TSTP Solution File: SEU696^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU696^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 03:39:08 EDT 2024

% Result   : Theorem 3.27s 1.72s
% Output   : Refutation 3.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   18 (   6 unt;   9 typ;   5 def)
%            Number of atoms       :   58 (  18 equ;   4 cnn)
%            Maximal formula atoms :   18 (   6 avg)
%            Number of connectives :  187 (   2   ~;   0   |;   0   &; 148   @)
%                                         (   0 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   6 con; 0-4 aty)
%            Number of variables   :   52 (   7   ^  45   !;   0   ?;  52   :)

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

thf(dpsetconstr_type,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(func_type,type,
    func: $i > $i > $i > $o ).

thf(ap_type,type,
    ap: $i > $i > $i > $i > $i ).

thf(app_type,type,
    app: $o ).

thf(app_def,definition,
    ( app
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( func @ A @ B @ C )
         => ! [D: $i] :
              ( ( in @ D @ A )
             => ( in @ ( ap @ A @ B @ C @ D ) @ B ) ) ) ) ) ).

thf(lam_type,type,
    lam: $i > $i > ( $i > $i ) > $i ).

thf(lam_def,definition,
    ( lam
    = ( ^ [A: $i,B: $i,C: $i > $i] :
          ( dpsetconstr @ A @ B
          @ ^ [D: $i] : ( (=) @ $i @ ( C @ D ) ) ) ) ) ).

thf(lamp_type,type,
    lamp: $o ).

thf(lamp_def,definition,
    ( lamp
    = ( ! [A: $i,B: $i,C: $i > $i] :
          ( ! [D: $i] :
              ( ( in @ D @ A )
             => ( in @ ( C @ D ) @ B ) )
         => ( func @ A @ B @ ( lam @ A @ B @ C ) ) ) ) ) ).

thf(funcext_type,type,
    funcext: $o ).

thf(funcext_def,definition,
    ( funcext
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( func @ A @ B @ C )
         => ! [D: $i] :
              ( ( func @ A @ B @ D )
             => ( ! [E: $i] :
                    ( ( in @ E @ A )
                   => ( ( ap @ A @ B @ C @ E )
                      = ( ap @ A @ B @ D @ E ) ) )
               => ( C = D ) ) ) ) ) ) ).

thf(beta1_type,type,
    beta1: $o ).

thf(beta1_def,definition,
    ( beta1
    = ( ! [A: $i,B: $i,C: $i > $i] :
          ( ! [D: $i] :
              ( ( in @ D @ A )
             => ( in @ ( C @ D ) @ B ) )
         => ! [D: $i] :
              ( ( in @ D @ A )
             => ( ( ap @ A @ B @ ( lam @ A @ B @ C ) @ D )
                = ( C @ D ) ) ) ) ) ) ).

thf(1,conjecture,
    ( app
   => ( lamp
     => ( funcext
       => ( beta1
         => ! [A: $i,B: $i,C: $i] :
              ( ( func @ A @ B @ C )
             => ( ( lam @ A @ B @ ( ap @ A @ B @ C ) )
                = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).

thf(2,negated_conjecture,
    ~ ( app
     => ( lamp
       => ( funcext
         => ( beta1
           => ! [A: $i,B: $i,C: $i] :
                ( ( func @ A @ B @ C )
               => ( ( lam @ A @ B @ ( ap @ A @ B @ C ) )
                  = C ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(24,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU696^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n021.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 15:40:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.15/0.97  % [INFO] 	 Parsing done (105ms). 
% 1.15/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.01/1.29  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.01/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.01/1.29  % [INFO] 	 Type checking passed. 
% 2.01/1.29  % [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 ... 
% 3.27/1.71  % External prover 'cvc4' found a proof!
% 3.27/1.72  % [INFO] 	 Killing All external provers ... 
% 3.27/1.72  % Time passed: 1183ms (effective reasoning time: 732ms)
% 3.27/1.72  % 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)>
% 3.27/1.72  % Axioms used in derivation (0): 
% 3.27/1.72  % No. of inferences in proof: 4
% 3.27/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1183 ms resp. 732 ms w/o parsing
% 3.40/1.77  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.40/1.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------