%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV283-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:47:10 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 3 unt; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 75 ( 34 ~; 39 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_U,V_msg] :
( ~ c_lessequals(v_sko__upX(V_msg),V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(V_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_m,V_k,V_n] :
( c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_m,V_k,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [V_U] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [V_W,V_U] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_X,V_U] :
( c_in(c_Message_Omsg_ONonce(v_xd(V_U)),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(V_U)),c_Event_Oused(v_list),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(V_X)),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(V_X)),c_Event_Oused(v_list),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__upX(X1),X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(X1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [V_k,V_n] :
( c_lessequals(V_k,V_n,tc_nat)
| ! [V_m] : ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [V_m,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| ! [V_k] : ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] :
( ~ c_lessequals(v_x,X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ! [V_U] : c_lessequals(V_U,v_xd(V_U),tc_nat)
| ! [V_W] : c_lessequals(V_W,v_xd(V_W),tc_nat) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1] :
( c_lessequals(X1,v_xd(X1),tc_nat)
| c_lessequals(X0,v_xd(X0),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [V_U] :
( c_in(c_Message_Omsg_ONonce(v_xd(V_U)),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(V_U)),c_Event_Oused(v_list),tc_Message_Omsg)
| ! [V_X] :
( c_in(c_Message_Omsg_ONonce(v_xd(V_X)),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(V_X)),c_Event_Oused(v_list),tc_Message_Omsg) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1] :
( c_in(c_Message_Omsg_ONonce(v_xd(X1)),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(X1)),c_Event_Oused(v_list),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(X0)),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(X0)),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,definition,
! [X0] :
( sQ0_spl
<=> c_lessequals(X0,v_xd(X0),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f18,plain,
! [X0] :
( ~ sQ0_spl
| c_lessequals(X0,v_xd(X0),tc_nat) ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f14,f17]) ).
fof(f21,definition,
! [X0] :
( sQ1_spl
<=> ( c_in(c_Message_Omsg_ONonce(v_xd(X0)),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(X0)),c_Event_Oused(v_list),tc_Message_Omsg) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Message_Omsg_ONonce(v_xd(X0)),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(X0)),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
sQ1_spl,
inference(split_clause,[status(thm)],[f16,f21]) ).
fof(f25,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Message_Omsg_ONonce(v_xd(X0)),c_Event_Oused(v_list),tc_Message_Omsg)
| ~ c_lessequals(v_sko__upX(v_xc),v_xd(X0),tc_nat) ),
inference(resolution,[status(thm)],[f7,f22]) ).
fof(f26,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_lessequals(v_x,v_xd(X0),tc_nat)
| ~ c_lessequals(v_sko__upX(v_xc),v_xd(X0),tc_nat) ),
inference(resolution,[status(thm)],[f25,f12]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ c_lessequals(c_plus(v_x,X1,tc_nat),v_xd(X0),tc_nat)
| ~ c_lessequals(v_sko__upX(v_xc),v_xd(X0),tc_nat) ),
inference(resolution,[status(thm)],[f26,f11]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ c_lessequals(c_plus(X2,v_sko__upX(v_xc),tc_nat),v_xd(X1),tc_nat)
| ~ c_lessequals(c_plus(v_x,X0,tc_nat),v_xd(X1),tc_nat) ),
inference(resolution,[status(thm)],[f28,f9]) ).
fof(f49,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ1_spl
| ~ c_lessequals(c_plus(X0,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,X1,tc_nat)),tc_nat) ),
inference(resolution,[status(thm)],[f40,f18]) ).
fof(f75,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f49,f18]) ).
fof(f78,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f79,plain,
$false,
inference(sat_refutation,[status(thm)],[f20,f24,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV283-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:38:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.47 % Elapsed time: 0.100997 seconds
% 0.15/0.47 % CPU time: 0.073057 seconds
% 0.15/0.47 % Total memory used: 1.779 MB
% 0.15/0.47 % Net memory used: 1.770 MB
%------------------------------------------------------------------------------