TSTP Solution File: SWV061^7 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWV061^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% 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 : Mon Jun 24 17:27:37 EDT 2024

% Result   : Theorem 26.24s 7.36s
% Output   : Refutation 26.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   25 (  13 unt;   0 typ;   6 def)
%            Number of atoms       :  102 (   7 equ;   0 cnn)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  159 (  30   ~;  21   |;   0   &; 108   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   9 con; 0-3 aty)
%            Number of variables   :   30 (   8   ^  22   !;   0   ?;  30   :)

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

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: $i > $o,B: $i] :
          ~ ( A @ B ) ) ) ).

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(mreflexive_type,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(mreflexive_def,definition,
    ( mreflexive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i] : ( A @ B @ 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(true_type,type,
    true: $i > $o ).

thf(gt_type,type,
    gt: mu > mu > $i > $o ).

thf(loopcounter_type,type,
    loopcounter: mu ).

thf(n1_type,type,
    n1: mu ).

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

thf(sk6_type,type,
    sk6: $i ).

thf(sk8_type,type,
    sk8: $i ).

thf(1,conjecture,
    mvalid @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ true ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( gt @ loopcounter @ n1 ) ) ) ) @ ( mbox_s4 @ true ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ loopcounter @ n1 ) ) @ ( mbox_s4 @ true ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_array_0002) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ true ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( gt @ loopcounter @ n1 ) ) ) ) @ ( mbox_s4 @ true ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ loopcounter @ n1 ) ) @ ( mbox_s4 @ true ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(169,plain,
    ~ ! [A: $i,B: $i] :
        ( ~ ( rel_s4 @ A @ B )
        | ~ ! [C: $i] :
              ( ~ ( rel_s4 @ B @ C )
              | ( true @ C ) )
        | ~ ( ~ ! [C: $i] :
                  ( ~ ( rel_s4 @ B @ C )
                  | ~ ! [D: $i] :
                        ( ~ ( rel_s4 @ C @ D )
                        | ~ ! [E: $i] :
                              ( ~ ( rel_s4 @ D @ E )
                              | ( gt @ loopcounter @ n1 @ E ) ) )
                  | ! [D: $i] :
                      ( ~ ( rel_s4 @ C @ D )
                      | ( true @ D ) ) )
            | ~ ! [C: $i] :
                  ( ~ ( rel_s4 @ B @ C )
                  | ~ ! [D: $i] :
                        ( ~ ( rel_s4 @ C @ D )
                        | ( gt @ loopcounter @ n1 @ D ) )
                  | ! [D: $i] :
                      ( ~ ( rel_s4 @ C @ D )
                      | ( true @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(177,plain,
    ( ~ ( true @ sk6 )
    | sk3 ),
    inference(cnf,[status(esa)],[169]) ).

thf(136,axiom,
    mreflexive @ rel_s4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).

thf(865,plain,
    ! [A: $i] : ( rel_s4 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(866,plain,
    ! [A: $i] : ( rel_s4 @ A @ A ),
    inference(cnf,[status(esa)],[865]) ).

thf(121,axiom,
    mvalid @ ( mbox_s4 @ true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ttrue) ).

thf(822,plain,
    ! [A: $i,B: $i] :
      ( ~ ( rel_s4 @ A @ B )
      | ( true @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(823,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rel_s4 @ A @ B )
      | ( true @ B ) ),
    inference(cnf,[status(esa)],[822]) ).

thf(2507,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( true @ C )
      | ( ( rel_s4 @ A @ A )
       != ( rel_s4 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[866,823]) ).

thf(2508,plain,
    ! [A: $i] : ( true @ A ),
    inference(pattern_uni,[status(thm)],[2507:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(2534,plain,
    ( ~ $true
    | sk3 ),
    inference(rewrite,[status(thm)],[177,2508]) ).

thf(2535,plain,
    sk3,
    inference(simp,[status(thm)],[2534]) ).

thf(170,plain,
    ( ~ sk3
    | ~ ( true @ sk8 ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(2531,plain,
    ( ~ sk3
    | ~ $true ),
    inference(rewrite,[status(thm)],[170,2508]) ).

thf(2532,plain,
    ~ sk3,
    inference(simp,[status(thm)],[2531]) ).

thf(2578,plain,
    $false,
    inference(rewrite,[status(thm)],[2535,2532]) ).

thf(2579,plain,
    $false,
    inference(simp,[status(thm)],[2578]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWV061^7 : TPTP v8.2.0. Released v5.5.0.
% 0.04/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Jun 20 17:23:10 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.96/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.05/1.18  % [INFO] 	 Parsing done (260ms). 
% 2.05/1.19  % [INFO] 	 Running in sequential loop mode. 
% 2.60/1.40  % [INFO] 	 nitpick registered as external prover. 
% 2.60/1.40  % [INFO] 	 Scanning for conjecture ... 
% 3.15/1.55  % [INFO] 	 Found a conjecture (or negated_conjecture) and 166 axioms. Running axiom selection ... 
% 3.15/1.63  % [INFO] 	 Axiom selection finished. Selected 166 axioms (removed 0 axioms). 
% 3.71/1.74  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.71/1.75  % [INFO] 	 Type checking passed. 
% 3.71/1.75  % [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 ... 
% 26.23/7.35  % [INFO] 	 Killing All external provers ... 
% 26.23/7.35  % Time passed: 6805ms (effective reasoning time: 6160ms)
% 26.23/7.35  % 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)>
% 26.23/7.36  % Axioms used in derivation (2): a1, ttrue
% 26.24/7.36  % No. of inferences in proof: 19
% 26.24/7.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6805 ms resp. 6160 ms w/o parsing
% 26.35/7.41  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.35/7.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------