TSTP Solution File: SEU148+3 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 : Fri May 19 11:57:13 EDT 2023

% Result   : Theorem 2.62s 1.60s
% Output   : Refutation 3.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   25 (  11 unt;   5 typ;   0 def)
%            Number of atoms       :   43 (  19 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   88 (   8   ~;   3   |;   4   &;  57   @)
%                                         (   3 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   30 (   0   ^;  26   !;   4   ?;  30   :)

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

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

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

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

thf(empty_set_type,type,
    empty_set: $i ).

thf(8,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(52,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(10,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(57,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( singleton @ A )
     != empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).

thf(38,plain,
    ! [A: $i] :
      ( ( singleton @ A )
     != empty_set ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( singleton @ A ) )
    <=> ! [C: $i] :
          ( ( in @ C @ B )
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

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

thf(9,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(54,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).

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

thf(11,plain,
    ~ ! [A: $i,B: $i] :
        ( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
       => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(15,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ ( singleton @ B ) )
    <=> ( ( A = empty_set )
        | ( A
          = ( singleton @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).

thf(42,plain,
    ! [A: $i,B: $i] :
      ( ( ( subset @ A @ ( singleton @ B ) )
       => ( ( A = empty_set )
          | ( A
            = ( singleton @ B ) ) ) )
      & ( ( ( A = empty_set )
          | ( A
            = ( singleton @ B ) ) )
       => ( subset @ A @ ( singleton @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    empty @ empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(37,plain,
    empty @ empty_set,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(59,plain,
    $false,
    inference(e,[status(thm)],[52,57,38,17,54,11,15,42,37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n014.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 12:59:28 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.82/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.16/0.96  % [INFO] 	 Parsing done (109ms). 
% 1.16/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.44/1.15  % [INFO] 	 eprover registered as external prover. 
% 1.44/1.15  % [INFO] 	 cvc4 registered as external prover. 
% 1.44/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.21  % [INFO] 	 Found a conjecture and 8 axioms. Running axiom selection ... 
% 1.74/1.23  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.84/1.24  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.84/1.24  % [INFO] 	 Type checking passed. 
% 1.84/1.24  % [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 ... 
% 2.62/1.60  % External prover 'e' found a proof!
% 2.62/1.60  % [INFO] 	 Killing All external provers ... 
% 2.62/1.60  % Time passed: 1076ms (effective reasoning time: 634ms)
% 2.62/1.60  % 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)>
% 2.62/1.60  % Axioms used in derivation (8): d1_tarski, fc1_xboole_0, l4_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0, l1_zfmisc_1, antisymmetry_r2_hidden
% 2.62/1.60  % No. of inferences in proof: 20
% 2.62/1.60  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1076 ms resp. 634 ms w/o parsing
% 3.11/1.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.11/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------