TSTP Solution File: SYO049^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO049^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 08:55:35 EDT 2024

% Result   : Theorem 3.14s 1.61s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   15 (   6 unt;   6 typ;   5 def)
%            Number of atoms       :   36 (   5 equ;   0 cnn)
%            Maximal formula atoms :    9 (   4 avg)
%            Number of connectives :  102 (  23   ~;  14   |;   0   &;  65   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   46 (  46   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :   26 (  13   ^  13   !;   0   ?;  26   :)

% 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(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(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(mdia_type,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mdia_def,definition,
    ( mdia
    = ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).

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

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

thf(1,conjecture,
    ! [A: $i > $i > $o] :
      ( mvalid
      @ ( mforall_prop
        @ ^ [B: $i > $o] :
            ( mforall_prop
            @ ^ [C: $i > $o] : ( mequiv @ ( mdia @ A @ ( mor @ B @ C ) ) @ ( mor @ ( mdia @ A @ B ) @ ( mdia @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o] :
        ( mvalid
        @ ( mforall_prop
          @ ^ [B: $i > $o] :
              ( mforall_prop
              @ ^ [C: $i > $o] : ( mequiv @ ( mdia @ A @ ( mor @ B @ C ) ) @ ( mor @ ( mdia @ A @ B ) @ ( mdia @ A @ C ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(18,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SYO049^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.10  % Command  : run_Leo-III %s %d
% 0.09/0.29  % Computer : n016.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Mon May 20 08:48:09 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.86/0.76  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.14/0.90  % [INFO] 	 Parsing done (134ms). 
% 1.14/0.91  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.11  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.11  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.11  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.00/1.23  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.00/1.23  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.19/1.24  % [INFO] 	 Type checking passed. 
% 2.19/1.24  % [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 ... 
% 3.14/1.60  % External prover 'e' found a proof!
% 3.14/1.60  % [INFO] 	 Killing All external provers ... 
% 3.14/1.61  % Time passed: 1138ms (effective reasoning time: 697ms)
% 3.14/1.61  % 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)>
% 3.14/1.61  % Axioms used in derivation (0): 
% 3.14/1.61  % No. of inferences in proof: 4
% 3.14/1.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1138 ms resp. 697 ms w/o parsing
% 3.33/1.66  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.33/1.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------