TSTP Solution File: SEU735^2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU735^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 03:43:34 EDT 2024

% Result   : Theorem 5.58s 2.69s
% Output   : Refutation 5.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   30 (   9 unt;  10 typ;   2 def)
%            Number of atoms       :   59 (   5 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  257 (  14   ~;  11   |;   0   &; 214   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   35 (   0   ^  35   !;   0   ?;  35   :)

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

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

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

thf(powersetI1_type,type,
    powersetI1: $o ).

thf(powersetI1_def,definition,
    ( powersetI1
    = ( ! [A: $i,B: $i] :
          ( ( subset @ B @ A )
         => ( in @ B @ ( powerset @ A ) ) ) ) ) ).

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

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

thf(complementSubsetComplementIntersect_type,type,
    complementSubsetComplementIntersect: $o ).

thf(complementSubsetComplementIntersect_def,definition,
    ( complementSubsetComplementIntersect
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ( powersetI1
   => ( complementSubsetComplementIntersect
     => ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ( in @ ( setminus @ A @ B ) @ ( powerset @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).

thf(2,negated_conjecture,
    ~ ( powersetI1
     => ( complementSubsetComplementIntersect
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ( in @ ( setminus @ A @ B ) @ ( powerset @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

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

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

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ A ) )
      | ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ),
    inference(simp,[status(thm)],[7]) ).

thf(18,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) )
      | ( ( in @ sk3 @ ( powerset @ sk1 ) )
       != ( in @ C @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6,9]) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk1 ) )
      | ( subset @ ( setminus @ sk1 @ A ) @ ( setminus @ sk1 @ ( binintersect @ A @ sk3 ) ) ) ),
    inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).

thf(27,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk1 ) )
      | ( subset @ ( setminus @ sk1 @ A ) @ ( setminus @ sk1 @ ( binintersect @ A @ sk3 ) ) ) ),
    inference(simp,[status(thm)],[19]) ).

thf(82,plain,
    ! [A: $i] :
      ( ( subset @ ( setminus @ sk1 @ A ) @ ( setminus @ sk1 @ ( binintersect @ A @ sk3 ) ) )
      | ( ( in @ sk2 @ ( powerset @ sk1 ) )
       != ( in @ A @ ( powerset @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,27]) ).

thf(83,plain,
    subset @ ( setminus @ sk1 @ sk2 ) @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk2 ))]]) ).

thf(4,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ B @ A )
      | ( in @ B @ ( powerset @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(89,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( subset @ ( setminus @ sk1 @ sk2 ) @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) )
       != ( subset @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[83,4]) ).

thf(90,plain,
    in @ ( setminus @ sk1 @ sk2 ) @ ( powerset @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) )),bind(B,$thf( setminus @ sk1 @ sk2 ))]]) ).

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

thf(91,plain,
    $false,
    inference(rewrite,[status(thm)],[90,5]) ).

thf(92,plain,
    $false,
    inference(simp,[status(thm)],[91]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : SEU735^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n017.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Sun May 19 16:30:09 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 1.00/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/1.11  % [INFO] 	 Parsing done (167ms). 
% 1.32/1.13  % [INFO] 	 Running in sequential loop mode. 
% 1.89/1.49  % [INFO] 	 nitpick registered as external prover. 
% 1.89/1.49  % [INFO] 	 Scanning for conjecture ... 
% 2.06/1.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.16/1.63  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.16/1.63  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.16/1.64  % [INFO] 	 Type checking passed. 
% 2.16/1.64  % [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 ... 
% 5.58/2.68  % [INFO] 	 Killing All external provers ... 
% 5.58/2.69  % Time passed: 2211ms (effective reasoning time: 1552ms)
% 5.58/2.69  % 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)>
% 5.58/2.69  % Axioms used in derivation (0): 
% 5.58/2.69  % No. of inferences in proof: 18
% 5.58/2.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2211 ms resp. 1552 ms w/o parsing
% 5.58/2.74  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.58/2.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------