TSTP Solution File: SET904+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET904+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 03:04:27 EDT 2024

% Result   : Theorem 3.24s 2.13s
% Output   : Refutation 3.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   27 (  11 unt;   5 typ;   0 def)
%            Number of atoms       :   33 (   4 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  104 (  14   ~;   0   |;   0   &;  79   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   36 (   0   ^  32   !;   4   ?;  36   :)

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

thf(set_union2_type,type,
    set_union2: $i > $i > $i ).

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

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

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

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( set_union2 @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).

thf(24,plain,
    ! [A: $i] :
      ( ( set_union2 @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(29,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(7,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(27,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
     => ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
       => ( in @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(12,plain,
    ~ ! [A: $i,B: $i] :
        ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
       => ( in @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( empty @ A )
     => ~ ( empty @ ( set_union2 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).

thf(18,plain,
    ! [A: $i,B: $i] :
      ( ~ ( empty @ A )
     => ~ ( empty @ ( set_union2 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(31,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
     => ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).

thf(36,plain,
    ! [A: $i,B: $i] :
      ( ( subset @ ( set_union2 @ ( singleton @ A ) @ B ) @ B )
     => ( in @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( empty @ A )
     => ~ ( empty @ ( set_union2 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).

thf(15,plain,
    ! [A: $i,B: $i] :
      ( ~ ( empty @ A )
     => ~ ( empty @ ( set_union2 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( set_union2 @ A @ B )
      = ( set_union2 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

thf(21,plain,
    ! [A: $i,B: $i] :
      ( ( set_union2 @ A @ B )
      = ( set_union2 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

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

thf(33,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(40,plain,
    $false,
    inference(e,[status(thm)],[24,29,27,12,18,31,36,15,21,33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SET904+1 : TPTP v8.2.0. Released v3.2.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n012.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 12:00:09 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.97/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.26/1.10  % [INFO] 	 Parsing done (152ms). 
% 1.26/1.11  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.45  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.45  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.46  % [INFO] 	 Scanning for conjecture ... 
% 1.86/1.55  % [INFO] 	 Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ... 
% 2.04/1.58  % [INFO] 	 Axiom selection finished. Selected 9 axioms (removed 0 axioms). 
% 2.14/1.60  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.14/1.60  % [INFO] 	 Type checking passed. 
% 2.14/1.61  % [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 ... 
% 2.90/2.07  % External prover 'e' found a proof!
% 2.90/2.07  % [INFO] 	 Killing All external provers ... 
% 3.24/2.13  % Time passed: 1667ms (effective reasoning time: 1018ms)
% 3.24/2.13  % 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)>
% 3.24/2.13  % Axioms used in derivation (9): fc2_xboole_0, commutativity_k2_xboole_0, fc3_xboole_0, reflexivity_r1_tarski, l21_zfmisc_1, rc1_xboole_0, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 3.24/2.13  % No. of inferences in proof: 22
% 3.24/2.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1667 ms resp. 1018 ms w/o parsing
% 3.24/2.18  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.24/2.18  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------