TSTP Solution File: SEU534^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU534^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 03:42:33 EDT 2024

% Result   : Theorem 3.86s 2.22s
% Output   : Refutation 3.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   31 (  14 unt;   8 typ;   2 def)
%            Number of atoms       :   56 (  11 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  158 (  17   ~;  10   |;   4   &; 104   @)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   43 (   0   ^  38   !;   5   ?;  43   :)

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

thf(emptyset_type,type,
    emptyset: $i ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(dsetconstrI_type,type,
    dsetconstrI: $o ).

thf(dsetconstrI_def,definition,
    ( dsetconstrI
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ A )
         => ( ( B @ C )
           => ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).

thf(emptysetE_type,type,
    emptysetE: $o ).

thf(emptysetE_def,definition,
    ( emptysetE
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => ! [B: $o] : B ) ) ) ).

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

thf(sk2_type,type,
    sk2: $i > $o ).

thf(sk3_type,type,
    sk3: $i ).

thf(1,conjecture,
    ( dsetconstrI
   => ( emptysetE
     => ! [A: $i,B: $i > $o] :
          ( ? [C: $i] :
              ( ( in @ C @ A )
              & ( B @ C ) )
         => ( ( ( dsetconstr @ A @ B )
              = emptyset )
           => $false ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).

thf(2,negated_conjecture,
    ~ ( dsetconstrI
     => ( emptysetE
       => ! [A: $i,B: $i > $o] :
            ( ? [C: $i] :
                ( ( in @ C @ A )
                & ( B @ C ) )
           => ( ( ( dsetconstr @ A @ B )
                = emptyset )
             => $false ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ A )
         => ( ( B @ C )
           => ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
     => ( ! [A: $i] :
            ( ( in @ A @ emptyset )
           => ! [B: $o] : B )
       => ! [A: $i,B: $i > $o] :
            ( ? [C: $i] :
                ( ( in @ C @ A )
                & ( B @ C ) )
           => ( ( dsetconstr @ A @ B )
             != emptyset ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ A )
         => ( ( B @ C )
           => ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
     => ( ( ? [A: $i] : ( in @ A @ emptyset )
         => ! [A: $o] : A )
       => ! [A: $i,B: $i > $o] :
            ( ? [C: $i] :
                ( ( in @ C @ A )
                & ( B @ C ) )
           => ( ( dsetconstr @ A @ B )
             != emptyset ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(9,plain,
    sk2 @ sk3,
    inference(cnf,[status(esa)],[4]) ).

thf(8,plain,
    in @ sk3 @ sk1,
    inference(cnf,[status(esa)],[4]) ).

thf(7,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ A )
      | ~ ( B @ C )
      | ( in @ C @ ( dsetconstr @ A @ B ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(46,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( B @ C )
      | ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( ( in @ sk3 @ sk1 )
       != ( in @ C @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8,7]) ).

thf(47,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk3 )
      | ( in @ sk3 @ ( dsetconstr @ sk1 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).

thf(70,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk3 )
      | ( in @ sk3 @ ( dsetconstr @ sk1 @ A ) ) ),
    inference(simp,[status(thm)],[47]) ).

thf(92,plain,
    ! [A: $i > $o] :
      ( ( in @ sk3 @ ( dsetconstr @ sk1 @ A ) )
      | ( ( sk2 @ sk3 )
       != ( A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[9,70]) ).

thf(111,plain,
    in @ sk3 @ ( dsetconstr @ sk1 @ sk2 ),
    inference(pre_uni,[status(thm)],[92:[bind(A,$thf( sk2 ))]]) ).

thf(5,plain,
    ( ( dsetconstr @ sk1 @ sk2 )
    = emptyset ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ( ( dsetconstr @ sk1 @ sk2 )
    = emptyset ),
    inference(lifteq,[status(thm)],[5]) ).

thf(134,plain,
    in @ sk3 @ emptyset,
    inference(rewrite,[status(thm)],[111,10]) ).

thf(6,plain,
    ! [B: $o,A: $i] :
      ( ~ ( in @ A @ emptyset )
      | B ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [B: $o,A: $i] :
      ( ~ ( in @ A @ emptyset )
      | B ),
    inference(simp,[status(thm)],[6]) ).

thf(16,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ emptyset )
      | $false ),
    inference(prim_subst,[status(thm)],[11:[bind(A,$thf( A )),bind(B,$thf( $false ))]]) ).

thf(24,plain,
    ! [A: $i] :
      ~ ( in @ A @ emptyset ),
    inference(simp,[status(thm)],[16]) ).

thf(135,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ emptyset )
     != ( in @ A @ emptyset ) ),
    inference(paramod_ordered,[status(thm)],[134,24]) ).

thf(136,plain,
    $false,
    inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( sk3 ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEU534^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n026.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sun May 19 15:46:08 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 1.05/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.06  % [INFO] 	 Parsing done (121ms). 
% 1.41/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.37  % [INFO] 	 nitpick registered as external prover. 
% 1.80/1.38  % [INFO] 	 Scanning for conjecture ... 
% 2.09/1.46  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.09/1.48  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.09/1.49  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.09/1.49  % [INFO] 	 Type checking passed. 
% 2.09/1.49  % [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 ... 
% 3.77/2.22  % [INFO] 	 Killing All external provers ... 
% 3.86/2.22  % Time passed: 1675ms (effective reasoning time: 1141ms)
% 3.86/2.22  % 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)>
% 3.86/2.22  % Axioms used in derivation (0): 
% 3.86/2.22  % No. of inferences in proof: 21
% 3.86/2.22  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1675 ms resp. 1141 ms w/o parsing
% 3.87/2.26  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.87/2.26  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------