TSTP Solution File: SWW567_5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW567_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% 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 : Mon Jun 24 18:25:36 EDT 2024

% Result   : Theorem 11.13s 3.88s
% Output   : Refutation 11.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   13 (   5 unt;   0 typ;   0 def)
%            Number of atoms       :   66 (   1 equ;   0 cnn)
%            Maximal formula atoms :    9 (   5 avg)
%            Number of connectives :  255 (   8   ~;   2   |;   3   &; 242   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   9 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;  14 con; 0-5 aty)
%            Number of variables   :   14 (   0   ^  11   !;   3   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(bop1_type,type,
    bop1: $tType ).

thf(bool_type,type,
    bool: $tType ).

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

thf(char_type,type,
    char: $tType ).

thf(ty_type,type,
    ty: $tType ).

thf(val1_type,type,
    val1: $tType ).

thf(binOp_type,type,
    binOp: 
      !>[TA: $tType] : ( ( exp @ TA ) > bop1 > ( exp @ TA ) > ( exp @ TA ) ) ).

thf(val_type,type,
    val: 
      !>[TA: $tType] : ( val1 > ( exp @ TA ) ) ).

thf(widen_type,type,
    widen: 
      !>[TA: $tType] : ( ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ) ) > ty > ty > $o ) ).

thf(wTrt_type,type,
    wTrt: ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ) > ( fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ) > ( fun @ ( list @ char ) @ ( option @ ty ) ) > ( exp @ ( list @ char ) ) > ty > $o ).

thf(e_type,type,
    e: fun @ ( list @ char ) @ ( option @ ty ) ).

thf(p_type,type,
    p: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) ) ) ) ) ) ) ) ).

thf(t_type,type,
    t: ty ).

thf(bop_type,type,
    bop: bop1 ).

thf(e_2_type,type,
    e_2: exp @ ( list @ char ) ).

thf(h_a_type,type,
    h_a: fun @ nat @ ( option @ ( product_prod @ ( list @ char ) @ ( fun @ ( product_prod @ ( list @ char ) @ ( list @ char ) ) @ ( option @ val1 ) ) ) ) ).

thf(v_1_type,type,
    v_1: val1 ).

thf(35,axiom,
    wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ t,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096P_ME_Mh_H_A_092_060turnstile_062_AVal_Av_092_060_094isub_0621_A_092_060guillemotleft_062bop_092_060guillemotright_062_Ae_092_060_094isub_0622_H_A_058_AT_096) ).

thf(208,plain,
    wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(1,conjecture,
    ? [A: ty] :
      ( ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ A )
      & ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ? [A: ty] :
        ( ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ A )
        & ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(105,plain,
    ~ ? [A: ty] :
        ( ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ A )
        & ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(106,plain,
    ! [A: ty] :
      ( ~ ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ A )
      | ~ ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t ) ),
    inference(cnf,[status(esa)],[105]) ).

thf(413,plain,
    ! [A: ty] :
      ( ~ ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ A @ t )
      | ( ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ t )
       != ( wTrt @ p @ h_a @ e @ ( binOp @ ( list @ char ) @ ( val @ ( list @ char ) @ v_1 ) @ bop @ e_2 ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[208,106]) ).

thf(414,plain,
    ~ ( widen @ ( product_prod @ ( list @ ( list @ char ) ) @ ( exp @ ( list @ char ) ) ) @ p @ t @ t ),
    inference(pattern_uni,[status(thm)],[413:[bind(A,$thf( t ))]]) ).

thf(36,axiom,
    ! [TA: $tType,A: ty,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_widen__refl) ).

thf(209,plain,
    ! [TA: $tType,A: ty,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) )] : ( widen @ TA @ B @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(210,plain,
    ! [TA: $tType,B: list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ( product_prod @ ( list @ char ) @ ty ) ) @ ( list @ ( product_prod @ ( list @ char ) @ ( product_prod @ ( list @ ty ) @ ( product_prod @ ty @ TA ) ) ) ) ) ) ),A: ty] : ( widen @ TA @ B @ A @ A ),
    inference(cnf,[status(esa)],[209]) ).

thf(419,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[414,210]) ).

thf(420,plain,
    $false,
    inference(simp,[status(thm)],[419]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWW567_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.13  % Command  : run_Leo-III %s %d SAT
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jun 19 09:42:40 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.02/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.76/1.16  % [INFO] 	 Parsing done (269ms). 
% 1.76/1.17  % [INFO] 	 Running in sequential loop mode. 
% 2.65/1.40  % [INFO] 	 nitpick registered as external prover. 
% 2.65/1.40  % [INFO] 	 Scanning for conjecture ... 
% 3.19/1.56  % [INFO] 	 Found a conjecture (or negated_conjecture) and 102 axioms. Running axiom selection ... 
% 3.50/1.68  % [INFO] 	 Axiom selection finished. Selected 102 axioms (removed 0 axioms). 
% 4.57/1.96  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 4.85/1.99  % [INFO] 	 Type checking passed. 
% 4.85/1.99  % [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 ... 
% 11.13/3.88  % [INFO] 	 Killing All external provers ... 
% 11.13/3.88  % Time passed: 3330ms (effective reasoning time: 2706ms)
% 11.13/3.88  % 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)>
% 11.13/3.88  % Axioms used in derivation (2): fact_0__096P_ME_Mh_H_A_092_060turnstile_062_AVal_Av_092_060_094isub_0621_A_092_060guillemotleft_062bop_092_060guillemotright_062_Ae_092_060_094isub_0622_H_A_058_AT_096, fact_4_widen__refl
% 11.13/3.88  % No. of inferences in proof: 13
% 11.13/3.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3330 ms resp. 2706 ms w/o parsing
% 11.61/3.90  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.61/3.90  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------