%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL773-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:08:45 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.57s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 6 unt; 0 def)
% Number of atoms : 12 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1060,axiom,
! [V_r,V_i,V_j] :
( ~ c_InductTermi_OIT(V_r)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1066,negated_conjecture,
c_InductTermi_OIT(v_r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1068,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2785,plain,
! [V_r] :
( ~ c_InductTermi_OIT(V_r)
| ! [V_i,V_j] : c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) ),
inference(miniscoping,[status(thm)],[f1060]) ).
fof(f2786,plain,
! [X0,X1,X2] :
( ~ c_InductTermi_OIT(X0)
| c_InductTermi_OIT(c_Lambda_Osubst(X0,c_Lambda_OdB_OVar(X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f2785]) ).
fof(f2794,plain,
c_InductTermi_OIT(v_r),
inference(cnf_transformation,[status(thm)],[f1066]) ).
fof(f2796,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(cnf_transformation,[status(thm)],[f1068]) ).
fof(f2836,plain,
~ c_InductTermi_OIT(v_r),
inference(resolution,[status(thm)],[f2786,f2796]) ).
fof(f2838,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2836,f2794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL773-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n017.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 00:58:41 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.27/0.54 % Drodi V4.1.1
% 0.27/0.57 % Refutation found
% 0.27/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.27/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.62 % Elapsed time: 0.198753 seconds
% 0.27/0.62 % CPU time: 0.355462 seconds
% 0.27/0.62 % Total memory used: 118.255 MB
% 0.27/0.62 % Net memory used: 117.613 MB
%------------------------------------------------------------------------------