%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL852-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:08:59 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.70s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 29 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f563,axiom,
! [V_e,V_i,V_U,V_t,V_T] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f567,axiom,
! [V_env,V_s,V_t,V_U,V_T] :
( ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
| ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f571,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(f574,axiom,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f575,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(f579,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_U____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1483,plain,
! [V_e,V_t,V_T] :
( ~ c_Type_Otyping(V_e,V_t,V_T)
| ! [V_i,V_U] : c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T) ),
inference(miniscoping,[status(thm)],[f563]) ).
fof(f1484,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Type_Otyping(X0,X3,X4)
| c_Type_Otyping(c_Type_Oshift(X0,X1,X2,tc_Type_Otype),c_Lambda_Olift(X3,X1),X4) ),
inference(cnf_transformation,[status(thm)],[f1483]) ).
fof(f1490,plain,
! [V_env,V_s,V_U,V_T] :
( ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
| ! [V_t] :
( ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ) ),
inference(miniscoping,[status(thm)],[f567]) ).
fof(f1491,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,X4),X3))
| ~ c_Type_Otyping(X0,X2,X4)
| c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) ),
inference(cnf_transformation,[status(thm)],[f1490]) ).
fof(f1497,plain,
! [X0,X1,X2,X3] : hAPP(c_Type_Oshift(X0,X1,X2,X3),X1) = X2,
inference(cnf_transformation,[status(thm)],[f571]) ).
fof(f1500,plain,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
inference(cnf_transformation,[status(thm)],[f574]) ).
fof(f1501,plain,
! [X0,X1] : c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),hAPP(X0,X1)),
inference(cnf_transformation,[status(thm)],[f575]) ).
fof(f1505,plain,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_U____),
inference(cnf_transformation,[status(thm)],[f579]) ).
fof(f1540,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)],[f1497,f1501]) ).
fof(f1629,plain,
! [X0] :
( ~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,X0),v_U____))
| ~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),X0) ),
inference(resolution,[status(thm)],[f1491,f1505]) ).
fof(f1651,plain,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____),
inference(resolution,[status(thm)],[f1629,f1540]) ).
fof(f1652,plain,
~ c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
inference(resolution,[status(thm)],[f1651,f1484]) ).
fof(f1653,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1652,f1500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL852-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.59 % Computer : n009.cluster.edu
% 0.16/0.59 % Model : x86_64 x86_64
% 0.16/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.59 % Memory : 8046.5625MB
% 0.16/0.59 % OS : Linux 6.8.0-71-generic
% 0.16/0.59 % CPULimit : 300
% 0.16/0.59 % WCLimit : 300
% 0.16/0.59 % DateTime : Mon Sep 21 01:08:13 UTC 2026
% 0.16/0.59 % CPUTime :
% 0.21/0.67 % Drodi V4.1.1
% 0.21/0.70 % Refutation found
% 0.21/0.70 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.77 % Elapsed time: 0.157394 seconds
% 0.21/0.77 % CPU time: 0.260267 seconds
% 0.21/0.77 % Total memory used: 54.078 MB
% 0.21/0.77 % Net memory used: 53.982 MB
%------------------------------------------------------------------------------