TSTP Solution File: SEU652^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU652^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 03:43:10 EDT 2024

% Result   : Theorem 6.45s 3.06s
% Output   : Refutation 6.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   41 (  18 unt;   9 typ;   3 def)
%            Number of atoms       :   75 (  39 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  242 (  33   ~;  14   |;   0   &; 176   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :   57 (   0   ^  56   !;   1   ?;  57   :)

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

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

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

thf(setadjoinIL_type,type,
    setadjoinIL: $o ).

thf(setadjoinIL_def,definition,
    ( setadjoinIL
    = ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).

thf(uniqinunit_type,type,
    uniqinunit: $o ).

thf(uniqinunit_def,definition,
    ( uniqinunit
    = ( ! [A: $i,B: $i] :
          ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
         => ( A = B ) ) ) ) ).

thf(secondinupair_type,type,
    secondinupair: $o ).

thf(secondinupair_def,definition,
    ( secondinupair
    = ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).

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

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

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

thf(1,conjecture,
    ( setadjoinIL
   => ( uniqinunit
     => ( secondinupair
       => ! [A: $i,B: $i,C: $i] :
            ( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
              = ( setadjoin @ C @ emptyset ) )
           => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).

thf(2,negated_conjecture,
    ~ ( setadjoinIL
     => ( uniqinunit
       => ( secondinupair
         => ! [A: $i,B: $i,C: $i] :
              ( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
                = ( setadjoin @ C @ emptyset ) )
             => ( A = B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ~ ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
     => ( ! [A: $i,B: $i] :
            ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
           => ( A = B ) )
       => ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
         => ! [A: $i,B: $i] :
              ( ? [C: $i] :
                  ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
                  = ( setadjoin @ C @ emptyset ) )
             => ( A = B ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(9,plain,
    ! [B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(12,plain,
    ! [B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(simp,[status(thm)],[9]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(7,plain,
    ( ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
    = ( setadjoin @ sk3 @ emptyset ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(13,plain,
    ( ( setadjoin @ sk3 @ emptyset )
    = ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(6,plain,
    ! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(8,plain,
    sk1 != sk2,
    inference(cnf,[status(esa)],[4]) ).

thf(14,plain,
    sk2 != sk1,
    inference(lifteq,[status(thm)],[8]) ).

thf(45,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A != sk1 )
      | ( B != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[11,14]) ).

thf(46,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ sk2 @ emptyset ) )
      | ( A != sk1 ) ),
    inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(153,plain,
    ~ ( in @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ),
    inference(simp,[status(thm)],[46]) ).

thf(219,plain,
    ! [B: $i,A: $i] :
      ( ( in @ A @ ( setadjoin @ A @ B ) )
     != ( in @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[6,153]) ).

thf(241,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ( ( setadjoin @ A @ B )
       != ( setadjoin @ sk2 @ emptyset ) ) ),
    inference(simp,[status(thm)],[219]) ).

thf(249,plain,
    ! [A: $i] :
      ( ( setadjoin @ sk1 @ A )
     != ( setadjoin @ sk2 @ emptyset ) ),
    inference(simp,[status(thm)],[241]) ).

thf(275,plain,
    ! [A: $i] :
      ( ( ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
       != ( setadjoin @ sk1 @ A ) )
      | ( ( setadjoin @ sk3 @ emptyset )
       != ( setadjoin @ sk2 @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[13,249]) ).

thf(298,plain,
    ! [A: $i] :
      ( ( sk1 != sk1 )
      | ( ( setadjoin @ sk2 @ emptyset )
       != A )
      | ( sk3 != sk2 )
      | ( emptyset != emptyset ) ),
    inference(simp,[status(thm)],[275]) ).

thf(308,plain,
    sk3 != sk2,
    inference(simp,[status(thm)],[298]) ).

thf(320,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A != sk2 )
      | ( B != sk3 ) ),
    inference(paramod_ordered,[status(thm)],[11,308]) ).

thf(321,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ sk3 @ emptyset ) )
      | ( A != sk2 ) ),
    inference(pattern_uni,[status(thm)],[320:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).

thf(322,plain,
    ~ ( in @ sk2 @ ( setadjoin @ sk3 @ emptyset ) ),
    inference(simp,[status(thm)],[321]) ).

thf(324,plain,
    ~ ( in @ sk2 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ),
    inference(rewrite,[status(thm)],[322,13]) ).

thf(329,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
     != ( in @ sk2 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,324]) ).

thf(330,plain,
    $false,
    inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU652^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n017.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Sun May 19 16:41:54 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 1.08/1.06  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.39/1.23  % [INFO] 	 Parsing done (165ms). 
% 1.45/1.24  % [INFO] 	 Running in sequential loop mode. 
% 1.82/1.61  % [INFO] 	 nitpick registered as external prover. 
% 1.82/1.62  % [INFO] 	 Scanning for conjecture ... 
% 2.13/1.75  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.24/1.79  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.24/1.79  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.24/1.79  % [INFO] 	 Type checking passed. 
% 2.24/1.80  % [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 ... 
% 6.45/3.05  % [INFO] 	 Killing All external provers ... 
% 6.45/3.05  % Time passed: 2532ms (effective reasoning time: 1805ms)
% 6.45/3.06  % 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)>
% 6.45/3.06  % Axioms used in derivation (0): 
% 6.45/3.06  % No. of inferences in proof: 29
% 6.45/3.06  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2532 ms resp. 1805 ms w/o parsing
% 6.48/3.12  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.48/3.12  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------