TSTP Solution File: SEU594^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU594^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 03:38:27 EDT 2024

% Result   : Theorem 2.94s 1.61s
% Output   : Refutation 2.94s
% 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       :   43 (  13 equ;   0 cnn)
%            Maximal formula atoms :   11 (   5 avg)
%            Number of connectives :   76 (   2   ~;   0   |;   0   &;  52   @)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   31 (   5   ^  26   !;   0   ?;  31   :)

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

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

thf(in__Cong_type,type,
    in__Cong: $o ).

thf(in__Cong_def,definition,
    ( in__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [C: $i,D: $i] :
              ( ( C = D )
             => ( ( in @ C @ A )
                = ( in @ D @ B ) ) ) ) ) ) ).

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

thf(subsetI1_type,type,
    subsetI1: $o ).

thf(subsetI1_def,definition,
    ( subsetI1
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( subset @ A @ B ) ) ) ) ).

thf(binintersect_type,type,
    binintersect: $i > $i > $i ).

thf(binintersect_def,definition,
    ( binintersect
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ A
          @ ^ [C: $i] : ( in @ C @ B ) ) ) ) ).

thf(binintersectEL_type,type,
    binintersectEL: $o ).

thf(binintersectEL_def,definition,
    ( binintersectEL
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( binintersect @ A @ B ) )
         => ( in @ C @ A ) ) ) ) ).

thf(1,conjecture,
    ( in__Cong
   => ( subsetI1
     => ( binintersectEL
       => ! [A: $i,B: $i] :
            ( ( ( binintersect @ A @ B )
              = B )
           => ( subset @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).

thf(2,negated_conjecture,
    ~ ( in__Cong
     => ( subsetI1
       => ( binintersectEL
         => ! [A: $i,B: $i] :
              ( ( ( binintersect @ A @ B )
                = B )
             => ( subset @ B @ A ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(16,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SEU594^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n018.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Sun May 19 16:08:54 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.97  % [INFO] 	 Parsing done (100ms). 
% 1.18/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.90/1.27  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.90/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.90/1.27  % [INFO] 	 Type checking passed. 
% 1.90/1.27  % [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 ... 
% 2.94/1.60  % External prover 'e' found a proof!
% 2.94/1.60  % [INFO] 	 Killing All external provers ... 
% 2.94/1.60  % Time passed: 1062ms (effective reasoning time: 619ms)
% 2.94/1.60  % 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)>
% 2.94/1.61  % Axioms used in derivation (0): 
% 2.94/1.61  % No. of inferences in proof: 4
% 2.94/1.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1062 ms resp. 619 ms w/o parsing
% 2.94/1.63  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.94/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------