%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL800-1 : 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 01:08:50 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f346,axiom,
! [V_k,V_u] : c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f362,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(f367,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f368,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f931,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(f934,plain,
! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,X0) = X1,
inference(cnf_transformation,[status(thm)],[f346]) ).
fof(f957,plain,
! [X0,X1,X2] : c_Lambda_Osubst(c_Lambda_Olift(X0,X1),X2,X1) = X0,
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f963,plain,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(cnf_transformation,[status(thm)],[f367]) ).
fof(f964,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f1018,plain,
! [X0,X1,X2] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,c_Lambda_OdB_OVar(X1)),X2,X1) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X0,X2,X1),X2),
inference(paramodulation,[status(thm)],[f934,f931]) ).
fof(f1609,plain,
! [X0,X1,X2] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),c_Lambda_OdB_OVar(X1)),X2,X1) = c_Lambda_OdB_OApp(X0,X2),
inference(paramodulation,[status(thm)],[f957,f1018]) ).
fof(f1628,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
inference(backward_demodulation,[status(thm)],[f1609,f963]) ).
fof(f1653,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1628,f964]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL800-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.33 % Computer : n020.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 01:05:47 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.44 % Refutation found
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.096451 seconds
% 0.13/0.44 % CPU time: 0.404617 seconds
% 0.13/0.44 % Total memory used: 121.873 MB
% 0.13/0.44 % Net memory used: 121.529 MB
%------------------------------------------------------------------------------