%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL806-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 01:08:51 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.43s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 11 unt; 2 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 19 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f353,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_b____),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_b____),V_u),V_ia))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f385,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_b____),v_xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f386,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f387,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f388,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f931,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_b____),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_b____),V_u),V_ia))) ) ),
inference(miniscoping,[status(thm)],[f353]) ).
fof(f932,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_b____),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_b____),X0),X1))) ),
inference(cnf_transformation,[status(thm)],[f931]) ).
fof(f974,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f975,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f976,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f977,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f1060,plain,
! [X0] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X0),v_xc))) ),
inference(resolution,[status(thm)],[f932,f974]) ).
fof(f1073,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ),
inference(resolution,[status(thm)],[f1060,f977]) ).
fof(f1074,definition,
( sQ7_spl
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1076,plain,
( sQ7_spl
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ),
inference(component_clause,[status(thm)],[f1074]) ).
fof(f1077,definition,
( sQ8_spl
<=> hBOOL(hAPP(c_InductTermi_OIT,v_xb)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1079,plain,
( sQ8_spl
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb)) ),
inference(component_clause,[status(thm)],[f1077]) ).
fof(f1080,plain,
( ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1073,f1074,f1077]) ).
fof(f1081,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1076,f976]) ).
fof(f1082,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1081]) ).
fof(f1083,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1079,f975]) ).
fof(f1084,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1083]) ).
fof(f1085,plain,
$false,
inference(sat_refutation,[status(thm)],[f1080,f1082,f1084]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL806-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 01:10:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.39 % Drodi V4.1.1
% 0.08/0.43 % Refutation found
% 0.08/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.47 % Elapsed time: 0.099354 seconds
% 0.08/0.47 % CPU time: 0.215268 seconds
% 0.08/0.47 % Total memory used: 123.536 MB
% 0.08/0.47 % Net memory used: 123.288 MB
%------------------------------------------------------------------------------