TSTP Solution File: SEV293^5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV293^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n032.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 15:59:56 EDT 2024

% Result   : Theorem 13.62s 3.18s
% Output   : Refutation 13.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   41
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   75 (  17 unt;   0 typ;   1 def)
%            Number of atoms       :  329 ( 205 equ;  44 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  400 ( 114   ~;  92   |;  26   &; 168   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   9 con; 0-2 aty)
%            Number of variables   :   42 (  10   ^   8   !;  24   ?;  42   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cONE_type,type,
    cONE: ( $i > $o ) > $o ).

thf(cONE_def,definition,
    ( cONE
    = ( cSUCC @ cZERO ) ) ).

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

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

thf(sk11_type,type,
    sk11: $i ).

thf(sk12_type,type,
    sk12: $i ).

thf(sk13_type,type,
    sk13: $i ).

thf(sk20_type,type,
    sk20: $i ).

thf(1,conjecture,
    ( cONE
    = ( ^ [A: $i > $o] :
        ? [B: $i] :
          ( A
          = ( (=) @ $i @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6101_pme) ).

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

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

thf(4,plain,
    ( ( ^ [A: $i > $o] :
        ? [B: $i] :
          ( ( A @ B )
          & ~ ? [C: $i] :
                ( ( C != B )
                & ( A @ C ) ) ) )
   != ( ^ [A: $i > $o] :
        ? [B: $i] :
          ( A
          = ( (=) @ $i @ B ) ) ) ),
    inference(lifteq,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ^ [A: $i > $o,B: $i] :
          ( ( A @ B )
          & ~ ? [C: $i] :
                ( ( C != B )
                & ( A @ C ) ) ) )
   != ( ^ [A: $i > $o,B: $i] :
          ( A
          = ( (=) @ $i @ B ) ) ) ),
    inference(simp,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ( sk2 @ sk3 )
      & ~ ? [A: $i] :
            ( ( A != sk3 )
            & ( sk2 @ A ) ) )
   != ( sk2
      = ( (=) @ $i @ sk3 ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(20,plain,
    ( ( ( sk2 @ sk3 )
      & ~ ? [A: $i] :
            ( ( A != sk3 )
            & ( sk2 @ A ) ) )
    | ( sk2
      = ( (=) @ $i @ sk3 ) ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(22,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( ( sk2 @ sk3 )
      & ~ ? [A: $i] :
            ( ( A != sk3 )
            & ( sk2 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[20]) ).

thf(27,plain,
    ( ( sk2 @ sk3 )
    | ( sk2
      = ( (=) @ $i @ sk3 ) ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(33,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( ( ~ ? [A: $i] :
              ( ( A != sk3 )
              & ( sk2 @ A ) ) )
     != ( sk2
        = ( (=) @ $i @ sk3 ) ) )
    | ( ( sk2 @ sk3 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[27,7]) ).

thf(34,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( ( ~ ? [A: $i] :
              ( ( A != sk3 )
              & ( sk2 @ A ) ) )
     != ( sk2
        = ( (=) @ $i @ sk3 ) ) ) ),
    inference(pattern_uni,[status(thm)],[33:[]]) ).

thf(54,plain,
    ! [A: $i] :
      ( ( ( sk2 @ A )
        = ( sk3 = A ) )
      | ( ( ~ ? [B: $i] :
                ( ( B != sk3 )
                & ( sk2 @ B ) ) )
       != ( sk2
          = ( (=) @ $i @ sk3 ) ) ) ),
    inference(func_ext,[status(esa)],[34]) ).

thf(78,plain,
    ! [A: $i] :
      ( ( ( ~ ? [B: $i] :
                ( ( B != sk3 )
                & ( sk2 @ B ) ) )
       != ( sk2
          = ( (=) @ $i @ sk3 ) ) )
      | ( ( ( sk3 = A )
          & ~ ? [B: $i] :
                ( ( B != sk3 )
                & ( sk2 @ B ) ) )
       != ( sk2
          = ( (=) @ $i @ sk3 ) ) )
      | ( ( sk2 @ A )
       != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[54,7]) ).

thf(79,plain,
    ( ( ( ~ ? [A: $i] :
              ( ( A != sk3 )
              & ( sk2 @ A ) ) )
     != ( sk2
        = ( (=) @ $i @ sk3 ) ) )
    | ( ( ( sk3 = sk3 )
        & ~ ? [A: $i] :
              ( ( A != sk3 )
              & ( sk2 @ A ) ) )
     != ( sk2
        = ( (=) @ $i @ sk3 ) ) ) ),
    inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( sk3 ))]]) ).

thf(112,plain,
    ( ( ~ ? [A: $i] :
            ( ( A != sk3 )
            & ( sk2 @ A ) ) )
   != ( sk2
      = ( (=) @ $i @ sk3 ) ) ),
    inference(simp,[status(thm)],[79]) ).

thf(114,plain,
    ( ~ ~ ? [A: $i] :
            ( ( A != sk3 )
            & ( sk2 @ A ) )
    | ( sk2
     != ( (=) @ $i @ sk3 ) ) ),
    inference(bool_ext,[status(thm)],[112]) ).

thf(119,plain,
    ( ( sk2
     != ( (=) @ $i @ sk3 ) )
    | ~ ~ ? [A: $i] :
            ( ( A != sk3 )
            & ( sk2 @ A ) ) ),
    inference(lifteq,[status(thm)],[114]) ).

thf(125,plain,
    ( ( sk2 @ sk11 )
    | ( sk2
     != ( (=) @ $i @ sk3 ) ) ),
    inference(cnf,[status(esa)],[119]) ).

thf(183,plain,
    ( ( ( sk2 @ sk13 )
     != ( sk3 = sk13 ) )
    | ( sk2 @ sk11 ) ),
    inference(func_ext,[status(esa)],[125]) ).

thf(358,plain,
    ( ( sk2 @ sk11 )
    | ( sk2 @ sk13 )
    | ( sk3 = sk13 ) ),
    inference(bool_ext,[status(thm)],[183]) ).

thf(376,plain,
    ( ( sk13 = sk3 )
    | ( sk2 @ sk11 )
    | ( sk2 @ sk13 ) ),
    inference(lifteq,[status(thm)],[358]) ).

thf(26,plain,
    ! [A: $i] :
      ( ( A = sk3 )
      | ~ ( sk2 @ A )
      | ( sk2
        = ( (=) @ $i @ sk3 ) ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(28,plain,
    ! [A: $i] :
      ( ( A = sk3 )
      | ~ ( sk2 @ A )
      | ( sk2
        = ( (=) @ $i @ sk3 ) ) ),
    inference(lifteq,[status(thm)],[26]) ).

thf(453,plain,
    ! [A: $i] :
      ( ( sk13 = sk3 )
      | ( sk2 @ sk11 )
      | ( A = sk3 )
      | ( sk2
        = ( (=) @ $i @ sk3 ) )
      | ( ( sk2 @ sk13 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[376,28]) ).

thf(454,plain,
    ( ( sk13 = sk3 )
    | ( sk2 @ sk11 )
    | ( sk13 = sk3 )
    | ( sk2
      = ( (=) @ $i @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[453:[bind(A,$thf( sk13 ))]]) ).

thf(573,plain,
    ( ( sk13 = sk3 )
    | ( sk2 @ sk11 )
    | ( sk2
      = ( (=) @ $i @ sk3 ) ) ),
    inference(simp,[status(thm)],[454]) ).

thf(1074,plain,
    ( ( sk13 = sk3 )
    | ( sk2 @ sk11 )
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[573,125]) ).

thf(1075,plain,
    ( ( sk13 = sk3 )
    | ( sk2 @ sk11 ) ),
    inference(pattern_uni,[status(thm)],[1074:[]]) ).

thf(357,plain,
    ( ( sk2 @ sk11 )
    | ~ ( sk2 @ sk13 )
    | ( sk3 != sk13 ) ),
    inference(bool_ext,[status(thm)],[183]) ).

thf(370,plain,
    ( ( sk13 != sk3 )
    | ( sk2 @ sk11 )
    | ~ ( sk2 @ sk13 ) ),
    inference(lifteq,[status(thm)],[357]) ).

thf(423,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk13 != sk3 )
    | ( sk2 @ sk11 )
    | ( ( sk2 @ sk13 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[27,370]) ).

thf(431,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk2 @ sk11 )
    | ( sk13 != sk3 )
    | ( sk13 != sk3 ) ),
    inference(simp,[status(thm)],[423]) ).

thf(438,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk2 @ sk11 )
    | ( sk13 != sk3 ) ),
    inference(simp,[status(thm)],[431]) ).

thf(856,plain,
    ( ( sk2 @ sk11 )
    | ( sk13 != sk3 )
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[438,125]) ).

thf(857,plain,
    ( ( sk2 @ sk11 )
    | ( sk13 != sk3 ) ),
    inference(pattern_uni,[status(thm)],[856:[]]) ).

thf(1102,plain,
    ( ( sk2 @ sk11 )
    | ( sk13 != sk13 ) ),
    inference(paramod_ordered,[status(thm)],[1075,857]) ).

thf(1103,plain,
    sk2 @ sk11,
    inference(pattern_uni,[status(thm)],[1102:[]]) ).

thf(1132,plain,
    ! [A: $i] :
      ( ( A = sk3 )
      | ( sk2
        = ( (=) @ $i @ sk3 ) )
      | ( ( sk2 @ sk11 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1103,28]) ).

thf(1133,plain,
    ( ( sk11 = sk3 )
    | ( sk2
      = ( (=) @ $i @ sk3 ) ) ),
    inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( sk11 ))]]) ).

thf(1202,plain,
    ( ( sk11 = sk3 )
    | ? [A: $i] :
        ( ( A != sk3 )
        & ( sk2 @ A ) )
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[1133,112]) ).

thf(1203,plain,
    ( ( sk11 = sk3 )
    | ? [A: $i] :
        ( ( A != sk3 )
        & ( sk2 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[1202:[]]) ).

thf(1222,plain,
    ( ( sk2 @ sk20 )
    | ( sk11 = sk3 ) ),
    inference(cnf,[status(esa)],[1203]) ).

thf(126,plain,
    ( ( sk11 != sk3 )
    | ( sk2
     != ( (=) @ $i @ sk3 ) ) ),
    inference(cnf,[status(esa)],[119]) ).

thf(127,plain,
    ( ( sk11 != sk3 )
    | ( sk2
     != ( (=) @ $i @ sk3 ) ) ),
    inference(lifteq,[status(thm)],[126]) ).

thf(140,plain,
    ( ( ( sk2 @ sk12 )
     != ( sk3 = sk12 ) )
    | ( sk11 != sk3 ) ),
    inference(func_ext,[status(esa)],[127]) ).

thf(144,plain,
    ( ( sk11 != sk3 )
    | ( sk2 @ sk12 )
    | ( sk3 = sk12 ) ),
    inference(bool_ext,[status(thm)],[140]) ).

thf(149,plain,
    ( ( sk12 = sk3 )
    | ( sk11 != sk3 )
    | ( sk2 @ sk12 ) ),
    inference(lifteq,[status(thm)],[144]) ).

thf(141,plain,
    ( ( sk2 @ sk3 )
    | ( sk11 != sk3 )
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[27,127]) ).

thf(142,plain,
    ( ( sk2 @ sk3 )
    | ( sk11 != sk3 ) ),
    inference(pattern_uni,[status(thm)],[141:[]]) ).

thf(143,plain,
    ( ( sk11 != sk3 )
    | ~ ( sk2 @ sk12 )
    | ( sk3 != sk12 ) ),
    inference(bool_ext,[status(thm)],[140]) ).

thf(151,plain,
    ( ( sk12 != sk3 )
    | ( sk11 != sk3 )
    | ~ ( sk2 @ sk12 ) ),
    inference(lifteq,[status(thm)],[143]) ).

thf(217,plain,
    ( ( sk11 != sk3 )
    | ( sk12 != sk3 )
    | ( ( sk2 @ sk12 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[142,151]) ).

thf(224,plain,
    ( ( sk11 != sk3 )
    | ( sk12 != sk3 )
    | ( sk12 != sk3 ) ),
    inference(simp,[status(thm)],[217]) ).

thf(231,plain,
    ( ( sk11 != sk3 )
    | ( sk12 != sk3 ) ),
    inference(simp,[status(thm)],[224]) ).

thf(242,plain,
    ( ( sk11 != sk3 )
    | ( sk2 @ sk12 )
    | ( sk12 != sk12 ) ),
    inference(paramod_ordered,[status(thm)],[149,231]) ).

thf(243,plain,
    ( ( sk11 != sk3 )
    | ( sk2 @ sk12 ) ),
    inference(pattern_uni,[status(thm)],[242:[]]) ).

thf(1216,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk2 @ sk12 )
    | ( sk11 != sk11 ) ),
    inference(paramod_ordered,[status(thm)],[1133,243]) ).

thf(1217,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk2 @ sk12 ) ),
    inference(pattern_uni,[status(thm)],[1216:[]]) ).

thf(1442,plain,
    ! [A: $i] :
      ( ( sk2
        = ( (=) @ $i @ sk3 ) )
      | ( A = sk3 )
      | ( ( sk2 @ sk12 )
       != ( sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1217,28]) ).

thf(1443,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk12 = sk3 ) ),
    inference(pattern_uni,[status(thm)],[1442:[bind(A,$thf( sk12 ))]]) ).

thf(1208,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk12 != sk3 )
    | ( sk11 != sk11 ) ),
    inference(paramod_ordered,[status(thm)],[1133,231]) ).

thf(1209,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk12 != sk3 ) ),
    inference(pattern_uni,[status(thm)],[1208:[]]) ).

thf(1714,plain,
    ( ( sk2
      = ( (=) @ $i @ sk3 ) )
    | ( sk12 != sk12 ) ),
    inference(paramod_ordered,[status(thm)],[1443,1209]) ).

thf(1715,plain,
    ( sk2
    = ( (=) @ $i @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[1714:[]]) ).

thf(1729,plain,
    ( ( sk11 != sk3 )
    | ( ( (=) @ $i @ sk3 )
     != ( (=) @ $i @ sk3 ) ) ),
    inference(rewrite,[status(thm)],[127,1715]) ).

thf(1730,plain,
    sk11 != sk3,
    inference(simp,[status(thm)],[1729]) ).

thf(1748,plain,
    sk2 @ sk20,
    inference(simplifyReflect,[status(thm)],[1222,1730]) ).

thf(1741,plain,
    ! [A: $i] :
      ( ( sk2 @ A )
      = ( sk3 = A ) ),
    inference(func_ext,[status(esa)],[1715]) ).

thf(1837,plain,
    sk3 = sk20,
    inference(rewrite,[status(thm)],[1748,1741]) ).

thf(1846,plain,
    sk20 = sk3,
    inference(lifteq,[status(thm)],[1837]) ).

thf(1223,plain,
    ( ( sk20 != sk3 )
    | ( sk11 = sk3 ) ),
    inference(cnf,[status(esa)],[1203]) ).

thf(1224,plain,
    ( ( sk20 != sk3 )
    | ( sk11 = sk3 ) ),
    inference(lifteq,[status(thm)],[1223]) ).

thf(1749,plain,
    sk20 != sk3,
    inference(simplifyReflect,[status(thm)],[1224,1730]) ).

thf(1857,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[1846,1749]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SEV293^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.02/0.09  % Command  : run_Leo-III %s %d SAT
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Fri Jun 21 18:37:55 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.70/0.76  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.01/0.86  % [INFO] 	 Parsing done (100ms). 
% 1.01/0.87  % [INFO] 	 Running in sequential loop mode. 
% 1.24/1.07  % [INFO] 	 nitpick registered as external prover. 
% 1.24/1.07  % [INFO] 	 Scanning for conjecture ... 
% 1.39/1.13  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.39/1.14  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.39/1.15  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.39/1.15  % [INFO] 	 Type checking passed. 
% 1.39/1.15  % [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 ... 
% 13.62/3.18  % [INFO] 	 Killing All external provers ... 
% 13.62/3.18  % Time passed: 2723ms (effective reasoning time: 2310ms)
% 13.62/3.18  % 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)>
% 13.62/3.18  % Axioms used in derivation (0): 
% 13.62/3.18  % No. of inferences in proof: 74
% 13.62/3.18  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2723 ms resp. 2310 ms w/o parsing
% 13.62/3.24  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.62/3.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------