TSTP Solution File: SYO460^3 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SYO460^3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n029.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 20:51:42 EDT 2024

% Result   : Theorem 3.10s 1.70s
% Output   : Refutation 3.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   12 (   8 unt;   0 typ;   6 def)
%            Number of atoms       :   60 (   6 equ;   0 cnn)
%            Maximal formula atoms :   13 (   5 avg)
%            Number of connectives :   75 (  14   ~;   8   |;   0   &;  53   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   14 (   8   ^   6   !;   0   ?;  14   :)

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

thf(mor_type,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mor_def,definition,
    ( mor
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          | ( B @ C ) ) ) ) ).

thf(mand_type,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).

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(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 @ ( mor @ ( mdia_m @ ( mand @ p @ q ) ) @ ( mdia_m @ ( mand @ p @ r ) ) ) @ ( mdia_m @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).

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

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

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

thf(12,plain,
    ! [A: $i] : ( rel_m @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,plain,
    $false,
    inference(e,[status(thm)],[4,12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYO460^3 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n029.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 10:50:25 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.00/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/1.05  % [INFO] 	 Parsing done (158ms). 
% 1.32/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.92/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.92/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.17/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 2.33/1.40  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 2.33/1.40  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.33/1.40  % [INFO] 	 Type checking passed. 
% 2.33/1.41  % [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 ... 
% 3.10/1.70  % External prover 'e' found a proof!
% 3.10/1.70  % [INFO] 	 Killing All external provers ... 
% 3.10/1.70  % Time passed: 1170ms (effective reasoning time: 636ms)
% 3.10/1.70  % 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)>
% 3.10/1.70  % Axioms used in derivation (1): a1
% 3.10/1.70  % No. of inferences in proof: 6
% 3.10/1.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1170 ms resp. 636 ms w/o parsing
% 3.10/1.74  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.10/1.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------