TSTP Solution File: LCL879^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : LCL879^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 00:08:36 EDT 2024

% Result   : Theorem 3.47s 2.02s
% Output   : Refutation 3.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   13 (   8 unt;   5 typ;   4 def)
%            Number of atoms       :   27 (   7 equ;   0 cnn)
%            Maximal formula atoms :    1 (   3 avg)
%            Number of connectives :   72 (   7   ~;   5   |;   3   &;  54   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   41 (  41   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   30 (   8   ^  22   !;   0   ?;  30   :)

% 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(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(mforall_prop_def,definition,
    ( mforall_prop
    = ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
        ! [C: $i > $o] : ( A @ C @ B ) ) ) ).

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ! [D: $i] :
          ( ~ ( A @ C @ D )
          | ( B @ D ) ) ) ) ).

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

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

thf(1,conjecture,
    ! [A: $i > $i > $o,B: $i > $i > $o] :
      ( ( mvalid
        @ ( mforall_prop
          @ ^ [C: $i > $o] : ( mimplies @ ( mbox @ A @ C ) @ ( mbox @ B @ ( mbox @ A @ C ) ) ) ) )
      = ( ! [C: $i,D: $i,E: $i] :
            ( ( ( B @ C @ D )
              & ( A @ D @ E ) )
           => ( A @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o,B: $i > $i > $o] :
        ( ( mvalid
          @ ( mforall_prop
            @ ^ [C: $i > $o] : ( mimplies @ ( mbox @ A @ C ) @ ( mbox @ B @ ( mbox @ A @ C ) ) ) ) )
        = ( ! [C: $i,D: $i,E: $i] :
              ( ( ( B @ C @ D )
                & ( A @ D @ E ) )
             => ( A @ C @ E ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i > $i > $o,B: $i > $i > $o] :
        ( ( ! [C: $i,D: $i > $o] :
              ( ~ ! [E: $i] :
                    ( ~ ( A @ C @ E )
                    | ( D @ E ) )
              | ! [E: $i] :
                  ( ~ ( B @ C @ E )
                  | ! [F: $i] :
                      ( ~ ( A @ E @ F )
                      | ( D @ F ) ) ) ) )
        = ( ! [C: $i,D: $i,E: $i] :
              ( ( ( B @ C @ D )
                & ( A @ D @ E ) )
             => ( A @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(23,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LCL879^1 : TPTP v8.2.0. Released v5.2.0.
% 0.12/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n025.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
% 0.20/0.35  % CPULimit : 300
% 0.20/0.35  % WCLimit  : 300
% 0.20/0.35  % DateTime : Mon May 20 03:14:24 EDT 2024
% 0.20/0.35  % CPUTime  : 
% 0.92/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.36/1.10  % [INFO] 	 Parsing done (180ms). 
% 1.36/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.89/1.39  % [INFO] 	 eprover registered as external prover. 
% 1.89/1.39  % [INFO] 	 cvc4 registered as external prover. 
% 1.89/1.40  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.34/1.54  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.37/1.54  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.37/1.54  % [INFO] 	 Type checking passed. 
% 2.37/1.54  % [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 ... 
% 3.47/2.01  % External prover 'e' found a proof!
% 3.47/2.01  % [INFO] 	 Killing All external provers ... 
% 3.47/2.01  % Time passed: 1513ms (effective reasoning time: 892ms)
% 3.47/2.01  % 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)>
% 3.47/2.02  % Axioms used in derivation (0): 
% 3.47/2.02  % No. of inferences in proof: 4
% 3.47/2.02  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1513 ms resp. 892 ms w/o parsing
% 3.47/2.06  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.47/2.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------