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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---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 THM

% Computer : n021.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 15:58:55 EDT 2024

% Result   : Theorem 5.91s 2.40s
% Output   : Refutation 5.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   57 (   6 unt;   0 typ;   0 def)
%            Number of atoms       :  274 (  54 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  397 (  74   ~;  83   |;  32   &; 198   @)
%                                         (   0 <=>;  10  =>;   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     :   10 (   7 usr;   7 con; 0-2 aty)
%            Number of variables   :   39 (  23   ^  16   !;   0   ?;  39   :)

% 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(sk6_type,type,
    sk6: $i ).

thf(sk8_type,type,
    sk8: $i ).

thf(1,conjecture,
    ( ( ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) ) )
    = ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    file('/export/starexec/sandbox/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(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(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(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(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(166,plain,
    ( ( cS @ sk1 )
    | ~ ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
     != ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[144,4]) ).

thf(167,plain,
    ( ( cS @ sk1 )
    | ~ ! [A: $i] :
          ( ( cR @ A )
         => ( cS @ A ) ) ),
    inference(pattern_uni,[status(thm)],[166:[]]) ).

thf(169,plain,
    ( ( cR @ sk6 )
    | ( cS @ sk1 ) ),
    inference(cnf,[status(esa)],[167]) ).

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

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

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(177,plain,
    ( ( cR @ sk6 )
    | ( cR @ sk2 )
    | ( ( cS @ sk1 )
     != ( cS @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[169,20]) ).

thf(178,plain,
    ( ( cR @ sk6 )
    | ( cR @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[177:[]]) ).

thf(195,plain,
    ( ( cR @ sk2 )
    | ( ( cR @ sk6 )
     != ( cR @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[178]) ).

thf(202,plain,
    ( ( cR @ sk2 )
    | ( sk6 != sk2 ) ),
    inference(simp,[status(thm)],[195]) ).

thf(184,plain,
    ( ( cR @ sk6 )
    | ( ( ( cR @ sk2 )
        & ( cS @ sk2 ) )
     != ( cR @ sk2 ) )
    | ( ( cS @ sk1 )
     != ( cS @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[169,12]) ).

thf(185,plain,
    ( ( cR @ sk6 )
    | ( ( ( cR @ sk2 )
        & ( cS @ sk2 ) )
     != ( cR @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[184:[]]) ).

thf(201,plain,
    ( ( cR @ sk2 )
    | ( ( cR @ sk6 )
     != ( cR @ sk2 ) ) ),
    inference(simp,[status(thm)],[195]) ).

thf(192,plain,
    ! [A: $i] :
      ( ( cR @ sk2 )
      | ( cS @ A )
      | ( ( ^ [B: $i] :
              ( ( cR @ B )
              & ( cS @ B ) ) )
        = cR )
      | ( ( cR @ sk6 )
       != ( cR @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[178,11]) ).

thf(193,plain,
    ( ( cR @ sk2 )
    | ( cS @ sk6 )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
      = cR ) ),
    inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( sk6 ))]]) ).

thf(181,plain,
    ( ( cR @ sk6 )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
     != cR )
    | ( ( cS @ sk1 )
     != ( cS @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[169,9]) ).

thf(182,plain,
    ( ( cR @ sk6 )
    | ( ( ^ [A: $i] :
            ( ( cR @ A )
            & ( cS @ A ) ) )
     != cR ) ),
    inference(pattern_uni,[status(thm)],[181:[]]) ).

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(21,plain,
    ( ~ ( cR @ sk2 )
    | ~ ( cS @ sk1 )
    | ( ( cS @ sk2 )
     != ( cS @ sk1 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[17]) ).

thf(22,plain,
    ( ~ ( cR @ sk2 )
    | ~ ( cS @ sk1 )
    | ( ( cS @ sk2 )
     != ( cS @ sk1 ) ) ),
    inference(simp,[status(thm)],[21]) ).

thf(141,plain,
    ( ~ ( cS @ sk1 )
    | ( ( cS @ sk2 )
     != ( cS @ sk1 ) )
    | ( ( cR @ sk2 )
     != ( cR @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[113,22]) ).

thf(149,plain,
    ( ~ ( cS @ sk1 )
    | ( sk2 != sk1 )
    | ( sk2 != sk1 ) ),
    inference(simp,[status(thm)],[141]) ).

thf(152,plain,
    ( ~ ( cS @ sk1 )
    | ( sk2 != sk1 ) ),
    inference(simp,[status(thm)],[149]) ).

thf(179,plain,
    ( ( cR @ sk6 )
    | ( sk2 != sk1 )
    | ( ( cS @ sk1 )
     != ( cS @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[169,152]) ).

thf(180,plain,
    ( ( cR @ sk6 )
    | ( sk2 != sk1 ) ),
    inference(pattern_uni,[status(thm)],[179:[]]) ).

thf(281,plain,
    ( ( ( ( cR @ sk8 )
        & ( cS @ sk8 ) )
     != ( cR @ sk8 ) )
    | ( cR @ sk6 ) ),
    inference(func_ext,[status(esa)],[182]) ).

thf(235,plain,
    ( ( sk6 != sk2 )
    | ~ ( cS @ sk2 )
    | ~ ( cS @ sk1 )
    | ( ( cR @ sk2 )
     != ( cR @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[202,17]) ).

thf(236,plain,
    ( ( sk6 != sk2 )
    | ~ ( cS @ sk2 )
    | ~ ( cS @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[235:[]]) ).

thf(36,plain,
    ! [B: $i,A: $i] :
      ( ( ( ( cR @ B )
          & ( cS @ B ) )
        = ( cR @ B ) )
      | ~ ( cR @ A )
      | ( cS @ A ) ),
    inference(func_ext,[status(esa)],[11]) ).

thf(168,plain,
    ( ~ ( cS @ sk6 )
    | ( cS @ sk1 ) ),
    inference(cnf,[status(esa)],[167]) ).

thf(430,plain,
    $false,
    inference(e,[status(thm)],[202,185,201,193,113,3,182,11,4,178,20,152,9,169,180,17,22,281,12,144,236,36,168]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEV396^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Jun 21 18:37:10 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 1.07/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.27/1.06  % [INFO] 	 Parsing done (128ms). 
% 1.27/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.33  % [INFO] 	 eprover registered as external prover. 
% 1.84/1.33  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.39  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.02/1.41  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.02/1.41  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.02/1.41  % [INFO] 	 Type checking passed. 
% 2.02/1.41  % [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 ... 
% 5.91/2.39  % External prover 'e' found a proof!
% 5.91/2.40  % [INFO] 	 Killing All external provers ... 
% 5.91/2.40  % Time passed: 1867ms (effective reasoning time: 1316ms)
% 5.91/2.40  % 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)>
% 5.91/2.40  % Axioms used in derivation (0): 
% 5.91/2.40  % No. of inferences in proof: 57
% 5.91/2.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1867 ms resp. 1316 ms w/o parsing
% 5.97/2.43  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.97/2.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------