TSTP Solution File: SYO462^5 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO462^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 08:56:59 EDT 2024

% Result   : Theorem 3.34s 2.22s
% Output   : Refutation 3.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   24 (   8 unt;  10 typ;   6 def)
%            Number of atoms       :   63 (   6 equ;   0 cnn)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  104 (  19   ~;  13   |;   2   &;  68   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :   22 (   7   ^  15   !;   0   ?;  22   :)

% 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(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ 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(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(mtransitive_def,definition,
    ( mtransitive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i,D: $i] :
          ( ( ( A @ B @ C )
            & ( A @ C @ D ) )
         => ( A @ B @ D ) ) ) ) ).

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

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

thf(rel_s4_type,type,
    rel_s4: $i > $i > $o ).

thf(mbox_s4_type,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf(mbox_s4_def,definition,
    ( mbox_s4
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_s4 @ B @ C )
          | ( A @ C ) ) ) ) ).

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

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

thf(1,conjecture,
    mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ! [A: $i] :
        ( ~ ! [B: $i] :
              ( ~ ( rel_s4 @ A @ B )
              | ~ ( ~ ( ~ ( p @ B )
                      | ( q @ B ) )
                  | ~ ( ~ ( q @ B )
                      | ( p @ B ) ) ) )
        | ~ ( ~ ( ~ ! [B: $i] :
                      ( ~ ( rel_s4 @ A @ B )
                      | ( p @ B ) )
                | ! [B: $i] :
                    ( ~ ( rel_s4 @ A @ B )
                    | ( q @ B ) ) )
            | ~ ( ~ ! [B: $i] :
                      ( ~ ( rel_s4 @ A @ B )
                      | ( q @ B ) )
                | ! [B: $i] :
                    ( ~ ( rel_s4 @ A @ B )
                    | ( p @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    mreflexive @ rel_s4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).

thf(16,plain,
    ! [A: $i] : ( rel_s4 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    mtransitive @ rel_s4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).

thf(18,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rel_s4 @ A @ B )
        & ( rel_s4 @ B @ C ) )
     => ( rel_s4 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(20,plain,
    $false,
    inference(e,[status(thm)],[5,16,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SYO462^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n027.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon May 20 09:57:09 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.93/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/1.15  % [INFO] 	 Parsing done (218ms). 
% 1.60/1.18  % [INFO] 	 Running in sequential loop mode. 
% 2.12/1.53  % [INFO] 	 eprover registered as external prover. 
% 2.12/1.54  % [INFO] 	 cvc4 registered as external prover. 
% 2.12/1.54  % [INFO] 	 Scanning for conjecture ... 
% 2.51/1.71  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.51/1.74  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.51/1.74  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.51/1.75  % [INFO] 	 Type checking passed. 
% 2.51/1.75  % [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 ... 
% 3.34/2.22  % External prover 'e' found a proof!
% 3.34/2.22  % [INFO] 	 Killing All external provers ... 
% 3.34/2.22  % Time passed: 1762ms (effective reasoning time: 1037ms)
% 3.34/2.22  % 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)>
% 3.34/2.22  % Axioms used in derivation (2): a1, a2
% 3.34/2.22  % No. of inferences in proof: 8
% 3.34/2.22  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1762 ms resp. 1037 ms w/o parsing
% 3.75/2.27  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.75/2.27  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------