TSTP Solution File: SEU752^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU752^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 03:43:38 EDT 2024

% Result   : Theorem 178.94s 25.89s
% Output   : Refutation 178.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   65 (  14 unt;  14 typ;   5 def)
%            Number of atoms       :  212 (  16 equ;   0 cnn)
%            Maximal formula atoms :   23 (   4 avg)
%            Number of connectives :  740 (  91   ~;  78   |;   0   &; 520   @)
%                                         (   0 <=>;  51  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :  112 (   0   ^ 112   !;   0   ?; 112   :)

% 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(binunionE_type,type,
    binunionE: $o ).

thf(binunionE_def,definition,
    ( binunionE
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( binunion @ A @ B ) )
         => ( ( in @ C @ A )
            | ( in @ C @ B ) ) ) ) ) ).

thf(binintersect_type,type,
    binintersect: $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(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(binintersectTERcontra_type,type,
    binintersectTERcontra: $o ).

thf(binintersectTERcontra_def,definition,
    ( binintersectTERcontra
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ( ~ ( in @ D @ C )
                   => ~ ( 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,
    ( binunionE
   => ( setminusI
     => ( setminusER
       => ( binintersectTELcontra
         => ( binintersectTERcontra
           => ! [A: $i,B: $i] :
                ( ( in @ B @ ( powerset @ A ) )
               => ! [C: $i] :
                    ( ( in @ C @ ( powerset @ A ) )
                   => ! [D: $i] :
                        ( ( in @ D @ A )
                       => ( ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) )
                         => ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1b) ).

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

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

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

thf(13,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ B )
      | ( in @ C @ ( setminus @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(16,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ A )
      | ( in @ C @ B )
      | ( in @ C @ ( setminus @ A @ B ) ) ),
    inference(simp,[status(thm)],[13]) ).

thf(502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ B )
      | ( in @ C @ ( setminus @ A @ B ) )
      | ( ( in @ sk4 @ sk1 )
       != ( in @ C @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8,16]) ).

thf(503,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ A )
      | ( in @ sk4 @ ( setminus @ sk1 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[502:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).

thf(537,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ A )
      | ( in @ sk4 @ ( setminus @ sk1 @ A ) ) ),
    inference(simp,[status(thm)],[503]) ).

thf(4,plain,
    ~ ( in @ sk4 @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(619,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ A )
      | ( ( in @ sk4 @ ( setminus @ sk1 @ A ) )
       != ( in @ sk4 @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[537,4]) ).

thf(620,plain,
    in @ sk4 @ ( binintersect @ sk2 @ sk3 ),
    inference(pattern_uni,[status(thm)],[619:[bind(A,$thf( binintersect @ sk2 @ sk3 ))]]) ).

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

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

thf(15,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ( in @ D @ C )
      | ~ ( in @ D @ ( binintersect @ B @ C ) ) ),
    inference(simp,[status(thm)],[6]) ).

thf(255,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ( in @ D @ C )
      | ~ ( in @ D @ ( binintersect @ B @ C ) )
      | ( ( in @ sk2 @ ( powerset @ sk1 ) )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,15]) ).

thf(256,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk1 ) )
      | ~ ( in @ B @ sk1 )
      | ( in @ B @ A )
      | ~ ( in @ B @ ( binintersect @ sk2 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(307,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk1 ) )
      | ~ ( in @ B @ sk1 )
      | ( in @ B @ A )
      | ~ ( in @ B @ ( binintersect @ sk2 @ A ) ) ),
    inference(simp,[status(thm)],[256]) ).

thf(33890,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk1 ) )
      | ~ ( in @ B @ sk1 )
      | ( in @ B @ A )
      | ( ( in @ sk4 @ ( binintersect @ sk2 @ sk3 ) )
       != ( in @ B @ ( binintersect @ sk2 @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[620,307]) ).

thf(33891,plain,
    ( ~ ( in @ sk3 @ ( powerset @ sk1 ) )
    | ~ ( in @ sk4 @ sk1 )
    | ( in @ sk4 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[33890:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(11,plain,
    in @ sk4 @ ( binunion @ ( setminus @ sk1 @ sk2 ) @ ( setminus @ sk1 @ sk3 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | ( ( in @ sk4 @ ( binunion @ ( setminus @ sk1 @ sk2 ) @ ( setminus @ sk1 @ sk3 ) ) )
       != ( in @ C @ ( binunion @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,5]) ).

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

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( setminus @ A @ B ) )
      | ~ ( in @ C @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(17,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( setminus @ A @ B ) )
      | ~ ( in @ C @ B ) ),
    inference(simp,[status(thm)],[12]) ).

thf(72,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
      | ~ ( in @ C @ B )
      | ( ( in @ sk4 @ ( setminus @ sk1 @ sk3 ) )
       != ( in @ C @ ( setminus @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[31,17]) ).

thf(73,plain,
    ( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
    | ~ ( in @ sk4 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).

thf(372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ sk4 @ sk3 )
      | ~ ( in @ C @ B )
      | ( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
       != ( in @ C @ ( setminus @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[73,17]) ).

thf(373,plain,
    ( ~ ( in @ sk4 @ sk3 )
    | ~ ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[372:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).

thf(433,plain,
    ( ~ ( in @ sk4 @ sk2 )
    | ( ( in @ sk4 @ sk3 )
     != ( in @ sk4 @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[373]) ).

thf(441,plain,
    ( ~ ( in @ sk4 @ sk2 )
    | ( ( in @ sk4 @ sk3 )
     != ( in @ sk4 @ sk2 ) ) ),
    inference(simp,[status(thm)],[433]) ).

thf(9,plain,
    in @ sk3 @ ( powerset @ sk1 ),
    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(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 @ ( binintersect @ B @ C ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(109,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ D @ A )
      | ( in @ D @ B )
      | ~ ( in @ D @ ( binintersect @ B @ C ) )
      | ( ( in @ sk3 @ ( powerset @ sk1 ) )
       != ( in @ C @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9,14]) ).

thf(110,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk1 ) )
      | ~ ( in @ B @ sk1 )
      | ( in @ B @ A )
      | ~ ( in @ B @ ( binintersect @ A @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).

thf(195,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk1 ) )
      | ~ ( in @ B @ sk1 )
      | ( in @ B @ A )
      | ~ ( in @ B @ ( binintersect @ A @ sk3 ) ) ),
    inference(simp,[status(thm)],[110]) ).

thf(21327,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk1 ) )
      | ~ ( in @ B @ sk1 )
      | ( in @ B @ A )
      | ( ( in @ sk4 @ ( binintersect @ sk2 @ sk3 ) )
       != ( in @ B @ ( binintersect @ A @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[620,195]) ).

thf(21328,plain,
    ( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
    | ~ ( in @ sk4 @ sk1 )
    | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[21327:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).

thf(31414,plain,
    ( ~ $true
    | ~ $true
    | ( in @ sk4 @ sk2 ) ),
    inference(rewrite,[status(thm)],[21328,7,8]) ).

thf(31415,plain,
    in @ sk4 @ sk2,
    inference(simp,[status(thm)],[31414]) ).

thf(31446,plain,
    ( ~ $true
    | ~ ( in @ sk4 @ sk3 ) ),
    inference(rewrite,[status(thm)],[441,31415]) ).

thf(31447,plain,
    ~ ( in @ sk4 @ sk3 ),
    inference(simp,[status(thm)],[31446]) ).

thf(38657,plain,
    ( ~ $true
    | ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[33891,31447,8,9]) ).

thf(38658,plain,
    $false,
    inference(simp,[status(thm)],[38657]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU752^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun May 19 16:06:24 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.05/1.01  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.38/1.21  % [INFO] 	 Parsing done (195ms). 
% 1.38/1.22  % [INFO] 	 Running in sequential loop mode. 
% 2.04/1.61  % [INFO] 	 nitpick registered as external prover. 
% 2.04/1.61  % [INFO] 	 Scanning for conjecture ... 
% 2.44/1.75  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.48/1.79  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.48/1.79  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.48/1.79  % [INFO] 	 Type checking passed. 
% 2.48/1.80  % [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 ... 
% 178.94/25.88  % [INFO] 	 Killing All external provers ... 
% 178.94/25.88  % Time passed: 25380ms (effective reasoning time: 24645ms)
% 178.94/25.88  % 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)>
% 178.94/25.89  % Axioms used in derivation (0): 
% 178.94/25.89  % No. of inferences in proof: 46
% 178.94/25.89  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 25380 ms resp. 24645 ms w/o parsing
% 178.94/25.91  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 178.94/25.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------