%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL798-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 01:08:50 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.34s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 11 unt; 2 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 25 ~; 19 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f67,axiom,
c_InductTermi_OIT(v_u____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,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),v_a____,V_T_H)
| ~ c_InductTermi_OIT(V_u)
| ~ c_Type_Otyping(V_e,V_u,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u,V_i)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f172,plain,
c_InductTermi_OIT(v_u____),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f175,plain,
! [V_i,V_e] :
( ! [V_T_H] : ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H)
| ! [V_u] :
( ~ c_InductTermi_OIT(V_u)
| ~ c_Type_Otyping(V_e,V_u,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u,V_i)) ) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f176,plain,
! [X0,X1,X2,X3] :
( ~ c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),v_a____,X3)
| ~ c_InductTermi_OIT(X0)
| ~ c_Type_Otyping(X2,X0,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f177,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f179,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f180,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f1127,plain,
! [X0,X1] :
( ~ c_Type_Otyping(c_Type_Oshift(X0,v_i____,v_T____,tc_Type_Otype),v_a____,X1)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(X0,v_u____,v_T____) ),
inference(resolution,[status(thm)],[f176,f180]) ).
fof(f1128,definition,
! [X0,X1] :
( sQ21_spl
<=> ( ~ c_Type_Otyping(c_Type_Oshift(X0,v_i____,v_T____,tc_Type_Otype),v_a____,X1)
| ~ c_Type_Otyping(X0,v_u____,v_T____) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1129,plain,
! [X0,X1] :
( ~ sQ21_spl
| ~ c_Type_Otyping(c_Type_Oshift(X0,v_i____,v_T____,tc_Type_Otype),v_a____,X1)
| ~ c_Type_Otyping(X0,v_u____,v_T____) ),
inference(component_clause,[status(thm)],[f1128]) ).
fof(f1131,definition,
( sQ22_spl
<=> c_InductTermi_OIT(v_u____) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1133,plain,
( sQ22_spl
| ~ c_InductTermi_OIT(v_u____) ),
inference(component_clause,[status(thm)],[f1131]) ).
fof(f1134,plain,
( ~ sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1127,f1128,f1131]) ).
fof(f1140,plain,
! [X0] :
( ~ sQ21_spl
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0) ),
inference(resolution,[status(thm)],[f1129,f177]) ).
fof(f1141,plain,
( ~ sQ21_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f179,f1140]) ).
fof(f1142,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1141]) ).
fof(f1143,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1133,f172]) ).
fof(f1144,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f1143]) ).
fof(f1145,plain,
$false,
inference(sat_refutation,[status(thm)],[f1134,f1142,f1144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL798-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 01:04:36 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.07/0.34 % Refutation found
% 0.07/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.36 % Elapsed time: 0.055011 seconds
% 0.07/0.36 % CPU time: 0.195481 seconds
% 0.07/0.36 % Total memory used: 109.830 MB
% 0.07/0.36 % Net memory used: 109.542 MB
%------------------------------------------------------------------------------