TSTP Solution File: LCL754-1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : LCL754-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %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 : Wed May 31 12:20:22 EDT 2023

% Result   : Unsatisfiable 12.60s 2.05s
% Output   : CNFRefutation 13.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   27 (  18 unt;   0 def)
%            Number of atoms       :   36 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   17 (   8   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   59 (;  59   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f18,axiom,
    ! [V_n,V_t,V_k] : c_Lambda_Oliftn(c_Suc(V_n),V_t,V_k) = c_Lambda_Olift(c_Lambda_Oliftn(V_n,V_t,V_k),V_k),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f149,axiom,
    ! [V_n] : c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f194,axiom,
    ! [V_n,V_i,V_k] :
      ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(V_i,V_n,tc_nat))
      | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f259,axiom,
    ! [V_t,V_k] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f297,axiom,
    ! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f595,axiom,
    ! [V_t,V_s,V_k] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(V_t,c_Lambda_Olift(V_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f678,axiom,
    ! [V_r] :
      ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
      | ~ c_InductTermi_OIT(V_r) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f683,negated_conjecture,
    ! [V_i,V_j] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f684,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f747,plain,
    ! [X0,X1,X2] : c_Lambda_Oliftn(c_Suc(X0),X1,X2) = c_Lambda_Olift(c_Lambda_Oliftn(X0,X1,X2),X2),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f950,plain,
    ! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(cnf_transformation,[status(esa)],[f149]) ).

fof(f1014,plain,
    ! [V_i,V_k] :
      ( ! [V_n] : c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(V_i,V_n,tc_nat))
      | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ),
    inference(miniscoping,[status(esa)],[f194]) ).

fof(f1015,plain,
    ! [X0,X1,X2] :
      ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(cnf_transformation,[status(esa)],[f1014]) ).

fof(f1109,plain,
    ! [X0,X1] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1) = X0,
    inference(cnf_transformation,[status(esa)],[f259]) ).

fof(f1168,plain,
    ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(cnf_transformation,[status(esa)],[f297]) ).

fof(f1660,plain,
    ! [X0,X1,X2] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    inference(cnf_transformation,[status(esa)],[f595]) ).

fof(f1780,plain,
    ! [X0] :
      ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0))
      | ~ c_InductTermi_OIT(X0) ),
    inference(cnf_transformation,[status(esa)],[f678]) ).

fof(f1785,plain,
    ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
    inference(cnf_transformation,[status(esa)],[f683]) ).

fof(f1786,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
    inference(cnf_transformation,[status(esa)],[f684]) ).

fof(f2892,plain,
    ! [X0,X1,X2,X3] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X0,c_Lambda_Oliftn(c_Suc(X1),X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    inference(paramodulation,[status(thm)],[f747,f1660]) ).

fof(f3693,plain,
    ! [X0,X1,X2,X3] :
      ( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3))
      | ~ c_InductTermi_OIT(c_Lambda_Osubst(X0,c_Lambda_Oliftn(c_Suc(X1),X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    inference(paramodulation,[status(thm)],[f2892,f1780]) ).

fof(f10614,plain,
    ! [X0,X1,X2,X3] :
      ( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3))
      | ~ c_InductTermi_OIT(c_Lambda_Osubst(X0,c_Lambda_Oliftn(c_Suc(X1),X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X3))) ),
    inference(forward_demodulation,[status(thm)],[f950,f3693]) ).

fof(f36094,plain,
    ! [X0,X1,X2,X3] :
      ( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2),X3))
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(paramodulation,[status(thm)],[f1015,f1785]) ).

fof(f36130,plain,
    ! [X0,X1,X2] :
      ( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
      | c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
    inference(resolution,[status(thm)],[f36094,f10614]) ).

fof(f36131,plain,
    ! [X0,X1,X2] : c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2)),
    inference(forward_subsumption_resolution,[status(thm)],[f36130,f1168]) ).

fof(f36145,plain,
    ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X0),X1)),
    inference(paramodulation,[status(thm)],[f1109,f36131]) ).

fof(f36150,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f1786,f36145]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL754-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.33  % Computer : n007.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Tue May 30 09:35:02 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.38  % Drodi V3.5.1
% 12.60/2.05  % Refutation found
% 12.60/2.05  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.60/2.05  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.56/2.13  % Elapsed time: 1.777507 seconds
% 13.56/2.13  % CPU time: 13.520477 seconds
% 13.56/2.13  % Memory used: 304.436 MB
%------------------------------------------------------------------------------