TSTP Solution File: SEU732^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU732^2 : TPTP v8.2.0. Released v3.7.0.
% 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 03:43:33 EDT 2024

% Result   : Theorem 4.38s 1.97s
% Output   : Refutation 4.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   33 (   9 unt;  10 typ;   2 def)
%            Number of atoms       :   87 (   5 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  308 (  44   ~;  26   |;   0   &; 210   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   48 (   0   ^  48   !;   0   ?;  48   :)

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

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

thf(binintersect_type,type,
    binintersect: $i > $i > $i ).

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

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(binintersectTELcontra_type,type,
    binintersectTELcontra: $o ).

thf(binintersectTELcontra_def,definition,
    ( binintersectTELcontra
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ( ~ ( in @ D @ B )
                   => ~ ( in @ D @ ( binintersect @ 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,
    ( setminusER
   => ( binintersectTELcontra
     => ! [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 @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).

thf(2,negated_conjecture,
    ~ ( setminusER
     => ( binintersectTELcontra
       => ! [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 @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [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 @ ( binintersect @ 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 @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

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

thf(10,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 @ ( binintersect @ B @ C ) ) ),
    inference(cnf,[status(esa)],[3]) ).

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 @ ( binintersect @ B @ C ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(70,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ( in @ D @ B )
      | ( ( in @ sk4 @ ( binintersect @ sk2 @ sk3 ) )
       != ( in @ D @ ( binintersect @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5,11]) ).

thf(71,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ sk4 @ A )
      | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 )),bind(D,$thf( sk4 ))]]) ).

thf(8,plain,
    in @ sk4 @ ( setminus @ sk1 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( setminus @ A @ B ) )
      | ~ ( in @ C @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(47,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)],[8,9]) ).

thf(48,plain,
    ~ ( in @ sk4 @ sk2 ),
    inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).

thf(158,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ sk4 @ A )
      | $false ),
    inference(rewrite,[status(thm)],[71,48]) ).

thf(159,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ sk4 @ A ) ),
    inference(simp,[status(thm)],[158]) ).

thf(165,plain,
    ! [A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ sk4 @ A )
      | ( ( in @ sk3 @ ( powerset @ sk1 ) )
       != ( in @ sk3 @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,159]) ).

thf(166,plain,
    ( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
    | ~ ( in @ sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( sk1 ))]]) ).

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

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

thf(224,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[166,4,7]) ).

thf(225,plain,
    $false,
    inference(simp,[status(thm)],[224]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU732^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n019.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 17:44:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.91/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.02/0.92  % [INFO] 	 Parsing done (98ms). 
% 1.02/0.93  % [INFO] 	 Running in sequential loop mode. 
% 1.42/1.12  % [INFO] 	 nitpick registered as external prover. 
% 1.42/1.13  % [INFO] 	 Scanning for conjecture ... 
% 1.64/1.19  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.83/1.22  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.83/1.22  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.83/1.22  % [INFO] 	 Type checking passed. 
% 1.83/1.22  % [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 ... 
% 4.38/1.96  % [INFO] 	 Killing All external provers ... 
% 4.38/1.96  % Time passed: 1433ms (effective reasoning time: 1029ms)
% 4.38/1.96  % 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)>
% 4.38/1.97  % Axioms used in derivation (0): 
% 4.38/1.97  % No. of inferences in proof: 21
% 4.38/1.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1433 ms resp. 1029 ms w/o parsing
% 4.43/2.01  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.43/2.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------