.73/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.93/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.05/1.27  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.05/1.28  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.05/1.28  % [INFO] 	 Type checking passed. 
% 2.05/1.28  % [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 ... 
% 2.77/1.54  % External prover 'cvc4' found a proof!
% 2.77/1.54  % [INFO] 	 Killing All external provers ... 
% 2.77/1.54  % Time passed: 1024ms (effective reasoning time: 559ms)
% 2.77/1.54  % 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)>
% 2.77/1.54  % Axioms used in derivation (4): refl_axiom, axiom1, trans_axiom, axiom2
% 2.77/1.54  % No. of inferences in proof: 12
% 2.77/1.54  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1024 ms resp. 559 ms w/o parsing
% 2.96/1.61  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.96/1.61  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------