TSTP Solution File: ITP028^1 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : ITP028^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n019.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 09:27:38 EDT 2024

% Result   : Theorem 8.35s 2.83s
% Output   : Refutation 8.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   20 (  10 unt;   0 typ;   0 def)
%            Number of atoms       :   54 (   1 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  165 (  25   ~;  18   |;   6   &; 108   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :   16 (  15 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :    8 (   0   ^   6   !;   2   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_Pr1710391469_a_a_e_type,type,
    set_Pr1710391469_a_a_e: $tType ).

thf(produc169085773_a_a_e_type,type,
    produc169085773_a_a_e: $tType ).

thf(set_se821189730_a_a_e_type,type,
    set_se821189730_a_a_e: $tType ).

thf(set_Pr2045688071_set_a_type,type,
    set_Pr2045688071_set_a: $tType ).

thf(set_Pr204296108_a_a_e_type,type,
    set_Pr204296108_a_a_e: $tType ).

thf(set_Pr305929312_set_a_type,type,
    set_Pr305929312_set_a: $tType ).

thf(produc1691597095_set_a_type,type,
    produc1691597095_set_a: $tType ).

thf(produc715398134_a_a_e_type,type,
    produc715398134_a_a_e: $tType ).

thf(produc1965228714_set_a_type,type,
    produc1965228714_set_a: $tType ).

thf(set_set_set_a_type,type,
    set_set_set_a: $tType ).

thf(set_set_a_type,type,
    set_set_a: $tType ).

thf(set_a_e_type,type,
    set_a_e: $tType ).

thf(set_a_type,type,
    set_a: $tType ).

thf(e_type,type,
    e: $tType ).

thf(a_type,type,
    a: $tType ).

thf(ord_less_eq_set_a_type,type,
    ord_less_eq_set_a: set_a > set_a > $o ).

thf(produc1040928388_a_a_e_type,type,
    produc1040928388_a_a_e: produc715398134_a_a_e > set_a ).

thf(image_64240033_set_a_type,type,
    image_64240033_set_a: ( produc715398134_a_a_e > set_a ) > set_Pr204296108_a_a_e > set_set_a ).

thf(member_set_a_type,type,
    member_set_a: set_a > set_set_a > $o ).

thf(c_type,type,
    c: set_Pr204296108_a_a_e ).

thf(a1_type,type,
    a1: set_a ).

thf(a2_type,type,
    a2: set_a ).

thf(a3_type,type,
    a3: set_a ).

thf(thesis_type,type,
    thesis: $o ).

thf(sk30_type,type,
    sk30: set_a ).

thf(85,axiom,
    ? [A: set_a] :
      ( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
      & ( ord_less_eq_set_a @ a1 @ A )
      & ( ord_less_eq_set_a @ a2 @ A )
      & ( ord_less_eq_set_a @ a3 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062) ).

thf(392,plain,
    ? [A: set_a] :
      ( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
      & ( ord_less_eq_set_a @ a1 @ A )
      & ( ord_less_eq_set_a @ a2 @ A )
      & ( ord_less_eq_set_a @ a3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(396,plain,
    member_set_a @ sk30 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ),
    inference(cnf,[status(esa)],[392]) ).

thf(393,plain,
    ord_less_eq_set_a @ a3 @ sk30,
    inference(cnf,[status(esa)],[392]) ).

thf(102,axiom,
    ! [A: set_a] :
      ( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
     => ( ( ord_less_eq_set_a @ a1 @ A )
       => ( ( ord_less_eq_set_a @ a2 @ A )
         => ( ( ord_less_eq_set_a @ a3 @ A )
           => thesis ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(445,plain,
    ! [A: set_a] :
      ( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
     => ( ( ord_less_eq_set_a @ a1 @ A )
       => ( ( ord_less_eq_set_a @ a2 @ A )
         => ( ( ord_less_eq_set_a @ a3 @ A )
           => thesis ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(446,plain,
    ! [A: set_a] :
      ( ~ ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
      | ~ ( ord_less_eq_set_a @ a1 @ A )
      | ~ ( ord_less_eq_set_a @ a2 @ A )
      | ~ ( ord_less_eq_set_a @ a3 @ A )
      | thesis ),
    inference(cnf,[status(esa)],[445]) ).

thf(1,conjecture,
    thesis,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(2,negated_conjecture,
    ~ thesis,
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(103,plain,
    ~ thesis,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(448,plain,
    ! [A: set_a] :
      ( ~ ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
      | ~ ( ord_less_eq_set_a @ a1 @ A )
      | ~ ( ord_less_eq_set_a @ a2 @ A )
      | ~ ( ord_less_eq_set_a @ a3 @ A )
      | $false ),
    inference(rewrite,[status(thm)],[446,103]) ).

thf(449,plain,
    ! [A: set_a] :
      ( ~ ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
      | ~ ( ord_less_eq_set_a @ a1 @ A )
      | ~ ( ord_less_eq_set_a @ a2 @ A )
      | ~ ( ord_less_eq_set_a @ a3 @ A ) ),
    inference(simp,[status(thm)],[448]) ).

thf(456,plain,
    ! [A: set_a] :
      ( ~ ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
      | ~ ( ord_less_eq_set_a @ a1 @ A )
      | ~ ( ord_less_eq_set_a @ a2 @ A )
      | ( ( ord_less_eq_set_a @ a3 @ sk30 )
       != ( ord_less_eq_set_a @ a3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[393,449]) ).

thf(457,plain,
    ( ~ ( member_set_a @ sk30 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
    | ~ ( ord_less_eq_set_a @ a1 @ sk30 )
    | ~ ( ord_less_eq_set_a @ a2 @ sk30 ) ),
    inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( sk30 ))]]) ).

thf(394,plain,
    ord_less_eq_set_a @ a2 @ sk30,
    inference(cnf,[status(esa)],[392]) ).

thf(395,plain,
    ord_less_eq_set_a @ a1 @ sk30,
    inference(cnf,[status(esa)],[392]) ).

thf(512,plain,
    ( ~ ( member_set_a @ sk30 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[457,394,395]) ).

thf(513,plain,
    ~ ( member_set_a @ sk30 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ),
    inference(simp,[status(thm)],[512]) ).

thf(662,plain,
    $false,
    inference(rewrite,[status(thm)],[396,513]) ).

thf(663,plain,
    $false,
    inference(simp,[status(thm)],[662]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP028^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d SAT
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Jun 19 00:09:25 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.85/1.09  % [INFO] 	 Parsing done (226ms). 
% 1.85/1.10  % [INFO] 	 Running in sequential loop mode. 
% 2.58/1.31  % [INFO] 	 nitpick registered as external prover. 
% 2.58/1.31  % [INFO] 	 Scanning for conjecture ... 
% 2.73/1.40  % [INFO] 	 Found a conjecture (or negated_conjecture) and 353 axioms. Running axiom selection ... 
% 3.02/1.47  % [INFO] 	 Axiom selection finished. Selected 100 axioms (removed 253 axioms). 
% 3.30/1.56  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.30/1.57  % [INFO] 	 Type checking passed. 
% 3.30/1.57  % [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 ... 
% 8.35/2.82  % [INFO] 	 Killing All external provers ... 
% 8.35/2.82  % Time passed: 2292ms (effective reasoning time: 1719ms)
% 8.35/2.82  % 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)>
% 8.35/2.83  % Axioms used in derivation (2): fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062, conj_0
% 8.35/2.83  % No. of inferences in proof: 20
% 8.35/2.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2292 ms resp. 1719 ms w/o parsing
% 8.35/2.84  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.35/2.84  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------