TSTP Solution File: LCL755_5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LCL755_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 00:11:07 EDT 2024

% Result   : Theorem 206.32s 31.36s
% Output   : Refutation 206.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   38 (  20 unt;  13 typ;   0 def)
%            Number of atoms       :   32 (  11 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  192 (  11   ~;   3   |;   0   &; 176   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :   22 (   0   ^  20   !;   0   ?;  22   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(bool_type,type,
    bool: $tType ).

thf(dB_type,type,
    dB: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(one_one_type,type,
    one_one: 
      !>[TA: $tType] : TA ).

thf(plus_plus_type,type,
    plus_plus: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(it_type,type,
    it: dB > $o ).

thf(abs_type,type,
    abs: dB > dB ).

thf(var_type,type,
    var: nat > dB ).

thf(subst_type,type,
    subst: dB > dB > nat > dB ).

thf(suc_type,type,
    suc: nat > nat ).

thf(ia_type,type,
    ia: nat ).

thf(ja_type,type,
    ja: nat ).

thf(ra_type,type,
    ra: dB ).

thf(84,axiom,
    ! [A: dB] :
      ( ( it @ A )
     => ( it @ ( abs @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Lambda) ).

thf(380,plain,
    ! [A: dB] :
      ( ( it @ A )
     => ( it @ ( abs @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(381,plain,
    ! [A: dB] :
      ( ~ ( it @ A )
      | ( it @ ( abs @ A ) ) ),
    inference(cnf,[status(esa)],[380]) ).

thf(107,axiom,
    ! [A: nat] :
      ( ( suc @ A )
      = ( plus_plus @ nat @ ( one_one @ nat ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Suc__eq__plus1__left) ).

thf(468,plain,
    ! [A: nat] :
      ( ( suc @ A )
      = ( plus_plus @ nat @ ( one_one @ nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(469,plain,
    ! [A: nat] :
      ( ( suc @ A )
      = ( plus_plus @ nat @ ( one_one @ nat ) @ A ) ),
    inference(cnf,[status(esa)],[468]) ).

thf(470,plain,
    ! [A: nat] :
      ( ( suc @ A )
      = ( plus_plus @ nat @ ( one_one @ nat ) @ A ) ),
    inference(lifteq,[status(thm)],[469]) ).

thf(71,axiom,
    ! [A: nat] :
      ( ( suc @ A )
      = ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Suc__eq__plus1) ).

thf(335,plain,
    ! [A: nat] :
      ( ( suc @ A )
      = ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(336,plain,
    ! [A: nat] :
      ( ( suc @ A )
      = ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ),
    inference(cnf,[status(esa)],[335]) ).

thf(337,plain,
    ! [A: nat] :
      ( ( suc @ A )
      = ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ),
    inference(lifteq,[status(thm)],[336]) ).

thf(535,plain,
    ! [A: nat] :
      ( ( plus_plus @ nat @ A @ ( one_one @ nat ) )
      = ( plus_plus @ nat @ ( one_one @ nat ) @ A ) ),
    inference(rewrite,[status(thm)],[470,337]) ).

thf(1,conjecture,
    it @ ( abs @ ( subst @ ra @ ( var @ ( suc @ ia ) ) @ ( suc @ ja ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(2,negated_conjecture,
    ~ ( it @ ( abs @ ( subst @ ra @ ( var @ ( suc @ ia ) ) @ ( suc @ ja ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(115,plain,
    ~ ( it @ ( abs @ ( subst @ ra @ ( var @ ( suc @ ia ) ) @ ( suc @ ja ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(517,plain,
    ~ ( it @ ( abs @ ( subst @ ra @ ( var @ ( plus_plus @ nat @ ia @ ( one_one @ nat ) ) ) @ ( plus_plus @ nat @ ja @ ( one_one @ nat ) ) ) ) ),
    inference(rewrite,[status(thm)],[115,337]) ).

thf(576,plain,
    ! [A: nat] :
      ( ~ ( it @ ( abs @ ( subst @ ra @ ( var @ ( plus_plus @ nat @ ia @ ( one_one @ nat ) ) ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ A ) ) ) )
      | ( ( plus_plus @ nat @ A @ ( one_one @ nat ) )
       != ( plus_plus @ nat @ ja @ ( one_one @ nat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[535,517]) ).

thf(577,plain,
    ~ ( it @ ( abs @ ( subst @ ra @ ( var @ ( plus_plus @ nat @ ia @ ( one_one @ nat ) ) ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ ja ) ) ) ),
    inference(pattern_uni,[status(thm)],[576:[bind(A,$thf( ja ))]]) ).

thf(63815,plain,
    ! [A: dB] :
      ( ~ ( it @ A )
      | ( ( it @ ( abs @ A ) )
       != ( it @ ( abs @ ( subst @ ra @ ( var @ ( plus_plus @ nat @ ia @ ( one_one @ nat ) ) ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ ja ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[381,577]) ).

thf(63816,plain,
    ~ ( it @ ( subst @ ra @ ( var @ ( plus_plus @ nat @ ia @ ( one_one @ nat ) ) ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ ja ) ) ),
    inference(pattern_uni,[status(thm)],[63815:[bind(A,$thf( subst @ ra @ ( var @ ( plus_plus @ nat @ ia @ ( one_one @ nat ) ) ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ ja ) ))]]) ).

thf(83,axiom,
    ! [A: nat,B: nat] : ( it @ ( subst @ ra @ ( var @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(378,plain,
    ! [A: nat,B: nat] : ( it @ ( subst @ ra @ ( var @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(379,plain,
    ! [B: nat,A: nat] : ( it @ ( subst @ ra @ ( var @ A ) @ B ) ),
    inference(cnf,[status(esa)],[378]) ).

thf(66150,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[63816,379]) ).

thf(66151,plain,
    $false,
    inference(simp,[status(thm)],[66150]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL755_5 : TPTP v8.2.0. Released v6.0.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n023.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 : Mon May 20 01:40:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.87/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.55/1.02  % [INFO] 	 Parsing done (182ms). 
% 1.55/1.03  % [INFO] 	 Running in sequential loop mode. 
% 2.19/1.25  % [INFO] 	 nitpick registered as external prover. 
% 2.19/1.25  % [INFO] 	 Scanning for conjecture ... 
% 2.48/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 112 axioms. Running axiom selection ... 
% 2.67/1.41  % [INFO] 	 Axiom selection finished. Selected 112 axioms (removed 0 axioms). 
% 3.11/1.54  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.11/1.56  % [INFO] 	 Type checking passed. 
% 3.11/1.56  % [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 ... 
% 206.32/31.35  % [INFO] 	 Killing All external provers ... 
% 206.32/31.36  % Time passed: 30849ms (effective reasoning time: 30322ms)
% 206.32/31.36  % 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)>
% 206.32/31.36  % Axioms used in derivation (4): fact_0_Lambda, fact_89_Suc__eq__plus1__left, fact_88_Suc__eq__plus1, conj_1
% 206.32/31.36  % No. of inferences in proof: 25
% 206.32/31.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 30849 ms resp. 30322 ms w/o parsing
% 206.32/31.37  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 206.32/31.37  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------