%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL826-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 01:08:55 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 17 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f355,axiom,
! [V_u,V_ia,V_ea,V_T_H] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_a____),V_T_H))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),V_u),V_ia))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f387,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_a____),v_xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f388,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f389,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f390,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),v_xc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f935,plain,
! [V_ia,V_ea] :
( ! [V_T_H] : ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_a____),V_T_H))
| ! [V_u] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),V_u),V_ia))) ) ),
inference(miniscoping,[status(thm)],[f355]) ).
fof(f936,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X2),X1),v_T____)),v_a____),X3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),X0),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X0),X1))) ),
inference(cnf_transformation,[status(thm)],[f935]) ).
fof(f978,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_a____),v_xa)),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f979,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f980,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f981,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),v_xc))),
inference(cnf_transformation,[status(thm)],[f390]) ).
fof(f1018,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X0),v_xc),v_T____)),v_a____),X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X0),v_xb),v_T____)) ),
inference(resolution,[status(thm)],[f936,f981]) ).
fof(f1019,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X0),v_xc),v_T____)),v_a____),X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X0),v_xb),v_T____)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1018,f979]) ).
fof(f1024,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_a____),X0)),
inference(resolution,[status(thm)],[f1019,f980]) ).
fof(f1026,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f978,f1024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL826-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:06:12 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.089882 seconds
% 0.14/0.46 % CPU time: 0.229818 seconds
% 0.14/0.46 % Total memory used: 124.100 MB
% 0.14/0.46 % Net memory used: 123.827 MB
%------------------------------------------------------------------------------