TSTP Solution File: SET680^3 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET680^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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  7 10:50:20 EDT 2024

% Result   : Theorem 4.59s 2.44s
% Output   : Refutation 4.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   28 (  12 unt;   6 typ;   2 def)
%            Number of atoms       :   53 (  10 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  134 (  18   ~;   9   |;  11   &;  88   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   35 (   6   ^  20   !;   9   ?;  35   :)

% Comments : 
%------------------------------------------------------------------------------
thf(is_rel_on_type,type,
    is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).

thf(is_rel_on_def,definition,
    ( is_rel_on
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
        ! [D: $i,E: $i] :
          ( ( A @ D @ E )
         => ( ( B @ D )
            & ( C @ E ) ) ) ) ) ).

thf(rel_domain_type,type,
    rel_domain: ( $i > $i > $o ) > $i > $o ).

thf(rel_domain_def,definition,
    ( rel_domain
    = ( ^ [A: $i > $i > $o,B: $i] :
        ? [C: $i] : ( A @ B @ C ) ) ) ).

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

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

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

thf(sk7_type,type,
    sk7: $i ).

thf(1,conjecture,
    ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
      ( ( is_rel_on @ A @ B @ C )
     => ! [D: $i] :
          ( ( B @ D )
         => ( ( rel_domain @ A @ D )
            = ( ? [E: $i] :
                  ( ( C @ E )
                  & ( A @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
        ( ( is_rel_on @ A @ B @ C )
       => ! [D: $i] :
            ( ( B @ D )
           => ( ( rel_domain @ A @ D )
              = ( ? [E: $i] :
                    ( ( C @ E )
                    & ( A @ D @ E ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ( ( ? [A: $i] : ( sk1 @ sk4 @ A ) )
   != ( ? [A: $i] :
          ( ( sk3 @ A )
          & ( sk1 @ sk4 @ A ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ( ( ? [A: $i] :
          ( ( sk3 @ A )
          & ( sk1 @ sk4 @ A ) ) )
   != ( ? [A: $i] : ( sk1 @ sk4 @ A ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(9,plain,
    ( ( ^ [A: $i] :
          ( ( sk3 @ A )
          & ( sk1 @ sk4 @ A ) ) )
   != ( sk1 @ sk4 ) ),
    inference(simp,[status(thm)],[8]) ).

thf(15,plain,
    ( ( ( sk3 @ sk7 )
      & ( sk1 @ sk4 @ sk7 ) )
   != ( sk1 @ sk4 @ sk7 ) ),
    inference(func_ext,[status(esa)],[9]) ).

thf(17,plain,
    ( ( ( sk3 @ sk7 )
      & ( sk1 @ sk4 @ sk7 ) )
    | ( sk1 @ sk4 @ sk7 ) ),
    inference(bool_ext,[status(thm)],[15]) ).

thf(20,plain,
    ( ( sk1 @ sk4 @ sk7 )
    | ( sk1 @ sk4 @ sk7 ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(22,plain,
    sk1 @ sk4 @ sk7,
    inference(simp,[status(thm)],[20]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ( sk3 @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(76,plain,
    ! [B: $i,A: $i] :
      ( ( sk3 @ B )
      | ( ( sk1 @ sk4 @ sk7 )
       != ( sk1 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[22,7]) ).

thf(77,plain,
    sk3 @ sk7,
    inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( sk4 )),bind(B,$thf( sk7 ))]]) ).

thf(16,plain,
    ( ~ ( ( sk3 @ sk7 )
        & ( sk1 @ sk4 @ sk7 ) )
    | ~ ( sk1 @ sk4 @ sk7 ) ),
    inference(bool_ext,[status(thm)],[15]) ).

thf(18,plain,
    ( ~ ( sk1 @ sk4 @ sk7 )
    | ~ ( sk3 @ sk7 )
    | ~ ( sk1 @ sk4 @ sk7 ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(19,plain,
    ( ~ ( sk1 @ sk4 @ sk7 )
    | ~ ( sk3 @ sk7 ) ),
    inference(simp,[status(thm)],[18]) ).

thf(25,plain,
    ( ~ $true
    | ~ ( sk3 @ sk7 ) ),
    inference(rewrite,[status(thm)],[19,22]) ).

thf(26,plain,
    ~ ( sk3 @ sk7 ),
    inference(simp,[status(thm)],[25]) ).

thf(78,plain,
    $false,
    inference(rewrite,[status(thm)],[77,26]) ).

thf(79,plain,
    $false,
    inference(simp,[status(thm)],[78]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SET680^3 : TPTP v8.1.2. Released v3.6.0.
% 0.16/0.17  % Command  : run_Leo-III %s %d
% 0.16/0.38  % Computer : n022.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
% 0.16/0.39  % DateTime : Mon May  6 20:31:09 EDT 2024
% 0.16/0.39  % CPUTime  : 
% 0.92/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.60/1.19  % [INFO] 	 Parsing done (244ms). 
% 1.60/1.20  % [INFO] 	 Running in sequential loop mode. 
% 2.03/1.54  % [INFO] 	 nitpick registered as external prover. 
% 2.15/1.55  % [INFO] 	 Scanning for conjecture ... 
% 2.45/1.71  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.45/1.74  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.45/1.74  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.45/1.75  % [INFO] 	 Type checking passed. 
% 2.45/1.75  % [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 ... 
% 4.59/2.43  % [INFO] 	 Killing All external provers ... 
% 4.59/2.44  % Time passed: 1874ms (effective reasoning time: 1227ms)
% 4.59/2.44  % 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)>
% 4.59/2.44  % Axioms used in derivation (0): 
% 4.59/2.44  % No. of inferences in proof: 20
% 4.59/2.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1874 ms resp. 1227 ms w/o parsing
% 4.59/2.48  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.59/2.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------