TSTP Solution File: SET974+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 03:04:41 EDT 2024

% Result   : Theorem 3.42s 2.03s
% Output   : Refutation 3.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   34 (  15 unt;   8 typ;   0 def)
%            Number of atoms       :   48 (  10 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  192 (  20   ~;   3   |;  12   &; 150   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   1 con; 0-2 aty)
%            Number of variables   :   65 (   0   ^  59   !;   6   ?;  65   :)

% Comments : 
%------------------------------------------------------------------------------
thf(disjoint_type,type,
    disjoint: $i > $i > $o ).

thf(cartesian_product2_type,type,
    cartesian_product2: $i > $i > $i ).

thf(in_type,type,
    in: $i > $i > $o ).

thf(unordered_pair_type,type,
    unordered_pair: $i > $i > $i ).

thf(set_intersection2_type,type,
    set_intersection2: $i > $i > $i ).

thf(ordered_pair_type,type,
    ordered_pair: $i > $i > $i ).

thf(singleton_type,type,
    singleton: $i > $i ).

thf(empty_type,type,
    empty: $i > $o ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( ordered_pair @ A @ B )
      = ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

thf(25,plain,
    ! [A: $i,B: $i] :
      ( ( ordered_pair @ A @ B )
      = ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( disjoint @ A @ B )
        | ( disjoint @ C @ D ) )
     => ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( disjoint @ A @ B )
          | ( disjoint @ C @ D ) )
       => ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(14,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( disjoint @ A @ B )
          | ( disjoint @ C @ D ) )
       => ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ~ ( empty @ ( ordered_pair @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

thf(28,plain,
    ! [A: $i,B: $i] :
      ~ ( empty @ ( ordered_pair @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
        & ! [F: $i,G: $i] :
            ~ ( ( A
                = ( ordered_pair @ F @ G ) )
              & ( in @ F @ ( set_intersection2 @ B @ D ) )
              & ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).

thf(41,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
        & ! [F: $i,G: $i] :
            ~ ( ( A
                = ( ordered_pair @ F @ G ) )
              & ( in @ F @ ( set_intersection2 @ B @ D ) )
              & ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

thf(22,plain,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
     => ( disjoint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

thf(39,plain,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
     => ( disjoint @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

thf(31,plain,
    ! [A: $i] :
      ( ( set_intersection2 @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( disjoint @ A @ B )
          & ! [C: $i] :
              ~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
      & ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
          & ( disjoint @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).

thf(47,plain,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( disjoint @ A @ B )
          & ! [C: $i] :
              ~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
      & ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
          & ( disjoint @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(9,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(34,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(17,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(36,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(19,plain,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(54,plain,
    $false,
    inference(e,[status(thm)],[25,14,28,41,22,39,31,47,34,17,36,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% 0.09/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon May 20 12:39:53 EDT 2024
% 0.13/0.36  % CPUTime  : 
% 0.94/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.08  % [INFO] 	 Parsing done (122ms). 
% 1.28/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.36  % [INFO] 	 eprover registered as external prover. 
% 1.59/1.36  % [INFO] 	 cvc4 registered as external prover. 
% 1.59/1.37  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ... 
% 1.93/1.46  % [INFO] 	 Axiom selection finished. Selected 11 axioms (removed 0 axioms). 
% 1.93/1.48  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.93/1.49  % [INFO] 	 Type checking passed. 
% 1.93/1.49  % [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 ... 
% 3.42/2.02  % External prover 'e' found a proof!
% 3.42/2.02  % [INFO] 	 Killing All external provers ... 
% 3.42/2.02  % Time passed: 1486ms (effective reasoning time: 931ms)
% 3.42/2.03  % 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)>
% 3.42/2.03  % Axioms used in derivation (11): fc1_zfmisc_1, idempotence_k3_xboole_0, d5_tarski, commutativity_k3_xboole_0, t4_xboole_0, t104_zfmisc_1, commutativity_k2_tarski, rc1_xboole_0, symmetry_r1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 3.42/2.03  % No. of inferences in proof: 26
% 3.42/2.03  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1486 ms resp. 931 ms w/o parsing
% 3.50/2.08  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.50/2.08  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------