TSTP Solution File: SYO450^3 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SYO450^3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% 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 : Mon Jun 24 20:51:29 EDT 2024

% Result   : Theorem 3.10s 1.76s
% Output   : Refutation 3.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   11 (   7 unt;   0 typ;   5 def)
%            Number of atoms       :   66 (   5 equ;   0 cnn)
%            Maximal formula atoms :   17 (   6 avg)
%            Number of connectives :   92 (  19   ~;  11   |;   0   &;  62   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :   14 (   5   ^   9   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).

thf(mreflexive_type,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(mreflexive_def,definition,
    ( mreflexive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i] : ( A @ B @ B ) ) ) ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid_def,definition,
    ( mvalid
    = ( '!' @ $i ) ) ).

thf(rel_m_type,type,
    rel_m: $i > $i > $o ).

thf(mbox_m_type,type,
    mbox_m: ( $i > $o ) > $i > $o ).

thf(mbox_m_def,definition,
    ( mbox_m
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_m @ B @ C )
          | ( A @ C ) ) ) ) ).

thf(mdia_m_type,type,
    mdia_m: ( $i > $o ) > $i > $o ).

thf(mdia_m_def,definition,
    ( mdia_m
    = ( ^ [A: $i > $o] : ( mnot @ ( mbox_m @ ( mnot @ A ) ) ) ) ) ).

thf(p_type,type,
    p: $i > $o ).

thf(q_type,type,
    q: $i > $o ).

thf(r_type,type,
    r: $i > $o ).

thf(1,conjecture,
    mvalid @ ( mimplies @ ( mbox_m @ ( mimplies @ p @ ( mdia_m @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_m @ ( mimplies @ q @ ( mimplies @ ( mbox_m @ p ) @ ( mdia_m @ r ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mimplies @ ( mbox_m @ ( mimplies @ p @ ( mdia_m @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_m @ ( mimplies @ q @ ( mimplies @ ( mbox_m @ p ) @ ( mdia_m @ r ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ~ ! [A: $i] :
        ( ~ ! [B: $i] :
              ( ~ ( rel_m @ A @ B )
              | ~ ( p @ B )
              | ~ ! [C: $i] :
                    ( ~ ( rel_m @ B @ C )
                    | ~ ( ~ ( q @ C )
                        | ( r @ C ) ) ) )
        | ~ ! [B: $i] :
              ( ~ ( rel_m @ A @ B )
              | ~ ( ~ ( q @ B )
                  | ~ ! [C: $i] :
                        ( ~ ( rel_m @ B @ C )
                        | ( p @ C ) )
                  | ~ ! [C: $i] :
                        ( ~ ( rel_m @ B @ C )
                        | ~ ( r @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    mreflexive @ rel_m,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).

thf(13,plain,
    ! [A: $i] : ( rel_m @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(17,plain,
    $false,
    inference(e,[status(thm)],[4,13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO450^3 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 09:37:10 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.95/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.43/1.07  % [INFO] 	 Parsing done (162ms). 
% 1.43/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.92/1.28  % [INFO] 	 eprover registered as external prover. 
% 1.92/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.27/1.39  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 2.27/1.41  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 2.27/1.41  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.27/1.42  % [INFO] 	 Type checking passed. 
% 2.27/1.42  % [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 ... 
% 3.10/1.75  % External prover 'e' found a proof!
% 3.10/1.75  % [INFO] 	 Killing All external provers ... 
% 3.10/1.75  % Time passed: 1235ms (effective reasoning time: 674ms)
% 3.10/1.75  % 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)>
% 3.10/1.76  % Axioms used in derivation (1): a1
% 3.10/1.76  % No. of inferences in proof: 6
% 3.10/1.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1235 ms resp. 674 ms w/o parsing
% 3.34/1.78  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.34/1.78  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------