%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL763-1 : 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 01:08:44 PM UTC 2026
% Result : Unsatisfiable 40.33s 5.72s
% Output : CNFRefutation 40.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 10 unt; 0 def)
% Number of atoms : 16 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-5 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f198,axiom,
! [V_A,T_a] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f386,axiom,
! [V_n,V_rs] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f396,axiom,
! [V_f,V_a,T_b,T_a] : c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f401,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f714,plain,
! [X0,X1] : c_List_Olistsp(X0,c_List_Olist_ONil(X1),X1),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f999,plain,
! [V_rs] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| ! [V_n] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(miniscoping,[status(thm)],[f386]) ).
fof(f1000,plain,
! [X0,X1] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(cnf_transformation,[status(thm)],[f999]) ).
fof(f1015,plain,
! [X0,X1,X2,X3] : c_List_Ofoldl(X0,X1,c_List_Olist_ONil(X2),X3,X2) = X1,
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f1022,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f1047,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
inference(backward_demodulation,[status(thm)],[f1015,f1022]) ).
fof(f36333,plain,
! [X0] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(resolution,[status(thm)],[f1000,f714]) ).
fof(f36334,plain,
! [X0] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X0))),
inference(forward_demodulation,[status(thm)],[f1015,f36333]) ).
fof(f36435,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1047,f36334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 01:03:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.40 % Drodi V4.1.1
% 40.33/5.72 % Refutation found
% 40.33/5.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 40.33/5.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.08/6.08 % Elapsed time: 5.696545 seconds
% 3.08/6.08 % CPU time: 42.328511 seconds
% 3.08/6.08 % Total memory used: 536.273 MB
% 3.08/6.08 % Net memory used: 506.012 MB
%------------------------------------------------------------------------------