TSTP Solution File: SWC012-1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC012-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 04:33:42 EDT 2024

% Result   : Unsatisfiable 255.36s 45.14s
% Output   : Refutation 255.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   62 (  20 unt;  11 typ;   0 def)
%            Number of atoms       :  131 (  55 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  374 (  84   ~;  70   |;   0   &; 220   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   29 (   0   ^  29   !;   0   ?;  29   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ssList_type,type,
    ssList: $i > $o ).

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

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

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

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

thf(neq_type,type,
    neq: $i > $i > $o ).

thf(nil_type,type,
    nil: $i ).

thf(ssItem_type,type,
    ssItem: $i > $o ).

thf(app_type,type,
    app: $i > $i > $i ).

thf(cons_type,type,
    cons: $i > $i > $i ).

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

thf(43,axiom,
    ssList @ nil,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).

thf(293,plain,
    ssList @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(7,negated_conjecture,
    ( ( neq @ sk2 @ nil )
    | ( neq @ sk2 @ nil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).

thf(209,plain,
    neq @ sk2 @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(14,negated_conjecture,
    ( ( ( app @ sk3 @ ( cons @ sk5 @ nil ) )
      = sk4 )
    | ~ ( neq @ sk4 @ nil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).

thf(202,plain,
    ( ( ( app @ sk3 @ ( cons @ sk5 @ nil ) )
      = sk4 )
    | ~ ( neq @ sk4 @ nil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(214,plain,
    ( ( ( app @ sk3 @ ( cons @ sk5 @ nil ) )
      = sk4 )
    | ~ ( neq @ sk4 @ nil ) ),
    inference(cnf,[status(esa)],[202]) ).

thf(215,plain,
    ( ( ( app @ sk3 @ ( cons @ sk5 @ nil ) )
      = sk4 )
    | ~ ( neq @ sk4 @ nil ) ),
    inference(lifteq,[status(thm)],[214]) ).

thf(5,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).

thf(200,plain,
    sk2 = sk4,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(226,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[200]) ).

thf(6,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).

thf(204,plain,
    sk1 = sk3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(223,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[204]) ).

thf(651,plain,
    ( ( ( app @ sk1 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ~ ( neq @ sk2 @ nil ) ),
    inference(rewrite,[status(thm)],[215,226,223]) ).

thf(652,plain,
    ( ( ( app @ sk1 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( ( neq @ sk2 @ nil )
     != ( neq @ sk2 @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[209,651]) ).

thf(653,plain,
    ( ( app @ sk1 @ ( cons @ sk5 @ nil ) )
    = sk2 ),
    inference(pattern_uni,[status(thm)],[652:[]]) ).

thf(12,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ( ( app @ ( app @ B @ ( cons @ A @ nil ) ) @ C )
       != sk2 )
      | ( ( app @ B @ C )
       != sk1 )
      | ~ ( neq @ sk4 @ nil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).

thf(208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ( ( app @ ( app @ B @ ( cons @ A @ nil ) ) @ C )
       != sk2 )
      | ( ( app @ B @ C )
       != sk1 )
      | ~ ( neq @ sk4 @ nil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ( ( app @ ( app @ B @ ( cons @ A @ nil ) ) @ C )
       != sk2 )
      | ( ( app @ B @ C )
       != sk1 )
      | ~ ( neq @ sk4 @ nil ) ),
    inference(cnf,[status(esa)],[208]) ).

thf(225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ B @ ( cons @ A @ nil ) ) @ C )
       != sk2 )
      | ( ( app @ B @ C )
       != sk1 )
      | ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ~ ( neq @ sk4 @ nil ) ),
    inference(lifteq,[status(thm)],[224]) ).

thf(714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ B @ ( cons @ A @ nil ) ) @ C )
       != sk2 )
      | ( ( app @ B @ C )
       != sk1 )
      | ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ~ ( neq @ sk2 @ nil ) ),
    inference(rewrite,[status(thm)],[225,226]) ).

thf(731,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( app @ sk2 @ C )
       != sk2 )
      | ( ( app @ B @ C )
       != sk1 )
      | ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ~ ( neq @ sk2 @ nil )
      | ( ( app @ sk1 @ ( cons @ sk5 @ nil ) )
       != ( app @ B @ ( cons @ A @ nil ) ) ) ),
    inference(paramod_ordered,[status(thm)],[653,714]) ).

thf(732,plain,
    ! [A: $i] :
      ( ( ( app @ sk2 @ A )
       != sk2 )
      | ( ( app @ sk1 @ A )
       != sk1 )
      | ~ ( ssItem @ sk5 )
      | ~ ( ssList @ sk1 )
      | ~ ( ssList @ A )
      | ~ ( neq @ sk2 @ nil ) ),
    inference(pattern_uni,[status(thm)],[731:[bind(A,$thf( sk5 )),bind(B,$thf( sk1 ))]]) ).

thf(763,plain,
    ! [A: $i] :
      ( ( ( app @ sk2 @ A )
       != sk2 )
      | ( ( app @ sk1 @ A )
       != sk1 )
      | ~ ( ssItem @ sk5 )
      | ~ ( ssList @ sk1 )
      | ~ ( ssList @ A )
      | ~ ( neq @ sk2 @ nil ) ),
    inference(simp,[status(thm)],[732]) ).

thf(13,negated_conjecture,
    ( ( ssItem @ sk5 )
    | ~ ( neq @ sk4 @ nil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).

thf(206,plain,
    ( ( ssItem @ sk5 )
    | ~ ( neq @ sk4 @ nil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(218,plain,
    ( ( ssItem @ sk5 )
    | ~ ( neq @ sk4 @ nil ) ),
    inference(cnf,[status(esa)],[206]) ).

thf(678,plain,
    ( ( ssItem @ sk5 )
    | ~ ( neq @ sk2 @ nil ) ),
    inference(rewrite,[status(thm)],[218,226]) ).

thf(679,plain,
    ( ( ssItem @ sk5 )
    | ( ( neq @ sk2 @ nil )
     != ( neq @ sk2 @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[209,678]) ).

thf(680,plain,
    ssItem @ sk5,
    inference(pattern_uni,[status(thm)],[679:[]]) ).

thf(1,negated_conjecture,
    ssList @ sk1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).

thf(203,plain,
    ssList @ sk1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(809,plain,
    ! [A: $i] :
      ( ( ( app @ sk2 @ A )
       != sk2 )
      | ( ( app @ sk1 @ A )
       != sk1 )
      | ~ $true
      | ~ $true
      | ~ ( ssList @ A )
      | ~ $true ),
    inference(rewrite,[status(thm)],[763,209,680,203]) ).

thf(810,plain,
    ! [A: $i] :
      ( ( ( app @ sk2 @ A )
       != sk2 )
      | ( ( app @ sk1 @ A )
       != sk1 )
      | ~ ( ssList @ A ) ),
    inference(simp,[status(thm)],[809]) ).

thf(815,plain,
    ! [A: $i] :
      ( ( ( app @ sk2 @ A )
       != sk2 )
      | ( ( app @ sk1 @ A )
       != sk1 )
      | ( ( ssList @ nil )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[293,810]) ).

thf(816,plain,
    ( ( ( app @ sk2 @ nil )
     != sk2 )
    | ( ( app @ sk1 @ nil )
     != sk1 ) ),
    inference(pattern_uni,[status(thm)],[815:[bind(A,$thf( nil ))]]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ A @ nil )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).

thf(449,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ A @ nil )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(450,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ A @ nil )
        = A ) ),
    inference(cnf,[status(esa)],[449]) ).

thf(451,plain,
    ! [A: $i] :
      ( ( ( app @ A @ nil )
        = A )
      | ~ ( ssList @ A ) ),
    inference(lifteq,[status(thm)],[450]) ).

thf(115167,plain,
    ! [A: $i] :
      ( ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[203,451]) ).

thf(115168,plain,
    ( ( app @ sk1 @ nil )
    = sk1 ),
    inference(pattern_uni,[status(thm)],[115167:[bind(A,$thf( sk1 ))]]) ).

thf(115541,plain,
    ( ( ( app @ sk2 @ nil )
     != sk2 )
    | ( sk1 != sk1 ) ),
    inference(rewrite,[status(thm)],[816,115168]) ).

thf(115542,plain,
    ( ( app @ sk2 @ nil )
   != sk2 ),
    inference(simp,[status(thm)],[115541]) ).

thf(2,negated_conjecture,
    ssList @ sk2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).

thf(207,plain,
    ssList @ sk2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(115180,plain,
    ! [A: $i] :
      ( ( ( app @ A @ nil )
        = A )
      | ( ( ssList @ sk2 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[207,451]) ).

thf(115181,plain,
    ( ( app @ sk2 @ nil )
    = sk2 ),
    inference(pattern_uni,[status(thm)],[115180:[bind(A,$thf( sk2 ))]]) ).

thf(124067,plain,
    sk2 != sk2,
    inference(rewrite,[status(thm)],[115542,115181]) ).

thf(124068,plain,
    $false,
    inference(simp,[status(thm)],[124067]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09  % Problem  : SWC012-1 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n022.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Sun May 19 03:12:24 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.93/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.60/1.17  % [INFO] 	 Parsing done (245ms). 
% 1.60/1.19  % [INFO] 	 Running in sequential loop mode. 
% 2.19/1.54  % [INFO] 	 nitpick registered as external prover. 
% 2.19/1.55  % [INFO] 	 Scanning for conjecture ... 
% 2.47/1.70  % [INFO] 	 Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ... 
% 2.91/1.83  % [INFO] 	 Axiom selection finished. Selected 185 axioms (removed 0 axioms). 
% 3.19/1.96  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.19/1.97  % [INFO] 	 Type checking passed. 
% 3.39/1.98  % [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 ... 
% 255.36/45.13  % [INFO] 	 Killing All external provers ... 
% 255.36/45.14  % Time passed: 44671ms (effective reasoning time: 43941ms)
% 255.36/45.14  % Axioms used in derivation (2): clause8, clause73
% 255.36/45.14  % No. of inferences in proof: 51
% 255.36/45.14  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 44671 ms resp. 43941 ms w/o parsing
% 255.36/45.17  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 255.36/45.17  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------