TSTP Solution File: SEU631^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU631^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 03:43:04 EDT 2024

% Result   : Theorem 5.87s 2.33s
% Output   : Refutation 5.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   35 (  10 unt;  14 typ;   3 def)
%            Number of atoms       :   61 (  18 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  306 (  20   ~;  12   |;  16   &; 250   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   9 con; 0-2 aty)
%            Number of variables   :   53 (   8   ^  29   !;  16   ?;  53   :)

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

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

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

thf(powerset_type,type,
    powerset: $i > $i ).

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

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

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

thf(binunion_type,type,
    binunion: $i > $i > $i ).

thf(kpair_type,type,
    kpair: $i > $i > $i ).

thf(kpair_def,definition,
    ( kpair
    = ( ^ [A: $i,B: $i] : ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ).

thf(cartprod_type,type,
    cartprod: $i > $i > $i ).

thf(cartprod_def,definition,
    ( cartprod
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
          @ ^ [C: $i] :
            ? [D: $i] :
              ( ( in @ D @ A )
              & ? [E: $i] :
                  ( ( in @ E @ B )
                  & ( C
                    = ( kpair @ D @ E ) ) ) ) ) ) ) ).

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

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

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

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

thf(1,conjecture,
    ( dsetconstrER
   => ! [A: $i,B: $i,C: $i] :
        ( ( in @ C @ ( cartprod @ A @ B ) )
       => ? [D: $i] :
            ( ( in @ D @ A )
            & ? [E: $i] :
                ( ( in @ E @ B )
                & ( C
                  = ( kpair @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).

thf(2,negated_conjecture,
    ~ ( dsetconstrER
     => ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( cartprod @ A @ B ) )
         => ? [D: $i] :
              ( ( in @ D @ A )
              & ? [E: $i] :
                  ( ( in @ E @ B )
                  & ( C
                    = ( kpair @ D @ E ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(5,plain,
    ( in @ sk3
    @ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) )
      @ ^ [A: $i] :
        ? [B: $i] :
          ( ( in @ B @ sk1 )
          & ? [C: $i] :
              ( ( in @ C @ sk2 )
              & ( A
                = ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
      | ( B @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [C: $i,B: $i > $o,A: $i] :
      ( ( B @ C )
      | ( ( in @ sk3
          @ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) )
            @ ^ [D: $i] :
              ? [E: $i] :
                ( ( in @ E @ sk1 )
                & ? [F: $i] :
                    ( ( in @ F @ sk2 )
                    & ( D
                      = ( setadjoin @ ( setadjoin @ E @ emptyset ) @ ( setadjoin @ ( setadjoin @ E @ ( setadjoin @ F @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
       != ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5,6]) ).

thf(10,plain,
    ? [A: $i] :
      ( ( in @ A @ sk1 )
      & ? [B: $i] :
          ( ( in @ B @ sk2 )
          & ( sk3
            = ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[9:[bind(A,$thf( powerset @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) )),bind(B,$thf( ^ [D: $i] : ? [E: $i] : ( ( in @ E @ sk1 ) & ? [F: $i] : ( ( in @ F @ sk2 ) & ( D = ( setadjoin @ ( setadjoin @ E @ emptyset ) @ ( setadjoin @ ( setadjoin @ E @ ( setadjoin @ F @ emptyset ) ) @ emptyset ) ) ) ) ) )),bind(C,$thf( sk3 ))]]) ).

thf(25,plain,
    ( sk3
    = ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(28,plain,
    ( ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) )
    = sk3 ),
    inference(lifteq,[status(thm)],[25]) ).

thf(4,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk1 )
      | ~ ( in @ B @ sk2 )
      | ( sk3
       != ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
       != sk3 )
      | ~ ( in @ A @ sk1 )
      | ~ ( in @ B @ sk2 ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
       != sk3 )
      | ~ ( in @ A @ sk1 )
      | ~ ( in @ B @ sk2 ) ),
    inference(simp,[status(thm)],[7]) ).

thf(103,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk1 )
      | ~ ( in @ B @ sk2 )
      | ( ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[28,8]) ).

thf(104,plain,
    ( ~ ( in @ sk4 @ sk1 )
    | ~ ( in @ sk5 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).

thf(26,plain,
    in @ sk5 @ sk2,
    inference(cnf,[status(esa)],[10]) ).

thf(27,plain,
    in @ sk4 @ sk1,
    inference(cnf,[status(esa)],[10]) ).

thf(189,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[104,26,27]) ).

thf(190,plain,
    $false,
    inference(simp,[status(thm)],[189]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU631^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n016.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 17:30:39 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.17/0.98  % [INFO] 	 Parsing done (113ms). 
% 1.17/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.75/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.88/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.88/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.88/1.33  % [INFO] 	 Type checking passed. 
% 1.88/1.33  % [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 ... 
% 5.87/2.32  % [INFO] 	 Killing All external provers ... 
% 5.87/2.33  % Time passed: 1797ms (effective reasoning time: 1332ms)
% 5.87/2.33  % 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)>
% 5.87/2.33  % Axioms used in derivation (0): 
% 5.87/2.33  % No. of inferences in proof: 18
% 5.87/2.33  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1797 ms resp. 1332 ms w/o parsing
% 5.87/2.37  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.87/2.37  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------