TSTP Solution File: SYN357^7 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 08:18:12 EDT 2024

% Result   : Theorem 4.00s 2.00s
% Output   : Refutation 4.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   33 (   9 unt;  13 typ;   5 def)
%            Number of atoms       :   74 (   8 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  152 (  23   ~;  16   |;   0   &; 110   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :   28 (  11   ^  17   !;   0   ?;  28   :)

% 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(exists_in_world_type,type,
    exists_in_world: mu > $i > $o ).

thf(mforall_ind_type,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(mforall_ind_def,definition,
    ( mforall_ind
    = ( ^ [A: mu > $i > $o,B: $i] :
        ! [C: mu] :
          ( ( exists_in_world @ C @ B )
         => ( A @ C @ B ) ) ) ) ).

thf(mexists_ind_type,type,
    mexists_ind: ( mu > $i > $o ) > $i > $o ).

thf(mexists_ind_def,definition,
    ( mexists_ind
    = ( ^ [A: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [B: mu] : ( mnot @ ( A @ B ) ) ) ) ) ) ).

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(big_p_type,type,
    big_p: mu > $i > $o ).

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

thf(sk3_type,type,
    sk3: mu ).

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

thf(sk5_type,type,
    sk5: mu > $i ).

thf(1,conjecture,
    ( mvalid
    @ ( mbox_s4
      @ ( mforall_ind
        @ ^ [A: mu] :
            ( mexists_ind
            @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ A ) ) @ ( mbox_s4 @ ( big_p @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2108) ).

thf(2,negated_conjecture,
    ~ ( mvalid
      @ ( mbox_s4
        @ ( mforall_ind
          @ ^ [A: mu] :
              ( mexists_ind
              @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ A ) ) @ ( mbox_s4 @ ( big_p @ B ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ! [A: $i,B: $i] :
        ( ~ ( rel_s4 @ A @ B )
        | ! [C: mu] :
            ( ( exists_in_world @ C @ B )
           => ~ ! [D: mu] :
                  ( ( exists_in_world @ D @ B )
                 => ~ ! [E: $i] :
                        ( ~ ( rel_s4 @ B @ E )
                        | ~ ! [F: $i] :
                              ( ~ ( rel_s4 @ E @ F )
                              | ( big_p @ C @ F ) )
                        | ! [F: $i] :
                            ( ~ ( rel_s4 @ E @ F )
                            | ( big_p @ D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,plain,
    exists_in_world @ sk3 @ sk2,
    inference(cnf,[status(esa)],[7]) ).

thf(10,plain,
    ! [A: mu] :
      ( ~ ( exists_in_world @ A @ sk2 )
      | ( rel_s4 @ ( sk4 @ A ) @ ( sk5 @ A ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(92,plain,
    ! [A: mu] :
      ( ( rel_s4 @ ( sk4 @ A ) @ ( sk5 @ A ) )
      | ( ( exists_in_world @ sk3 @ sk2 )
       != ( exists_in_world @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,10]) ).

thf(93,plain,
    rel_s4 @ ( sk4 @ sk3 ) @ ( sk5 @ sk3 ),
    inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk3 ))]]) ).

thf(9,plain,
    ! [B: $i,A: mu] :
      ( ~ ( exists_in_world @ A @ sk2 )
      | ~ ( rel_s4 @ ( sk4 @ A ) @ B )
      | ( big_p @ sk3 @ B ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(97,plain,
    ! [B: $i,A: mu] :
      ( ~ ( exists_in_world @ A @ sk2 )
      | ( big_p @ sk3 @ B )
      | ( ( rel_s4 @ ( sk4 @ sk3 ) @ ( sk5 @ sk3 ) )
       != ( rel_s4 @ ( sk4 @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[93,9]) ).

thf(98,plain,
    ( ~ ( exists_in_world @ sk3 @ sk2 )
    | ( big_p @ sk3 @ ( sk5 @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( sk3 )),bind(B,$thf( sk5 @ sk3 ))]]) ).

thf(8,plain,
    ! [A: mu] :
      ( ~ ( exists_in_world @ A @ sk2 )
      | ~ ( big_p @ A @ ( sk5 @ A ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(22,plain,
    ! [A: mu] :
      ( ~ ( big_p @ A @ ( sk5 @ A ) )
      | ( ( exists_in_world @ sk3 @ sk2 )
       != ( exists_in_world @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,8]) ).

thf(23,plain,
    ~ ( big_p @ sk3 @ ( sk5 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( sk3 ))]]) ).

thf(101,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[98,23,11]) ).

thf(102,plain,
    $false,
    inference(simp,[status(thm)],[101]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n019.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May 20 13:42:39 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/1.02  % [INFO] 	 Parsing done (153ms). 
% 1.50/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.78/1.23  % [INFO] 	 Scanning for conjecture ... 
% 2.14/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.14/1.35  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.14/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.14/1.35  % [INFO] 	 Type checking passed. 
% 2.14/1.36  % [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 ... 
% 4.00/2.00  % [INFO] 	 Killing All external provers ... 
% 4.00/2.00  % Time passed: 1461ms (effective reasoning time: 965ms)
% 4.00/2.00  % 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)>
% 4.00/2.00  % Axioms used in derivation (0): 
% 4.00/2.00  % No. of inferences in proof: 15
% 4.00/2.00  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1461 ms resp. 965 ms w/o parsing
% 4.00/2.04  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.00/2.04  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------