%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 01:08:56 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.72s
% Output : CNFRefutation 0.22s
% 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f435,axiom,
! [V_s,V_t] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f436,axiom,
! [V_r,V_ss,V_s] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f444,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1124,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f1125,plain,
! [V_r,V_s] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| ! [V_ss] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(miniscoping,[status(thm)],[f436]) ).
fof(f1126,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(cnf_transformation,[status(thm)],[f1125]) ).
fof(f1139,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[status(thm)],[f444]) ).
fof(f1532,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(resolution,[status(thm)],[f1126,f1139]) ).
fof(f1543,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1532,f1124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.57 % Computer : n010.cluster.edu
% 0.17/0.57 % Model : x86_64 x86_64
% 0.17/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.57 % Memory : 8046.5625MB
% 0.17/0.57 % OS : Linux 6.8.0-71-generic
% 0.17/0.58 % CPULimit : 300
% 0.17/0.58 % WCLimit : 300
% 0.17/0.58 % DateTime : Mon Sep 21 01:07:25 UTC 2026
% 0.17/0.58 % CPUTime :
% 0.22/0.64 % Drodi V4.1.1
% 0.22/0.72 % Refutation found
% 0.22/0.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.22/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.74 % Elapsed time: 0.147097 seconds
% 0.22/0.74 % CPU time: 0.623726 seconds
% 0.22/0.74 % Total memory used: 131.867 MB
% 0.22/0.74 % Net memory used: 131.563 MB
%------------------------------------------------------------------------------