TSTP Solution File: SEU460^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU460^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 03:42:13 EDT 2024

% Result   : Theorem 2.95s 1.79s
% Output   : Refutation 3.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   23 (   8 unt;   6 typ;   2 def)
%            Number of atoms       :   33 (   4 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   84 (  10   ~;  10   |;   0   &;  60   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   18 (   4   ^  14   !;   0   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mono_type,type,
    mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).

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

thf(sc_type,type,
    sc: ( $i > $i > $o ) > $i > $i > $o ).

thf(sc_def,definition,
    ( sc
    = ( ^ [A: $i > $i > $o,B: $i,C: $i] :
          ( ( A @ C @ B )
          | ( A @ B @ C ) ) ) ) ).

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

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

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

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

thf(1,conjecture,
    mono @ sc,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_closure_op_is_monotonic) ).

thf(2,negated_conjecture,
    ~ ( mono @ sc ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ( sk2 @ A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk2 @ sk3 @ sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ( ( sk2 @ A @ B )
       != ( sk2 @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[7,4]) ).

thf(27,plain,
    ~ ( sk1 @ sk3 @ sk4 ),
    inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(6,plain,
    ( ( sk1 @ sk4 @ sk3 )
    | ( sk1 @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(22,plain,
    ! [B: $i,A: $i] :
      ( ( sk1 @ sk3 @ sk4 )
      | ( sk2 @ A @ B )
      | ( ( sk1 @ sk4 @ sk3 )
       != ( sk1 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[6,7]) ).

thf(23,plain,
    ( ( sk1 @ sk3 @ sk4 )
    | ( sk2 @ sk4 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).

thf(5,plain,
    ~ ( sk2 @ sk4 @ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(28,plain,
    ( ( sk1 @ sk3 @ sk4 )
    | $false ),
    inference(rewrite,[status(thm)],[23,5]) ).

thf(29,plain,
    sk1 @ sk3 @ sk4,
    inference(simp,[status(thm)],[28]) ).

thf(37,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[27,29]) ).

thf(38,plain,
    $false,
    inference(simp,[status(thm)],[37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEU460^1 : TPTP v8.2.0. Released v3.6.0.
% 0.12/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.33  % Computer : n032.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sun May 19 15:41:23 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.80/0.79  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.94  % [INFO] 	 Parsing done (157ms). 
% 1.22/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.23  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.91/1.37  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.91/1.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.10/1.37  % [INFO] 	 Type checking passed. 
% 2.10/1.37  % [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 ... 
% 2.95/1.79  % [INFO] 	 Killing All external provers ... 
% 2.95/1.79  % Time passed: 1333ms (effective reasoning time: 828ms)
% 2.95/1.79  % 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)>
% 2.95/1.79  % Axioms used in derivation (0): 
% 2.95/1.79  % No. of inferences in proof: 15
% 2.95/1.79  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1333 ms resp. 828 ms w/o parsing
% 3.01/1.82  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.01/1.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------