TSTP Solution File: SYO464^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO464^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 09:00:31 EDT 2024

% Result   : Theorem 6.47s 2.96s
% Output   : Refutation 6.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   46 (  14 unt;  14 typ;   6 def)
%            Number of atoms       :  111 (  11 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  208 (  40   ~;  26   |;   2   &; 138   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   9 con; 0-3 aty)
%            Number of variables   :   38 (   7   ^  31   !;   0   ?;  38   :)

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

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(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

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

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

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

thf(rel_s4_type,type,
    rel_s4: $i > $i > $o ).

thf(mbox_s4_type,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf(mbox_s4_def,definition,
    ( mbox_s4
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_s4 @ B @ C )
          | ( A @ C ) ) ) ) ).

thf(mdia_s4_type,type,
    mdia_s4: ( $i > $o ) > $i > $o ).

thf(mdia_s4_def,definition,
    ( mdia_s4
    = ( ^ [A: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ A ) ) ) ) ) ).

thf(p_type,type,
    p: $i > $o ).

thf(q_type,type,
    q: $i > $o ).

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

thf(sk2_type,type,
    sk2: $i ).

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

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

thf(1,conjecture,
    mvalid @ ( mimplies @ ( mbox_s4 @ ( mand @ p @ q ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mimplies @ ( mdia_s4 @ p ) @ ( mdia_s4 @ q ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mand @ p @ q ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mimplies @ ( mdia_s4 @ p ) @ ( mdia_s4 @ q ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ! [A: $i] :
        ( ~ ! [B: $i] :
              ( ~ ( rel_s4 @ A @ B )
              | ~ ( ~ ( p @ B )
                  | ~ ( q @ B ) ) )
        | ! [B: $i] :
            ( ~ ( rel_s4 @ A @ B )
            | ! [C: $i] :
                ( ~ ( rel_s4 @ B @ C )
                | ! [D: $i] :
                    ( ~ ( rel_s4 @ C @ D )
                    | ~ ( p @ D ) )
                | ~ ! [D: $i] :
                      ( ~ ( rel_s4 @ C @ D )
                      | ~ ( q @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    rel_s4 @ sk2 @ sk3,
    inference(cnf,[status(esa)],[5]) ).

thf(4,axiom,
    mtransitive @ rel_s4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).

thf(16,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rel_s4 @ A @ B )
        & ( rel_s4 @ B @ C ) )
     => ( rel_s4 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(17,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rel_s4 @ A @ B )
      | ~ ( rel_s4 @ B @ C )
      | ( rel_s4 @ A @ C ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(98,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rel_s4 @ A @ B )
      | ( rel_s4 @ A @ C )
      | ( ( rel_s4 @ sk2 @ sk3 )
       != ( rel_s4 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[9,17]) ).

thf(99,plain,
    ! [A: $i] :
      ( ~ ( rel_s4 @ A @ sk2 )
      | ( rel_s4 @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(10,plain,
    rel_s4 @ sk3 @ sk4,
    inference(cnf,[status(esa)],[5]) ).

thf(92,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rel_s4 @ A @ B )
      | ( rel_s4 @ A @ C )
      | ( ( rel_s4 @ sk3 @ sk4 )
       != ( rel_s4 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[10,17]) ).

thf(93,plain,
    ! [A: $i] :
      ( ~ ( rel_s4 @ A @ sk3 )
      | ( rel_s4 @ A @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).

thf(6,plain,
    ! [A: $i] :
      ( ~ ( rel_s4 @ sk1 @ A )
      | ( q @ A ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(133,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rel_s4 @ A @ sk3 )
      | ( q @ B )
      | ( ( rel_s4 @ A @ sk4 )
       != ( rel_s4 @ sk1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[93,6]) ).

thf(134,plain,
    ( ~ ( rel_s4 @ sk1 @ sk3 )
    | ( q @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( rel_s4 @ sk3 @ A )
      | ~ ( q @ A ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(13,plain,
    ! [A: $i] :
      ( ~ ( rel_s4 @ sk3 @ A )
      | ~ ( q @ A ) ),
    inference(simp,[status(thm)],[12]) ).

thf(18,plain,
    ! [A: $i] :
      ( ~ ( q @ A )
      | ( ( rel_s4 @ sk3 @ sk4 )
       != ( rel_s4 @ sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10,13]) ).

thf(19,plain,
    ~ ( q @ sk4 ),
    inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk4 ))]]) ).

thf(191,plain,
    ( ~ ( rel_s4 @ sk1 @ sk3 )
    | $false ),
    inference(rewrite,[status(thm)],[134,19]) ).

thf(192,plain,
    ~ ( rel_s4 @ sk1 @ sk3 ),
    inference(simp,[status(thm)],[191]) ).

thf(215,plain,
    ! [A: $i] :
      ( ~ ( rel_s4 @ A @ sk2 )
      | ( ( rel_s4 @ A @ sk3 )
       != ( rel_s4 @ sk1 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[99,192]) ).

thf(216,plain,
    ~ ( rel_s4 @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( sk1 ))]]) ).

thf(11,plain,
    rel_s4 @ sk1 @ sk2,
    inference(cnf,[status(esa)],[5]) ).

thf(254,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[216,11]) ).

thf(255,plain,
    $false,
    inference(simp,[status(thm)],[254]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.09  % Problem  : SYO464^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n027.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Mon May 20 10:01:54 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.99/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.61/1.21  % [INFO] 	 Parsing done (255ms). 
% 1.61/1.22  % [INFO] 	 Running in sequential loop mode. 
% 2.10/1.59  % [INFO] 	 nitpick registered as external prover. 
% 2.10/1.59  % [INFO] 	 Scanning for conjecture ... 
% 2.44/1.77  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.65/1.80  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.65/1.80  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.65/1.80  % [INFO] 	 Type checking passed. 
% 2.65/1.81  % [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 ... 
% 6.47/2.96  % [INFO] 	 Killing All external provers ... 
% 6.47/2.96  % Time passed: 2487ms (effective reasoning time: 1731ms)
% 6.47/2.96  % 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)>
% 6.47/2.96  % Axioms used in derivation (1): a2
% 6.47/2.96  % No. of inferences in proof: 26
% 6.47/2.96  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2487 ms resp. 1731 ms w/o parsing
% 6.47/3.02  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.47/3.02  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------