TSTP Solution File: LCL710^1 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : LCL710^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 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 11:15:28 EDT 2024

% Result   : Theorem 5.58s 2.33s
% Output   : Refutation 5.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   24 (  16 unt;   0 typ;   6 def)
%            Number of atoms       :   57 (  13 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  172 (  36   ~;  19   |;   0   &; 112   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   8 con; 0-3 aty)
%            Number of variables   :   44 (  14   ^  30   !;   0   ?;  44   :)

% 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(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(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

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

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

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

thf(sk1_type,type,
    sk1: $i > $i > $o ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

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

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

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

thf(5,plain,
    sk1 @ sk3 @ sk4,
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk1 @ sk4 @ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ( ( sk1 @ sk4 @ sk3 )
   != ( sk1 @ sk3 @ sk4 ) ),
    inference(paramod_ordered,[status(thm)],[5,4]) ).

thf(9,plain,
    ( ( sk4 != sk3 )
    | ( sk4 != sk3 ) ),
    inference(simp,[status(thm)],[8]) ).

thf(10,plain,
    sk4 != sk3,
    inference(simp,[status(thm)],[9]) ).

thf(6,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ A )
      | ~ ( sk1 @ A @ C )
      | ( B @ ( sk2 @ C @ B @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(17,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ A )
      | ~ ( sk1 @ A @ C )
      | ( ( B @ ( sk2 @ C @ B @ A ) )
       != ( ~ ( B @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[6]) ).

thf(24,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ A )
      | ~ ( sk1 @ A @ C )
      | ( ( B @ ( sk2 @ C @ B @ A ) )
       != ( ~ ( B @ A ) ) ) ),
    inference(simp,[status(thm)],[17]) ).

thf(13,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ A )
      | ( B @ ( sk2 @ C @ B @ A ) )
      | ( ( sk1 @ sk3 @ sk4 )
       != ( sk1 @ A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[5,6]) ).

thf(14,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk3 )
      | ( A @ ( sk2 @ sk4 @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).

thf(34,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk3 )
      | ( A @ ( sk2 @ sk4 @ A @ sk3 ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(100,plain,
    ! [A: $i > $o] :
      ( ~ ~ ( A @ sk3 )
      | ~ ( A
          @ ( sk2 @ sk4
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) ) ),
    inference(prim_subst,[status(thm)],[34:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).

thf(120,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ sk4
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk3 ) ),
    inference(cnf,[status(esa)],[100]) ).

thf(121,plain,
    ! [A: $i > $o] :
      ( ~ ( A
          @ ( sk2 @ sk4
            @ ^ [B: $i] :
                ~ ( A @ B )
            @ sk3 ) )
      | ( A @ sk3 ) ),
    inference(simp,[status(thm)],[120]) ).

thf(235,plain,
    $false,
    inference(e,[status(thm)],[5,10,24,121,6,34,3,4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL710^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d THM
% 0.11/0.32  % Computer : n017.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sat Jun 22 17:23:10 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.95/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.42/1.07  % [INFO] 	 Parsing done (158ms). 
% 1.42/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.90/1.29  % [INFO] 	 eprover registered as external prover. 
% 1.90/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.27/1.40  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.27/1.41  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.27/1.42  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.27/1.42  % [INFO] 	 Type checking passed. 
% 2.27/1.42  % [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 ... 
% 5.58/2.32  % External prover 'e' found a proof!
% 5.58/2.33  % [INFO] 	 Killing All external provers ... 
% 5.58/2.33  % Time passed: 1809ms (effective reasoning time: 1245ms)
% 5.58/2.33  % 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)>
% 5.58/2.33  % Axioms used in derivation (0): 
% 5.58/2.33  % No. of inferences in proof: 18
% 5.58/2.33  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1809 ms resp. 1245 ms w/o parsing
% 5.58/2.35  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.58/2.35  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------