%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 01:08:47 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f221,axiom,
! [V_k,V_u] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f245,axiom,
! [V_f,V_a,T_b,T_a] : c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f248,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f274,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f283,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f297,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f658,plain,
! [X0,X1] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0)),X1),X0) = X1,
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f700,plain,
! [X0,X1,X2,X3] : c_List_Ofoldl(X0,X1,c_List_Olist_ONil(X2),X3,X2) = X1,
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f703,plain,
v_n____ = v_i____,
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f736,plain,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f750,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f766,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f790,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(backward_demodulation,[status(thm)],[f703,f766]) ).
fof(f1297,plain,
! [X0,X1,X2] : c_List_Ofoldl(X0,X1,v_rs____,X2,tc_Lambda_OdB) = X1,
inference(paramodulation,[status(thm)],[f736,f700]) ).
fof(f1330,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____))),
inference(backward_demodulation,[status(thm)],[f1297,f790]) ).
fof(f1344,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(forward_demodulation,[status(thm)],[f658,f1330]) ).
fof(f1345,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1344,f750]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n001.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 01:09:33 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.15/5.42 % Drodi V4.1.1
% 0.15/5.45 % Refutation found
% 0.15/5.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.49 % Elapsed time: 0.085016 seconds
% 0.15/5.49 % CPU time: 0.269554 seconds
% 0.15/5.49 % Total memory used: 120.196 MB
% 0.15/5.49 % Net memory used: 119.951 MB
%------------------------------------------------------------------------------