%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 01:08:42 PM UTC 2026
% Result : Unsatisfiable 2.18s 1.09s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 20 unt; 0 def)
% Number of atoms : 40 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 56 ( 56 !; 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(f28,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
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_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
| 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)) ),
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(V_r)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(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(thm)],[f18]) ).
fof(f762,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(cnf_transformation,[status(thm)],[f28]) ).
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(thm)],[f149]) ).
fof(f1014,plain,
! [V_i,V_k] :
( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
| ! [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)) ),
inference(miniscoping,[status(thm)],[f194]) ).
fof(f1015,plain,
! [X0,X1,X2] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) ),
inference(cnf_transformation,[status(thm)],[f1014]) ).
fof(f1109,plain,
! [X0,X1] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1) = X0,
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f1168,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[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(thm)],[f595]) ).
fof(f1780,plain,
! [X0] :
( ~ c_InductTermi_OIT(X0)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0)) ),
inference(cnf_transformation,[status(thm)],[f678]) ).
fof(f1785,plain,
! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
inference(cnf_transformation,[status(thm)],[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(thm)],[f684]) ).
fof(f1834,plain,
! [X0,X1,X2] :
( ~ c_InductTermi_OIT(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)))
| c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2)) ),
inference(paramodulation,[status(thm)],[f1660,f1780]) ).
fof(f2725,plain,
! [X0,X1] : c_Lambda_Oliftn(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1) = c_Lambda_Olift(X0,X1),
inference(paramodulation,[status(thm)],[f1109,f747]) ).
fof(f2727,plain,
! [X0,X1] : c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X1) = c_Lambda_Olift(X0,X1),
inference(forward_demodulation,[status(thm)],[f762,f2725]) ).
fof(f5552,plain,
! [X0,X1,X2] :
( ~ c_InductTermi_OIT(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X2)))
| c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2)) ),
inference(backward_demodulation,[status(thm)],[f950,f1834]) ).
fof(f8156,plain,
! [X0,X1,X2,X3] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2),X3)) ),
inference(paramodulation,[status(thm)],[f1015,f1785]) ).
fof(f8223,plain,
! [X0,X1,X2] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2)) ),
inference(paramodulation,[status(thm)],[f2727,f8156]) ).
fof(f8236,plain,
! [X0,X1] :
( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X0),X1))
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f8223,f5552]) ).
fof(f8239,plain,
! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X0),X1)),
inference(forward_subsumption_resolution,[status(thm)],[f8236,f1168]) ).
fof(f8251,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1786,f8239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL754-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n020.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Mon Sep 21 01:02:47 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.26/0.51 % Drodi V4.1.1
% 2.18/1.09 % Refutation found
% 2.18/1.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.18/1.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.73/1.15 % Elapsed time: 0.699362 seconds
% 1.73/1.15 % CPU time: 4.559742 seconds
% 1.73/1.15 % Total memory used: 204.844 MB
% 1.73/1.15 % Net memory used: 201.824 MB
%------------------------------------------------------------------------------