TSTP Solution File: SEU162+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU162+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 11:57:18 EDT 2023

% Result   : Theorem 2.65s 1.66s
% Output   : Refutation 3.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   22 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :   35 (   7 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   97 (  12   ~;   0   |;   4   &;  68   @)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   26 (   0   ^;  26   !;   0   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_difference_type,type,
    set_difference: $i > $i > $i ).

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

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

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

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( set_difference @ A @ ( singleton @ B ) )
        = A )
    <=> ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).

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

thf(10,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( ( set_difference @ A @ ( singleton @ B ) )
            = A )
         => ~ ( in @ B @ A ) )
        & ( ~ ( in @ B @ A )
         => ( ( set_difference @ A @ ( singleton @ B ) )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).

thf(22,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
     => ( disjoint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

thf(28,plain,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
     => ( disjoint @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(4,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).

thf(21,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( in @ A @ B )
     => ( disjoint @ ( singleton @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).

thf(26,plain,
    ! [A: $i,B: $i] :
      ( ~ ( in @ A @ B )
     => ( disjoint @ ( singleton @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( disjoint @ ( singleton @ A ) @ B )
        & ( in @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).

thf(23,plain,
    ! [A: $i,B: $i] :
      ~ ( ( disjoint @ ( singleton @ A ) @ B )
        & ( in @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
    <=> ( ( set_difference @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).

thf(30,plain,
    ! [A: $i,B: $i] :
      ( ( ( disjoint @ A @ B )
       => ( ( set_difference @ A @ B )
          = A ) )
      & ( ( ( set_difference @ A @ B )
          = A )
       => ( disjoint @ A @ B ) ) ),
    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(19,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(44,plain,
    $false,
    inference(cvc4,[status(thm)],[10,22,28,21,26,23,30,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU162+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu May 18 12:46:37 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.83/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.14/0.95  % [INFO] 	 Parsing done (107ms). 
% 1.14/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.47/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.47/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.66/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.24  % [INFO] 	 Found a conjecture and 7 axioms. Running axiom selection ... 
% 1.76/1.26  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.76/1.27  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.76/1.28  % [INFO] 	 Type checking passed. 
% 1.76/1.28  % [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 ... 
% 2.65/1.66  % External prover 'cvc4' found a proof!
% 2.65/1.66  % [INFO] 	 Killing All external provers ... 
% 2.65/1.66  % Time passed: 1136ms (effective reasoning time: 692ms)
% 2.65/1.66  % 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)>
% 2.65/1.66  % Axioms used in derivation (7): dt_k1_tarski, l25_zfmisc_1, antisymmetry_r2_hidden, t83_xboole_1, l28_zfmisc_1, dt_k4_xboole_0, symmetry_r1_xboole_0
% 2.65/1.66  % No. of inferences in proof: 18
% 2.65/1.66  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1136 ms resp. 692 ms w/o parsing
% 3.01/1.73  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.01/1.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------