TSTP Solution File: SEU156+1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : SEU156+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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  7 08:08:58 EDT 2024

% Result   : Theorem 2.82s 1.92s
% Output   : Refutation 3.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   37 (  21 unt;   5 typ;   0 def)
%            Number of atoms       :   48 (  31 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  110 (  12   ~;   0   |;   7   &;  82   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   57 (   0   ^  53   !;   4   ?;  57   :)

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

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

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

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

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

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ordered_pair @ A @ B )
      = ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
    file('/export/starexec/sandbox/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)],[4]) ).

thf(6,axiom,
    $true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).

thf(29,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    $true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).

thf(28,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( ( unordered_pair @ A @ B )
          = ( unordered_pair @ C @ D ) )
        & ( A != C )
        & ( A != D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).

thf(41,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( ( unordered_pair @ A @ B )
          = ( unordered_pair @ C @ D ) )
        & ( A != C )
        & ( A != D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(22,plain,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

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

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).

thf(48,plain,
    ! [A: $i,B: $i] :
      ( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ~ ( empty @ ( ordered_pair @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

thf(31,plain,
    ! [A: $i,B: $i] :
      ~ ( empty @ ( ordered_pair @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( singleton @ A )
        = ( unordered_pair @ B @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).

thf(55,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( singleton @ A )
        = ( unordered_pair @ B @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

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

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

thf(13,axiom,
    ! [A: $i] :
      ( ( unordered_pair @ A @ A )
      = ( singleton @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

thf(45,plain,
    ! [A: $i] :
      ( ( unordered_pair @ A @ A )
      = ( singleton @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ordered_pair @ A @ B )
        = ( ordered_pair @ C @ D ) )
     => ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).

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

thf(17,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( ordered_pair @ A @ B )
          = ( ordered_pair @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

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

thf(7,axiom,
    $true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).

thf(30,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( singleton @ A )
        = ( unordered_pair @ B @ C ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).

thf(51,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( singleton @ A )
        = ( unordered_pair @ B @ C ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(64,plain,
    $false,
    inference(cvc4,[status(thm)],[25,29,28,41,22,39,48,31,55,34,45,17,36,30,51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : SEU156+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon May  6 10:37:54 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.89/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.11/1.02  % [INFO] 	 Parsing done (150ms). 
% 1.11/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.33  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.34  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.34  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.42  % [INFO] 	 Found a conjecture and 14 axioms. Running axiom selection ... 
% 1.86/1.45  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 1.94/1.48  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.94/1.48  % [INFO] 	 Type checking passed. 
% 1.94/1.48  % [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 ... 
% 2.82/1.92  % External prover 'cvc4' found a proof!
% 2.82/1.92  % [INFO] 	 Killing All external provers ... 
% 2.82/1.92  % Time passed: 1464ms (effective reasoning time: 883ms)
% 2.82/1.92  % 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)>
% 2.82/1.92  % Axioms used in derivation (14): fc1_zfmisc_1, dt_k4_tarski, dt_k2_tarski, t8_zfmisc_1, t9_zfmisc_1, commutativity_k2_tarski, t69_enumset1, reflexivity_r1_tarski, t6_zfmisc_1, rc1_xboole_0, t10_zfmisc_1, rc2_xboole_0, dt_k1_tarski, d5_tarski
% 2.82/1.92  % No. of inferences in proof: 32
% 2.82/1.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1464 ms resp. 883 ms w/o parsing
% 3.17/1.94  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.17/1.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------