TSTP Solution File: SWV283-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV283-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:10:50 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 51
% Syntax : Number of formulae : 100 ( 16 unt; 15 typ; 0 def)
% Number of atoms : 387 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 448 ( 162 ~; 245 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 9 >; 8 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 213 ( 193 !; 0 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(v_xc_type,type,
v_xc: $i ).
tff(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_xd_type,type,
v_xd: $i > $i ).
tff(c_plus_type,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_sko__upX_type,type,
v_sko__upX: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
tff(v_list_type,type,
v_list: $i ).
tff(1,plain,
^ [V_W: $i,V_U: $i] :
refl(
( ( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
<=> ( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
<=> ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
<=> ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [V_W: $i,V_U: $i] :
rewrite(
( ( c_lessequals(V_W,v_xd(V_W),tc_nat)
| c_lessequals(V_U,v_xd(V_U),tc_nat) )
<=> ( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_W: $i,V_U: $i] :
( c_lessequals(V_W,v_xd(V_W),tc_nat)
| c_lessequals(V_U,v_xd(V_U),tc_nat) )
<=> ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_W: $i,V_U: $i] :
( c_lessequals(V_W,v_xd(V_W),tc_nat)
| c_lessequals(V_U,v_xd(V_U),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(7,plain,
! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) )
<=> ( ~ ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) )
<=> c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( ~ ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) )
<=> ( ~ ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) )
<=> ( ~ ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_W: $i,V_U: $i] :
( c_lessequals(V_U,v_xd(V_U),tc_nat)
| c_lessequals(V_W,v_xd(V_W),tc_nat) )
| c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat),
inference(unit_resolution,[status(thm)],[16,10]) ).
tff(18,plain,
^ [V_n: $i,V_m: $i,V_k: $i] :
refl(
( ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) )
<=> ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_0) ).
tff(22,plain,
! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) )
| ~ c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) )
<=> ( ~ ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) )
| ~ c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) )
| ~ c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) )
| ~ c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [V_U: $i,V_msg: $i] :
refl(
( ( ~ 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) )
<=> ( ~ 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(bind,[status(th)],]) ).
tff(30,plain,
( ! [V_U: $i,V_msg: $i] :
( ~ 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) )
<=> ! [V_U: $i,V_msg: $i] :
( ~ 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(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V_U: $i,V_msg: $i] :
( ~ 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) )
<=> ! [V_U: $i,V_msg: $i] :
( ~ 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(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [V_U: $i,V_msg: $i] :
rewrite(
( ( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(V_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(v_sko__upX(V_msg),V_U,tc_nat) )
<=> ( ~ 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(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_U: $i,V_msg: $i] :
( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(V_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(v_sko__upX(V_msg),V_U,tc_nat) )
<=> ! [V_U: $i,V_msg: $i] :
( ~ 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(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [V_U: $i,V_msg: $i] :
( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(V_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(v_sko__upX(V_msg),V_U,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg__Nonce__supply_0) ).
tff(35,plain,
! [V_U: $i,V_msg: $i] :
( ~ 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(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V_U: $i,V_msg: $i] :
( ~ 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(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [V_U: $i,V_msg: $i] :
( ~ 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(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_U: $i,V_msg: $i] :
( ~ 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(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [V_U: $i,V_msg: $i] :
( ~ 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) )
| ~ c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) )
<=> ( ~ ! [V_U: $i,V_msg: $i] :
( ~ 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) )
| ~ c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V_U: $i,V_msg: $i] :
( ~ 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) )
| ~ c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [V_U: $i,V_msg: $i] :
( ~ 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) )
| ~ c_lessequals(v_sko__upX(v_xc),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[41,38,28]) ).
tff(43,plain,
^ [V_n: $i,V_m: $i,V_k: $i] :
refl(
( ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) )
<=> ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) )
<=> ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_1) ).
tff(47,plain,
! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) )
| ~ c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) )
<=> ( ~ ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) )
| ~ c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) )
| ~ c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [V_n: $i,V_m: $i,V_k: $i] :
( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) )
| ~ c_lessequals(c_plus(v_x,v_sko__upX(v_xc),tc_nat),v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat),
inference(unit_resolution,[status(thm)],[52,49,17]) ).
tff(54,plain,
^ [V_U: $i] :
refl(
( ( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg) )
<=> ( ~ 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(bind,[status(th)],]) ).
tff(55,plain,
( ! [V_U: $i] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg) )
<=> ! [V_U: $i] :
( ~ 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(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [V_U: $i] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg) )
<=> ! [V_U: $i] :
( ~ 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(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [V_U: $i] :
rewrite(
( ( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg)
| ~ c_lessequals(v_x,V_U,tc_nat) )
<=> ( ~ 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(bind,[status(th)],]) ).
tff(58,plain,
( ! [V_U: $i] :
( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg)
| ~ c_lessequals(v_x,V_U,tc_nat) )
<=> ! [V_U: $i] :
( ~ 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(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [V_U: $i] :
( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg)
| ~ c_lessequals(v_x,V_U,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(60,plain,
! [V_U: $i] :
( ~ 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(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [V_U: $i] :
( ~ 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(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [V_U: $i] :
( ~ 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(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [V_U: $i] :
( ~ 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(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
( ( ~ ! [V_U: $i] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg) )
| ~ c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) )
<=> ( ~ ! [V_U: $i] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg) )
| ~ c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [V_U: $i] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg) )
| ~ c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [V_U: $i] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg) )
| ~ c_lessequals(v_x,v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat)),tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
~ c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[66,63,53]) ).
tff(68,plain,
^ [V_U: $i,V_X: $i] :
refl(
( ( 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) )
<=> ( 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(bind,[status(th)],]) ).
tff(69,plain,
( ! [V_U: $i,V_X: $i] :
( 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) )
<=> ! [V_U: $i,V_X: $i] :
( 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(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [V_U: $i,V_X: $i] :
( 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) )
<=> ! [V_U: $i,V_X: $i] :
( 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(rewrite,[status(thm)],]) ).
tff(71,plain,
^ [V_U: $i,V_X: $i] :
trans(
monotonicity(
rewrite(
( ( c_in(c_Message_Omsg_ONonce(v_xd(V_X)),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_U)),c_Event_Oused(v_list),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) ) )),
( ( c_in(c_Message_Omsg_ONonce(v_xd(V_X)),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_U)),c_Event_Oused(v_list),tc_Message_Omsg)
| 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)
| 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) ) )),
rewrite(
( ( 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)
| 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_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) ) )),
( ( c_in(c_Message_Omsg_ONonce(v_xd(V_X)),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_U)),c_Event_Oused(v_list),tc_Message_Omsg)
| 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_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(bind,[status(th)],]) ).
tff(72,plain,
( ! [V_U: $i,V_X: $i] :
( c_in(c_Message_Omsg_ONonce(v_xd(V_X)),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_U)),c_Event_Oused(v_list),tc_Message_Omsg)
| 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) )
<=> ! [V_U: $i,V_X: $i] :
( 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(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [V_U: $i,V_X: $i] :
( c_in(c_Message_Omsg_ONonce(v_xd(V_X)),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_U)),c_Event_Oused(v_list),tc_Message_Omsg)
| 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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).
tff(74,plain,
! [V_U: $i,V_X: $i] :
( 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(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [V_U: $i,V_X: $i] :
( 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(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [V_U: $i,V_X: $i] :
( 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(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [V_U: $i,V_X: $i] :
( 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(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [V_U: $i,V_X: $i] :
( 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) )
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) )
<=> ( ~ ! [V_U: $i,V_X: $i] :
( 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) )
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ ! [V_U: $i,V_X: $i] :
( 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) )
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) )
<=> ( ~ ! [V_U: $i,V_X: $i] :
( 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) )
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [V_U: $i,V_X: $i] :
( 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) )
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) )
<=> ( ~ ! [V_U: $i,V_X: $i] :
( 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) )
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [V_U: $i,V_X: $i] :
( 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) )
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [V_U: $i,V_X: $i] :
( 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) )
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Message_Oparts(c_insert(v_xc,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x,v_sko__upX(v_xc),tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ),
inference(unit_resolution,[status(thm)],[83,77]) ).
tff(85,plain,
$false,
inference(unit_resolution,[status(thm)],[84,67,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV283-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 02:08:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------