TSTP Solution File: SEU619^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU619^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 03:38:38 EDT 2024

% Result   : Theorem 2.72s 1.64s
% Output   : Refutation 3.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   14 (   4 unt;   7 typ;   3 def)
%            Number of atoms       :   23 (   5 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  148 (   2   ~;   0   |;   4   &; 136   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   19 (   1   ^  14   !;   4   ?;  19   :)

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

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

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

thf(setunion_type,type,
    setunion: $i > $i ).

thf(iskpair_type,type,
    iskpair: $i > $o ).

thf(iskpair_def,definition,
    ( iskpair
    = ( ^ [A: $i] :
        ? [B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
          & ? [C: $i] :
              ( ( in @ C @ ( setunion @ A ) )
              & ( A
                = ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).

thf(setukpairIL_type,type,
    setukpairIL: $o ).

thf(setukpairIL_def,definition,
    ( setukpairIL
    = ( ! [A: $i,B: $i] : ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).

thf(setukpairIR_type,type,
    setukpairIR: $o ).

thf(setukpairIR_def,definition,
    ( setukpairIR
    = ( ! [A: $i,B: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).

thf(1,conjecture,
    ( setukpairIL
   => ( setukpairIR
     => ! [A: $i,B: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).

thf(2,negated_conjecture,
    ~ ( setukpairIL
     => ( setukpairIR
       => ! [A: $i,B: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(10,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU619^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n002.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 16:23:24 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 1.03/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.33/1.04  % [INFO] 	 Parsing done (118ms). 
% 1.33/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.73/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.73/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.73/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.96/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.96/1.34  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.96/1.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.96/1.34  % [INFO] 	 Type checking passed. 
% 1.96/1.34  % [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 ... 
% 2.72/1.64  % External prover 'cvc4' found a proof!
% 2.72/1.64  % [INFO] 	 Killing All external provers ... 
% 2.72/1.64  % Time passed: 1112ms (effective reasoning time: 589ms)
% 2.72/1.64  % 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)>
% 2.72/1.64  % Axioms used in derivation (0): 
% 2.72/1.64  % No. of inferences in proof: 4
% 2.72/1.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1112 ms resp. 589 ms w/o parsing
% 3.07/1.72  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.07/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------