TSTP Solution File: SET626+3 by Leo-III-SAT---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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  7 10:50:10 EDT 2024

% Result   : Theorem 277.28s 47.73s
% Output   : Refutation 277.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   41 (   9 unt;   7 typ;   0 def)
%            Number of atoms       :   92 (   6 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  306 (  20   ~;  16   |;  14   &; 240   @)
%                                         (   2 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   7 avg)
%            Number of types       :    2 (   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   :   70 (   0   ^  64   !;   6   ?;  70   :)

% Comments : 
%------------------------------------------------------------------------------
thf(intersect_type,type,
    intersect: $i > $i > $o ).

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

thf(member_type,type,
    member: $i > $i > $o ).

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

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

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

thf(sk4_type,type,
    sk4: $i > $i > $i ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( intersect @ A @ ( intersection @ B @ C ) )
     => ( intersect @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th102) ).

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

thf(8,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( intersect @ A @ ( intersection @ B @ C ) )
       => ( intersect @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ~ ! [A: $i,B: $i] :
        ( ? [C: $i] : ( intersect @ A @ ( intersection @ B @ C ) )
       => ( intersect @ A @ B ) ),
    inference(miniscope,[status(thm)],[8]) ).

thf(11,plain,
    intersect @ sk1 @ ( intersection @ sk2 @ sk3 ),
    inference(cnf,[status(esa)],[9]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( intersect @ A @ B )
    <=> ? [C: $i] :
          ( ( member @ C @ A )
          & ( member @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).

thf(18,plain,
    ! [A: $i,B: $i] :
      ( ( ( intersect @ A @ B )
       => ? [C: $i] :
            ( ( member @ C @ A )
            & ( member @ C @ B ) ) )
      & ( ? [C: $i] :
            ( ( member @ C @ A )
            & ( member @ C @ B ) )
       => ( intersect @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(19,plain,
    ( ! [A: $i,B: $i] :
        ( ( intersect @ A @ B )
       => ? [C: $i] :
            ( ( member @ C @ A )
            & ( member @ C @ B ) ) )
    & ! [A: $i,B: $i] :
        ( ? [C: $i] :
            ( ( member @ C @ A )
            & ( member @ C @ B ) )
       => ( intersect @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[18]) ).

thf(22,plain,
    ! [B: $i,A: $i] :
      ( ~ ( intersect @ A @ B )
      | ( member @ ( sk4 @ B @ A ) @ B ) ),
    inference(cnf,[status(esa)],[19]) ).

thf(1561,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk4 @ B @ A ) @ B )
      | ( ( intersect @ sk1 @ ( intersection @ sk2 @ sk3 ) )
       != ( intersect @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[11,22]) ).

thf(1562,plain,
    member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ ( intersection @ sk2 @ sk3 ),
    inference(pattern_uni,[status(thm)],[1561:[bind(A,$thf( sk1 )),bind(B,$thf( intersection @ sk2 @ sk3 ))]]) ).

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

thf(12,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( member @ C @ ( intersection @ A @ B ) )
       => ( ( member @ C @ A )
          & ( member @ C @ B ) ) )
      & ( ( ( member @ C @ A )
          & ( member @ C @ B ) )
       => ( member @ C @ ( intersection @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(13,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( member @ C @ ( intersection @ A @ B ) )
       => ( ( member @ C @ A )
          & ( member @ C @ B ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( ( member @ C @ A )
          & ( member @ C @ B ) )
       => ( member @ C @ ( intersection @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[12]) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ ( intersection @ A @ B ) )
      | ( member @ C @ A ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(2809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ C @ A )
      | ( ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ ( intersection @ sk2 @ sk3 ) )
       != ( member @ C @ ( intersection @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1562,15]) ).

thf(2810,plain,
    member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ sk2,
    inference(pattern_uni,[status(thm)],[2809:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ))]]) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ~ ( intersect @ A @ B )
      | ( member @ ( sk4 @ B @ A ) @ A ) ),
    inference(cnf,[status(esa)],[19]) ).

thf(1173,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk4 @ B @ A ) @ A )
      | ( ( intersect @ sk1 @ ( intersection @ sk2 @ sk3 ) )
       != ( intersect @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[11,21]) ).

thf(1174,plain,
    member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ sk1,
    inference(pattern_uni,[status(thm)],[1173:[bind(A,$thf( sk1 )),bind(B,$thf( intersection @ sk2 @ sk3 ))]]) ).

thf(20,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ A )
      | ~ ( member @ C @ B )
      | ( intersect @ A @ B ) ),
    inference(cnf,[status(esa)],[19]) ).

thf(23,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ A )
      | ~ ( member @ C @ B )
      | ( intersect @ A @ B ) ),
    inference(simp,[status(thm)],[20]) ).

thf(1349,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ A )
      | ( intersect @ A @ B )
      | ( ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ sk1 )
       != ( member @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1174,23]) ).

thf(1350,plain,
    ! [A: $i] :
      ( ~ ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ A )
      | ( intersect @ A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[1349:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ))]]) ).

thf(127429,plain,
    ! [A: $i] :
      ( ( intersect @ A @ sk1 )
      | ( ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ sk2 )
       != ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2810,1350]) ).

thf(127430,plain,
    intersect @ sk2 @ sk1,
    inference(pattern_uni,[status(thm)],[127429:[bind(A,$thf( sk2 ))]]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( intersect @ A @ B )
     => ( intersect @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).

thf(27,plain,
    ! [A: $i,B: $i] :
      ( ( intersect @ A @ B )
     => ( intersect @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ~ ( intersect @ A @ B )
      | ( intersect @ B @ A ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(127946,plain,
    ! [B: $i,A: $i] :
      ( ( intersect @ B @ A )
      | ( ( intersect @ sk2 @ sk1 )
       != ( intersect @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[127430,28]) ).

thf(127947,plain,
    intersect @ sk1 @ sk2,
    inference(pattern_uni,[status(thm)],[127946:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).

thf(10,plain,
    ~ ( intersect @ sk1 @ sk2 ),
    inference(cnf,[status(esa)],[9]) ).

thf(128252,plain,
    $false,
    inference(rewrite,[status(thm)],[127947,10]) ).

thf(128253,plain,
    $false,
    inference(simp,[status(thm)],[128252]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.32  % Computer : n028.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon May  6 20:52:24 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.99/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.19/1.07  % [INFO] 	 Parsing done (154ms). 
% 1.19/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.39  % [INFO] 	 nitpick registered as external prover. 
% 1.76/1.40  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.48  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.96/1.51  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 2.05/1.53  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.10/1.54  % [INFO] 	 Type checking passed. 
% 2.10/1.54  % [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 ... 
% 277.28/47.73  % [INFO] 	 Killing All external provers ... 
% 277.28/47.73  % Time passed: 47259ms (effective reasoning time: 46646ms)
% 277.28/47.73  % 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)>
% 277.28/47.73  % Axioms used in derivation (3): intersect_defn, intersection_defn, symmetry_of_intersect
% 277.28/47.73  % No. of inferences in proof: 34
% 277.28/47.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 47259 ms resp. 46646 ms w/o parsing
% 277.28/47.82  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 277.28/47.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------