%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV283-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 03:12:44 PM UTC 2026
% Result : Unsatisfiable 65.55s 9.96s
% Output : Proof 65.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 6 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 62 ( 26 ~; 36 |; 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 : 62 ( 8 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1438,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_0) ).
fof(f1438_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)],[f1438]) ).
fof(f1438_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)],[f1438_nnf]) ).
cnf(c1438,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f1438_sk]) ).
cnf(f1472,negated_conjecture,
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1472_nnf,plain,
! [V_W,V_U] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ),
inference(nnf_transformation,[status(thm)],[f1472]) ).
fof(f1472_sk,plain,
! [V_W,V_U] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ),
inference(skolemisation,[status(esa)],[f1472_nnf]) ).
cnf(c1472,plain,
( c_lessequals(X1,v_xd(X1),tc_nat)
| c_lessequals(X0,v_xd(X0),tc_nat) ),
inference(cnf_transformation,[status(esa)],[f1472_sk]) ).
cnf(p362,plain,
c_lessequals(X0,v_xd(X0),tc_nat),
inference(factoring,[status(thm)],[c1472]) ).
cnf(p3792,plain,
c_lessequals(X0,v_xd(c_plus(X1,X0,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[c1438,p362]) ).
cnf(f1437,axiom,
( ~ 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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg__Nonce__supply_0) ).
fof(f1437_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f1437]) ).
fof(f1437_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f1437_nnf]) ).
cnf(c1437,plain,
( ~ 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(esa)],[f1437_sk]) ).
cnf(f1477,negated_conjecture,
( 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/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
fof(f1477_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f1477]) ).
fof(f1477_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f1477_nnf]) ).
cnf(c1477,plain,
( 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(esa)],[f1477_sk]) ).
cnf(p342,plain,
( c_in(c_Message_Omsg_ONonce(v_xd(X0)),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(factoring,[status(thm)],[c1477]) ).
cnf(p343,plain,
( 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(factoring,[status(thm)],[p342]) ).
cnf(p3768,plain,
( 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)],[c1437,p343]) ).
cnf(p3794,plain,
c_in(c_Message_Omsg_ONonce(v_xd(c_plus(X0,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg),
inference(resolution,[status(thm)],[p3792,p3768]) ).
cnf(f1468,negated_conjecture,
( ~ 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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1468_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f1468]) ).
fof(f1468_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f1468_nnf]) ).
cnf(c1468,plain,
( ~ 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(esa)],[f1468_sk]) ).
cnf(p3951,plain,
~ c_lessequals(v_x,v_xd(c_plus(X0,v_sko__upX(v_xc),tc_nat)),tc_nat),
inference(resolution,[status(thm)],[p3794,c1468]) ).
cnf(f1439,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_1) ).
fof(f1439_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)],[f1439]) ).
fof(f1439_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)],[f1439_nnf]) ).
cnf(c1439,plain,
( c_lessequals(X0,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f1439_sk]) ).
cnf(p3830,plain,
c_lessequals(X0,v_xd(c_plus(X0,X1,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[c1439,p362]) ).
cnf(p3962,plain,
$false,
inference(resolution,[status(thm)],[p3951,p3830]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV283-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 19:00:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 65.55/9.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 65.55/9.96 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------