TSTP Solution File: SEU805^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 03:40:01 EDT 2024

% Result   : Theorem 2.52s 1.51s
% Output   : Refutation 2.78s
% 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 (  12 equ;   0 cnn)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :   83 (   9   ~;   0   |;   9   &;  47   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   25 (   1   ^  11   !;  13   ?;  25   :)

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

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

thf(foundationAx_type,type,
    foundationAx: $o ).

thf(foundationAx_def,definition,
    ( foundationAx
    = ( ! [A: $i] :
          ( ? [B: $i] : ( in @ B @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [C: $i] :
                    ( ( in @ C @ B )
                    & ( in @ C @ A ) ) ) ) ) ) ).

thf(nonempty_type,type,
    nonempty: $i > $o ).

thf(nonempty_def,definition,
    ( nonempty
    = ( ^ [A: $i] : ( A != emptyset ) ) ) ).

thf(nonemptyE1_type,type,
    nonemptyE1: $o ).

thf(nonemptyE1_def,definition,
    ( nonemptyE1
    = ( ! [A: $i] :
          ( ( nonempty @ A )
         => ? [B: $i] : ( in @ B @ A ) ) ) ) ).

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

thf(disjointsetsI1_type,type,
    disjointsetsI1: $o ).

thf(disjointsetsI1_def,definition,
    ( disjointsetsI1
    = ( ! [A: $i,B: $i] :
          ( ~ ? [C: $i] :
                ( ( in @ C @ A )
                & ( in @ C @ B ) )
         => ( ( binintersect @ A @ B )
            = emptyset ) ) ) ) ).

thf(1,conjecture,
    ( foundationAx
   => ( nonemptyE1
     => ( disjointsetsI1
       => ! [A: $i] :
            ( ( nonempty @ A )
           => ? [B: $i] :
                ( ( in @ B @ A )
                & ( ( binintersect @ B @ A )
                  = emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundation2) ).

thf(2,negated_conjecture,
    ~ ( foundationAx
     => ( nonemptyE1
       => ( disjointsetsI1
         => ! [A: $i] :
              ( ( nonempty @ A )
             => ? [B: $i] :
                  ( ( in @ B @ A )
                  & ( ( binintersect @ B @ A )
                    = emptyset ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i] :
          ( ? [B: $i] : ( in @ B @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [C: $i] :
                    ( ( in @ C @ B )
                    & ( in @ C @ A ) ) ) )
     => ( ! [A: $i] :
            ( ( A != emptyset )
           => ? [B: $i] : ( in @ B @ A ) )
       => ( ! [A: $i,B: $i] :
              ( ~ ? [C: $i] :
                    ( ( in @ C @ A )
                    & ( in @ C @ B ) )
             => ( ( binintersect @ A @ B )
                = emptyset ) )
         => ! [A: $i] :
              ( ( A != emptyset )
             => ? [B: $i] :
                  ( ( in @ B @ A )
                  & ( ( binintersect @ B @ A )
                    = emptyset ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(20,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08  % Problem  : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.10  % Command  : run_Leo-III %s %d
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Sun May 19 18:16:09 EDT 2024
% 0.08/0.28  % CPUTime  : 
% 0.71/0.71  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.87/0.82  % [INFO] 	 Parsing done (108ms). 
% 1.07/0.83  % [INFO] 	 Running in sequential loop mode. 
% 1.42/1.05  % [INFO] 	 eprover registered as external prover. 
% 1.42/1.06  % [INFO] 	 cvc4 registered as external prover. 
% 1.42/1.06  % [INFO] 	 Scanning for conjecture ... 
% 1.53/1.13  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.69/1.16  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.69/1.16  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.69/1.16  % [INFO] 	 Type checking passed. 
% 1.69/1.16  % [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 ... 
% 2.52/1.51  % External prover 'e' found a proof!
% 2.52/1.51  % [INFO] 	 Killing All external provers ... 
% 2.52/1.51  % Time passed: 1105ms (effective reasoning time: 676ms)
% 2.52/1.51  % 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)>
% 2.52/1.51  % Axioms used in derivation (0): 
% 2.52/1.51  % No. of inferences in proof: 4
% 2.52/1.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1105 ms resp. 676 ms w/o parsing
% 2.78/1.54  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.78/1.54  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------