%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV255-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 : Fri Sep 25 03:12:38 PM UTC 2026
% Result : Unsatisfiable 0.07s 7.85s
% Output : Proof 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 47 ( 26 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 47 ( 8 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,negated_conjecture,
( 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',cls_conjecture_3) ).
fof(f3_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( 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(esa)],[f3_sk]) ).
cnf(f2,negated_conjecture,
( ~ 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',cls_conjecture_2) ).
fof(f2_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ 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(esa)],[f2_sk]) ).
cnf(p6,plain,
( ~ 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)],[c3,c2]) ).
cnf(f4,axiom,
( 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',cls_Nat_Oadd__leE_0) ).
fof(f4_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f0,negated_conjecture,
c_lessequals(V_U,v_xb(V_U),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
! [V_U] : c_lessequals(V_U,v_xb(V_U),tc_nat),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_U] : c_lessequals(V_U,v_xb(V_U),tc_nat),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
c_lessequals(X0,v_xb(X0),tc_nat),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p7,plain,
c_lessequals(X0,v_xb(c_plus(X1,X0,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(p12,plain,
c_in(c_Message_Omsg_ONonce(v_xb(c_plus(X0,v_xa,tc_nat))),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolution,[status(thm)],[p6,p7]) ).
cnf(f1,negated_conjecture,
( ~ 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',cls_conjecture_1) ).
fof(f1_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ 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(esa)],[f1_sk]) ).
cnf(p35,plain,
~ c_lessequals(v_x,v_xb(c_plus(X0,v_xa,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[p12,c1]) ).
cnf(f5,axiom,
( 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',cls_Nat_Oadd__leE_1) ).
fof(f5_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_lessequals(X0,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p15,plain,
c_lessequals(X0,v_xb(c_plus(X0,X1,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(p36,plain,
$false,
inference(resolution,[status(thm)],[p35,p15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV255-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.05/7.37 % Computer : n012.cluster.edu
% 0.05/7.37 % Model : x86_64 x86_64
% 0.05/7.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/7.37 % Memory : 8046.5625MB
% 0.05/7.37 % OS : Linux 6.8.0-71-generic
% 0.05/7.38 % CPULimit : 300
% 0.05/7.38 % WCLimit : 300
% 0.05/7.38 % DateTime : Thu Sep 24 18:54:50 UTC 2026
% 0.05/7.38 % CPUTime :
% 0.05/7.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/7.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/7.85 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------