TSTP Solution File: LCL707^1 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n017.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 11:15:27 EDT 2024

% Result   : Theorem 2.87s 1.50s
% Output   : Refutation 2.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   11 (   9 unt;   0 typ;   7 def)
%            Number of atoms       :   50 (   9 equ;   0 cnn)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  122 (  11   ~;  15   |;   2   &;  89   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   34 (  16   ^  18   !;   0   ?;  34   :)

% 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(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(mweakly_connected_type,type,
    mweakly_connected: ( $i > $i > $o ) > $o ).

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

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

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

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

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

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

thf(16,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% 0.00/0.07  % Command  : run_Leo-III %s %d THM
% 0.07/0.26  % Computer : n017.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Sat Jun 22 16:51:25 EDT 2024
% 0.07/0.26  % CPUTime  : 
% 0.65/0.70  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.97/0.85  % [INFO] 	 Parsing done (150ms). 
% 0.97/0.86  % [INFO] 	 Running in sequential loop mode. 
% 1.61/1.06  % [INFO] 	 eprover registered as external prover. 
% 1.61/1.07  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.17  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.10/1.19  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.10/1.19  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.10/1.19  % [INFO] 	 Type checking passed. 
% 2.10/1.19  % [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 ... 
% 2.87/1.50  % External prover 'e' found a proof!
% 2.87/1.50  % [INFO] 	 Killing All external provers ... 
% 2.87/1.50  % Time passed: 1130ms (effective reasoning time: 633ms)
% 2.87/1.50  % 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)>
% 2.87/1.50  % Axioms used in derivation (0): 
% 2.87/1.50  % No. of inferences in proof: 4
% 2.87/1.50  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1130 ms resp. 633 ms w/o parsing
% 2.87/1.53  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.87/1.53  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------