%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.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 04:58:15 EDT 2022

% Result   : Unsatisfiable 0.19s 0.51s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   15 (   8 unt;   3 typ;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   5   ~;   1   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   2 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   10 (   9   !;   0   ?;  10   :)

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

tff(c_Lambda_OdB_OVar_type,type,
    c_Lambda_OdB_OVar: $i > $i ).

tff(v_i_type,type,
    v_i: $i ).

tff(1,plain,
    ( ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i))
  <=> ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(3,plain,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [V_n: $i] :
      refl(
        ( c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n))
      <=> c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n))
  <=> ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n))
  <=> ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).

tff(8,plain,
    ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ~ ! [V_n: $i] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n))
    | c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    $false,
    inference(unit_resolution,[status(thm)],[11,10,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Sep  2 00:53:54 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.51  % SZS status Unsatisfiable
% 0.19/0.51  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------