TSTP Solution File: SWW469+1 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SWW469+1 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n022.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 : Mon Jun 24 18:22:37 EDT 2024

% Result   : Theorem 2.96s 2.10s
% Output   : Refutation 3.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   16 (  11 unt;   0 typ;   0 def)
%            Number of atoms       :   32 (   6 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   42 (  10   ~;   0   |;   7   &;  16   @)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   12 (   0   ^   6   !;   6   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(is_state_type,type,
    is_state: $i > $o ).

thf(undefined_state_type,type,
    undefined_state: $i > $i ).

thf(state_type,type,
    state: $i ).

thf(hoare_165779456gleton_type,type,
    hoare_165779456gleton: $o ).

thf(induct_false_type,type,
    induct_false: $o ).

thf(induct_true_type,type,
    induct_true: $o ).

thf(4,axiom,
    ( hoare_165779456gleton
  <=> ? [A: $i,B: $i] :
        ( ( is_state @ A )
        & ( is_state @ B )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).

thf(14,plain,
    ( ( hoare_165779456gleton
     => ? [A: $i,B: $i] :
          ( ( is_state @ A )
          & ( is_state @ B )
          & ( A != B ) ) )
    & ( ? [A: $i,B: $i] :
          ( ( is_state @ A )
          & ( is_state @ B )
          & ( A != B ) )
     => hoare_165779456gleton ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( is_state @ A )
     => ~ ! [B: $i] :
            ( ( is_state @ B )
           => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

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

thf(9,plain,
    ~ ! [A: $i] :
        ( ( is_state @ A )
       => ~ ! [B: $i] :
              ( ( is_state @ B )
             => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    is_state @ ( undefined_state @ state ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Ostate) ).

thf(13,plain,
    is_state @ ( undefined_state @ state ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ~ induct_false,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_induct__false__def) ).

thf(22,plain,
    ~ induct_false,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    hoare_165779456gleton,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(26,plain,
    hoare_165779456gleton,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    induct_true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_induct__trueI) ).

thf(24,plain,
    induct_true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(7,axiom,
    induct_true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_induct__true__def) ).

thf(25,plain,
    induct_true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(28,plain,
    $false,
    inference(e,[status(thm)],[14,9,13,22,26,24,25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SWW469+1 : TPTP v8.2.0. Released v5.3.0.
% 0.06/0.11  % Command  : run_Leo-III %s %d THM
% 0.10/0.31  % Computer : n022.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Wed Jun 19 04:48:40 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.99/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.33/1.13  % [INFO] 	 Parsing done (154ms). 
% 1.33/1.14  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.52  % [INFO] 	 eprover registered as external prover. 
% 1.80/1.53  % [INFO] 	 Scanning for conjecture ... 
% 2.05/1.61  % [INFO] 	 Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ... 
% 2.05/1.64  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 2.21/1.66  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.21/1.66  % [INFO] 	 Type checking passed. 
% 2.21/1.66  % [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 ... 
% 2.96/2.10  % External prover 'e' found a proof!
% 2.96/2.10  % [INFO] 	 Killing All external provers ... 
% 2.96/2.10  % Time passed: 1610ms (effective reasoning time: 950ms)
% 2.96/2.10  % 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)>
% 2.96/2.10  % Axioms used in derivation (6): gsy_c_HOL_Oundefined_000tc__Com__Ostate, fact_0_state__not__singleton__def, fact_3_induct__true__def, fact_1_induct__false__def, conj_0, fact_2_induct__trueI
% 2.96/2.10  % No. of inferences in proof: 16
% 2.96/2.10  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1610 ms resp. 950 ms w/o parsing
% 3.09/2.14  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.09/2.14  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------