TSTP Solution File: SET658+3 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET658+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 03:06:42 EDT 2024

% Result   : Theorem 23.00s 4.93s
% Output   : Refutation 23.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   32 (   9 unt;   8 typ;   0 def)
%            Number of atoms       :   53 (   2 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  188 (  17   ~;  14   |;   0   &; 146   @)
%                                         (   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     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   26 (   0   ^  26   !;   0   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ilf_type_type,type,
    ilf_type: $i > $i > $o ).

thf(binary_relation_type_type,type,
    binary_relation_type: $i ).

thf(relation_type_type,type,
    relation_type: $i > $i > $i ).

thf(domain_of_type,type,
    domain_of: $i > $i ).

thf(range_of_type,type,
    range_of: $i > $i ).

thf(set_type_type,type,
    set_type: $i ).

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

thf(sk1_type,type,
    sk1: $i ).

thf(25,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( subset @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).

thf(90,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( subset @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(91,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ( subset @ A @ A ) ),
    inference(cnf,[status(esa)],[90]) ).

thf(20,axiom,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).

thf(75,plain,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(76,plain,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    inference(cnf,[status(esa)],[75]) ).

thf(158,plain,
    ! [A: $i] :
      ( ~ $true
      | ( subset @ A @ A ) ),
    inference(rewrite,[status(thm)],[91,76]) ).

thf(159,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(simp,[status(thm)],[158]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ( ilf_type @ A @ ( relation_type @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_20) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ilf_type @ A @ binary_relation_type )
       => ( ilf_type @ A @ ( relation_type @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(31,plain,
    ~ ! [A: $i] :
        ( ( ilf_type @ A @ binary_relation_type )
       => ( ilf_type @ A @ ( relation_type @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(33,plain,
    ilf_type @ sk1 @ binary_relation_type,
    inference(cnf,[status(esa)],[31]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ binary_relation_type )
         => ( ( subset @ ( domain_of @ B ) @ A )
           => ( ilf_type @ B @ ( relation_type @ A @ ( range_of @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

thf(58,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ binary_relation_type )
         => ( ( subset @ ( domain_of @ B ) @ A )
           => ( ilf_type @ B @ ( relation_type @ A @ ( range_of @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(59,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( ilf_type @ B @ binary_relation_type )
      | ~ ( subset @ ( domain_of @ B ) @ A )
      | ( ilf_type @ B @ ( relation_type @ A @ ( range_of @ B ) ) ) ),
    inference(cnf,[status(esa)],[58]) ).

thf(1257,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ~ ( ilf_type @ B @ binary_relation_type )
      | ~ ( subset @ ( domain_of @ B ) @ A )
      | ( ilf_type @ B @ ( relation_type @ A @ ( range_of @ B ) ) ) ),
    inference(rewrite,[status(thm)],[59,76]) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ilf_type @ B @ binary_relation_type )
      | ~ ( subset @ ( domain_of @ B ) @ A )
      | ( ilf_type @ B @ ( relation_type @ A @ ( range_of @ B ) ) ) ),
    inference(simp,[status(thm)],[1257]) ).

thf(1273,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ ( domain_of @ B ) @ A )
      | ( ilf_type @ B @ ( relation_type @ A @ ( range_of @ B ) ) )
      | ( ( ilf_type @ sk1 @ binary_relation_type )
       != ( ilf_type @ B @ binary_relation_type ) ) ),
    inference(paramod_ordered,[status(thm)],[33,1258]) ).

thf(1274,plain,
    ! [A: $i] :
      ( ~ ( subset @ ( domain_of @ sk1 ) @ A )
      | ( ilf_type @ sk1 @ ( relation_type @ A @ ( range_of @ sk1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1273:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(1406,plain,
    ! [B: $i,A: $i] :
      ( ( ilf_type @ sk1 @ ( relation_type @ B @ ( range_of @ sk1 ) ) )
      | ( ( subset @ A @ A )
       != ( subset @ ( domain_of @ sk1 ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[159,1274]) ).

thf(1407,plain,
    ilf_type @ sk1 @ ( relation_type @ ( domain_of @ sk1 ) @ ( range_of @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[1406:[bind(A,$thf( domain_of @ sk1 )),bind(B,$thf( domain_of @ sk1 ))]]) ).

thf(32,plain,
    ~ ( ilf_type @ sk1 @ ( relation_type @ ( domain_of @ sk1 ) @ ( range_of @ sk1 ) ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(1410,plain,
    $false,
    inference(rewrite,[status(thm)],[1407,32]) ).

thf(1411,plain,
    $false,
    inference(simp,[status(thm)],[1410]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET658+3 : TPTP v8.2.0. Released v2.2.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n017.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 11:22:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.07/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.47/1.09  % [INFO] 	 Parsing done (131ms). 
% 1.47/1.10  % [INFO] 	 Running in sequential loop mode. 
% 2.04/1.37  % [INFO] 	 nitpick registered as external prover. 
% 2.04/1.37  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.44  % [INFO] 	 Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ... 
% 2.31/1.50  % [INFO] 	 Axiom selection finished. Selected 28 axioms (removed 0 axioms). 
% 2.59/1.57  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.59/1.58  % [INFO] 	 Type checking passed. 
% 2.59/1.58  % [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 ... 
% 23.00/4.93  % [INFO] 	 Killing All external provers ... 
% 23.00/4.93  % Time passed: 4387ms (effective reasoning time: 3829ms)
% 23.00/4.93  % 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)>
% 23.00/4.93  % Axioms used in derivation (3): p15, p28, p1
% 23.00/4.93  % No. of inferences in proof: 24
% 23.00/4.93  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4387 ms resp. 3829 ms w/o parsing
% 23.09/4.97  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.09/4.97  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------