TSTP Solution File: ALG256^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ALG256^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 18:14:36 EDT 2024

% Result   : Theorem 6.52s 2.90s
% Output   : Refutation 6.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   17 (   4 unt;  12 typ;   1 def)
%            Number of atoms       :   74 (  29 equ;   0 cnn)
%            Maximal formula atoms :   40 (  14 avg)
%            Number of connectives :  293 (   5   ~;   0   |;   3   &; 191   @)
%                                         (   0 <=>;  94  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   40 (   9 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   41 (  39 usr;  34 con; 0-2 aty)
%            Number of variables   :   83 (   0   ^  83   !;   0   ?;  83   :)

% Comments : 
%------------------------------------------------------------------------------
thf(term_type,type,
    term: $tType ).

thf(subst_type,type,
    subst: $tType ).

thf(one_type,type,
    one: term ).

thf(ap_type,type,
    ap: term > term > term ).

thf(lam_type,type,
    lam: term > term ).

thf(sub_type,type,
    sub: term > subst > term ).

thf(id_type,type,
    id: subst ).

thf(sh_type,type,
    sh: subst ).

thf(push_type,type,
    push: term > subst > subst ).

thf(comp_type,type,
    comp: subst > subst > subst ).

thf(var_type,type,
    var: term > $o ).

thf(hoasapinj1_gthm_type,type,
    hoasapinj1_gthm: $o ).

thf(hoasapinj1_gthm_def,definition,
    ( hoasapinj1_gthm
    = ( axapp
     => ( axvarcons
       => ( axvarid
         => ( axabs
           => ( axclos
             => ( axidl
               => ( axshiftcons
                 => ( axassoc
                   => ( axmap
                     => ( axidr
                       => ( axvarshift
                         => ( axscons
                           => ( ulamvar1
                             => ( ulamvarsh
                               => ( ulamvarind
                                 => ( apinj1
                                   => ( apinj2
                                     => ( laminj
                                       => ( shinj
                                         => ( lamnotap
                                           => ( apnotvar
                                             => ( lamnotvar
                                               => ( induction
                                                 => ( pushprop
                                                   => ( induction2lem
                                                     => ( induction2
                                                       => ( substmonoid
                                                         => ( termmset
                                                           => hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(1,conjecture,
    hoasapinj1_gthm,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ hoasapinj1_gthm,
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: term,B: term,C: subst] :
          ( ( sub @ ( ap @ A @ B ) @ C )
          = ( ap @ ( sub @ A @ C ) @ ( sub @ B @ C ) ) )
     => ( ! [A: term,B: subst] :
            ( ( sub @ one @ ( push @ A @ B ) )
            = A )
       => ( ! [A: term] :
              ( ( sub @ A @ id )
              = A )
         => ( ! [A: term,B: subst] :
                ( ( sub @ ( lam @ A ) @ B )
                = ( lam @ ( sub @ A @ ( push @ one @ ( comp @ B @ sh ) ) ) ) )
           => ( ! [A: term,B: subst,C: subst] :
                  ( ( sub @ ( sub @ A @ B ) @ C )
                  = ( sub @ A @ ( comp @ B @ C ) ) )
             => ( ! [A: subst] :
                    ( ( comp @ id @ A )
                    = A )
               => ( ! [A: term,B: subst] :
                      ( ( comp @ sh @ ( push @ A @ B ) )
                      = B )
                 => ( ! [A: subst,B: subst,C: subst] :
                        ( ( comp @ ( comp @ A @ B ) @ C )
                        = ( comp @ A @ ( comp @ B @ C ) ) )
                   => ( ! [A: term,B: subst,C: subst] :
                          ( ( comp @ ( push @ A @ B ) @ C )
                          = ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) )
                     => ( ! [A: subst] :
                            ( ( comp @ A @ id )
                            = A )
                       => ( ( ( push @ one @ sh )
                            = id )
                         => ( ! [A: subst] :
                                ( ( push @ ( sub @ one @ A ) @ ( comp @ sh @ A ) )
                                = A )
                           => ( ( var @ one )
                             => ( ! [A: term] :
                                    ( ( var @ A )
                                   => ( var @ ( sub @ A @ sh ) ) )
                               => ( ! [A: term > $o] :
                                      ( ( A @ one )
                                     => ( ! [B: term] :
                                            ( ( var @ B )
                                           => ( ( A @ B )
                                             => ( A @ ( sub @ B @ sh ) ) ) )
                                       => ! [B: term] :
                                            ( ( var @ B )
                                           => ( A @ B ) ) ) )
                                 => ( ! [A: term,B: term,C: term,D: term] :
                                        ( ( ( ap @ A @ C )
                                          = ( ap @ B @ D ) )
                                       => ( A = B ) )
                                   => ( ! [A: term,B: term,C: term,D: term] :
                                          ( ( ( ap @ A @ C )
                                            = ( ap @ B @ D ) )
                                         => ( C = D ) )
                                     => ( ! [A: term,B: term] :
                                            ( ( ( lam @ A )
                                              = ( lam @ B ) )
                                           => ( A = B ) )
                                       => ( ! [A: term,B: term] :
                                              ( ( ( sub @ A @ sh )
                                                = ( sub @ B @ sh ) )
                                             => ( A = B ) )
                                         => ( ! [A: term,B: term,C: term] :
                                                ( ( lam @ A )
                                               != ( ap @ B @ C ) )
                                           => ( ! [A: term,B: term] :
                                                  ~ ( var @ ( ap @ A @ B ) )
                                             => ( ! [A: term] :
                                                    ~ ( var @ ( lam @ A ) )
                                               => ( ! [A: term > $o] :
                                                      ( ! [B: term] :
                                                          ( ( var @ B )
                                                         => ( A @ B ) )
                                                     => ( ! [B: term,C: term] :
                                                            ( ( A @ B )
                                                           => ( ( A @ C )
                                                             => ( A @ ( ap @ B @ C ) ) ) )
                                                       => ( ! [B: term] :
                                                              ( ( A @ B )
                                                             => ( A @ ( lam @ B ) ) )
                                                         => ! [B: term] : ( A @ B ) ) ) )
                                                 => ( ! [A: term > $o,B: term,C: subst] :
                                                        ( ! [D: term] :
                                                            ( ( var @ D )
                                                           => ( A @ ( sub @ D @ C ) ) )
                                                       => ( ( A @ B )
                                                         => ! [D: term] :
                                                              ( ( var @ D )
                                                             => ( A @ ( sub @ D @ ( push @ B @ C ) ) ) ) ) )
                                                   => ( ! [A: term > $o] :
                                                          ( ! [B: term,C: term] :
                                                              ( ( A @ B )
                                                             => ( ( A @ C )
                                                               => ( A @ ( ap @ B @ C ) ) ) )
                                                         => ( ! [B: term] :
                                                                ( ! [C: term] :
                                                                    ( ( A @ C )
                                                                   => ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
                                                               => ( A @ ( lam @ B ) ) )
                                                           => ! [B: term,C: subst] :
                                                                ( ! [D: term] :
                                                                    ( ( var @ D )
                                                                   => ( A @ ( sub @ D @ C ) ) )
                                                               => ( A @ ( sub @ B @ C ) ) ) ) )
                                                     => ( ! [A: term > $o] :
                                                            ( ! [B: term] :
                                                                ( ( var @ B )
                                                               => ( A @ B ) )
                                                           => ( ! [B: term,C: term] :
                                                                  ( ( A @ B )
                                                                 => ( ( A @ C )
                                                                   => ( A @ ( ap @ B @ C ) ) ) )
                                                             => ( ! [B: term] :
                                                                    ( ! [C: term] :
                                                                        ( ( A @ C )
                                                                       => ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
                                                                   => ( A @ ( lam @ B ) ) )
                                                               => ! [B: term] : ( A @ B ) ) ) )
                                                       => ( ( ! [A: subst,B: subst,C: subst] :
                                                                ( ( comp @ ( comp @ A @ B ) @ C )
                                                                = ( comp @ A @ ( comp @ B @ C ) ) )
                                                            & ! [A: subst] :
                                                                ( ( comp @ id @ A )
                                                                = A )
                                                            & ! [A: subst] :
                                                                ( ( comp @ A @ id )
                                                                = A ) )
                                                         => ( ( ! [A: term,B: subst,C: subst] :
                                                                  ( ( sub @ ( sub @ A @ B ) @ C )
                                                                  = ( sub @ A @ ( comp @ B @ C ) ) )
                                                              & ! [A: term] :
                                                                  ( ( sub @ A @ id )
                                                                  = A ) )
                                                           => ! [A: term,B: term,C: term,D: term] :
                                                                ( ( ( ap @ ( sub @ A @ id ) @ C )
                                                                  = ( ap @ ( sub @ B @ id ) @ D ) )
                                                               => ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(155,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem  : ALG256^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.10/0.16  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n009.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sat May 18 23:35:24 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.90/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.71/1.22  % [INFO] 	 Parsing done (304ms). 
% 1.84/1.23  % [INFO] 	 Running in sequential loop mode. 
% 2.61/1.54  % [INFO] 	 eprover registered as external prover. 
% 2.61/1.55  % [INFO] 	 cvc4 registered as external prover. 
% 2.61/1.55  % [INFO] 	 Scanning for conjecture ... 
% 3.71/1.95  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 3.71/1.97  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 3.71/1.97  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.71/1.97  % [INFO] 	 Type checking passed. 
% 3.71/1.97  % [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 ... 
% 6.52/2.89  % External prover 'e' found a proof!
% 6.52/2.89  % [INFO] 	 Killing All external provers ... 
% 6.52/2.89  % Time passed: 2383ms (effective reasoning time: 1659ms)
% 6.52/2.89  % 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)>
% 6.52/2.89  % Axioms used in derivation (0): 
% 6.52/2.89  % No. of inferences in proof: 4
% 6.52/2.90  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2383 ms resp. 1659 ms w/o parsing
% 6.52/2.94  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.52/2.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------