TSTP Solution File: SEU123+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU123+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 11:57:05 EDT 2023

% Result   : Theorem 2.70s 1.61s
% Output   : Refutation 3.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   30 (  13 unt;   4 typ;   0 def)
%            Number of atoms       :   46 (  10 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   84 (  12   ~;   0   |;  10   &;  52   @)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (   0   ^;  26   !;   4   ?;  30   :)

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

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

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

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

thf(11,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(42,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( subset @ A @ empty_set )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

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

thf(14,plain,
    ~ ! [A: $i] :
        ( ( subset @ A @ empty_set )
       => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( subset @ A @ B )
        & ( subset @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(20,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( subset @ A @ B )
          & ( subset @ B @ A ) ) )
      & ( ( ( subset @ A @ B )
          & ( subset @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(35,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(5,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).

thf(31,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,axiom,
    ! [A: $i] : ( subset @ empty_set @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

thf(40,plain,
    ! [A: $i] : ( subset @ empty_set @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(9,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(38,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(7,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(33,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(6,axiom,
    empty @ empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(32,plain,
    empty @ empty_set,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(45,plain,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(48,plain,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

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

thf(18,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(56,plain,
    $false,
    inference(cvc4,[status(thm)],[42,14,20,35,31,40,38,33,32,45,48,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU123+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n020.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 13:30:18 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.92/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.96  % [INFO] 	 Parsing done (110ms). 
% 1.19/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.58/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.58/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.68/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.68/1.22  % [INFO] 	 Found a conjecture and 11 axioms. Running axiom selection ... 
% 1.84/1.24  % [INFO] 	 Axiom selection finished. Selected 11 axioms (removed 0 axioms). 
% 1.84/1.26  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.94/1.26  % [INFO] 	 Type checking passed. 
% 1.94/1.26  % [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 ... 
% 2.70/1.60  % External prover 'cvc4' found a proof!
% 2.70/1.60  % [INFO] 	 Killing All external provers ... 
% 2.70/1.61  % Time passed: 1079ms (effective reasoning time: 635ms)
% 2.70/1.61  % 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)>
% 2.70/1.61  % Axioms used in derivation (11): fc1_xboole_0, t6_boole, t7_boole, dt_k1_xboole_0, reflexivity_r1_tarski, t2_xboole_1, d10_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, t8_boole, rc1_xboole_0
% 2.70/1.61  % No. of inferences in proof: 26
% 2.70/1.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1079 ms resp. 635 ms w/o parsing
% 3.08/1.68  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.08/1.68  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------