TSTP Solution File: SYO309^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO309^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 08:56:23 EDT 2024

% Result   : Theorem 12.79s 3.47s
% Output   : Refutation 12.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (   8 unt;   6 typ;   0 def)
%            Number of atoms       :   84 (  17 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  394 (  48   ~;  25   |;   0   &; 318   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   82 (  12   ^  53   !;  17   ?;  82   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cS_type,type,
    cS: $i > $i ).

thf(cQ_type,type,
    cQ: $i > $i ).

thf(cR_type,type,
    cR: $i > $i > $o ).

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

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

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

thf(1,conjecture,
    ( ! [A: $i] :
        ( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
        = ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
   => ? [A: $i > $o] :
      ! [B: $i] :
        ( ( A @ B )
        = ( ~ ( A @ ( cS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEO1) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
          = ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
     => ? [A: $i > $o] :
        ! [B: $i] :
          ( ( A @ B )
          = ( ~ ( A @ ( cS @ B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i] :
          ( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
          = ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
     => ? [A: $i > $o] :
        ! [B: $i] :
          ( ( A @ B )
          = ( ~ ( A @ ( cS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk1 @ A ) )
     != ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [A: $i > $o] :
      ( ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) )
     != ( A @ ( sk1 @ A ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ! [A: $i > $o] :
      ( ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) )
     != ( A @ ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[6]) ).

thf(9,plain,
    ! [A: $i > $o] :
      ( ~ ~ ( A @ ( cS @ ( sk1 @ A ) ) )
      | ~ ( A @ ( sk1 @ A ) ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(11,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ ( sk1 @ A ) )
      | ( A @ ( cS @ ( sk1 @ A ) ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(5,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
      = ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [A: $i] :
      ( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
      = ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(14,plain,
    ! [A: $i] :
      ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) )
      | ~ ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ),
    inference(bool_ext,[status(thm)],[8]) ).

thf(28,plain,
    ! [A: $i] :
      ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) )
      | ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(13,plain,
    ! [A: $i] :
      ( ~ ? [B: $i] : ( cR @ A @ ( cQ @ B ) )
      | ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ),
    inference(bool_ext,[status(thm)],[8]) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cR @ ( cS @ A ) @ ( cQ @ C ) )
      | ~ ( cR @ A @ ( cQ @ B ) ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
      | ~ ( cR @ B @ ( cQ @ C ) )
      | ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) )
       != ( cR @ ( cS @ B ) @ ( cQ @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[28,27]) ).

thf(592,plain,
    ! [B: $i,A: $i] :
      ( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
      | ~ ( cR @ B @ ( cQ @ A ) ) ),
    inference(pattern_uni,[status(thm)],[591:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( sk3 @ E ))]]) ).

thf(613,plain,
    ! [B: $i,A: $i] :
      ( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
      | ~ ( cR @ B @ ( cQ @ A ) ) ),
    inference(simp,[status(thm)],[592]) ).

thf(753,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
      | ( cR @ C @ ( cQ @ ( sk2 @ C ) ) )
      | ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) )
       != ( cR @ C @ ( cQ @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[28,613]) ).

thf(754,plain,
    ! [A: $i] :
      ( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
      | ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[753:[bind(A,$thf( E )),bind(B,$thf( sk3 @ E )),bind(C,$thf( cS @ E ))]]) ).

thf(797,plain,
    ! [A: $i] :
      ( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
      | ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) ) ),
    inference(simp,[status(thm)],[754]) ).

thf(10,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ ( cS @ ( sk1 @ A ) ) )
      | ( A @ ( sk1 @ A ) ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(12,plain,
    ! [A: $i > $o] :
      ( ( A @ ( sk1 @ A ) )
      | ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(1507,plain,
    ! [B: $i > $o,A: $i] :
      ( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
      | ( B @ ( sk1 @ B ) )
      | ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) )
       != ( B @ ( cS @ ( sk1 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[797,12]) ).

thf(1544,plain,
    ( ( cR
      @ ( sk1
        @ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
      @ ( cQ
        @ ( sk2
          @ ( sk1
            @ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) )
    | ( cR
      @ ( sk1
        @ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
      @ ( cQ
        @ ( sk2
          @ ( sk1
            @ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ) ),
    inference(pre_uni,[status(thm)],[1507:[bind(A,$thf( sk1 @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )),bind(B,$thf( ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ))]]) ).

thf(1577,plain,
    ( cR
    @ ( sk1
      @ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
    @ ( cQ
      @ ( sk2
        @ ( sk1
          @ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ),
    inference(simp,[status(thm)],[1544]) ).

thf(758,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( cR @ B @ ( cQ @ A ) )
      | ~ ( cR @ C @ ( cQ @ D ) )
      | ( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
       != ( cR @ ( cS @ C ) @ ( cQ @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[613,27]) ).

thf(759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
      | ~ ( cR @ C @ ( cQ @ B ) ) ),
    inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( A )),bind(B,$thf( cS @ H )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( sk2 @ ( cS @ H ) ))]]) ).

thf(800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
      | ~ ( cR @ C @ ( cQ @ B ) ) ),
    inference(simp,[status(thm)],[759]) ).

thf(1634,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
      | ( ( cR
          @ ( sk1
            @ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) )
          @ ( cQ
            @ ( sk2
              @ ( sk1
                @ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ) ) ) )
       != ( cR @ C @ ( cQ @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1577,800]) ).

thf(1635,plain,
    ! [A: $i] :
      ~ ( cR
        @ ( cS
          @ ( sk1
            @ ^ [B: $i] : ( cR @ B @ ( cQ @ ( sk2 @ B ) ) ) ) )
        @ ( cQ @ A ) ),
    inference(pattern_uni,[status(thm)],[1634:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ) )),bind(C,$thf( sk1 @ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ))]]) ).

thf(1661,plain,
    ! [B: $i,A: $i > $o] :
      ( ~ ( A @ ( sk1 @ A ) )
      | ( ( A @ ( cS @ ( sk1 @ A ) ) )
       != ( cR
          @ ( cS
            @ ( sk1
              @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) )
          @ ( cQ @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,1635]) ).

thf(1666,plain,
    ~ ( cR
      @ ( sk1
        @ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
      @ ( cQ
        @ ( sk2
          @ ( sk1
            @ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ),
    inference(pre_uni,[status(thm)],[1661:[bind(A,$thf( ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )),bind(B,$thf( sk2 @ ( cS @ ( sk1 @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) ) ))]]) ).

thf(1729,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[1666,1577]) ).

thf(1730,plain,
    $false,
    inference(simp,[status(thm)],[1729]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO309^5 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n027.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 09:29:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.96/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.95  % [INFO] 	 Parsing done (92ms). 
% 1.25/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.48/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.63/1.16  % [INFO] 	 cvc4 registered as external prover. 
% 1.63/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.70/1.21  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.70/1.23  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.70/1.23  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.70/1.23  % [INFO] 	 Type checking passed. 
% 1.83/1.24  % [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 ... 
% 12.79/3.46  % [INFO] 	 Killing All external provers ... 
% 12.79/3.46  % Time passed: 2939ms (effective reasoning time: 2497ms)
% 12.79/3.46  % 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)>
% 12.79/3.46  % Axioms used in derivation (0): 
% 12.79/3.46  % No. of inferences in proof: 34
% 12.79/3.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2939 ms resp. 2497 ms w/o parsing
% 12.79/3.51  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.79/3.51  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------