TSTP Solution File: LCL836-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : LCL836-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n017.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 Apr 30 20:28:15 EDT 2024

% Result   : Unsatisfiable 3.38s 0.84s
% Output   : CNFRefutation 3.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   21 (  14 unt;   0 def)
%            Number of atoms       :   39 (   2 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   41 (  23   ~;  18   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;  14 con; 0-5 aty)
%            Number of variables   :   30 (  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f462,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f569,axiom,
    ! [V_t,V_s] : c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f582,axiom,
    ! [V_u,V_i,V_e,V_T_H] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)))
      | ~ c_Type_Otyping(V_e,V_u,v_T____)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
      | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),V_T_H) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f590,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f593,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f594,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1382,plain,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    inference(cnf_transformation,[status(esa)],[f462]) ).

fof(f1528,plain,
    ! [X0,X1] : c_Lambda_Osubstn(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(cnf_transformation,[status(esa)],[f569]) ).

fof(f1551,plain,
    ! [V_i,V_e] :
      ( ! [V_u] :
          ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)))
          | ~ c_Type_Otyping(V_e,V_u,v_T____)
          | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) )
      | ! [V_T_H] : ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),V_T_H) ),
    inference(miniscoping,[status(esa)],[f582]) ).

fof(f1552,plain,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X0),X1)))
      | ~ c_Type_Otyping(X2,X0,v_T____)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
      | ~ c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    inference(cnf_transformation,[status(esa)],[f1551]) ).

fof(f1563,plain,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    inference(cnf_transformation,[status(esa)],[f590]) ).

fof(f1566,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
    inference(cnf_transformation,[status(esa)],[f593]) ).

fof(f1567,plain,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
    inference(cnf_transformation,[status(esa)],[f594]) ).

fof(f1619,plain,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X0),X1)))
      | ~ c_Type_Otyping(X2,X0,v_T____)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
      | ~ c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    inference(forward_demodulation,[status(thm)],[f1528,f1552]) ).

fof(f1620,plain,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X0),X1)))
      | ~ c_Type_Otyping(X2,X0,v_T____)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
      | ~ c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    inference(forward_demodulation,[status(thm)],[f1528,f1619]) ).

fof(f1624,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
    inference(forward_demodulation,[status(thm)],[f1528,f1566]) ).

fof(f1625,plain,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
    inference(forward_demodulation,[status(thm)],[f1528,f1567]) ).

fof(f1790,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),X0)))
      | ~ c_Type_Otyping(X1,v_u____,v_T____)
      | ~ c_Type_Otyping(c_Type_Oshift(X1,X0,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X2) ),
    inference(resolution,[status(thm)],[f1620,f1563]) ).

fof(f2802,plain,
    ! [X0,X1] :
      ( ~ c_Type_Otyping(X0,v_u____,v_T____)
      | ~ c_Type_Otyping(c_Type_Oshift(X0,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
    inference(resolution,[status(thm)],[f1790,f1625]) ).

fof(f2814,plain,
    ! [X0] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X0),
    inference(resolution,[status(thm)],[f2802,f1382]) ).

fof(f2815,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f1624,f2814]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : LCL836-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33  % Computer : n017.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Apr 29 20:01:18 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.38  % Drodi V3.6.0
% 3.38/0.84  % Refutation found
% 3.38/0.84  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.38/0.84  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.38/0.87  % Elapsed time: 0.524106 seconds
% 3.38/0.87  % CPU time: 3.782714 seconds
% 3.38/0.87  % Total memory used: 145.639 MB
% 3.38/0.87  % Net memory used: 143.691 MB
%------------------------------------------------------------------------------