TSTP Solution File: SYN386^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN386^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 08:18:20 EDT 2024

% Result   : Theorem 4.12s 2.20s
% Output   : Refutation 4.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   37 (  12 unt;  10 typ;   0 def)
%            Number of atoms       :   85 (   5 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  347 (  34   ~;  21   |;   9   &; 265   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   2 con; 0-3 aty)
%            Number of variables   :  121 (   0   ^ 103   !;  18   ?; 121   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cD_type,type,
    cD: $i > $i > $i > $o ).

thf(cF_type,type,
    cF: $i > $i > $o ).

thf(cS_type,type,
    cS: $i > $i > $o ).

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

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

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

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

thf(sk5_type,type,
    sk5: $i > $i ).

thf(sk6_type,type,
    sk6: $i > $i > $i ).

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

thf(1,conjecture,
    ( ( ! [A: $i] :
        ? [B: $i] : ( cF @ A @ B )
      & ? [A: $i] :
        ! [B: $i] :
        ? [C: $i] :
        ! [D: $i] :
          ( ( cS @ C @ D )
         => ( cD @ D @ A @ B ) )
      & ! [A: $i] :
        ? [B: $i] :
        ! [C: $i,D: $i] :
          ( ( cD @ C @ D @ B )
         => ! [E: $i,F: $i] :
              ( ( ( cF @ C @ E )
                & ( cF @ D @ F ) )
             => ( cD @ E @ F @ A ) ) ) )
   => ? [A: $i] :
      ! [B: $i] :
      ? [C: $i] :
      ! [D: $i] :
        ( ( cS @ C @ D )
       => ! [E: $i] :
            ( ( cF @ D @ E )
           => ( cD @ E @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2138) ).

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

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

thf(6,plain,
    ! [A: $i] : ( cF @ A @ ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [B: $i,A: $i] : ( cF @ ( sk6 @ B @ A ) @ ( sk7 @ B @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [B: $i,A: $i] : ( cF @ ( sk6 @ B @ A ) @ ( sk7 @ B @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(7,plain,
    ! [B: $i,A: $i] : ( cS @ B @ ( sk6 @ B @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [B: $i,A: $i] : ( cS @ B @ ( sk6 @ B @ A ) ),
    inference(simp,[status(thm)],[7]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cS @ ( sk3 @ A ) @ B )
      | ( cD @ B @ sk2 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cS @ ( sk3 @ A ) @ B )
      | ( cD @ B @ sk2 @ A ) ),
    inference(simp,[status(thm)],[9]) ).

thf(61,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( cD @ D @ sk2 @ C )
      | ( ( cS @ B @ ( sk6 @ B @ A ) )
       != ( cS @ ( sk3 @ C ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[12,11]) ).

thf(62,plain,
    ! [B: $i,A: $i] : ( cD @ ( sk6 @ ( sk3 @ B ) @ A ) @ sk2 @ B ),
    inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( G )),bind(B,$thf( sk3 @ H )),bind(C,$thf( H )),bind(D,$thf( sk6 @ ( sk3 @ H ) @ G ))]]) ).

thf(66,plain,
    ! [B: $i,A: $i] : ( cD @ ( sk6 @ ( sk3 @ B ) @ A ) @ sk2 @ B ),
    inference(simp,[status(thm)],[62]) ).

thf(4,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cD @ B @ C @ ( sk4 @ A ) )
      | ~ ( cF @ B @ D )
      | ~ ( cF @ C @ E )
      | ( cD @ D @ E @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cD @ B @ C @ ( sk4 @ A ) )
      | ~ ( cF @ B @ D )
      | ~ ( cF @ C @ E )
      | ( cD @ D @ E @ A ) ),
    inference(simp,[status(thm)],[4]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ~ ( cD @ ( sk7 @ B @ A ) @ A @ ( sk5 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ~ ( cD @ ( sk7 @ B @ A ) @ A @ ( sk5 @ A ) ),
    inference(simp,[status(thm)],[5]) ).

thf(15,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cD @ B @ C @ ( sk4 @ A ) )
      | ~ ( cF @ B @ D )
      | ~ ( cF @ C @ E )
      | ( ( cD @ D @ E @ A )
       != ( cD @ ( sk7 @ G @ F ) @ F @ ( sk5 @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,10]) ).

thf(16,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cD @ A @ B @ ( sk4 @ ( sk5 @ D ) ) )
      | ~ ( cF @ A @ ( sk7 @ C @ D ) )
      | ~ ( cF @ B @ D ) ),
    inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( sk5 @ J )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk7 @ H @ J )),bind(E,$thf( J )),bind(F,$thf( J )),bind(G,$thf( H ))]]) ).

thf(29,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cD @ A @ B @ ( sk4 @ ( sk5 @ D ) ) )
      | ~ ( cF @ A @ ( sk7 @ C @ D ) )
      | ~ ( cF @ B @ D ) ),
    inference(simp,[status(thm)],[16]) ).

thf(73,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cF @ C @ ( sk7 @ E @ F ) )
      | ~ ( cF @ D @ F )
      | ( ( cD @ ( sk6 @ ( sk3 @ B ) @ A ) @ sk2 @ B )
       != ( cD @ C @ D @ ( sk4 @ ( sk5 @ F ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[66,29]) ).

thf(74,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cF @ ( sk6 @ ( sk3 @ ( sk4 @ ( sk5 @ C ) ) ) @ B ) @ ( sk7 @ A @ C ) )
      | ~ ( cF @ sk2 @ C ) ),
    inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( H )),bind(B,$thf( sk4 @ ( sk5 @ K ) )),bind(C,$thf( sk6 @ ( sk3 @ ( sk4 @ ( sk5 @ K ) ) ) @ H )),bind(D,$thf( sk2 )),bind(E,$thf( E )),bind(F,$thf( K ))]]) ).

thf(77,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cF @ ( sk6 @ ( sk3 @ ( sk4 @ ( sk5 @ C ) ) ) @ B ) @ ( sk7 @ A @ C ) )
      | ~ ( cF @ sk2 @ C ) ),
    inference(simp,[status(thm)],[74]) ).

thf(145,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cF @ sk2 @ E )
      | ( ( cF @ ( sk6 @ B @ A ) @ ( sk7 @ B @ A ) )
       != ( cF @ ( sk6 @ ( sk3 @ ( sk4 @ ( sk5 @ E ) ) ) @ D ) @ ( sk7 @ C @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13,77]) ).

thf(146,plain,
    ! [A: $i] :
      ~ ( cF @ sk2 @ A ),
    inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk4 @ ( sk5 @ A ) ) )),bind(C,$thf( sk3 @ ( sk4 @ ( sk5 @ A ) ) )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).

thf(156,plain,
    ! [B: $i,A: $i] :
      ( ( cF @ A @ ( sk1 @ A ) )
     != ( cF @ sk2 @ B ) ),
    inference(paramod_ordered,[status(thm)],[6,146]) ).

thf(157,plain,
    $false,
    inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 @ sk2 ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYN386^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n023.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 13:40:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.03/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.35/1.04  % [INFO] 	 Parsing done (119ms). 
% 1.35/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.26  % [INFO] 	 nitpick registered as external prover. 
% 1.69/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.93/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.93/1.36  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.93/1.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.93/1.36  % [INFO] 	 Type checking passed. 
% 1.93/1.37  % [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 ... 
% 4.12/2.20  % [INFO] 	 Killing All external provers ... 
% 4.12/2.20  % Time passed: 1665ms (effective reasoning time: 1152ms)
% 4.12/2.20  % 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)>
% 4.12/2.20  % Axioms used in derivation (0): 
% 4.12/2.20  % No. of inferences in proof: 27
% 4.12/2.20  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1665 ms resp. 1152 ms w/o parsing
% 4.44/2.25  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.44/2.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------