%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 5.60s 6.18s
% Output : CNFRefutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 15 unt; 0 def)
% Number of atoms : 21 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f290,axiom,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f324,axiom,
! [V_t,V_k,V_s] : c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f326,axiom,
! [V_x,V_s] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s
| c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f343,axiom,
! [V_t,V_u,V_s,V_k] : c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f361,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(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_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f362,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f860,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f899,plain,
! [X0,X1,X2] : c_Lambda_Osubst(c_Lambda_Olift(X0,X1),X2,X1) = X0,
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f902,plain,
! [V_x] :
( ! [V_s] : c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s
| c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
inference(miniscoping,[status(thm)],[f326]) ).
fof(f903,plain,
! [X0,X1] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,X0) = X1
| c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f902]) ).
fof(f925,plain,
! [X0,X1,X2,X3] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X1),X2,X3) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X0,X2,X3),c_Lambda_Osubst(X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f343]) ).
fof(f949,plain,
c_InductTermi_OIT(c_Lambda_Osubst(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_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(cnf_transformation,[status(thm)],[f361]) ).
fof(f950,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f988,plain,
! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,X0) = X1,
inference(forward_subsumption_resolution,[status(thm)],[f903,f860]) ).
fof(f4691,plain,
! [X0,X1,X2] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X0),X1),X2,X0) = c_Lambda_OdB_OApp(X2,c_Lambda_Osubst(X1,X2,X0)),
inference(paramodulation,[status(thm)],[f988,f925]) ).
fof(f4702,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(backward_demodulation,[status(thm)],[f4691,f949]) ).
fof(f4707,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
inference(forward_demodulation,[status(thm)],[f899,f4702]) ).
fof(f4708,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4707,f950]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n016.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 01:13:29 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 5.60/6.18 % Refutation found
% 5.60/6.18 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.60/6.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.60/6.21 % Elapsed time: 0.818137 seconds
% 5.60/6.21 % CPU time: 6.190967 seconds
% 5.60/6.21 % Total memory used: 219.973 MB
% 5.60/6.21 % Net memory used: 213.639 MB
%------------------------------------------------------------------------------