%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL787-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 01:08:48 PM UTC 2026
% Result : Unsatisfiable 12.60s 2.03s
% Output : CNFRefutation 12.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 15 unt; 2 def)
% Number of atoms : 56 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 31 ~; 22 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f219,axiom,
! [V_e,V_u,V_T,V_t] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f315,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/sandbox/benchmark/theBenchmark.p') ).
fof(f329,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f335,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f346,axiom,
! [V_T_H_H] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),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)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,V_T_H_H)
| v_thesis____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f353,axiom,
! [V_e,V_t,V_T,V_u] :
( ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T)
| c_Type_Otyping(V_e,V_t,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)),V_T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f356,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f711,plain,
! [X0,X1,X2,X3] :
( ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),X2)
| c_Type_Otyping(X0,X1,c_Type_Osko__Type__Xtyping__elims__2__1(X2,X0,X3,X1)) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f853,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)],[f315]) ).
fof(f875,plain,
v_n____ = v_i____,
inference(cnf_transformation,[status(thm)],[f329]) ).
fof(f881,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f893,plain,
! [X0] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),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(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
| v_thesis____ ),
inference(cnf_transformation,[status(thm)],[f346]) ).
fof(f903,plain,
! [X0,X1,X2,X3] :
( ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),X2)
| c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X2,X0,X1,X3)),X2)) ),
inference(cnf_transformation,[status(thm)],[f353]) ).
fof(f906,plain,
~ v_thesis____,
inference(cnf_transformation,[status(thm)],[f356]) ).
fof(f932,definition,
( sQ0_spl
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( ~ sQ0_spl
| v_thesis____ ),
inference(component_clause,[status(thm)],[f932]) ).
fof(f935,definition,
! [X0] :
( sQ1_spl
<=> ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),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(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f936,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),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(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0) ),
inference(component_clause,[status(thm)],[f935]) ).
fof(f938,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f893,f932,f935]) ).
fof(f973,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(forward_demodulation,[status(thm)],[f875,f881]) ).
fof(f978,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f933,f906]) ).
fof(f979,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f978]) ).
fof(f983,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),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(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,X0) ),
inference(forward_demodulation,[status(thm)],[f875,f936]) ).
fof(f984,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),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(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,X0) ),
inference(forward_demodulation,[status(thm)],[f875,f983]) ).
fof(f985,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),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(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,X0) ),
inference(forward_demodulation,[status(thm)],[f853,f984]) ).
fof(f2456,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_a____)),
inference(resolution,[status(thm)],[f973,f711]) ).
fof(f2581,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(resolution,[status(thm)],[f903,f973]) ).
fof(f2586,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_a____),v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(forward_demodulation,[status(thm)],[f853,f2581]) ).
fof(f6875,plain,
( ~ sQ1_spl
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_a____)) ),
inference(resolution,[status(thm)],[f2586,f985]) ).
fof(f6884,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6875,f2456]) ).
fof(f6885,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f6884]) ).
fof(f6886,plain,
$false,
inference(sat_refutation,[status(thm)],[f938,f979,f6885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL787-1 : 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 : n008.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 01:04:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 12.60/2.03 % Refutation found
% 12.60/2.03 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.60/2.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.60/2.08 % Elapsed time: 1.717419 seconds
% 12.60/2.08 % CPU time: 13.184396 seconds
% 12.60/2.08 % Total memory used: 285.246 MB
% 12.60/2.08 % Net memory used: 273.993 MB
%------------------------------------------------------------------------------