TSTP Solution File: SEU781^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 03:43:45 EDT 2024

% Result   : Theorem 31.97s 6.21s
% Output   : Refutation 32.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   48 (  12 unt;  14 typ;   2 def)
%            Number of atoms       :  153 (   6 equ;   0 cnn)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  715 (  77   ~;  69   |;   4   &; 525   @)
%                                         (   0 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;  10 con; 0-5 aty)
%            Number of variables   :   69 (   1   ^  66   !;   2   ?;  69   :)

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

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

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

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

thf(breln1_type,type,
    breln1: $i > $i > $o ).

thf(breln1_def,definition,
    ( breln1
    = ( ^ [A: $i] : ( breln @ A @ A ) ) ) ).

thf(breln1compset_type,type,
    breln1compset: $i > $i > $i > $i ).

thf(breln1compE_type,type,
    breln1compE: $o ).

thf(breln1compE_def,definition,
    ( breln1compE
    = ( ! [A: $i,B: $i] :
          ( ( breln1 @ A @ B )
         => ! [C: $i] :
              ( ( breln1 @ A @ C )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                       => ? [F: $i] :
                            ( ( in @ F @ A )
                            & ( in @ ( kpair @ D @ F ) @ B )
                            & ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i > $i > $i > $i > $i > $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(sk6_type,type,
    sk6: $i ).

thf(sk7_type,type,
    sk7: $o ).

thf(1,conjecture,
    ( breln1compE
   => ! [A: $i,B: $i] :
        ( ( breln1 @ A @ B )
       => ! [C: $i] :
            ( ( breln1 @ A @ C )
           => ! [D: $i] :
                ( ( in @ D @ A )
               => ! [E: $i] :
                    ( ( in @ E @ A )
                   => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                     => ! [F: $o] :
                          ( ! [G: $i] :
                              ( ( in @ G @ A )
                             => ( ( in @ ( kpair @ D @ G ) @ B )
                               => ( ( in @ ( kpair @ G @ E ) @ C )
                                 => F ) ) )
                         => F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compEex) ).

thf(2,negated_conjecture,
    ~ ( breln1compE
     => ! [A: $i,B: $i] :
          ( ( breln1 @ A @ B )
         => ! [C: $i] :
              ( ( breln1 @ A @ C )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                       => ! [F: $o] :
                            ( ! [G: $i] :
                                ( ( in @ G @ A )
                               => ( ( in @ ( kpair @ D @ G ) @ B )
                                 => ( ( in @ ( kpair @ G @ E ) @ C )
                                   => F ) ) )
                           => F ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( subset @ B @ ( cartprod @ A @ A ) )
         => ! [C: $i] :
              ( ( subset @ C @ ( cartprod @ A @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                       => ? [F: $i] :
                            ( ( in @ F @ A )
                            & ( in @ ( kpair @ D @ F ) @ B )
                            & ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) )
     => ! [A: $i,B: $i] :
          ( ( subset @ B @ ( cartprod @ A @ A ) )
         => ! [C: $i] :
              ( ( subset @ C @ ( cartprod @ A @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
                       => ! [F: $o] :
                            ( ! [G: $i] :
                                ( ( in @ G @ A )
                               => ( ( in @ ( kpair @ D @ G ) @ B )
                                 => ( ( in @ ( kpair @ G @ E ) @ C )
                                   => F ) ) )
                           => F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,plain,
    in @ ( kpair @ sk5 @ sk6 ) @ ( breln1compset @ sk2 @ sk3 @ sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( subset @ B @ ( cartprod @ A @ A ) )
      | ~ ( subset @ C @ ( cartprod @ A @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( in @ E @ A )
      | ~ ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
      | ( in @ ( kpair @ ( sk1 @ E @ D @ C @ B @ A ) @ E ) @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(620,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( subset @ B @ ( cartprod @ A @ A ) )
      | ~ ( subset @ C @ ( cartprod @ A @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( in @ E @ A )
      | ( in @ ( kpair @ ( sk1 @ E @ D @ C @ B @ A ) @ E ) @ C )
      | ( ( in @ ( kpair @ sk5 @ sk6 ) @ ( breln1compset @ sk2 @ sk3 @ sk4 ) )
       != ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,9]) ).

thf(621,plain,
    ( ~ ( subset @ sk3 @ ( cartprod @ sk2 @ sk2 ) )
    | ~ ( subset @ sk4 @ ( cartprod @ sk2 @ sk2 ) )
    | ~ ( in @ sk5 @ sk2 )
    | ~ ( in @ sk6 @ sk2 )
    | ( in @ ( kpair @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk6 ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[620:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 )),bind(E,$thf( sk6 ))]]) ).

thf(4,plain,
    in @ sk5 @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    subset @ sk4 @ ( cartprod @ sk2 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    subset @ sk3 @ ( cartprod @ sk2 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    in @ sk6 @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( subset @ B @ ( cartprod @ A @ A ) )
      | ~ ( subset @ C @ ( cartprod @ A @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( in @ E @ A )
      | ~ ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
      | ( in @ ( sk1 @ E @ D @ C @ B @ A ) @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(165,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( subset @ B @ ( cartprod @ A @ A ) )
      | ~ ( subset @ C @ ( cartprod @ A @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( in @ E @ A )
      | ( in @ ( sk1 @ E @ D @ C @ B @ A ) @ A )
      | ( ( in @ ( kpair @ sk5 @ sk6 ) @ ( breln1compset @ sk2 @ sk3 @ sk4 ) )
       != ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,13]) ).

thf(166,plain,
    ( ~ ( subset @ sk3 @ ( cartprod @ sk2 @ sk2 ) )
    | ~ ( subset @ sk4 @ ( cartprod @ sk2 @ sk2 ) )
    | ~ ( in @ sk5 @ sk2 )
    | ~ ( in @ sk6 @ sk2 )
    | ( in @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 )),bind(E,$thf( sk6 ))]]) ).

thf(456,plain,
    ( ~ $true
    | ~ $true
    | ~ $true
    | ~ $true
    | ( in @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk2 ) ),
    inference(rewrite,[status(thm)],[166,4,5,6,7]) ).

thf(457,plain,
    in @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk2,
    inference(simp,[status(thm)],[456]) ).

thf(10,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk2 )
      | ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
      | ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 )
      | sk7 ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk2 )
      | ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
      | ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 )
      | sk7 ),
    inference(simp,[status(thm)],[10]) ).

thf(11,plain,
    ~ sk7,
    inference(cnf,[status(esa)],[3]) ).

thf(174,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk2 )
      | ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
      | ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 )
      | $false ),
    inference(rewrite,[status(thm)],[14,11]) ).

thf(175,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk2 )
      | ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
      | ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 ) ),
    inference(simp,[status(thm)],[174]) ).

thf(482,plain,
    ! [A: $i] :
      ( ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
      | ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 )
      | ( ( in @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk2 )
       != ( in @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[457,175]) ).

thf(483,plain,
    ( ~ ( in @ ( kpair @ sk5 @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) ) @ sk3 )
    | ~ ( in @ ( kpair @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk6 ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ))]]) ).

thf(8,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( subset @ B @ ( cartprod @ A @ A ) )
      | ~ ( subset @ C @ ( cartprod @ A @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( in @ E @ A )
      | ~ ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
      | ( in @ ( kpair @ D @ ( sk1 @ E @ D @ C @ B @ A ) ) @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(260,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( subset @ B @ ( cartprod @ A @ A ) )
      | ~ ( subset @ C @ ( cartprod @ A @ A ) )
      | ~ ( in @ D @ A )
      | ~ ( in @ E @ A )
      | ( in @ ( kpair @ D @ ( sk1 @ E @ D @ C @ B @ A ) ) @ B )
      | ( ( in @ ( kpair @ sk5 @ sk6 ) @ ( breln1compset @ sk2 @ sk3 @ sk4 ) )
       != ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,8]) ).

thf(261,plain,
    ( ~ ( subset @ sk3 @ ( cartprod @ sk2 @ sk2 ) )
    | ~ ( subset @ sk4 @ ( cartprod @ sk2 @ sk2 ) )
    | ~ ( in @ sk5 @ sk2 )
    | ~ ( in @ sk6 @ sk2 )
    | ( in @ ( kpair @ sk5 @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) ) @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 )),bind(E,$thf( sk6 ))]]) ).

thf(1688,plain,
    ( ~ $true
    | ~ $true
    | ~ $true
    | ~ $true
    | ( in @ ( kpair @ sk5 @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) ) @ sk3 ) ),
    inference(rewrite,[status(thm)],[261,4,5,6,7]) ).

thf(1689,plain,
    in @ ( kpair @ sk5 @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) ) @ sk3,
    inference(simp,[status(thm)],[1688]) ).

thf(1690,plain,
    ( ~ $true
    | ~ ( in @ ( kpair @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk6 ) @ sk4 ) ),
    inference(rewrite,[status(thm)],[483,1689]) ).

thf(1691,plain,
    ~ ( in @ ( kpair @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk6 ) @ sk4 ),
    inference(simp,[status(thm)],[1690]) ).

thf(2073,plain,
    ( ~ $true
    | ~ $true
    | ~ $true
    | ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[621,4,5,6,7,1691]) ).

thf(2074,plain,
    $false,
    inference(simp,[status(thm)],[2073]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n008.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Sun May 19 18:18:09 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.94/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.10  % [INFO] 	 Parsing done (178ms). 
% 1.29/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.94/1.48  % [INFO] 	 nitpick registered as external prover. 
% 1.94/1.49  % [INFO] 	 Scanning for conjecture ... 
% 2.08/1.61  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.27/1.65  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.27/1.65  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.27/1.65  % [INFO] 	 Type checking passed. 
% 2.27/1.65  % [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 ... 
% 31.97/6.20  % [INFO] 	 Killing All external provers ... 
% 31.97/6.20  % Time passed: 5741ms (effective reasoning time: 5076ms)
% 31.97/6.21  % 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)>
% 31.97/6.21  % Axioms used in derivation (0): 
% 31.97/6.21  % No. of inferences in proof: 32
% 31.97/6.21  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5741 ms resp. 5076 ms w/o parsing
% 32.24/6.37  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.24/6.38  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------