TSTP Solution File: SEU807^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU807^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 03:40:02 EDT 2024

% Result   : Theorem 4.21s 2.72s
% Output   : Refutation 4.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   17 (   6 unt;   8 typ;   5 def)
%            Number of atoms       :   57 (  15 equ;   0 cnn)
%            Maximal formula atoms :   15 (   6 avg)
%            Number of connectives :  109 (   7   ~;   2   |;   4   &;  68   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   38 (   0   ^  32   !;   6   ?;  38   :)

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

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

thf(setadjoin_type,type,
    setadjoin: $i > $i > $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(setadjoinIL_type,type,
    setadjoinIL: $o ).

thf(setadjoinIL_def,definition,
    ( setadjoinIL
    = ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).

thf(setadjoinIR_type,type,
    setadjoinIR: $o ).

thf(setadjoinIR_def,definition,
    ( setadjoinIR
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ B )
         => ( in @ C @ ( setadjoin @ A @ B ) ) ) ) ) ).

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(upairset2E_type,type,
    upairset2E: $o ).

thf(upairset2E_def,definition,
    ( upairset2E
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
         => ( ( C = A )
            | ( C = B ) ) ) ) ) ).

thf(1,conjecture,
    ( foundationAx
   => ( setadjoinIL
     => ( setadjoinIR
       => ( in__Cong
         => ( upairset2E
           => ! [A: $i,B: $i] :
                ( ( in @ A @ B )
               => ~ ( in @ B @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinself2) ).

thf(2,negated_conjecture,
    ~ ( foundationAx
     => ( setadjoinIL
       => ( setadjoinIR
         => ( in__Cong
           => ( upairset2E
             => ! [A: $i,B: $i] :
                  ( ( in @ A @ B )
                 => ~ ( in @ B @ A ) ) ) ) ) ) ),
    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,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
       => ( ! [A: $i,B: $i,C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ ( setadjoin @ A @ B ) ) )
         => ( ! [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 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
                 => ( ( C = A )
                    | ( C = B ) ) )
             => ! [A: $i,B: $i] :
                  ( ( in @ A @ B )
                 => ~ ( in @ B @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU807^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun May 19 17:54:53 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.19/1.16  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.63/1.37  % [INFO] 	 Parsing done (203ms). 
% 1.63/1.38  % [INFO] 	 Running in sequential loop mode. 
% 2.34/1.85  % [INFO] 	 eprover registered as external prover. 
% 2.34/1.86  % [INFO] 	 cvc4 registered as external prover. 
% 2.34/1.86  % [INFO] 	 Scanning for conjecture ... 
% 2.74/2.01  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.74/2.05  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.74/2.05  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.74/2.05  % [INFO] 	 Type checking passed. 
% 2.74/2.06  % [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 ... 
% 4.21/2.71  % External prover 'e' found a proof!
% 4.21/2.71  % [INFO] 	 Killing All external provers ... 
% 4.21/2.71  % Time passed: 2180ms (effective reasoning time: 1324ms)
% 4.21/2.71  % 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)>
% 4.21/2.72  % Axioms used in derivation (0): 
% 4.21/2.72  % No. of inferences in proof: 4
% 4.21/2.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2180 ms resp. 1324 ms w/o parsing
% 4.21/2.76  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.21/2.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------