TSTP Solution File: LCL809-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL809-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 : Sun Sep 18 04:58:28 EDT 2022

% Result   : Unsatisfiable 0.68s 0.73s
% Output   : Proof 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   25 (   6 unt;   8 typ;   0 def)
%            Number of atoms       :   46 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   54 (  26   ~;  22   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   26 (  24   !;   0   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_InductTermi_OIT_type,type,
    c_InductTermi_OIT: $i > $o ).

tff(c_Lambda_Olift_type,type,
    c_Lambda_Olift: ( $i * $i ) > $i ).

tff(c_HOL_Ozero__class_Ozero_type,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(tc_nat_type,type,
    tc_nat: $i ).

tff(c_Lambda_Osubst_type,type,
    c_Lambda_Osubst: ( $i * $i * $i ) > $i ).

tff(v_i_____type,type,
    v_i____: $i ).

tff(v_u_____type,type,
    v_u____: $i ).

tff(v_b_____type,type,
    v_b____: $i ).

tff(1,plain,
    ( ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))
  <=> ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(3,plain,
    ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
  <=> c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

tff(6,plain,
    c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ^ [V_i: $i,V_t: $i] :
      refl(
        ( ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
          | ~ c_InductTermi_OIT(V_t) )
      <=> ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
          | ~ c_InductTermi_OIT(V_t) ) )),
    inference(bind,[status(th)],]) ).

tff(8,plain,
    ( ! [V_i: $i,V_t: $i] :
        ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
        | ~ c_InductTermi_OIT(V_t) )
  <=> ! [V_i: $i,V_t: $i] :
        ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
        | ~ c_InductTermi_OIT(V_t) ) ),
    inference(quant_intro,[status(thm)],[7]) ).

tff(9,plain,
    ( ! [V_i: $i,V_t: $i] :
        ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
        | ~ c_InductTermi_OIT(V_t) )
  <=> ! [V_i: $i,V_t: $i] :
        ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
        | ~ c_InductTermi_OIT(V_t) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(10,axiom,
    ! [V_i: $i,V_t: $i] :
      ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
      | ~ c_InductTermi_OIT(V_t) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).

tff(11,plain,
    ! [V_i: $i,V_t: $i] :
      ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
      | ~ c_InductTermi_OIT(V_t) ),
    inference(modus_ponens,[status(thm)],[10,9]) ).

tff(12,plain,
    ! [V_i: $i,V_t: $i] :
      ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
      | ~ c_InductTermi_OIT(V_t) ),
    inference(skolemize,[status(sab)],[11]) ).

tff(13,plain,
    ! [V_i: $i,V_t: $i] :
      ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
      | ~ c_InductTermi_OIT(V_t) ),
    inference(modus_ponens,[status(thm)],[12,8]) ).

tff(14,plain,
    ( ( ~ ! [V_i: $i,V_t: $i] :
            ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
            | ~ c_InductTermi_OIT(V_t) )
      | c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) )
  <=> ( ~ ! [V_i: $i,V_t: $i] :
            ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
            | ~ c_InductTermi_OIT(V_t) )
      | c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ~ ! [V_i: $i,V_t: $i] :
          ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
          | ~ c_InductTermi_OIT(V_t) )
    | c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(16,plain,
    ( ~ ! [V_i: $i,V_t: $i] :
          ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
          | ~ c_InductTermi_OIT(V_t) )
    | c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    $false,
    inference(unit_resolution,[status(thm)],[16,13,6,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL809-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Sep  2 00:52:18 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35  Usage: tptp [options] [-file:]file
% 0.12/0.35    -h, -?       prints this message.
% 0.12/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.35    -m, -model   generate model.
% 0.12/0.35    -p, -proof   generate proof.
% 0.12/0.35    -c, -core    generate unsat core of named formulas.
% 0.12/0.35    -st, -statistics display statistics.
% 0.12/0.35    -t:timeout   set timeout (in second).
% 0.12/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35    -<param>:<value> configuration parameter and value.
% 0.12/0.35    -o:<output-file> file to place output in.
% 0.68/0.73  % SZS status Unsatisfiable
% 0.68/0.73  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------