TSTP Solution File: SET619+3 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET619+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 03:06:31 EDT 2024

% Result   : Theorem 93.72s 14.56s
% Output   : Refutation 93.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   54 (  39 unt;   6 typ;   0 def)
%            Number of atoms       :   60 (  59 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  380 (  32   ~;  12   |;   0   &; 336   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   80 (   0   ^  80   !;   0   ?;  80   :)

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

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

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

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

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

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

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_difference) ).

thf(28,plain,
    ! [A: $i,B: $i] :
      ( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
      = A ),
    inference(cnf,[status(esa)],[28]) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
      = A ),
    inference(lifteq,[status(thm)],[29]) ).

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

thf(22,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( union @ ( union @ A @ B ) @ C )
      = ( union @ A @ ( union @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(23,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( union @ ( union @ A @ B ) @ C )
      = ( union @ A @ ( union @ B @ C ) ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( union @ ( union @ A @ B ) @ C )
      = ( union @ A @ ( union @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[23]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( union @ A @ B )
      = ( union @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).

thf(55,plain,
    ! [A: $i,B: $i] :
      ( ( union @ A @ B )
      = ( union @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(56,plain,
    ! [B: $i,A: $i] :
      ( ( union @ A @ B )
      = ( union @ B @ A ) ),
    inference(cnf,[status(esa)],[55]) ).

thf(57,plain,
    ! [B: $i,A: $i] :
      ( ( union @ A @ B )
      = ( union @ B @ A ) ),
    inference(lifteq,[status(thm)],[56]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( symmetric_difference @ A @ B )
      = ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).

thf(19,plain,
    ! [A: $i,B: $i] :
      ( ( symmetric_difference @ A @ B )
      = ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ( symmetric_difference @ A @ B )
      = ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
    inference(cnf,[status(esa)],[19]) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ( symmetric_difference @ A @ B )
      = ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[20]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( union @ A @ B )
      = ( union @ ( symmetric_difference @ A @ B ) @ ( intersection @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th95) ).

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

thf(16,plain,
    ~ ! [A: $i,B: $i] :
        ( ( union @ A @ B )
        = ( union @ ( symmetric_difference @ A @ B ) @ ( intersection @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(17,plain,
    ( ( union @ sk1 @ sk2 )
   != ( union @ ( symmetric_difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk2 ) ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(18,plain,
    ( ( union @ ( symmetric_difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk2 ) )
   != ( union @ sk1 @ sk2 ) ),
    inference(lifteq,[status(thm)],[17]) ).

thf(256,plain,
    ! [B: $i,A: $i] :
      ( ( ( union @ ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) @ ( intersection @ sk1 @ sk2 ) )
       != ( union @ sk1 @ sk2 ) )
      | ( ( symmetric_difference @ A @ B )
       != ( symmetric_difference @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[21,18]) ).

thf(257,plain,
    ( ( union @ ( union @ ( difference @ sk1 @ sk2 ) @ ( difference @ sk2 @ sk1 ) ) @ ( intersection @ sk1 @ sk2 ) )
   != ( union @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(724,plain,
    ( ( union @ ( difference @ sk1 @ sk2 ) @ ( union @ ( difference @ sk2 @ sk1 ) @ ( intersection @ sk1 @ sk2 ) ) )
   != ( union @ sk1 @ sk2 ) ),
    inference(rewrite,[status(thm)],[257,24]) ).

thf(862,plain,
    ! [B: $i,A: $i] :
      ( ( ( union @ B @ A )
       != ( union @ sk1 @ sk2 ) )
      | ( ( union @ A @ B )
       != ( union @ ( difference @ sk1 @ sk2 ) @ ( union @ ( difference @ sk2 @ sk1 ) @ ( intersection @ sk1 @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[57,724]) ).

thf(863,plain,
    ( ( union @ ( union @ ( difference @ sk2 @ sk1 ) @ ( intersection @ sk1 @ sk2 ) ) @ ( difference @ sk1 @ sk2 ) )
   != ( union @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[862:[bind(A,$thf( difference @ sk1 @ sk2 )),bind(B,$thf( union @ ( difference @ sk2 @ sk1 ) @ ( intersection @ sk1 @ sk2 ) ))]]) ).

thf(907,plain,
    ( ( union @ ( difference @ sk2 @ sk1 ) @ ( union @ ( intersection @ sk1 @ sk2 ) @ ( difference @ sk1 @ sk2 ) ) )
   != ( union @ sk1 @ sk2 ) ),
    inference(rewrite,[status(thm)],[863,24]) ).

thf(1330,plain,
    ( ( union @ ( difference @ sk2 @ sk1 ) @ sk1 )
   != ( union @ sk1 @ sk2 ) ),
    inference(rewrite,[status(thm)],[907,30]) ).

thf(1468,plain,
    ! [B: $i,A: $i] :
      ( ( ( union @ B @ A )
       != ( union @ sk1 @ sk2 ) )
      | ( ( union @ A @ B )
       != ( union @ ( difference @ sk2 @ sk1 ) @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[57,1330]) ).

thf(1469,plain,
    ( ( union @ sk1 @ ( difference @ sk2 @ sk1 ) )
   != ( union @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[1468:[bind(A,$thf( difference @ sk2 @ sk1 )),bind(B,$thf( sk1 ))]]) ).

thf(1495,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( union @ A @ ( union @ B @ C ) )
       != ( union @ sk1 @ sk2 ) )
      | ( ( union @ ( union @ A @ B ) @ C )
       != ( union @ sk1 @ ( difference @ sk2 @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,1469]) ).

thf(1526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != sk1 )
      | ( ( union @ B @ C )
       != sk2 )
      | ( ( union @ A @ B )
       != sk1 )
      | ( C
       != ( difference @ sk2 @ sk1 ) ) ),
    inference(simp,[status(thm)],[1495]) ).

thf(1537,plain,
    ! [A: $i] :
      ( ( ( union @ A @ ( difference @ sk2 @ sk1 ) )
       != sk2 )
      | ( ( union @ sk1 @ A )
       != sk1 ) ),
    inference(simp,[status(thm)],[1526]) ).

thf(18954,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != sk2 )
      | ( ( union @ sk1 @ C )
       != sk1 )
      | ( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
       != ( union @ C @ ( difference @ sk2 @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30,1537]) ).

thf(18955,plain,
    ( ( sk2 != sk2 )
    | ( ( union @ sk1 @ ( intersection @ sk2 @ sk1 ) )
     != sk1 ) ),
    inference(pattern_uni,[status(thm)],[18954:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( intersection @ sk2 @ sk1 ))]]) ).

thf(18989,plain,
    ( ( union @ sk1 @ ( intersection @ sk2 @ sk1 ) )
   != sk1 ),
    inference(simp,[status(thm)],[18955]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( intersection @ A @ B )
      = ( intersection @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

thf(58,plain,
    ! [A: $i,B: $i] :
      ( ( intersection @ A @ B )
      = ( intersection @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(59,plain,
    ! [B: $i,A: $i] :
      ( ( intersection @ A @ B )
      = ( intersection @ B @ A ) ),
    inference(cnf,[status(esa)],[58]) ).

thf(60,plain,
    ! [B: $i,A: $i] :
      ( ( intersection @ A @ B )
      = ( intersection @ B @ A ) ),
    inference(lifteq,[status(thm)],[59]) ).

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

thf(25,plain,
    ! [A: $i,B: $i] :
      ( ( union @ A @ ( intersection @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ( union @ A @ ( intersection @ A @ B ) )
      = A ),
    inference(cnf,[status(esa)],[25]) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ( union @ A @ ( intersection @ A @ B ) )
      = A ),
    inference(lifteq,[status(thm)],[26]) ).

thf(631,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( union @ C @ ( intersection @ B @ A ) )
        = C )
      | ( ( intersection @ A @ B )
       != ( intersection @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[60,27]) ).

thf(632,plain,
    ! [B: $i,A: $i] :
      ( ( union @ A @ ( intersection @ B @ A ) )
      = A ),
    inference(pattern_uni,[status(thm)],[631:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(19575,plain,
    sk1 != sk1,
    inference(rewrite,[status(thm)],[18989,632]) ).

thf(19576,plain,
    $false,
    inference(simp,[status(thm)],[19575]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET619+3 : TPTP v8.2.0. Released v2.2.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon May 20 12:47:24 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 1.01/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/1.15  % [INFO] 	 Parsing done (167ms). 
% 1.28/1.17  % [INFO] 	 Running in sequential loop mode. 
% 1.98/1.54  % [INFO] 	 nitpick registered as external prover. 
% 1.98/1.54  % [INFO] 	 Scanning for conjecture ... 
% 2.13/1.64  % [INFO] 	 Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ... 
% 2.13/1.67  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 2.28/1.71  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.28/1.71  % [INFO] 	 Type checking passed. 
% 2.28/1.72  % [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 ... 
% 93.72/14.55  % [INFO] 	 Killing All external provers ... 
% 93.72/14.55  % Time passed: 14052ms (effective reasoning time: 13374ms)
% 93.72/14.55  % 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)>
% 93.72/14.56  % Axioms used in derivation (6): union_intersection, associativity_of_union, union_intersection_difference, symmetric_difference_defn, commutativity_of_intersection, commutativity_of_union
% 93.72/14.56  % No. of inferences in proof: 48
% 93.72/14.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14052 ms resp. 13374 ms w/o parsing
% 93.72/14.60  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 93.72/14.60  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------