%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL836-1 : 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 01:08:57 PM UTC 2026
% Result : Unsatisfiable 11.32s 6.96s
% Output : CNFRefutation 11.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 39 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 23 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-5 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f462,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f569,axiom,
! [V_t,V_s] : c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f582,axiom,
! [V_u,V_i,V_e,V_T_H] :
( ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),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),V_T_H)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ c_Type_Otyping(V_e,V_u,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),V_u),V_i))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f590,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f593,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),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),v_T_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f594,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),v_u____),v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1382,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnf_transformation,[status(thm)],[f462]) ).
fof(f1528,plain,
! [X0,X1] : c_Lambda_Osubstn(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(cnf_transformation,[status(thm)],[f569]) ).
fof(f1551,plain,
! [V_i,V_e] :
( ! [V_T_H] : ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),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),V_T_H)
| ! [V_u] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ c_Type_Otyping(V_e,V_u,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),V_u),V_i))) ) ),
inference(miniscoping,[status(thm)],[f582]) ).
fof(f1552,plain,
! [X0,X1,X2,X3] :
( ~ c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),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),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ c_Type_Otyping(X2,X0,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),X0),X1))) ),
inference(cnf_transformation,[status(thm)],[f1551]) ).
fof(f1563,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(cnf_transformation,[status(thm)],[f590]) ).
fof(f1566,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),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),v_T_H____),
inference(cnf_transformation,[status(thm)],[f593]) ).
fof(f1567,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),v_u____),v_i____))),
inference(cnf_transformation,[status(thm)],[f594]) ).
fof(f1634,plain,
! [X0,X1,X2,X3] :
( ~ c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),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),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ c_Type_Otyping(X2,X0,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X0),X1))) ),
inference(forward_demodulation,[status(thm)],[f1528,f1552]) ).
fof(f1635,plain,
! [X0,X1,X2,X3] :
( ~ c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ c_Type_Otyping(X2,X0,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X0),X1))) ),
inference(forward_demodulation,[status(thm)],[f1528,f1634]) ).
fof(f1639,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(forward_demodulation,[status(thm)],[f1528,f1566]) ).
fof(f1640,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(forward_demodulation,[status(thm)],[f1528,f1567]) ).
fof(f1727,plain,
! [X0,X1,X2] :
( ~ c_Type_Otyping(c_Type_Oshift(X1,X0,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X2)
| ~ c_Type_Otyping(X1,v_u____,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),X0))) ),
inference(resolution,[status(thm)],[f1635,f1563]) ).
fof(f2036,plain,
! [X0,X1] :
( ~ c_Type_Otyping(c_Type_Oshift(X0,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X1)
| ~ c_Type_Otyping(X0,v_u____,v_T____) ),
inference(resolution,[status(thm)],[f1727,f1640]) ).
fof(f3299,plain,
! [X0] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X0),
inference(resolution,[status(thm)],[f1382,f2036]) ).
fof(f3301,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1639,f3299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/5.40 % Computer : n017.cluster.edu
% 0.04/5.40 % Model : x86_64 x86_64
% 0.04/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.40 % Memory : 8046.5625MB
% 0.04/5.40 % OS : Linux 6.8.0-71-generic
% 0.04/5.40 % CPULimit : 300
% 0.04/5.40 % WCLimit : 300
% 0.04/5.40 % DateTime : Mon Sep 21 01:02:32 UTC 2026
% 0.04/5.40 % CPUTime :
% 0.04/5.47 % Drodi V4.1.1
% 11.32/6.96 % Refutation found
% 11.32/6.96 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 11.32/6.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.11/7.03 % Elapsed time: 1.604906 seconds
% 4.11/7.03 % CPU time: 12.042668 seconds
% 4.11/7.03 % Total memory used: 242.071 MB
% 4.11/7.03 % Net memory used: 234.802 MB
%------------------------------------------------------------------------------