%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL818-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 01:08:53 PM UTC 2026
% Result : Unsatisfiable 0.23s 5.92s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 14 unt; 2 def)
% Number of atoms : 43 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 14 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-5 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f314,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f325,axiom,
! [V_f,V_x,V_xs,T_b,V_a,T_a] : c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f329,axiom,
! [V_env,V_s,V_t,V_U,V_T] :
( ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
| ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f354,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f373,axiom,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f375,negated_conjecture,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f881,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f897,plain,
! [X0,X1,X2,X3,X4,X5] : c_List_Ofoldr(X0,c_List_Olist_OCons(X1,X2,X3),X4,X3,X5) = hAPP(hAPP(X0,X1),c_List_Ofoldr(X0,X2,X4,X3,X5)),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f904,plain,
! [V_env,V_s,V_U,V_T] :
( ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
| ! [V_t] :
( ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ) ),
inference(miniscoping,[status(thm)],[f329]) ).
fof(f905,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,X4),X3))
| ~ c_Type_Otyping(X0,X2,X4)
| c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) ),
inference(cnf_transformation,[status(thm)],[f904]) ).
fof(f937,plain,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f962,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f964,plain,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f1037,plain,
v_T____ = c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype),
inference(forward_demodulation,[status(thm)],[f897,f937]) ).
fof(f1074,plain,
! [X0] :
( ~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,X0),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),X0) ),
inference(resolution,[status(thm)],[f905,f964]) ).
fof(f1077,plain,
! [X0] :
( ~ c_Type_Otyping(v_e____,v_u____,c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(X0,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),X0) ),
inference(forward_demodulation,[status(thm)],[f897,f1074]) ).
fof(f1160,plain,
( ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) ),
inference(paramodulation,[status(thm)],[f1037,f1077]) ).
fof(f1164,definition,
( sQ2_spl
<=> c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1166,plain,
( sQ2_spl
| ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) ),
inference(component_clause,[status(thm)],[f1164]) ).
fof(f1167,definition,
( sQ3_spl
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1169,plain,
( sQ3_spl
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(component_clause,[status(thm)],[f1167]) ).
fof(f1170,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1160,f1164,f1167]) ).
fof(f1171,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1166,f962]) ).
fof(f1172,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f1171]) ).
fof(f1173,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1169,f881]) ).
fof(f1174,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1173]) ).
fof(f1175,plain,
$false,
inference(sat_refutation,[status(thm)],[f1170,f1172,f1174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL818-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.61 % Computer : n006.cluster.edu
% 0.17/5.61 % Model : x86_64 x86_64
% 0.17/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.61 % Memory : 8046.5625MB
% 0.17/5.61 % OS : Linux 6.8.0-71-generic
% 0.17/5.61 % CPULimit : 300
% 0.17/5.61 % WCLimit : 300
% 0.17/5.61 % DateTime : Mon Sep 21 01:06:02 UTC 2026
% 0.17/5.62 % CPUTime :
% 0.17/5.66 % Drodi V4.1.1
% 0.23/5.92 % Refutation found
% 0.23/5.92 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/5.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.96 % Elapsed time: 0.324293 seconds
% 0.23/5.96 % CPU time: 2.076587 seconds
% 0.23/5.96 % Total memory used: 154.315 MB
% 0.23/5.96 % Net memory used: 153.547 MB
%------------------------------------------------------------------------------