TSTP Solution File: SEU611^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.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 03:38:34 EDT 2024

% Result   : Theorem 3.71s 2.34s
% Output   : Refutation 3.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   15 (   5 unt;   7 typ;   4 def)
%            Number of atoms       :   45 (   4 equ;   0 cnn)
%            Maximal formula atoms :   13 (   5 avg)
%            Number of connectives :  140 (  12   ~;   4   |;   0   &;  88   @)
%                                         (   0 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   34 (   4   ^  30   !;   0   ?;  34   :)

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

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

thf(dsetconstrEL_type,type,
    dsetconstrEL: $o ).

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

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(binunionE_type,type,
    binunionE: $o ).

thf(binunionE_def,definition,
    ( binunionE
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( binunion @ A @ B ) )
         => ( ( in @ C @ A )
            | ( in @ C @ B ) ) ) ) ) ).

thf(symdiff_type,type,
    symdiff: $i > $i > $i ).

thf(symdiff_def,definition,
    ( symdiff
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ ( binunion @ A @ B )
          @ ^ [C: $i] :
              ( ~ ( in @ C @ A )
              | ~ ( in @ C @ B ) ) ) ) ) ).

thf(1,conjecture,
    ( dsetconstrEL
   => ( dsetconstrER
     => ( binunionE
       => ! [A: $i,B: $i,C: $i] :
            ( ( in @ C @ ( symdiff @ A @ B ) )
           => ! [D: $o] :
                ( ( ( in @ C @ A )
                 => ( ~ ( in @ C @ B )
                   => D ) )
               => ( ( ~ ( in @ C @ A )
                   => ( ( in @ C @ B )
                     => D ) )
                 => D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).

thf(2,negated_conjecture,
    ~ ( dsetconstrEL
     => ( dsetconstrER
       => ( binunionE
         => ! [A: $i,B: $i,C: $i] :
              ( ( in @ C @ ( symdiff @ A @ B ) )
             => ! [D: $o] :
                  ( ( ( in @ C @ A )
                   => ( ~ ( in @ C @ B )
                     => D ) )
                 => ( ( ~ ( in @ C @ A )
                     => ( ( in @ C @ B )
                       => D ) )
                   => D ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(13,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 16:16:24 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.00/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.13  % [INFO] 	 Parsing done (172ms). 
% 1.45/1.15  % [INFO] 	 Running in sequential loop mode. 
% 1.87/1.53  % [INFO] 	 eprover registered as external prover. 
% 1.98/1.53  % [INFO] 	 cvc4 registered as external prover. 
% 1.98/1.54  % [INFO] 	 Scanning for conjecture ... 
% 2.22/1.66  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.34/1.69  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.34/1.69  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.34/1.70  % [INFO] 	 Type checking passed. 
% 2.34/1.70  % [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 ... 
% 3.71/2.34  % External prover 'e' found a proof!
% 3.71/2.34  % [INFO] 	 Killing All external provers ... 
% 3.71/2.34  % Time passed: 1865ms (effective reasoning time: 1183ms)
% 3.71/2.34  % 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)>
% 3.71/2.34  % Axioms used in derivation (0): 
% 3.71/2.34  % No. of inferences in proof: 4
% 3.71/2.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1865 ms resp. 1183 ms w/o parsing
% 3.96/2.38  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.96/2.38  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------