TSTP Solution File: SEV396^5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV396^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n029.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 : Mon Jun 24 16:00:09 EDT 2024

% Result   : Theorem 8.17s 2.80s
% Output   : Refutation 8.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   49 (  11 unt;   0 typ;   0 def)
%            Number of atoms       :  202 (  31 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  294 (  53   ~;  58   |;  25   &; 150   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   37 (  19   ^  18   !;   0   ?;  37   :)

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

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

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

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

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

thf(1,conjecture,
    ( ( ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) ) )
    = ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM31_pme) ).

thf(2,negated_conjecture,
    ( ( ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) ) )
   != ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) ) )
   != ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) ) )
   != ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    inference(lifteq,[status(thm)],[3]) ).

thf(6,plain,
    ( ! [A: $i] :
        ( ( cR @ A )
       => ( cS @ A ) )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    inference(bool_ext,[status(thm)],[4]) ).

thf(8,plain,
    ( ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR )
    | ! [A: $i] :
        ( ( cR @ A )
       => ( cS @ A ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(11,plain,
    ! [A: $i] :
      ( ~ ( cR @ A )
      | ( cS @ A )
      | ( ( ^ [B: $i] :
              ( ( cR @ B )
              & ( cS @ B ) ) )
        = cR ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(5,plain,
    ( ~ ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
     != cR ) ),
    inference(bool_ext,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
     != cR )
    | ~ ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(9,plain,
    ( ~ ( cS @ sk1 )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
     != cR ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(39,plain,
    ! [A: $i] :
      ( ~ ( cR @ A )
      | ( cS @ A )
      | ~ ( cS @ sk1 )
      | ( ( ^ [B: $i] :
              ( ( cR @ B )
              & ( cS @ B ) ) )
       != ( ^ [B: $i] :
              ( ( cR @ B )
              & ( cS @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,9]) ).

thf(40,plain,
    ! [A: $i] :
      ( ~ ( cR @ A )
      | ( cS @ A )
      | ~ ( cS @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[39:[]]) ).

thf(10,plain,
    ( ( cR @ sk1 )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
     != cR ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(13,plain,
    ( ( ( ( cR @ sk3 )
        & ( cS @ sk3 ) )
     != ( cR @ sk3 ) )
    | ( cR @ sk1 ) ),
    inference(func_ext,[status(esa)],[10]) ).

thf(46,plain,
    ( ( cR @ sk1 )
    | ( ( cR @ sk3 )
      & ( cS @ sk3 ) )
    | ( cR @ sk3 ) ),
    inference(bool_ext,[status(thm)],[13]) ).

thf(50,plain,
    ( ( cR @ sk3 )
    | ( cR @ sk3 )
    | ( cR @ sk1 ) ),
    inference(cnf,[status(esa)],[46]) ).

thf(51,plain,
    ( ( cR @ sk3 )
    | ( cR @ sk1 ) ),
    inference(simp,[status(thm)],[50]) ).

thf(56,plain,
    ! [A: $i] :
      ( ( cR @ sk1 )
      | ( cS @ A )
      | ( ( ^ [B: $i] :
              ( ( cR @ B )
              & ( cS @ B ) ) )
        = cR )
      | ( ( cR @ sk3 )
       != ( cR @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[51,11]) ).

thf(57,plain,
    ( ( cR @ sk1 )
    | ( cS @ sk3 )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( sk3 ))]]) ).

thf(99,plain,
    ( ( cR @ sk1 )
    | ( cS @ sk3 )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
     != ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[57,10]) ).

thf(100,plain,
    ( ( cR @ sk1 )
    | ( cS @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[99:[]]) ).

thf(112,plain,
    ( ( cR @ sk1 )
    | ( ( cS @ sk3 )
     != ( cS @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[100,13]) ).

thf(113,plain,
    cR @ sk1,
    inference(pattern_uni,[status(thm)],[112:[]]) ).

thf(143,plain,
    ! [A: $i] :
      ( ( cS @ A )
      | ( ( ^ [B: $i] :
              ( ( cR @ B )
              & ( cS @ B ) ) )
        = cR )
      | ( ( cR @ sk1 )
       != ( cR @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[113,11]) ).

thf(144,plain,
    ( ( cS @ sk1 )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( sk1 ))]]) ).

thf(159,plain,
    ! [A: $i] :
      ( ( ( ( cR @ A )
          & ( cS @ A ) )
        = ( cR @ A ) )
      | ( cS @ sk1 ) ),
    inference(func_ext,[status(esa)],[144]) ).

thf(436,plain,
    ! [A: $i] :
      ( ( ( cS @ A )
        = ( cR @ A ) )
      | ( cS @ sk1 )
      | ( ( cR @ sk1 )
       != ( cR @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[113,159]) ).

thf(437,plain,
    ( ( ( cS @ sk1 )
      = ( cR @ sk1 ) )
    | ( cS @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[436:[bind(A,$thf( sk1 ))]]) ).

thf(465,plain,
    ( ( cS @ sk1 )
    | ( cS @ sk1 ) ),
    inference(rewrite,[status(thm)],[437,113]) ).

thf(466,plain,
    cS @ sk1,
    inference(simp,[status(thm)],[465]) ).

thf(509,plain,
    ! [A: $i] :
      ( ~ ( cR @ A )
      | ( cS @ A )
      | ~ $true ),
    inference(rewrite,[status(thm)],[40,466]) ).

thf(510,plain,
    ! [A: $i] :
      ( ~ ( cR @ A )
      | ( cS @ A ) ),
    inference(simp,[status(thm)],[509]) ).

thf(12,plain,
    ( ( ( ( cR @ sk2 )
        & ( cS @ sk2 ) )
     != ( cR @ sk2 ) )
    | ~ ( cS @ sk1 ) ),
    inference(func_ext,[status(esa)],[9]) ).

thf(14,plain,
    ( ~ ( cS @ sk1 )
    | ~ ( ( cR @ sk2 )
        & ( cS @ sk2 ) )
    | ~ ( cR @ sk2 ) ),
    inference(bool_ext,[status(thm)],[12]) ).

thf(16,plain,
    ( ~ ( cR @ sk2 )
    | ~ ( cR @ sk2 )
    | ~ ( cS @ sk2 )
    | ~ ( cS @ sk1 ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(17,plain,
    ( ~ ( cR @ sk2 )
    | ~ ( cS @ sk2 )
    | ~ ( cS @ sk1 ) ),
    inference(simp,[status(thm)],[16]) ).

thf(473,plain,
    ( ~ ( cR @ sk2 )
    | ~ ( cS @ sk2 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[17,466]) ).

thf(474,plain,
    ( ~ ( cR @ sk2 )
    | ~ ( cS @ sk2 ) ),
    inference(simp,[status(thm)],[473]) ).

thf(15,plain,
    ( ~ ( cS @ sk1 )
    | ( ( cR @ sk2 )
      & ( cS @ sk2 ) )
    | ( cR @ sk2 ) ),
    inference(bool_ext,[status(thm)],[12]) ).

thf(19,plain,
    ( ( cR @ sk2 )
    | ( cR @ sk2 )
    | ~ ( cS @ sk1 ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(20,plain,
    ( ( cR @ sk2 )
    | ~ ( cS @ sk1 ) ),
    inference(simp,[status(thm)],[19]) ).

thf(469,plain,
    ( ( cR @ sk2 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[20,466]) ).

thf(470,plain,
    cR @ sk2,
    inference(simp,[status(thm)],[469]) ).

thf(502,plain,
    ( ~ $true
    | ~ ( cS @ sk2 ) ),
    inference(rewrite,[status(thm)],[474,470]) ).

thf(503,plain,
    ~ ( cS @ sk2 ),
    inference(simp,[status(thm)],[502]) ).

thf(511,plain,
    ! [A: $i] :
      ( ~ ( cR @ A )
      | ( ( cS @ A )
       != ( cS @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[510,503]) ).

thf(512,plain,
    ~ ( cR @ sk2 ),
    inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( sk2 ))]]) ).

thf(528,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[512,470]) ).

thf(529,plain,
    $false,
    inference(simp,[status(thm)],[528]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.09  % Problem  : SEV396^5 : TPTP v8.2.0. Released v4.0.0.
% 0.01/0.09  % Command  : run_Leo-III %s %d SAT
% 0.08/0.28  % Computer : n029.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Fri Jun 21 18:36:55 EDT 2024
% 0.08/0.28  % CPUTime  : 
% 0.79/0.81  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.06/0.92  % [INFO] 	 Parsing done (108ms). 
% 1.06/0.94  % [INFO] 	 Running in sequential loop mode. 
% 1.55/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.55/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.55/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.80/1.35  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.80/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.80/1.35  % [INFO] 	 Type checking passed. 
% 1.80/1.35  % [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 ... 
% 8.14/2.79  % [INFO] 	 Killing All external provers ... 
% 8.17/2.79  % Time passed: 2373ms (effective reasoning time: 1847ms)
% 8.17/2.79  % 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)>
% 8.17/2.79  % Axioms used in derivation (0): 
% 8.17/2.79  % No. of inferences in proof: 49
% 8.17/2.80  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2373 ms resp. 1847 ms w/o parsing
% 8.21/2.85  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.21/2.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------