TSTP Solution File: SET194+3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET194+3 : TPTP v8.2.0. Released v2.2.0.
% 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 03:05:40 EDT 2024

% Result   : Theorem 8.19s 3.10s
% Output   : Refutation 8.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   30 (   7 unt;   6 typ;   0 def)
%            Number of atoms       :   65 (   2 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  223 (  10   ~;  18   |;   4   &; 176   @)
%                                         (   2 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   65 (   0   ^  65   !;   0   ?;  65   :)

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

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

thf(1,conjecture,
    ! [A: $i,B: $i] : ( subset @ A @ ( union @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_of_union) ).

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

thf(8,plain,
    ~ ! [A: $i,B: $i] : ( subset @ A @ ( union @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ~ ( subset @ sk1 @ ( union @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
    <=> ! [C: $i] :
          ( ( member @ C @ A )
         => ( member @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

thf(17,plain,
    ! [A: $i,B: $i] :
      ( ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) ) )
      & ( ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) )
       => ( subset @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(18,plain,
    ( ! [A: $i,B: $i] :
        ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) ) )
    & ! [A: $i,B: $i] :
        ( ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) )
       => ( subset @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[17]) ).

thf(19,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk3 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[18]) ).

thf(22,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk3 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[19]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( member @ C @ ( union @ A @ B ) )
    <=> ( ( member @ C @ A )
        | ( member @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

thf(10,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( member @ C @ ( union @ A @ B ) )
       => ( ( member @ C @ A )
          | ( member @ C @ B ) ) )
      & ( ( ( member @ C @ A )
          | ( member @ C @ B ) )
       => ( member @ C @ ( union @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( member @ C @ ( union @ A @ B ) )
       => ( ( member @ C @ A )
          | ( member @ C @ B ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( ( member @ C @ A )
          | ( member @ C @ B ) )
       => ( member @ C @ ( union @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[10]) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ A )
      | ( member @ C @ ( union @ A @ B ) ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ C @ A )
      | ( member @ C @ ( union @ A @ B ) ) ),
    inference(simp,[status(thm)],[12]) ).

thf(89,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( subset @ A @ B )
      | ( member @ E @ ( union @ C @ D ) )
      | ( ( member @ ( sk3 @ B @ A ) @ A )
       != ( member @ E @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[22,15]) ).

thf(90,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset @ C @ B )
      | ( member @ ( sk3 @ B @ C ) @ ( union @ C @ A ) ) ),
    inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( sk3 @ F @ G ))]]) ).

thf(106,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset @ C @ B )
      | ( member @ ( sk3 @ B @ C ) @ ( union @ C @ A ) ) ),
    inference(simp,[status(thm)],[90]) ).

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ~ ( member @ ( sk3 @ B @ A ) @ B )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[18]) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ~ ( member @ ( sk3 @ B @ A ) @ B )
      | ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[20]) ).

thf(509,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( subset @ C @ B )
      | ( subset @ D @ E )
      | ( ( member @ ( sk3 @ B @ C ) @ ( union @ C @ A ) )
       != ( member @ ( sk3 @ E @ D ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[106,23]) ).

thf(510,plain,
    ! [B: $i,A: $i] :
      ( ( subset @ A @ ( union @ A @ B ) )
      | ( subset @ A @ ( union @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[509:[bind(A,$thf( G )),bind(B,$thf( union @ F @ G )),bind(C,$thf( F )),bind(D,$thf( F )),bind(E,$thf( union @ F @ G ))]]) ).

thf(526,plain,
    ! [B: $i,A: $i] : ( subset @ A @ ( union @ A @ B ) ),
    inference(simp,[status(thm)],[510]) ).

thf(527,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[9,526]) ).

thf(528,plain,
    $false,
    inference(simp,[status(thm)],[527]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET194+3 : TPTP v8.2.0. Released v2.2.0.
% 0.02/0.12  % Command  : run_Leo-III %s %d
% 0.13/0.32  % Computer : n017.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Mon May 20 12:21:09 EDT 2024
% 0.13/0.32  % CPUTime  : 
% 0.98/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.27/1.09  % [INFO] 	 Parsing done (150ms). 
% 1.27/1.11  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.45  % [INFO] 	 nitpick registered as external prover. 
% 1.71/1.46  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.54  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 1.98/1.57  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.98/1.58  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.98/1.59  % [INFO] 	 Type checking passed. 
% 1.98/1.59  % [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 ... 
% 8.19/3.09  % [INFO] 	 Killing All external provers ... 
% 8.19/3.10  % Time passed: 2618ms (effective reasoning time: 1979ms)
% 8.19/3.10  % 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)>
% 8.19/3.10  % Axioms used in derivation (2): subset_defn, union_defn
% 8.19/3.10  % No. of inferences in proof: 24
% 8.19/3.10  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2618 ms resp. 1979 ms w/o parsing
% 8.19/3.16  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.19/3.16  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------