TSTP Solution File: SET899+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET899+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 03:07:18 EDT 2024

% Result   : Theorem 4.29s 2.38s
% Output   : Refutation 4.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   22 (   4 unt;   7 typ;   0 def)
%            Number of atoms       :   37 (   1 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  129 (  10   ~;  13   |;   0   &;  99   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   27 (   0   ^  27   !;   0   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
thf(subset_type,type,
    subset: $i > $i > $o ).

thf(in_type,type,
    in: $i > $i > $o ).

thf(set_difference_type,type,
    set_difference: $i > $i > $i ).

thf(singleton_type,type,
    singleton: $i > $i ).

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

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

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

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( subset @ A @ B )
     => ( ( in @ C @ A )
        | ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).

thf(22,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( subset @ A @ B )
     => ( ( in @ C @ A )
        | ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(23,plain,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
     => ! [C: $i] :
          ( ( in @ C @ A )
          | ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
    inference(miniscope,[status(thm)],[22]) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ( in @ C @ A )
      | ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( subset @ A @ B )
     => ( ( in @ C @ A )
        | ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( subset @ A @ B )
       => ( ( in @ C @ A )
          | ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(8,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( subset @ A @ B )
       => ( ( in @ C @ A )
          | ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ~ ! [A: $i,B: $i] :
        ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( in @ C @ A )
            | ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
    inference(miniscope,[status(thm)],[8]) ).

thf(10,plain,
    ~ ( subset @ sk1 @ ( set_difference @ sk2 @ ( singleton @ sk3 ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(36,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ( in @ C @ A )
      | ( ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) )
       != ( subset @ sk1 @ ( set_difference @ sk2 @ ( singleton @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,10]) ).

thf(37,plain,
    ( ~ ( subset @ sk1 @ sk2 )
    | ( in @ sk3 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(11,plain,
    ~ ( in @ sk3 @ sk1 ),
    inference(cnf,[status(esa)],[9]) ).

thf(12,plain,
    subset @ sk1 @ sk2,
    inference(cnf,[status(esa)],[9]) ).

thf(56,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[37,11,12]) ).

thf(57,plain,
    $false,
    inference(simp,[status(thm)],[56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SET899+1 : TPTP v8.2.0. Released v3.2.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n004.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 : Mon May 20 11:33:39 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.99/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.26/1.11  % [INFO] 	 Parsing done (156ms). 
% 1.26/1.13  % [INFO] 	 Running in sequential loop mode. 
% 1.87/1.49  % [INFO] 	 nitpick registered as external prover. 
% 1.87/1.50  % [INFO] 	 Scanning for conjecture ... 
% 2.02/1.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 2.02/1.63  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 2.17/1.64  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.17/1.64  % [INFO] 	 Type checking passed. 
% 2.17/1.65  % [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 ... 
% 4.29/2.37  % [INFO] 	 Killing All external provers ... 
% 4.29/2.38  % Time passed: 1907ms (effective reasoning time: 1240ms)
% 4.29/2.38  % 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)>
% 4.29/2.38  % Axioms used in derivation (1): l3_zfmisc_1
% 4.29/2.38  % No. of inferences in proof: 15
% 4.29/2.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1907 ms resp. 1240 ms w/o parsing
% 4.29/2.42  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.29/2.42  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------