TSTP Solution File: SYO035^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO035^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 08:55:30 EDT 2024

% Result   : Theorem 3.16s 1.82s
% Output   : Refutation 3.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   23 (  10 unt;   5 typ;   2 def)
%            Number of atoms       :   46 (  35 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   44 (  10   ~;   5   |;   0   &;  22   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   36 (  22   ^  14   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(leibeq1_type,type,
    leibeq1: $i > $i > $o ).

thf(leibeq1_def,definition,
    ( leibeq1
    = ( ^ [A: $i,B: $i] :
        ! [C: $i > $o] :
          ( ( C @ A )
         => ( C @ B ) ) ) ) ).

thf(leibeq2_type,type,
    leibeq2: ( $i > $o ) > ( $i > $o ) > $o ).

thf(leibeq2_def,definition,
    ( leibeq2
    = ( ^ [A: $i > $o,B: $i > $o] :
        ! [C: ( $i > $o ) > $o] :
          ( ( C @ A )
         => ( C @ B ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( leibeq2
        @ ^ [C: $i] : ( C = A )
        @ ^ [C: $i] : ( C = B ) )
     => ( leibeq1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( leibeq2
          @ ^ [C: $i] : ( C = A )
          @ ^ [C: $i] : ( C = B ) )
       => ( leibeq1 @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(6,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ~ ( A
          @ ^ [B: $i] : ( B = sk1 ) )
      | ( A
        @ ^ [B: $i] : ( B = sk2 ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ( ( ( ^ [A: $i] : ( A = sk1 ) )
     != ( ^ [A: $i] : ( A = sk1 ) ) )
    | ( ( ^ [A: $i] : ( A = sk1 ) )
      = ( ^ [A: $i] : ( A = sk2 ) ) ) ),
    inference(replace_leibeq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $o ) @ ^ [B: $i] : ( B = sk1 ) ))]]) ).

thf(8,plain,
    ( ( ( ^ [A: $i] : ( A = sk1 ) )
     != ( ^ [A: $i] : ( A = sk1 ) ) )
    | ( ( ^ [A: $i] : ( A = sk2 ) )
      = ( ^ [A: $i] : ( A = sk1 ) ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ^ [A: $i] : ( A = sk2 ) )
    = ( ^ [A: $i] : ( A = sk1 ) ) ),
    inference(simp,[status(thm)],[8]) ).

thf(12,plain,
    ! [A: $i] :
      ( ( A = sk2 )
      = ( A = sk1 ) ),
    inference(func_ext,[status(esa)],[9]) ).

thf(16,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( A = sk1 ) ),
    inference(bool_ext,[status(thm)],[12]) ).

thf(18,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( A = sk1 ) ),
    inference(lifteq,[status(thm)],[16]) ).

thf(20,plain,
    sk2 = sk1,
    inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk2 ))]]) ).

thf(5,plain,
    sk3 @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk3 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ( ( sk3 @ sk2 )
   != ( sk3 @ sk1 ) ),
    inference(paramod_ordered,[status(thm)],[5,4]) ).

thf(11,plain,
    sk2 != sk1,
    inference(simp,[status(thm)],[10]) ).

thf(22,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[20,11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SYO035^1 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.17  % Command  : run_Leo-III %s %d
% 0.16/0.38  % Computer : n028.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit : 300
% 0.16/0.38  % WCLimit  : 300
% 0.16/0.38  % DateTime : Mon May 20 09:49:39 EDT 2024
% 0.16/0.39  % CPUTime  : 
% 1.05/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.05  % [INFO] 	 Parsing done (111ms). 
% 1.29/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.89/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.89/1.35  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.89/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.89/1.36  % [INFO] 	 Type checking passed. 
% 1.89/1.36  % [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 ... 
% 3.16/1.81  % [INFO] 	 Killing All external provers ... 
% 3.16/1.82  % Time passed: 1256ms (effective reasoning time: 752ms)
% 3.16/1.82  % 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)>
% 3.16/1.82  % Axioms used in derivation (0): 
% 3.16/1.82  % No. of inferences in proof: 16
% 3.16/1.82  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1256 ms resp. 752 ms w/o parsing
% 3.19/1.85  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.19/1.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------