%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV255-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 09:07:09 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 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 : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 31 ( 9 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_lessequals(VAR_0,v_xb(VAR_0),tc_nat),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_lessequals(A,v_xb(A),tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] :
( ~ c_lessequals(v_x,VAR_0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(VAR_0),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
( ~ c_lessequals(v_x,A,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(A),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( ~ c_lessequals(v_xa,VAR_0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(VAR_0),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,plain,
( ~ c_lessequals(v_xa,A,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(A),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0] :
( c_in(c_Message_Omsg_ONonce(v_xb(VAR_0)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(VAR_0)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_4,plain,
( c_in(c_Message_Omsg_ONonce(v_xb(A)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(A)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
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_5,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_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_6,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]) ).
cnf(c_9,plain,
( ~ c_lessequals(v_xa,v_xb(A),tc_nat)
| c_in(c_Message_Omsg_ONonce(v_xb(A)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_10,plain,
c_lessequals(A,v_xb(c_plus(B,A,tc_nat)),tc_nat),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
c_lessequals(A,v_xb(c_plus(A,B,tc_nat)),tc_nat),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_13,plain,
c_lessequals(A,v_xb(c_plus(B,c_plus(A,C,tc_nat),tc_nat)),tc_nat),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_20,plain,
~ c_in(c_Message_Omsg_ONonce(v_xb(c_plus(v_x,A,tc_nat))),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_2,c_11]) ).
cnf(c_26,plain,
c_in(c_Message_Omsg_ONonce(v_xb(c_plus(A,c_plus(v_xa,B,tc_nat),tc_nat))),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_9,c_13]) ).
cnf(c_27,plain,
$false,
inference(resolve,[status(thm)],[c_26,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV255-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 26 13:22:51 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 2837049 was started by sandbox2 on n013,
% 0.09/0.38 % Sat Sep 26 13:22:51 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 13.
% 0.09/0.40 % Level of proof is 4.
% 0.09/0.40 % Maximum clause weight is 20.000.
% 0.09/0.40 % Given clauses 13.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------