%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV255-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 02:47:02 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] : c_lessequals(V_U,v_xb(V_U),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] :
( ~ c_lessequals(v_xa,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [V_U] :
( c_in(c_Message_Omsg_ONonce(v_xb(V_U)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(V_U)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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(f6,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(f7,plain,
! [X0] : c_lessequals(X0,v_xb(X0),tc_nat),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0] :
( ~ c_lessequals(v_x,X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0] :
( ~ c_lessequals(v_xa,X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0] :
( c_in(c_Message_Omsg_ONonce(v_xb(X0)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(X0)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,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)],[f5]) ).
fof(f12,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)],[f11]) ).
fof(f13,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)],[f6]) ).
fof(f14,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)],[f13]) ).
fof(f15,plain,
! [X0] :
( ~ c_lessequals(v_xa,v_xb(X0),tc_nat)
| c_in(c_Message_Omsg_ONonce(v_xb(X0)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f10,f9]) ).
fof(f16,plain,
! [X0] :
( ~ c_lessequals(v_x,v_xb(X0),tc_nat)
| ~ c_lessequals(v_xa,v_xb(X0),tc_nat) ),
inference(resolution,[status(thm)],[f15,f8]) ).
fof(f18,plain,
! [X0,X1] : c_lessequals(X0,v_xb(c_plus(X1,X0,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[f12,f7]) ).
fof(f20,plain,
! [X0] : ~ c_lessequals(v_x,v_xb(c_plus(X0,v_xa,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f28,plain,
! [X0,X1] : c_lessequals(X0,v_xb(c_plus(X0,X1,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[f14,f7]) ).
fof(f31,plain,
$false,
inference(resolution,[status(thm)],[f28,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV255-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 08:38:01 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.042918 seconds
% 0.13/0.41 % CPU time: 0.102027 seconds
% 0.13/0.41 % Total memory used: 13.074 MB
% 0.13/0.41 % Net memory used: 12.666 MB
%------------------------------------------------------------------------------