TSTP Solution File: SET622+3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET622+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 03:06:32 EDT 2024

% Result   : Theorem 5.90s 2.37s
% Output   : Refutation 5.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   29 (  21 unt;   7 typ;   0 def)
%            Number of atoms       :   23 (  22 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  246 (   9   ~;   1   |;   0   &; 236   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   43 (   0   ^  43   !;   0   ?;  43   :)

% Comments : 
%------------------------------------------------------------------------------
thf(difference_type,type,
    difference: $i > $i > $i ).

thf(symmetric_difference_type,type,
    symmetric_difference: $i > $i > $i ).

thf(union_type,type,
    union: $i > $i > $i ).

thf(intersection_type,type,
    intersection: $i > $i > $i ).

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

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

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

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( symmetric_difference @ A @ B )
      = ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).

thf(26,plain,
    ! [A: $i,B: $i] :
      ( ( symmetric_difference @ A @ B )
      = ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ( symmetric_difference @ A @ B )
      = ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) ),
    inference(cnf,[status(esa)],[26]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( symmetric_difference @ A @ B )
      = ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) ),
    inference(lifteq,[status(thm)],[27]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( difference @ A @ ( symmetric_difference @ B @ C ) )
      = ( union @ ( difference @ A @ ( union @ B @ C ) ) @ ( intersection @ ( intersection @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( difference @ A @ ( symmetric_difference @ B @ C ) )
        = ( union @ ( difference @ A @ ( union @ B @ C ) ) @ ( intersection @ ( intersection @ A @ B ) @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(17,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( difference @ A @ ( symmetric_difference @ B @ C ) )
        = ( union @ ( difference @ A @ ( union @ B @ C ) ) @ ( intersection @ ( intersection @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(18,plain,
    ( ( difference @ sk1 @ ( symmetric_difference @ sk2 @ sk3 ) )
   != ( union @ ( difference @ sk1 @ ( union @ sk2 @ sk3 ) ) @ ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(19,plain,
    ( ( union @ ( difference @ sk1 @ ( union @ sk2 @ sk3 ) ) @ ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) )
   != ( difference @ sk1 @ ( symmetric_difference @ sk2 @ sk3 ) ) ),
    inference(lifteq,[status(thm)],[18]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( intersection @ ( intersection @ A @ B ) @ C )
      = ( intersection @ A @ ( intersection @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).

thf(20,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( intersection @ ( intersection @ A @ B ) @ C )
      = ( intersection @ A @ ( intersection @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(21,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( intersection @ ( intersection @ A @ B ) @ C )
      = ( intersection @ A @ ( intersection @ B @ C ) ) ),
    inference(cnf,[status(esa)],[20]) ).

thf(22,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( intersection @ ( intersection @ A @ B ) @ C )
      = ( intersection @ A @ ( intersection @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[21]) ).

thf(122,plain,
    ( ( union @ ( difference @ sk1 @ ( union @ sk2 @ sk3 ) ) @ ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) )
   != ( difference @ sk1 @ ( symmetric_difference @ sk2 @ sk3 ) ) ),
    inference(rewrite,[status(thm)],[19,22]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( difference @ A @ ( difference @ B @ C ) )
      = ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).

thf(23,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( difference @ A @ ( difference @ B @ C ) )
      = ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( difference @ A @ ( difference @ B @ C ) )
      = ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) )
      = ( difference @ A @ ( difference @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[24]) ).

thf(334,plain,
    ( ( difference @ sk1 @ ( difference @ ( union @ sk2 @ sk3 ) @ ( intersection @ sk2 @ sk3 ) ) )
   != ( difference @ sk1 @ ( symmetric_difference @ sk2 @ sk3 ) ) ),
    inference(rewrite,[status(thm)],[122,25]) ).

thf(389,plain,
    ! [B: $i,A: $i] :
      ( ( ( difference @ sk1 @ ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) )
       != ( difference @ sk1 @ ( difference @ ( union @ sk2 @ sk3 ) @ ( intersection @ sk2 @ sk3 ) ) ) )
      | ( ( symmetric_difference @ A @ B )
       != ( symmetric_difference @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[28,334]) ).

thf(390,plain,
    ( ( difference @ sk1 @ ( difference @ ( union @ sk2 @ sk3 ) @ ( intersection @ sk2 @ sk3 ) ) )
   != ( difference @ sk1 @ ( difference @ ( union @ sk2 @ sk3 ) @ ( intersection @ sk2 @ sk3 ) ) ) ),
    inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(415,plain,
    $false,
    inference(simp,[status(thm)],[390]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SET622+3 : TPTP v8.2.0. Released v2.2.0.
% 0.08/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n026.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon May 20 11:34:39 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.94/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.04  % [INFO] 	 Parsing done (130ms). 
% 1.25/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.75/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.86/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ... 
% 2.03/1.36  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 2.10/1.38  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.10/1.39  % [INFO] 	 Type checking passed. 
% 2.10/1.39  % [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 ... 
% 5.90/2.36  % [INFO] 	 Killing All external provers ... 
% 5.90/2.37  % Time passed: 1837ms (effective reasoning time: 1313ms)
% 5.90/2.37  % 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)>
% 5.90/2.37  % Axioms used in derivation (3): symmetric_difference_and_difference, associativity_of_intersection, difference_difference_union2
% 5.90/2.37  % No. of inferences in proof: 22
% 5.90/2.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1837 ms resp. 1313 ms w/o parsing
% 5.90/2.40  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.90/2.40  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------