TSTP Solution File: ITP029^1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : ITP029^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 22:27:41 EDT 2024

% Result   : ContradictoryAxioms 6.93s 2.72s
% Output   : Refutation 6.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   24 (   9 unt;  11 typ;   0 def)
%            Number of atoms       :   19 (   8 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   46 (   8   ~;   2   |;   0   &;  34   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    8 (   7 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   10 (   0   ^  10   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
thf(binary594033953_set_a_type,type,
    binary594033953_set_a: $tType ).

thf(binary1439146945Tree_a_type,type,
    binary1439146945Tree_a: $tType ).

thf(set_set_set_a_type,type,
    set_set_set_a: $tType ).

thf(set_set_a_type,type,
    set_set_a: $tType ).

thf(set_a_type,type,
    set_a: $tType ).

thf(int_type,type,
    int: $tType ).

thf(a_type,type,
    a: $tType ).

thf(ord_less_int_type,type,
    ord_less_int: int > int > $o ).

thf(a2_type,type,
    a2: a ).

thf(b_type,type,
    b: a ).

thf(h_type,type,
    h: a > int ).

thf(92,axiom,
    ord_less_int @ ( h @ b ) @ ( h @ a2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062) ).

thf(410,plain,
    ord_less_int @ ( h @ b ) @ ( h @ a2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(83,axiom,
    ( ( h @ a2 )
    = ( h @ b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hahb) ).

thf(396,plain,
    ( ( h @ a2 )
    = ( h @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(397,plain,
    ( ( h @ b )
    = ( h @ a2 ) ),
    inference(lifteq,[status(thm)],[396]) ).

thf(534,plain,
    ord_less_int @ ( h @ a2 ) @ ( h @ a2 ),
    inference(rewrite,[status(thm)],[410,397]) ).

thf(18,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_dual__order_Ostrict__implies__not__eq) ).

thf(140,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(141,plain,
    ! [B: int,A: int] :
      ( ~ ( ord_less_int @ A @ B )
      | ( B != A ) ),
    inference(cnf,[status(esa)],[140]) ).

thf(142,plain,
    ! [B: int,A: int] :
      ( ( B != A )
      | ~ ( ord_less_int @ A @ B ) ),
    inference(lifteq,[status(thm)],[141]) ).

thf(143,plain,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ),
    inference(simp,[status(thm)],[142]) ).

thf(537,plain,
    ! [A: int] :
      ( ( ord_less_int @ ( h @ a2 ) @ ( h @ a2 ) )
     != ( ord_less_int @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[534,143]) ).

thf(538,plain,
    $false,
    inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( h @ a2 ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ITP029^1 : TPTP v8.2.0. Released v7.5.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n010.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sat May 18 15:24:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.98/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.97/1.17  % [INFO] 	 Parsing done (290ms). 
% 1.97/1.18  % [INFO] 	 Running in sequential loop mode. 
% 2.47/1.42  % [INFO] 	 nitpick registered as external prover. 
% 2.47/1.42  % [INFO] 	 Scanning for conjecture ... 
% 2.76/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 350 axioms. Running axiom selection ... 
% 3.00/1.57  % [INFO] 	 Axiom selection finished. Selected 91 axioms (removed 259 axioms). 
% 3.30/1.67  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.43/1.68  % [INFO] 	 Type checking passed. 
% 3.43/1.68  % [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 ... 
% 6.93/2.72  % [INFO] 	 Killing All external provers ... 
% 6.93/2.72  % Time passed: 2197ms (effective reasoning time: 1533ms)
% 6.93/2.72  % Axioms used in derivation (3): fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062, fact_0_hahb, fact_44_dual__order_Ostrict__implies__not__eq
% 6.93/2.72  % No. of inferences in proof: 13
% 6.93/2.72  % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2197 ms resp. 1533 ms w/o parsing
% 6.93/2.74  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.93/2.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------