%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO483^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 08:57:07 EDT 2024

% Result   : Theorem 2.80s 1.55s
% Output   : Refutation 2.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   18 (   7 unt;   7 typ;   4 def)
%            Number of atoms       :   29 (   9 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   37 (  12   ~;   3   |;   0   &;  22   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   18 (   9   ^   6   !;   3   ?;  18   :)

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

thf(meq_ind_type,type,
    meq_ind: mu > mu > $i > $o ).

thf(meq_ind_def,definition,
    ( meq_ind
    = ( ^ [A: mu,B: mu,C: $i] : ( A = B ) ) ) ).

thf(mexists_ind_type,type,
    mexists_ind: ( mu > $i > $o ) > $i > $o ).

thf(mexists_ind_def,definition,
    ( mexists_ind
    = ( ^ [A: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [B: mu] : ( mnot @ ( A @ B ) ) ) ) ) ) ).

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

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

thf(rel_s5_type,type,
    rel_s5: $i > $i > $o ).

thf(mbox_s5_type,type,
    mbox_s5: ( $i > $o ) > $i > $o ).

thf(mbox_s5_def,definition,
    ( mbox_s5
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_s5 @ B @ C )
          | ( A @ C ) ) ) ) ).

thf(a_type,type,
    a: mu ).

thf(1,conjecture,
    ( mvalid
    @ ( mexists_ind
      @ ^ [A: mu] : ( mbox_s5 @ ( meq_ind @ A @ a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid
      @ ( mexists_ind
        @ ^ [A: mu] : ( mbox_s5 @ ( meq_ind @ A @ a ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: $i] :
        ~ ! [B: mu] :
            ~ ! [C: $i] :
                ( ~ ( rel_s5 @ A @ C )
                | ( B = a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ~ ~ ~ ( ~ ? [A: $i,B: $i] : ( rel_s5 @ A @ B )
          | ? [A: mu] : ( A = a ) ),
    inference(miniscope,[status(thm)],[6]) ).

thf(8,plain,
    ! [A: mu] : ( A != a ),
    inference(cnf,[status(esa)],[7]) ).

thf(10,plain,
    ! [A: mu] : ( A != a ),
    inference(lifteq,[status(thm)],[8]) ).

thf(11,plain,
    $false,
    inference(simp,[status(thm)],[10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO483^6 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n010.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May 20 10:36:24 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 1.01/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.50/1.03  % [INFO] 	 Parsing done (153ms). 
% 1.50/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.97/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.97/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 1.97/1.27  % [INFO] 	 Scanning for conjecture ... 
% 2.39/1.39  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.39/1.41  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.39/1.41  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.39/1.41  % [INFO] 	 Type checking passed. 
% 2.39/1.41  % [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 ... 
% 2.80/1.55  % [INFO] 	 Killing All external provers ... 
% 2.80/1.55  % Time passed: 1008ms (effective reasoning time: 501ms)
% 2.80/1.55  % 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)>
% 2.80/1.55  % Axioms used in derivation (0): 
% 2.80/1.55  % No. of inferences in proof: 7
% 2.80/1.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1008 ms resp. 501 ms w/o parsing
% 2.80/1.59  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.80/1.59  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------