%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL816-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:08:53 PM UTC 2026
% Result : Unsatisfiable 39.48s 5.41s
% Output : CNFRefutation 39.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 15 unt; 0 def)
% Number of atoms : 26 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-5 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f387,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f445,axiom,
! [V_e,V_t,V_ts,V_T,V_Ts] :
( ~ c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(V_e,V_ts,V_Ts)
| c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f465,axiom,
! [V_e,V_x,V_T,T_a] : hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f470,axiom,
! [V_env,V_x] : c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f475,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f477,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1085,plain,
v_n____ = v_i____,
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f1168,plain,
! [V_e,V_t,V_T,V_Ts] :
( ~ c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype))
| ! [V_ts] :
( ~ c_Type_Otypings(V_e,V_ts,V_Ts)
| c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ),
inference(miniscoping,[status(thm)],[f445]) ).
fof(f1169,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Type_Otyping(X0,X1,c_List_Ofoldr(c_Type_Otype_OFun,X4,X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X0,X2,X4)
| c_Type_Otyping(X0,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
inference(cnf_transformation,[status(thm)],[f1168]) ).
fof(f1200,plain,
! [X0,X1,X2,X3] : hAPP(c_Type_Oshift(X0,X1,X2,X3),X1) = X2,
inference(cnf_transformation,[status(thm)],[f465]) ).
fof(f1205,plain,
! [X0,X1] : c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),hAPP(X0,X1)),
inference(cnf_transformation,[status(thm)],[f470]) ).
fof(f1212,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(cnf_transformation,[status(thm)],[f475]) ).
fof(f1214,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(cnf_transformation,[status(thm)],[f477]) ).
fof(f1250,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(backward_demodulation,[status(thm)],[f1085,f1214]) ).
fof(f1259,plain,
! [X0,X1,X2,X3] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2),
inference(paramodulation,[status(thm)],[f1200,f1205]) ).
fof(f1784,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(forward_demodulation,[status(thm)],[f1085,f1212]) ).
fof(f30066,plain,
! [X0] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,X0,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),X0) ),
inference(resolution,[status(thm)],[f1169,f1250]) ).
fof(f30111,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(resolution,[status(thm)],[f30066,f1259]) ).
fof(f30118,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f30111,f1784]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL816-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 01:05:50 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 39.48/5.41 % Refutation found
% 39.48/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 39.48/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.08/5.99 % Elapsed time: 5.607682 seconds
% 3.08/5.99 % CPU time: 40.783847 seconds
% 3.08/5.99 % Total memory used: 632.267 MB
% 3.08/5.99 % Net memory used: 566.207 MB
%------------------------------------------------------------------------------