%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV284-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Sun Sep 27 09:07:16 AM UTC 2026
% Result : Unsatisfiable 20.23s 3.10s
% Output : CNFRefutation 20.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 30 ( 7 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( c_in(c_Message_Omsg_ONonce(v_x(VAR_0)),c_Message_Oparts(c_insert(v_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_x(VAR_0)),c_Event_Oused(v_list),tc_Message_Omsg) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_2265,plain,
( c_in(c_Message_Omsg_ONonce(v_x(A)),c_Message_Oparts(c_insert(v_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_x(A)),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] :
( ~ c_lessequals(v_N,VAR_0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(VAR_0),c_Event_Oused(v_list),tc_Message_Omsg) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2266,plain,
( ~ c_lessequals(v_N,A,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_lessequals(VAR_0,v_x(VAR_0),tc_nat),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2267,plain,
c_lessequals(A,v_x(A),tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Nat_Oadd__leE_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_2,tc_nat)
| ~ c_lessequals(c_plus(VAR_0,VAR_1,tc_nat),VAR_2,tc_nat) ),
file('theBenchmark.p',cls_Nat_Oadd__leE_1) ).
cnf(c_2274,plain,
( c_lessequals(A,C,tc_nat)
| ~ c_lessequals(c_plus(A,B,tc_nat),C,tc_nat) ),
inference(clausify,[status(thm)],[cls_Nat_Oadd__leE_1]) ).
fof(cls_Nat_Oadd__leE_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_1,VAR_2,tc_nat)
| ~ c_lessequals(c_plus(VAR_0,VAR_1,tc_nat),VAR_2,tc_nat) ),
file('theBenchmark.p',cls_Nat_Oadd__leE_0) ).
cnf(c_2275,plain,
( c_lessequals(B,C,tc_nat)
| ~ c_lessequals(c_plus(A,B,tc_nat),C,tc_nat) ),
inference(clausify,[status(thm)],[cls_Nat_Oadd__leE_0]) ).
fof(cls_Message_Omsg__Nonce__supply_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_lessequals(v_sko__upX(VAR_1),VAR_0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(VAR_0),c_Message_Oparts(c_insert(VAR_1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Omsg__Nonce__supply_0) ).
cnf(c_2276,plain,
( ~ c_lessequals(v_sko__upX(B),A,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(A),c_Message_Oparts(c_insert(B,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Omsg__Nonce__supply_0]) ).
cnf(c_2738,plain,
c_lessequals(A,v_x(c_plus(A,B,tc_nat)),tc_nat),
inference(resolve,[status(thm)],[c_2274,c_2267]) ).
cnf(c_2740,plain,
c_lessequals(A,v_x(c_plus(B,A,tc_nat)),tc_nat),
inference(resolve,[status(thm)],[c_2275,c_2267]) ).
cnf(c_3960,plain,
~ c_in(c_Message_Omsg_ONonce(v_x(c_plus(v_sko__upX(A),B,tc_nat))),c_Message_Oparts(c_insert(A,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_2738,c_2276]) ).
cnf(c_4064,plain,
~ c_in(c_Message_Omsg_ONonce(v_x(c_plus(A,v_N,tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_2740,c_2266]) ).
cnf(c_4084,plain,
c_in(c_Message_Omsg_ONonce(v_x(c_plus(v_sko__upX(v_msg),A,tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_3960,c_2265]) ).
cnf(c_4085,plain,
$false,
inference(resolve,[status(thm)],[c_4084,c_4064]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV284-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n002.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 13:30:20 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.41 % Process 1842867 was started by sandbox on n002,
% 0.14/0.41 % Sat Sep 26 13:30:20 2026
% 0.14/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 20.23/3.10
% 20.23/3.10 % SZS status Unsatisfiable for theBenchmark
% 20.23/3.10
% 20.23/3.10 % Proof 1 at 2.57 (+ 0.04) seconds.
% 20.23/3.10 % Length of proof is 12.
% 20.23/3.10 % Level of proof is 4.
% 20.23/3.10 % Maximum clause weight is 39.000.
% 20.23/3.10 % Given clauses 480.
% 20.23/3.10
% 20.23/3.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------