TSTP Solution File: SEU515^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU515^2 : 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 03:42:25 EDT 2024

% Result   : Theorem 2.75s 1.75s
% Output   : Refutation 3.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   28 (   9 unt;   7 typ;   1 def)
%            Number of atoms       :   53 (  21 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   99 (  10   ~;  13   |;   0   &;  58   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  24   !;   0   ?;  24   :)

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

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

thf(setadjoinAx_type,type,
    setadjoinAx: $o ).

thf(setadjoinAx_def,definition,
    ( setadjoinAx
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setadjoin @ A @ B ) )
          = ( ( C = A )
            | ( in @ C @ B ) ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $o ).

thf(1,conjecture,
    ( setadjoinAx
   => ! [A: $i,B: $i,C: $i] :
        ( ( in @ C @ ( setadjoin @ A @ B ) )
       => ! [D: $o] :
            ( ( ( C = A )
             => D )
           => ( ( ( in @ C @ B )
               => D )
             => D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).

thf(2,negated_conjecture,
    ~ ( setadjoinAx
     => ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setadjoin @ A @ B ) )
         => ! [D: $o] :
              ( ( ( C = A )
               => D )
             => ( ( ( in @ C @ B )
                 => D )
               => D ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(7,plain,
    in @ sk3 @ ( setadjoin @ sk1 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ ( setadjoin @ A @ B ) )
      = ( ( C = A )
        | ( in @ C @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ ( setadjoin @ A @ B ) )
      = ( ( C = A )
        | ( in @ C @ B ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(11,plain,
    ( ( sk3 = sk1 )
    | ( in @ sk3 @ sk2 ) ),
    inference(rewrite,[status(thm)],[7,10]) ).

thf(14,plain,
    ( ( sk3 = sk1 )
    | ( in @ sk3 @ sk2 ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(15,plain,
    ( ( sk3 = sk1 )
    | ( in @ sk3 @ sk2 ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(5,plain,
    ( ~ ( in @ sk3 @ sk2 )
    | sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ~ sk4,
    inference(cnf,[status(esa)],[3]) ).

thf(26,plain,
    ( ~ ( in @ sk3 @ sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[5,8]) ).

thf(27,plain,
    ~ ( in @ sk3 @ sk2 ),
    inference(simp,[status(thm)],[26]) ).

thf(35,plain,
    ( ( sk3 = sk1 )
    | $false ),
    inference(rewrite,[status(thm)],[15,27]) ).

thf(36,plain,
    sk3 = sk1,
    inference(simp,[status(thm)],[35]) ).

thf(6,plain,
    ( ( sk3 != sk1 )
    | sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ( ( sk3 != sk1 )
    | sk4 ),
    inference(lifteq,[status(thm)],[6]) ).

thf(24,plain,
    ( ( sk3 != sk1 )
    | $false ),
    inference(rewrite,[status(thm)],[9,8]) ).

thf(25,plain,
    sk3 != sk1,
    inference(simp,[status(thm)],[24]) ).

thf(37,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[36,25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU515^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 17:15:39 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 1.00/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/1.02  % [INFO] 	 Parsing done (141ms). 
% 1.28/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.32  % [INFO] 	 nitpick registered as external prover. 
% 1.74/1.32  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.39  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.88/1.41  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.88/1.41  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.88/1.42  % [INFO] 	 Type checking passed. 
% 1.88/1.42  % [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 ... 
% 2.75/1.71  % [INFO] 	 Killing All external provers ... 
% 2.75/1.75  % Time passed: 1224ms (effective reasoning time: 707ms)
% 2.75/1.75  % 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)>
% 2.75/1.75  % Axioms used in derivation (0): 
% 2.75/1.75  % No. of inferences in proof: 20
% 2.75/1.75  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1224 ms resp. 707 ms w/o parsing
% 2.75/1.77  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.00/1.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------