TSTP Solution File: QUA002^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : QUA002^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 02:30:25 EDT 2024

% Result   : Theorem 14.54s 4.44s
% Output   : Refutation 14.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   25 (  11 unt;   5 typ;   1 def)
%            Number of atoms       :   60 (  56 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :   64 (  18   ~;  27   |;   0   &;  19   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 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   :   16 (  10   ^   6   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sup_type,type,
    sup: ( $i > $o ) > $i ).

thf(addition_type,type,
    addition: $i > $i > $i ).

thf(addition_def,definition,
    ( addition
    = ( ^ [A: $i,B: $i] : ( sup @ ( union @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( addition @ A @ B )
      = ( addition @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_comm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( addition @ A @ B )
        = ( addition @ B @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: $i,B: $i] :
        ( ( sup
          @ ^ [C: $i] :
              ( ( C = A )
              | ( C = B ) ) )
        = ( sup
          @ ^ [C: $i] :
              ( ( C = B )
              | ( C = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,plain,
    ( ( sup
      @ ^ [A: $i] :
          ( ( A = sk1 )
          | ( A = sk2 ) ) )
   != ( sup
      @ ^ [A: $i] :
          ( ( A = sk2 )
          | ( A = sk1 ) ) ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(12,plain,
    ( ( sup
      @ ^ [A: $i] :
          ( ( A = sk1 )
          | ( A = sk2 ) ) )
   != ( sup
      @ ^ [A: $i] :
          ( ( A = sk2 )
          | ( A = sk1 ) ) ) ),
    inference(lifteq,[status(thm)],[11]) ).

thf(50,plain,
    ( ( ^ [A: $i] :
          ( ( A = sk1 )
          | ( A = sk2 ) ) )
   != ( ^ [A: $i] :
          ( ( A = sk2 )
          | ( A = sk1 ) ) ) ),
    inference(simp,[status(thm)],[12]) ).

thf(68,plain,
    ( ( ( sk3 = sk1 )
      | ( sk3 = sk2 ) )
   != ( ( sk3 = sk2 )
      | ( sk3 = sk1 ) ) ),
    inference(func_ext,[status(esa)],[50]) ).

thf(302,plain,
    ( ( sk3 = sk1 )
    | ( sk3 = sk2 )
    | ( sk3 = sk2 )
    | ( sk3 = sk1 ) ),
    inference(bool_ext,[status(thm)],[68]) ).

thf(341,plain,
    ( ( sk3 = sk2 )
    | ( sk3 = sk1 )
    | ( sk3 = sk1 )
    | ( sk3 = sk2 ) ),
    inference(cnf,[status(esa)],[302]) ).

thf(342,plain,
    ( ( sk3 = sk2 )
    | ( sk3 = sk1 )
    | ( sk3 = sk1 )
    | ( sk3 = sk2 ) ),
    inference(lifteq,[status(thm)],[341]) ).

thf(343,plain,
    ( ( sk3 = sk2 )
    | ( sk3 = sk1 ) ),
    inference(simp,[status(thm)],[342]) ).

thf(301,plain,
    ( ~ ( ( sk3 = sk1 )
        | ( sk3 = sk2 ) )
    | ~ ( ( sk3 = sk2 )
        | ( sk3 = sk1 ) ) ),
    inference(bool_ext,[status(thm)],[68]) ).

thf(333,plain,
    ( ( sk3 != sk1 )
    | ( sk3 != sk1 ) ),
    inference(cnf,[status(esa)],[301]) ).

thf(336,plain,
    ( ( sk3 != sk1 )
    | ( sk3 != sk1 ) ),
    inference(lifteq,[status(thm)],[333]) ).

thf(337,plain,
    sk3 != sk1,
    inference(simp,[status(thm)],[336]) ).

thf(335,plain,
    ( ( sk3 != sk2 )
    | ( sk3 != sk2 ) ),
    inference(cnf,[status(esa)],[301]) ).

thf(339,plain,
    ( ( sk3 != sk2 )
    | ( sk3 != sk2 ) ),
    inference(lifteq,[status(thm)],[335]) ).

thf(340,plain,
    sk3 != sk2,
    inference(simp,[status(thm)],[339]) ).

thf(349,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[343,337,340]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : QUA002^1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n008.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 : Mon May 20 13:37:09 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.14/1.07  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.63/1.27  % [INFO] 	 Parsing done (193ms). 
% 1.63/1.29  % [INFO] 	 Running in sequential loop mode. 
% 2.26/1.67  % [INFO] 	 eprover registered as external prover. 
% 2.26/1.67  % [INFO] 	 cvc4 registered as external prover. 
% 2.26/1.68  % [INFO] 	 Scanning for conjecture ... 
% 2.48/1.81  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 2.59/1.85  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 2.71/1.86  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.71/1.86  % [INFO] 	 Type checking passed. 
% 2.71/1.87  % [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 ... 
% 14.54/4.43  % [INFO] 	 Killing All external provers ... 
% 14.54/4.44  % Time passed: 3917ms (effective reasoning time: 3143ms)
% 14.54/4.44  % 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)>
% 14.54/4.44  % Axioms used in derivation (0): 
% 14.54/4.44  % No. of inferences in proof: 19
% 14.54/4.44  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3917 ms resp. 3143 ms w/o parsing
% 14.57/4.47  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.57/4.47  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------