TSTP Solution File: SEU755^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU755^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 03:43:39 EDT 2024

% Result   : Theorem 37.73s 7.19s
% Output   : Refutation 38.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   44 (  13 unt;  11 typ;   3 def)
%            Number of atoms       :  128 (   8 equ;   0 cnn)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  451 (  56   ~;  39   |;   0   &; 316   @)
%                                         (   0 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   66 (   0   ^  66   !;   0   ?;  66   :)

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

thf(powerset_type,type,
    powerset: $i > $i ).

thf(binunion_type,type,
    binunion: $i > $i > $i ).

thf(setminus_type,type,
    setminus: $i > $i > $i ).

thf(setminusI_type,type,
    setminusI: $o ).

thf(setminusI_def,definition,
    ( setminusI
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ A )
         => ( ~ ( in @ C @ B )
           => ( in @ C @ ( setminus @ A @ B ) ) ) ) ) ) ).

thf(setminusER_type,type,
    setminusER: $o ).

thf(setminusER_def,definition,
    ( setminusER
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setminus @ A @ B ) )
         => ~ ( in @ C @ B ) ) ) ) ).

thf(binunionTEcontra_type,type,
    binunionTEcontra: $o ).

thf(binunionTEcontra_def,definition,
    ( binunionTEcontra
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ( ~ ( in @ D @ B )
                   => ( ~ ( in @ D @ C )
                     => ~ ( in @ D @ ( binunion @ B @ C ) ) ) ) ) ) ) ) ) ).

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,
    ( setminusI
   => ( setminusER
     => ( binunionTEcontra
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ! [D: $i] :
                    ( ( in @ D @ A )
                   => ( ( in @ D @ ( setminus @ A @ B ) )
                     => ( ( in @ D @ ( setminus @ A @ C ) )
                       => ( in @ D @ ( setminus @ A @ ( binunion @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2) ).

thf(2,negated_conjecture,
    ~ ( setminusI
     => ( setminusER
       => ( binunionTEcontra
         => ! [A: $i,B: $i] :
              ( ( in @ B @ ( powerset @ A ) )
             => ! [C: $i] :
                  ( ( in @ C @ ( powerset @ A ) )
                 => ! [D: $i] :
                      ( ( in @ D @ A )
                     => ( ( in @ D @ ( setminus @ A @ B ) )
                       => ( ( in @ D @ ( setminus @ A @ C ) )
                         => ( in @ D @ ( setminus @ A @ ( binunion @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(12,plain,
    in @ sk3 @ ( powerset @ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ B )
      | ( in @ C @ ( setminus @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ~ ( in @ sk4 @ ( setminus @ sk1 @ ( binunion @ sk2 @ sk3 ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ B )
      | ( ( in @ C @ ( setminus @ A @ B ) )
       != ( in @ sk4 @ ( setminus @ sk1 @ ( binunion @ sk2 @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,5]) ).

thf(31,plain,
    ( ~ ( in @ sk4 @ sk1 )
    | ( in @ sk4 @ ( binunion @ sk2 @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk1 )),bind(B,$thf( binunion @ sk2 @ sk3 )),bind(C,$thf( sk4 ))]]) ).

thf(9,plain,
    in @ sk4 @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(56,plain,
    ( ~ $true
    | ( in @ sk4 @ ( binunion @ sk2 @ sk3 ) ) ),
    inference(rewrite,[status(thm)],[31,9]) ).

thf(57,plain,
    in @ sk4 @ ( binunion @ sk2 @ sk3 ),
    inference(simp,[status(thm)],[56]) ).

thf(11,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | ~ ( in @ D @ ( binunion @ B @ C ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | ~ ( in @ D @ ( binunion @ B @ C ) ) ),
    inference(simp,[status(thm)],[11]) ).

thf(231,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | ( ( in @ sk4 @ ( binunion @ sk2 @ sk3 ) )
       != ( in @ D @ ( binunion @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[57,14]) ).

thf(232,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ sk4 @ A )
      | ( in @ sk4 @ sk2 )
      | ( in @ sk4 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 )),bind(D,$thf( sk4 ))]]) ).

thf(10,plain,
    in @ sk4 @ ( setminus @ sk1 @ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( setminus @ A @ B ) )
      | ~ ( in @ C @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( setminus @ A @ B ) )
      | ~ ( in @ C @ B ) ),
    inference(simp,[status(thm)],[6]) ).

thf(82,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( ( in @ sk4 @ ( setminus @ sk1 @ sk3 ) )
       != ( in @ C @ ( setminus @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,13]) ).

thf(83,plain,
    ~ ( in @ sk4 @ sk3 ),
    inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).

thf(7,plain,
    in @ sk4 @ ( setminus @ sk1 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(89,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
       != ( in @ C @ ( setminus @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,13]) ).

thf(90,plain,
    ~ ( in @ sk4 @ sk2 ),
    inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).

thf(2299,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ sk4 @ A )
      | $false
      | $false ),
    inference(rewrite,[status(thm)],[232,83,90]) ).

thf(2300,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ sk4 @ A ) ),
    inference(simp,[status(thm)],[2299]) ).

thf(2331,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ sk4 @ A )
      | ( ( in @ sk3 @ ( powerset @ sk1 ) )
       != ( in @ sk3 @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,2300]) ).

thf(2332,plain,
    ( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
    | ~ ( in @ sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[2331:[bind(A,$thf( sk1 ))]]) ).

thf(4,plain,
    in @ sk2 @ ( powerset @ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(2463,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[2332,4,9]) ).

thf(2464,plain,
    $false,
    inference(simp,[status(thm)],[2463]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SEU755^2 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.33  % Computer : n023.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 16:05:39 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 1.07/1.02  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.37/1.21  % [INFO] 	 Parsing done (185ms). 
% 1.37/1.22  % [INFO] 	 Running in sequential loop mode. 
% 2.01/1.62  % [INFO] 	 nitpick registered as external prover. 
% 2.01/1.62  % [INFO] 	 Scanning for conjecture ... 
% 2.40/1.76  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.40/1.80  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.40/1.80  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.40/1.80  % [INFO] 	 Type checking passed. 
% 2.40/1.81  % [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 ... 
% 37.73/7.16  % [INFO] 	 Killing All external provers ... 
% 37.73/7.19  % Time passed: 6688ms (effective reasoning time: 5957ms)
% 37.73/7.19  % 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)>
% 37.73/7.19  % Axioms used in derivation (0): 
% 37.73/7.19  % No. of inferences in proof: 30
% 37.73/7.19  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6688 ms resp. 5957 ms w/o parsing
% 38.04/7.42  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.04/7.42  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------