TSTP Solution File: SEU734^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU734^2 : 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 03:39:26 EDT 2024

% Result   : Theorem 3.20s 1.81s
% Output   : Refutation 3.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   17 (   5 unt;   9 typ;   4 def)
%            Number of atoms       :   58 (   4 equ;   0 cnn)
%            Maximal formula atoms :   19 (   7 avg)
%            Number of connectives :  188 (   2   ~;   0   |;   0   &; 144   @)
%                                         (   0 <=>;  42  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   5 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(binintersect_type,type,
    binintersect: $i > $i > $i ).

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

thf(binintersectT_lem_type,type,
    binintersectT_lem: $o ).

thf(binintersectT_lem_def,definition,
    ( binintersectT_lem
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ( in @ ( binintersect @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ).

thf(complementT_lem_type,type,
    complementT_lem: $o ).

thf(complementT_lem_def,definition,
    ( complementT_lem
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( in @ ( setminus @ A @ B ) @ ( powerset @ A ) ) ) ) ) ).

thf(subsetTI_type,type,
    subsetTI: $o ).

thf(subsetTI_def,definition,
    ( subsetTI
    = ( ! [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 ) ) )
               => ( subset @ B @ C ) ) ) ) ) ) ).

thf(complementImpComplementIntersect_type,type,
    complementImpComplementIntersect: $o ).

thf(complementImpComplementIntersect_def,definition,
    ( complementImpComplementIntersect
    = ( ! [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 @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ) ).

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

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

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

thf(25,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU734^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n017.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 18:13:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.98/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.38/1.00  % [INFO] 	 Parsing done (126ms). 
% 1.38/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.94/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.94/1.35  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.94/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.94/1.35  % [INFO] 	 Type checking passed. 
% 1.94/1.35  % [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 ... 
% 3.20/1.81  % External prover 'e' found a proof!
% 3.20/1.81  % [INFO] 	 Killing All external provers ... 
% 3.20/1.81  % Time passed: 1271ms (effective reasoning time: 790ms)
% 3.20/1.81  % 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)>
% 3.20/1.81  % Axioms used in derivation (0): 
% 3.20/1.81  % No. of inferences in proof: 4
% 3.20/1.81  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1271 ms resp. 790 ms w/o parsing
% 3.37/1.84  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.37/1.84  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------