TSTP Solution File: SEU681^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 03:39:02 EDT 2024

% Result   : Theorem 2.92s 1.81s
% Output   : Refutation 3.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   14 (   4 unt;   7 typ;   3 def)
%            Number of atoms       :   41 (   5 equ;   0 cnn)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  124 (   2   ~;   0   |;   4   &;  88   @)
%                                         (   0 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   40 (   3   ^  33   !;   4   ?;  40   :)

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

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

thf(subsetE_type,type,
    subsetE: $o ).

thf(subsetE_def,definition,
    ( subsetE
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ A @ B )
         => ( ( in @ C @ A )
           => ( in @ C @ B ) ) ) ) ) ).

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

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

thf(cartprodmempair1_type,type,
    cartprodmempair1: $o ).

thf(cartprodmempair1_def,definition,
    ( cartprodmempair1
    = ( ! [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 ) ) ) ) ) ) ) ).

thf(breln_type,type,
    breln: $i > $i > $i > $o ).

thf(breln_def,definition,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).

thf(1,conjecture,
    ( subsetE
   => ( cartprodmempair1
     => ! [A: $i,B: $i,C: $i] :
          ( ( breln @ A @ B @ C )
         => ! [D: $i > $o] :
              ( ! [E: $i] :
                  ( ( in @ E @ A )
                 => ! [F: $i] :
                      ( ( in @ F @ B )
                     => ( ( in @ ( kpair @ E @ F ) @ C )
                       => ( D @ ( kpair @ E @ F ) ) ) ) )
             => ! [E: $i] :
                  ( ( in @ E @ C )
                 => ( D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).

thf(2,negated_conjecture,
    ~ ( subsetE
     => ( cartprodmempair1
       => ! [A: $i,B: $i,C: $i] :
            ( ( breln @ A @ B @ C )
           => ! [D: $i > $o] :
                ( ! [E: $i] :
                    ( ( in @ E @ A )
                   => ! [F: $i] :
                        ( ( in @ F @ B )
                       => ( ( in @ ( kpair @ E @ F ) @ C )
                         => ( D @ ( kpair @ E @ F ) ) ) ) )
               => ! [E: $i] :
                    ( ( in @ E @ C )
                   => ( D @ E ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(18,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 15:32:23 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.92/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/0.98  % [INFO] 	 Parsing done (144ms). 
% 1.29/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.77/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.06/1.37  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.06/1.38  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.06/1.38  % [INFO] 	 Type checking passed. 
% 2.06/1.38  % [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 ... 
% 2.92/1.80  % External prover 'cvc4' found a proof!
% 2.92/1.80  % [INFO] 	 Killing All external provers ... 
% 2.92/1.81  % Time passed: 1302ms (effective reasoning time: 802ms)
% 2.92/1.81  % 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)>
% 2.92/1.81  % Axioms used in derivation (0): 
% 2.92/1.81  % No. of inferences in proof: 4
% 2.92/1.81  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1302 ms resp. 802 ms w/o parsing
% 3.06/1.83  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.06/1.83  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------