TSTP Solution File: DAT130^1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : DAT130^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 May 20 19:48:52 EDT 2024

% Result   : Theorem 43.89s 10.98s
% Output   : Refutation 43.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   23 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :   19 (  10 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  176 (   6   ~;   1   |;   0   &; 169   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    3 (   0   ^   0   !;   0   ?;   3   :)
%                                         (   3  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(coindu526335360e_lSup_type,type,
    coindu526335360e_lSup: 
      !>[TA: $tType] : ( ( set @ ( coindu1593790203_llist @ TA ) ) > ( coindu1593790203_llist @ TA ) ) ).

thf(coindu1046438764le_lhd_type,type,
    coindu1046438764le_lhd: 
      !>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > TA ) ).

thf(coindu1047225960le_ltl_type,type,
    coindu1047225960le_ltl: 
      !>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).

thf(ya_type,type,
    ya: set @ ( coindu1593790203_llist @ a ) ).

thf(less_eq_type,type,
    less_eq: a > a > $o ).

thf(xs_type,type,
    xs: coindu1593790203_llist @ a ).

thf(182,axiom,
    ( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
    = ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062) ).

thf(855,plain,
    ( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
    = ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(856,plain,
    ( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) )
    = ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
    inference(lifteq,[status(thm)],[855]) ).

thf(188,axiom,
    less_eq @ ( coindu1046438764le_lhd @ a @ xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062) ).

thf(878,plain,
    less_eq @ ( coindu1046438764le_lhd @ a @ xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(149,axiom,
    ( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
    = ( coindu1046438764le_lhd @ a @ xs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062) ).

thf(739,plain,
    ( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
    = ( coindu1046438764le_lhd @ a @ xs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(740,plain,
    ( ( coindu1046438764le_lhd @ a @ xs )
    = ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ),
    inference(lifteq,[status(thm)],[739]) ).

thf(1372,plain,
    less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
    inference(rewrite,[status(thm)],[878,740]) ).

thf(1,conjecture,
    less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(241,plain,
    ~ ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1377,plain,
    ( ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) )
   != ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1372,241]) ).

thf(1382,plain,
    ( ( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
     != ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
    | ( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) )
     != ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ) ),
    inference(simp,[status(thm)],[1377]) ).

thf(1388,plain,
    ( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) )
   != ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
    inference(simp,[status(thm)],[1382]) ).

thf(1482,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[856,1388]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15  % Problem  : DAT130^1 : TPTP v8.2.0. Released v7.0.0.
% 0.18/0.18  % Command  : run_Leo-III %s %d
% 0.18/0.41  % Computer : n005.cluster.edu
% 0.18/0.41  % Model    : x86_64 x86_64
% 0.18/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41  % Memory   : 8042.1875MB
% 0.18/0.41  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.41  % CPULimit : 300
% 0.18/0.41  % WCLimit  : 300
% 0.18/0.41  % DateTime : Sun May 19 23:20:09 EDT 2024
% 0.18/0.41  % CPUTime  : 
% 1.49/1.36  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.87/1.91  % [INFO] 	 Parsing done (542ms). 
% 3.32/1.93  % [INFO] 	 Running in sequential loop mode. 
% 4.71/2.47  % [INFO] 	 nitpick registered as external prover. 
% 4.71/2.48  % [INFO] 	 Scanning for conjecture ... 
% 5.32/2.70  % [INFO] 	 Found a conjecture (or negated_conjecture) and 263 axioms. Running axiom selection ... 
% 5.63/2.91  % [INFO] 	 Axiom selection finished. Selected 238 axioms (removed 25 axioms). 
% 7.26/3.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 7.26/3.38  % [INFO] 	 Type checking passed. 
% 7.26/3.39  % [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 ... 
% 43.89/10.97  % [INFO] 	 Killing All external provers ... 
% 43.89/10.98  % Time passed: 10349ms (effective reasoning time: 9033ms)
% 43.89/10.98  % 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)>
% 43.89/10.98  % Axioms used in derivation (3): fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062, fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062, fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062
% 43.89/10.98  % No. of inferences in proof: 16
% 43.89/10.98  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10349 ms resp. 9033 ms w/o parsing
% 43.89/11.01  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 43.89/11.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------