TSTP Solution File: SWV457+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV457+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 15:17:40 EDT 2022
% Result : Theorem 16.27s 10.34s
% Output : Proof 16.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV457+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 04:07:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 16.27/10.34 % SZS status Theorem
% 16.27/10.34 % SZS output start Proof
% 16.27/10.34 tff(elem_type, type, (
% 16.27/10.34 elem: ( $i * $i ) > $o)).
% 16.27/10.34 tff(queue_type, type, (
% 16.27/10.34 queue: $i > $i)).
% 16.27/10.34 tff(host_type, type, (
% 16.27/10.34 host: $i > $i)).
% 16.27/10.34 tff(tptp_fun_W_4_type, type, (
% 16.27/10.34 tptp_fun_W_4: $i)).
% 16.27/10.34 tff(m_Halt_type, type, (
% 16.27/10.34 m_Halt: $i > $i)).
% 16.27/10.34 tff(tptp_fun_X_3_type, type, (
% 16.27/10.34 tptp_fun_X_3: $i)).
% 16.27/10.34 tff(cons_type, type, (
% 16.27/10.34 cons: ( $i * $i ) > $i)).
% 16.27/10.34 tff(tptp_fun_V_5_type, type, (
% 16.27/10.34 tptp_fun_V_5: $i)).
% 16.27/10.34 tff(index_type, type, (
% 16.27/10.34 index: ( $i * $i ) > $i)).
% 16.27/10.34 tff(pendack_type, type, (
% 16.27/10.34 pendack: $i)).
% 16.27/10.34 tff(elec_2_type, type, (
% 16.27/10.34 elec_2: $i)).
% 16.27/10.34 tff(status_type, type, (
% 16.27/10.34 status: $i)).
% 16.27/10.34 tff(leq_type, type, (
% 16.27/10.34 leq: ( $i * $i ) > $o)).
% 16.27/10.34 tff(nbr_proc_type, type, (
% 16.27/10.34 nbr_proc: $i)).
% 16.27/10.34 tff(m_Ack_type, type, (
% 16.27/10.34 m_Ack: ( $i * $i ) > $i)).
% 16.27/10.34 tff(setIn_type, type, (
% 16.27/10.34 setIn: ( $i * $i ) > $o)).
% 16.27/10.34 tff(alive_type, type, (
% 16.27/10.34 alive: $i)).
% 16.27/10.34 tff(norm_type, type, (
% 16.27/10.34 norm: $i)).
% 16.27/10.34 tff(ldr_type, type, (
% 16.27/10.34 ldr: $i)).
% 16.27/10.34 tff(down_type, type, (
% 16.27/10.34 down: $i)).
% 16.27/10.34 tff(m_Down_type, type, (
% 16.27/10.34 m_Down: $i > $i)).
% 16.27/10.34 tff(elid_type, type, (
% 16.27/10.34 elid: $i)).
% 16.27/10.34 tff(elec_1_type, type, (
% 16.27/10.34 elec_1: $i)).
% 16.27/10.34 tff(m_Ldr_type, type, (
% 16.27/10.34 m_Ldr: $i > $i)).
% 16.27/10.34 tff(pids_type, type, (
% 16.27/10.34 pids: $i)).
% 16.27/10.34 tff(tptp_fun_X0_7_type, type, (
% 16.27/10.34 tptp_fun_X0_7: $i)).
% 16.27/10.34 tff(tptp_fun_Z_8_type, type, (
% 16.27/10.34 tptp_fun_Z_8: $i)).
% 16.27/10.34 tff(snoc_type, type, (
% 16.27/10.34 snoc: ( $i * $i ) > $i)).
% 16.27/10.34 tff(tptp_fun_Y_6_type, type, (
% 16.27/10.34 tptp_fun_Y_6: $i)).
% 16.27/10.34 tff(1,plain,
% 16.27/10.34 ((setIn(W!4, alive) & ((~(host(W!4) = host(Y!6))) & (~((~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (host(W!4) = host(X0!7)) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7)))))) & (![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5)))) <=> (setIn(W!4, alive) & (~(host(W!4) = host(Y!6))) & (~((~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (host(W!4) = host(X0!7)) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7))))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5)))),
% 16.27/10.35 inference(rewrite,[status(thm)],[])).
% 16.27/10.35 tff(2,plain,
% 16.27/10.35 ((![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5))) <=> (![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5)))),
% 16.27/10.35 inference(rewrite,[status(thm)],[])).
% 16.27/10.35 tff(3,plain,
% 16.27/10.35 (((~(host(W!4) = host(Y!6))) & (~((host(W!4) = host(X0!7)) | (~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7)))))) <=> ((~(host(W!4) = host(Y!6))) & (~((~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (host(W!4) = host(X0!7)) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7))))))),
% 16.27/10.35 inference(rewrite,[status(thm)],[])).
% 16.27/10.35 tff(4,plain,
% 16.27/10.35 ((~(~setIn(W!4, alive))) <=> setIn(W!4, alive)),
% 16.27/10.35 inference(rewrite,[status(thm)],[])).
% 16.27/10.35 tff(5,plain,
% 16.27/10.35 (((~(~setIn(W!4, alive))) & ((~(host(W!4) = host(Y!6))) & (~((host(W!4) = host(X0!7)) | (~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7)))))) & (![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5)))) <=> (setIn(W!4, alive) & ((~(host(W!4) = host(Y!6))) & (~((~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (host(W!4) = host(X0!7)) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7)))))) & (![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5))))),
% 16.27/10.36 inference(monotonicity,[status(thm)],[4, 3, 2])).
% 16.27/10.36 tff(6,plain,
% 16.27/10.36 (((~(~setIn(W!4, alive))) & ((~(host(W!4) = host(Y!6))) & (~((host(W!4) = host(X0!7)) | (~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7)))))) & (![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5)))) <=> (setIn(W!4, alive) & (~(host(W!4) = host(Y!6))) & (~((~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (host(W!4) = host(X0!7)) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7))))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5)))),
% 16.34/10.36 inference(transitivity,[status(thm)],[5, 1])).
% 16.34/10.36 tff(7,plain,
% 16.34/10.36 ((~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V)))))) <=> (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V))))))),
% 16.34/10.36 inference(rewrite,[status(thm)],[])).
% 16.34/10.36 tff(8,plain,
% 16.34/10.36 ((~![V: $i, W: $i, X: $i] : ((((((((((((((((![Y: $i, Z: $i] : (elem(m_Ack(Z, Y), queue(host(Z))) => setIn(Z, pids)) & ![Y: $i, Z: $i] : (elem(m_Down(Z), queue(host(Y))) => (~setIn(Z, alive)))) & ![Y: $i, Z: $i] : (elem(m_Ldr(Z), queue(host(Y))) => (~leq(host(Y), host(Z))))) & ![Y: $i, Z: $i, Pid0: $i] : (elem(m_Ack(Pid0, Y), queue(host(Z))) => (~leq(host(Y), host(Pid0))))) & ![Y: $i, Z: $i] : ((((~setIn(Y, alive)) & leq(Z, Y)) & (host(Z) = host(Y))) => (~setIn(Z, alive)))) & ![Y: $i, Z: $i] : (((~(Z = Y)) & (host(Z) = host(Y))) => ((~setIn(Y, alive)) | (~setIn(Z, alive))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z)))) => leq(host(Y), index(pendack, host(Z))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & (index(status, host(Z)) = elec_1)) => (~elem(m_Ack(Y, Z), queue(host(Y)))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & (index(status, host(Z)) = elec_1)) => (~elem(m_Ack(Z, Y), queue(host(Z)))))) & ![Y: $i] : ((((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive)) => (index(elid, host(Y)) = Y))) & ![Y: $i, Z: $i, Pid0: $i] : (((elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) & (host(Pid0) = host(Y))) => (~setIn(Pid0, alive)))) & ![Y: $i, Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Ack(Pid0, Y), queue(host(Pid0)))) & (host(Z) = host(Y))) => (~setIn(host(Pid0), index(down, host(Z)))))) & ![Y: $i, Z: $i] : ((((((~leq(host(Y), host(Z))) & setIn(Y, alive)) & setIn(Z, alive)) & (index(status, host(Y)) = elec_2)) & (index(status, host(Z)) = elec_2)) => (~leq(index(pendack, host(Y)), index(pendack, host(Z)))))) & ![Y: $i, Z: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Z)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & ![Y: $i, Z: $i, Pid0: $i] : (((((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) & leq(nbr_proc, index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2)) & (host(Z) = index(pendack, host(Pid0)))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & (queue(host(W)) = cons(m_Halt(X), V))) => (setIn(W, alive) => ![Y: $i] : ((~(host(W) = host(Y))) => ![Z: $i, X0: $i] : ((host(X) = host(X0)) => ((~(host(W) = host(X0))) => (((((setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0)))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W)))) & (index(status, host(X0)) = elec_2)) & (host(Z) = index(pendack, host(X0)))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm)))))))))) <=> (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V))))))),
% 16.34/10.37 inference(rewrite,[status(thm)],[])).
% 16.34/10.37 tff(9,axiom,(~![V: $i, W: $i, X: $i] : ((((((((((((((((![Y: $i, Z: $i] : (elem(m_Ack(Z, Y), queue(host(Z))) => setIn(Z, pids)) & ![Y: $i, Z: $i] : (elem(m_Down(Z), queue(host(Y))) => (~setIn(Z, alive)))) & ![Y: $i, Z: $i] : (elem(m_Ldr(Z), queue(host(Y))) => (~leq(host(Y), host(Z))))) & ![Y: $i, Z: $i, Pid0: $i] : (elem(m_Ack(Pid0, Y), queue(host(Z))) => (~leq(host(Y), host(Pid0))))) & ![Y: $i, Z: $i] : ((((~setIn(Y, alive)) & leq(Z, Y)) & (host(Z) = host(Y))) => (~setIn(Z, alive)))) & ![Y: $i, Z: $i] : (((~(Z = Y)) & (host(Z) = host(Y))) => ((~setIn(Y, alive)) | (~setIn(Z, alive))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z)))) => leq(host(Y), index(pendack, host(Z))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & (index(status, host(Z)) = elec_1)) => (~elem(m_Ack(Y, Z), queue(host(Y)))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & (index(status, host(Z)) = elec_1)) => (~elem(m_Ack(Z, Y), queue(host(Z)))))) & ![Y: $i] : ((((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive)) => (index(elid, host(Y)) = Y))) & ![Y: $i, Z: $i, Pid0: $i] : (((elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) & (host(Pid0) = host(Y))) => (~setIn(Pid0, alive)))) & ![Y: $i, Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Ack(Pid0, Y), queue(host(Pid0)))) & (host(Z) = host(Y))) => (~setIn(host(Pid0), index(down, host(Z)))))) & ![Y: $i, Z: $i] : ((((((~leq(host(Y), host(Z))) & setIn(Y, alive)) & setIn(Z, alive)) & (index(status, host(Y)) = elec_2)) & (index(status, host(Z)) = elec_2)) => (~leq(index(pendack, host(Y)), index(pendack, host(Z)))))) & ![Y: $i, Z: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Z)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & ![Y: $i, Z: $i, Pid0: $i] : (((((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) & leq(nbr_proc, index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2)) & (host(Z) = index(pendack, host(Pid0)))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & (queue(host(W)) = cons(m_Halt(X), V))) => (setIn(W, alive) => ![Y: $i] : ((~(host(W) = host(Y))) => ![Z: $i, X0: $i] : ((host(X) = host(X0)) => ((~(host(W) = host(X0))) => (((((setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0)))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W)))) & (index(status, host(X0)) = elec_2)) & (host(Z) = index(pendack, host(X0)))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 16.34/10.37 tff(10,plain,
% 16.34/10.37 (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V)))))),
% 16.34/10.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 16.34/10.38 tff(11,plain,
% 16.34/10.38 (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V)))))),
% 16.34/10.38 inference(modus_ponens,[status(thm)],[10, 7])).
% 16.34/10.38 tff(12,plain,
% 16.34/10.38 (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V)))))),
% 16.34/10.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 16.34/10.38 tff(13,plain,
% 16.34/10.38 (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V)))))),
% 16.34/10.38 inference(modus_ponens,[status(thm)],[12, 7])).
% 16.34/10.38 tff(14,plain,
% 16.34/10.38 (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V)))))),
% 16.34/10.39 inference(modus_ponens,[status(thm)],[13, 7])).
% 16.34/10.39 tff(15,plain,
% 16.34/10.39 (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V)))))),
% 16.34/10.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 16.34/10.39 tff(16,plain,
% 16.34/10.39 (~![V: $i, W: $i, X: $i] : ((~setIn(W, alive)) | ![Y: $i] : ((host(W) = host(Y)) | ![Z: $i, X0: $i] : ((host(W) = host(X0)) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(X0, alive) & leq(nbr_proc, index(pendack, host(X0))) & elem(m_Ack(X0, Z), snoc(queue(host(X0)), m_Ack(X, W))) & (index(status, host(X0)) = elec_2) & (host(Z) = index(pendack, host(X0))))) | (~(host(X) = host(X0))))) | (~(![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W)) = cons(m_Halt(X), V)))))),
% 16.34/10.39 inference(modus_ponens,[status(thm)],[15, 7])).
% 16.34/10.39 tff(17,plain,
% 16.34/10.39 (setIn(W!4, alive) & (~(host(W!4) = host(Y!6))) & (~((~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (host(W!4) = host(X0!7)) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7))))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | setIn(Z, pids)) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~((~setIn(Y, alive)) & leq(Z, Y) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(elem(m_Down(Y), queue(host(Z))) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & (host(Pid0) = host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(host(Pid0), index(down, host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) & (queue(host(W!4)) = cons(m_Halt(X!3), V!5))),
% 16.34/10.39 inference(modus_ponens,[status(thm)],[16, 6])).
% 16.34/10.39 tff(18,plain,
% 16.34/10.39 (queue(host(W!4)) = cons(m_Halt(X!3), V!5)),
% 16.34/10.39 inference(and_elim,[status(thm)],[17])).
% 16.34/10.39 tff(19,plain,
% 16.34/10.39 (elem(m_Halt(X!3), queue(host(W!4))) <=> elem(m_Halt(X!3), cons(m_Halt(X!3), V!5))),
% 16.34/10.39 inference(monotonicity,[status(thm)],[18])).
% 16.34/10.39 tff(20,plain,
% 16.34/10.39 (elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)) <=> elem(m_Halt(X!3), queue(host(W!4)))),
% 16.34/10.39 inference(symmetry,[status(thm)],[19])).
% 16.34/10.39 tff(21,plain,
% 16.34/10.39 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))))),
% 16.34/10.39 inference(bind,[status(th)],[])).
% 16.34/10.39 tff(22,plain,
% 16.34/10.39 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.39 inference(quant_intro,[status(thm)],[21])).
% 16.34/10.39 tff(23,plain,
% 16.34/10.39 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.39 inference(rewrite,[status(thm)],[])).
% 16.34/10.39 tff(24,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 16.34/10.39 tff(25,plain,
% 16.34/10.39 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 16.34/10.39 tff(26,plain,(
% 16.34/10.39 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.39 inference(skolemize,[status(sab)],[25])).
% 16.34/10.39 tff(27,plain,
% 16.34/10.39 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 16.34/10.39 tff(28,plain,
% 16.34/10.39 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Halt(X!3), cons(m_Halt(X!3), V!5))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)))),
% 16.34/10.39 inference(rewrite,[status(thm)],[])).
% 16.34/10.39 tff(29,plain,
% 16.34/10.39 ((elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)) <=> $true) <=> elem(m_Halt(X!3), cons(m_Halt(X!3), V!5))),
% 16.34/10.39 inference(rewrite,[status(thm)],[])).
% 16.34/10.39 tff(30,plain,
% 16.34/10.39 (($true | elem(m_Halt(X!3), V!5)) <=> $true),
% 16.34/10.39 inference(rewrite,[status(thm)],[])).
% 16.34/10.39 tff(31,plain,
% 16.34/10.39 ((m_Halt(X!3) = m_Halt(X!3)) <=> $true),
% 16.34/10.39 inference(rewrite,[status(thm)],[])).
% 16.34/10.39 tff(32,plain,
% 16.34/10.39 (((m_Halt(X!3) = m_Halt(X!3)) | elem(m_Halt(X!3), V!5)) <=> ($true | elem(m_Halt(X!3), V!5))),
% 16.34/10.39 inference(monotonicity,[status(thm)],[31])).
% 16.34/10.39 tff(33,plain,
% 16.34/10.39 (((m_Halt(X!3) = m_Halt(X!3)) | elem(m_Halt(X!3), V!5)) <=> $true),
% 16.34/10.39 inference(transitivity,[status(thm)],[32, 30])).
% 16.34/10.39 tff(34,plain,
% 16.34/10.39 ((elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)) <=> ((m_Halt(X!3) = m_Halt(X!3)) | elem(m_Halt(X!3), V!5))) <=> (elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)) <=> $true)),
% 16.34/10.40 inference(monotonicity,[status(thm)],[33])).
% 16.34/10.40 tff(35,plain,
% 16.34/10.40 ((elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)) <=> ((m_Halt(X!3) = m_Halt(X!3)) | elem(m_Halt(X!3), V!5))) <=> elem(m_Halt(X!3), cons(m_Halt(X!3), V!5))),
% 16.34/10.40 inference(transitivity,[status(thm)],[34, 29])).
% 16.34/10.40 tff(36,plain,
% 16.34/10.40 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)) <=> ((m_Halt(X!3) = m_Halt(X!3)) | elem(m_Halt(X!3), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)))),
% 16.34/10.40 inference(monotonicity,[status(thm)],[35])).
% 16.34/10.40 tff(37,plain,
% 16.34/10.40 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)) <=> ((m_Halt(X!3) = m_Halt(X!3)) | elem(m_Halt(X!3), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)))),
% 16.34/10.40 inference(transitivity,[status(thm)],[36, 28])).
% 16.34/10.40 tff(38,plain,
% 16.34/10.40 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Halt(X!3), cons(m_Halt(X!3), V!5)) <=> ((m_Halt(X!3) = m_Halt(X!3)) | elem(m_Halt(X!3), V!5)))),
% 16.34/10.40 inference(quant_inst,[status(thm)],[])).
% 16.34/10.40 tff(39,plain,
% 16.34/10.40 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Halt(X!3), cons(m_Halt(X!3), V!5))),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 16.34/10.40 tff(40,plain,
% 16.34/10.40 (elem(m_Halt(X!3), cons(m_Halt(X!3), V!5))),
% 16.34/10.40 inference(unit_resolution,[status(thm)],[39, 27])).
% 16.34/10.40 tff(41,plain,
% 16.34/10.40 (elem(m_Halt(X!3), queue(host(W!4)))),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[40, 20])).
% 16.34/10.40 tff(42,plain,
% 16.34/10.40 (^[X: $i, Y: $i] : refl(((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 16.34/10.40 inference(bind,[status(th)],[])).
% 16.34/10.40 tff(43,plain,
% 16.34/10.40 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 16.34/10.40 inference(quant_intro,[status(thm)],[42])).
% 16.34/10.40 tff(44,plain,
% 16.34/10.40 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 16.34/10.40 inference(bind,[status(th)],[])).
% 16.34/10.40 tff(45,plain,
% 16.34/10.40 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 16.34/10.40 inference(quant_intro,[status(thm)],[44])).
% 16.34/10.40 tff(46,plain,
% 16.34/10.40 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 16.34/10.40 inference(rewrite,[status(thm)],[])).
% 16.34/10.40 tff(47,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_61')).
% 16.34/10.40 tff(48,plain,
% 16.34/10.40 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 16.34/10.40 tff(49,plain,(
% 16.34/10.40 ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 16.34/10.40 inference(skolemize,[status(sab)],[48])).
% 16.34/10.40 tff(50,plain,
% 16.34/10.40 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[49, 45])).
% 16.34/10.40 tff(51,plain,
% 16.34/10.40 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[50, 43])).
% 16.34/10.40 tff(52,plain,
% 16.34/10.40 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) <=> (index(pendack, host(X0!7)) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) <=> (index(pendack, host(X0!7)) = nbr_proc)))),
% 16.34/10.40 inference(rewrite,[status(thm)],[])).
% 16.34/10.40 tff(53,plain,
% 16.34/10.40 (((~((~leq(index(pendack, host(X0!7)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X0!7)))))) <=> (index(pendack, host(X0!7)) = nbr_proc)) <=> ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) <=> (index(pendack, host(X0!7)) = nbr_proc))),
% 16.34/10.40 inference(rewrite,[status(thm)],[])).
% 16.34/10.40 tff(54,plain,
% 16.34/10.40 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(index(pendack, host(X0!7)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X0!7)))))) <=> (index(pendack, host(X0!7)) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) <=> (index(pendack, host(X0!7)) = nbr_proc)))),
% 16.34/10.40 inference(monotonicity,[status(thm)],[53])).
% 16.34/10.40 tff(55,plain,
% 16.34/10.40 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(index(pendack, host(X0!7)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X0!7)))))) <=> (index(pendack, host(X0!7)) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) <=> (index(pendack, host(X0!7)) = nbr_proc)))),
% 16.34/10.40 inference(transitivity,[status(thm)],[54, 52])).
% 16.34/10.40 tff(56,plain,
% 16.34/10.40 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(index(pendack, host(X0!7)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X0!7)))))) <=> (index(pendack, host(X0!7)) = nbr_proc))),
% 16.34/10.40 inference(quant_inst,[status(thm)],[])).
% 16.34/10.40 tff(57,plain,
% 16.34/10.40 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) <=> (index(pendack, host(X0!7)) = nbr_proc))),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 16.34/10.40 tff(58,plain,
% 16.34/10.40 ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) <=> (index(pendack, host(X0!7)) = nbr_proc)),
% 16.34/10.40 inference(unit_resolution,[status(thm)],[57, 51])).
% 16.34/10.40 tff(59,plain,
% 16.34/10.40 (~((~(setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm))) | (host(W!4) = host(X0!7)) | (~(setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7))))) | (~(host(X!3) = host(X0!7))))),
% 16.34/10.40 inference(and_elim,[status(thm)],[17])).
% 16.34/10.40 tff(60,plain,
% 16.34/10.40 (setIn(X0!7, alive) & leq(nbr_proc, index(pendack, host(X0!7))) & elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) & (index(status, host(X0!7)) = elec_2) & (host(Z!8) = index(pendack, host(X0!7)))),
% 16.34/10.40 inference(or_elim,[status(thm)],[59])).
% 16.34/10.40 tff(61,plain,
% 16.34/10.40 (host(Z!8) = index(pendack, host(X0!7))),
% 16.34/10.40 inference(and_elim,[status(thm)],[60])).
% 16.34/10.40 tff(62,plain,
% 16.34/10.40 (index(pendack, host(X0!7)) = host(Z!8)),
% 16.34/10.40 inference(symmetry,[status(thm)],[61])).
% 16.34/10.40 tff(63,plain,
% 16.34/10.40 (leq(index(pendack, host(X0!7)), nbr_proc) <=> leq(host(Z!8), nbr_proc)),
% 16.34/10.40 inference(monotonicity,[status(thm)],[62])).
% 16.34/10.40 tff(64,plain,
% 16.34/10.40 (leq(host(Z!8), nbr_proc) <=> leq(index(pendack, host(X0!7)), nbr_proc)),
% 16.34/10.40 inference(symmetry,[status(thm)],[63])).
% 16.34/10.40 tff(65,plain,
% 16.34/10.40 (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 16.34/10.40 inference(bind,[status(th)],[])).
% 16.34/10.40 tff(66,plain,
% 16.34/10.40 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 16.34/10.40 inference(quant_intro,[status(thm)],[65])).
% 16.34/10.40 tff(67,plain,
% 16.34/10.40 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 16.34/10.40 inference(rewrite,[status(thm)],[])).
% 16.34/10.40 tff(68,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 16.34/10.40 tff(69,plain,
% 16.34/10.40 (![P: $i] : leq(host(P), nbr_proc)),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 16.34/10.40 tff(70,plain,(
% 16.34/10.40 ![P: $i] : leq(host(P), nbr_proc)),
% 16.34/10.40 inference(skolemize,[status(sab)],[69])).
% 16.34/10.40 tff(71,plain,
% 16.34/10.40 (![P: $i] : leq(host(P), nbr_proc)),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[70, 66])).
% 16.34/10.40 tff(72,plain,
% 16.34/10.40 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(Z!8), nbr_proc)),
% 16.34/10.40 inference(quant_inst,[status(thm)],[])).
% 16.34/10.40 tff(73,plain,
% 16.34/10.40 (leq(host(Z!8), nbr_proc)),
% 16.34/10.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 16.34/10.40 tff(74,plain,
% 16.34/10.40 (leq(index(pendack, host(X0!7)), nbr_proc)),
% 16.34/10.40 inference(modus_ponens,[status(thm)],[73, 64])).
% 16.34/10.40 tff(75,plain,
% 16.34/10.40 (leq(nbr_proc, index(pendack, host(X0!7)))),
% 16.34/10.40 inference(and_elim,[status(thm)],[60])).
% 16.34/10.40 tff(76,plain,
% 16.34/10.40 ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc))),
% 16.34/10.40 inference(tautology,[status(thm)],[])).
% 16.34/10.40 tff(77,plain,
% 16.34/10.40 ((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) | (~leq(index(pendack, host(X0!7)), nbr_proc))),
% 16.34/10.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 16.34/10.40 tff(78,plain,
% 16.34/10.40 (~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))),
% 16.34/10.40 inference(unit_resolution,[status(thm)],[77, 74])).
% 16.34/10.40 tff(79,plain,
% 16.34/10.40 ((~((~((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc)))) <=> (index(pendack, host(X0!7)) = nbr_proc))) | ((~leq(nbr_proc, index(pendack, host(X0!7)))) | (~leq(index(pendack, host(X0!7)), nbr_proc))) | (index(pendack, host(X0!7)) = nbr_proc)),
% 16.34/10.40 inference(tautology,[status(thm)],[])).
% 16.34/10.40 tff(80,plain,
% 16.34/10.40 (index(pendack, host(X0!7)) = nbr_proc),
% 16.34/10.40 inference(unit_resolution,[status(thm)],[79, 78, 58])).
% 16.34/10.40 tff(81,plain,
% 16.34/10.40 (host(X!3) = host(X0!7)),
% 16.34/10.40 inference(or_elim,[status(thm)],[59])).
% 16.34/10.40 tff(82,plain,
% 16.34/10.40 (index(pendack, host(X!3)) = index(pendack, host(X0!7))),
% 16.34/10.40 inference(monotonicity,[status(thm)],[81])).
% 16.34/10.40 tff(83,plain,
% 16.34/10.40 (index(pendack, host(X!3)) = nbr_proc),
% 16.34/10.40 inference(transitivity,[status(thm)],[82, 80])).
% 16.34/10.40 tff(84,plain,
% 16.34/10.40 (leq(index(pendack, host(X!3)), host(Y!6)) <=> leq(nbr_proc, host(Y!6))),
% 16.34/10.40 inference(monotonicity,[status(thm)],[83])).
% 16.34/10.40 tff(85,plain,
% 16.34/10.40 (leq(nbr_proc, host(Y!6)) <=> leq(index(pendack, host(X!3)), host(Y!6))),
% 16.34/10.40 inference(symmetry,[status(thm)],[84])).
% 16.34/10.40 tff(86,plain,
% 16.34/10.40 ((~leq(nbr_proc, host(Y!6))) <=> (~leq(index(pendack, host(X!3)), host(Y!6)))),
% 16.34/10.40 inference(monotonicity,[status(thm)],[85])).
% 16.34/10.40 tff(87,plain,
% 16.34/10.40 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, host(Y!6))) | (~leq(host(Y!6), nbr_proc)))) <=> (nbr_proc = host(Y!6)))),
% 16.34/10.40 inference(quant_inst,[status(thm)],[])).
% 16.34/10.40 tff(88,plain,
% 16.34/10.40 ((~((~leq(nbr_proc, host(Y!6))) | (~leq(host(Y!6), nbr_proc)))) <=> (nbr_proc = host(Y!6))),
% 16.34/10.40 inference(unit_resolution,[status(thm)],[87, 51])).
% 16.34/10.40 tff(89,plain,
% 16.34/10.40 ((host(Z!8) = host(Y!6)) <=> (host(Y!6) = host(Z!8))),
% 16.34/10.40 inference(commutativity,[status(thm)],[])).
% 16.34/10.40 tff(90,plain,
% 16.34/10.40 (nbr_proc = index(pendack, host(X0!7))),
% 16.34/10.40 inference(symmetry,[status(thm)],[80])).
% 16.34/10.40 tff(91,plain,
% 16.34/10.40 (nbr_proc = host(Z!8)),
% 16.34/10.40 inference(transitivity,[status(thm)],[90, 62])).
% 16.34/10.40 tff(92,plain,
% 16.34/10.40 ((nbr_proc = host(Y!6)) <=> (host(Z!8) = host(Y!6))),
% 16.34/10.40 inference(monotonicity,[status(thm)],[91])).
% 16.34/10.40 tff(93,plain,
% 16.34/10.40 ((nbr_proc = host(Y!6)) <=> (host(Y!6) = host(Z!8))),
% 16.34/10.40 inference(transitivity,[status(thm)],[92, 89])).
% 16.34/10.40 tff(94,plain,
% 16.34/10.40 ((host(Y!6) = host(Z!8)) <=> (nbr_proc = host(Y!6))),
% 16.34/10.40 inference(symmetry,[status(thm)],[93])).
% 16.34/10.40 tff(95,plain,
% 16.34/10.40 ((~(host(Y!6) = host(Z!8))) <=> (~(nbr_proc = host(Y!6)))),
% 16.34/10.40 inference(monotonicity,[status(thm)],[94])).
% 16.34/10.40 tff(96,plain,
% 16.34/10.40 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))))),
% 16.34/10.40 inference(bind,[status(th)],[])).
% 16.34/10.40 tff(97,plain,
% 16.34/10.40 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.40 inference(quant_intro,[status(thm)],[96])).
% 16.34/10.40 tff(98,plain,
% 16.34/10.40 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.40 inference(rewrite,[status(thm)],[])).
% 16.34/10.40 tff(99,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 16.34/10.41 tff(100,plain,
% 16.34/10.41 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 16.34/10.41 tff(101,plain,(
% 16.34/10.41 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.41 inference(skolemize,[status(sab)],[100])).
% 16.34/10.41 tff(102,plain,
% 16.34/10.41 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 16.34/10.41 inference(modus_ponens,[status(thm)],[101, 97])).
% 16.34/10.41 tff(103,plain,
% 16.34/10.41 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) <=> ((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))))),
% 16.34/10.41 inference(quant_inst,[status(thm)],[])).
% 16.34/10.41 tff(104,plain,
% 16.34/10.41 (elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) <=> ((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7))))),
% 16.34/10.41 inference(unit_resolution,[status(thm)],[103, 102])).
% 16.34/10.41 tff(105,plain,
% 16.34/10.41 (elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4)))),
% 16.34/10.41 inference(and_elim,[status(thm)],[60])).
% 16.34/10.41 tff(106,plain,
% 16.34/10.41 ((~(elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) <=> ((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))))) | (~elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4)))) | ((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7))))),
% 16.34/10.41 inference(tautology,[status(thm)],[])).
% 16.34/10.41 tff(107,plain,
% 16.34/10.41 ((~(elem(m_Ack(X0!7, Z!8), snoc(queue(host(X0!7)), m_Ack(X!3, W!4))) <=> ((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))))) | ((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7))))),
% 16.34/10.41 inference(unit_resolution,[status(thm)],[106, 105])).
% 16.34/10.41 tff(108,plain,
% 16.34/10.41 ((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))),
% 16.34/10.41 inference(unit_resolution,[status(thm)],[107, 104])).
% 16.34/10.41 tff(109,plain,
% 16.34/10.41 (^[Y: $i, Z: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0))))))),
% 16.34/10.41 inference(bind,[status(th)],[])).
% 16.34/10.41 tff(110,plain,
% 16.34/10.41 (![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0))))) <=> ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))),
% 16.34/10.41 inference(quant_intro,[status(thm)],[109])).
% 16.34/10.41 tff(111,plain,
% 16.34/10.41 (^[Y: $i, Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)) <=> (~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))), ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) <=> (~(~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))))), rewrite((~(~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))) <=> ((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)))), ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) <=> ((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))), trans(monotonicity(rewrite((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))) <=> (~((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0))))))), ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))))) <=> (~(~((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0))))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))), ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0))))))), (((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) <=> (((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))) | ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))))), rewrite((((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))) | ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))), (((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))))),
% 16.34/10.41 inference(bind,[status(th)],[])).
% 16.34/10.41 tff(112,plain,
% 16.34/10.41 (![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0)))))) <=> ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))),
% 16.34/10.41 inference(quant_intro,[status(thm)],[111])).
% 16.34/10.41 tff(113,plain,
% 16.34/10.41 (![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & leq(nbr_proc, index(pendack, host(Pid0))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))))))),
% 16.34/10.41 inference(and_elim,[status(thm)],[17])).
% 16.34/10.41 tff(114,plain,
% 16.34/10.41 (![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))),
% 16.34/10.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 16.34/10.41 tff(115,plain,
% 16.34/10.41 (![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))),
% 16.34/10.41 inference(modus_ponens,[status(thm)],[114, 110])).
% 16.34/10.41 tff(116,plain,
% 16.34/10.41 (index(status, host(X0!7)) = elec_2),
% 16.34/10.41 inference(and_elim,[status(thm)],[60])).
% 16.34/10.41 tff(117,plain,
% 16.34/10.41 (setIn(X0!7, alive)),
% 16.34/10.41 inference(and_elim,[status(thm)],[60])).
% 16.34/10.41 tff(118,plain,
% 16.34/10.41 (setIn(Y!6, alive) & (index(ldr, host(Y!6)) = host(Y!6)) & (index(status, host(Y!6)) = norm)),
% 16.34/10.41 inference(or_elim,[status(thm)],[59])).
% 16.34/10.41 tff(119,plain,
% 16.34/10.41 (index(status, host(Y!6)) = norm),
% 16.34/10.41 inference(and_elim,[status(thm)],[118])).
% 16.34/10.41 tff(120,plain,
% 16.34/10.41 (index(ldr, host(Y!6)) = host(Y!6)),
% 16.34/10.41 inference(and_elim,[status(thm)],[118])).
% 16.34/10.41 tff(121,plain,
% 16.34/10.41 (setIn(Y!6, alive)),
% 16.34/10.41 inference(and_elim,[status(thm)],[118])).
% 16.34/10.41 tff(122,plain,
% 16.34/10.41 (((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) | ((~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)))) <=> ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) | (~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)))),
% 16.34/10.41 inference(rewrite,[status(thm)],[])).
% 16.34/10.41 tff(123,plain,
% 16.34/10.41 (((~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7))))) <=> ((~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)))),
% 16.34/10.42 inference(rewrite,[status(thm)],[])).
% 16.34/10.42 tff(124,plain,
% 16.34/10.42 (((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) | ((~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))))) <=> ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) | ((~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm))))),
% 16.34/10.42 inference(monotonicity,[status(thm)],[123])).
% 16.34/10.42 tff(125,plain,
% 16.34/10.42 (((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) | ((~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))))) <=> ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) | (~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)))),
% 16.34/10.42 inference(transitivity,[status(thm)],[124, 122])).
% 16.34/10.42 tff(126,plain,
% 16.34/10.42 ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) | ((~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))))),
% 16.34/10.42 inference(quant_inst,[status(thm)],[])).
% 16.34/10.42 tff(127,plain,
% 16.34/10.42 ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~leq(nbr_proc, index(pendack, host(Pid0)))) | (~(host(Z) = index(pendack, host(Pid0)))))) | (~setIn(X0!7, alive)) | (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))) | (~(index(status, host(X0!7)) = elec_2)) | (~leq(nbr_proc, index(pendack, host(X0!7)))) | (~(host(Z!8) = index(pendack, host(X0!7)))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[126, 125])).
% 16.34/10.42 tff(128,plain,
% 16.34/10.42 (~elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[127, 121, 120, 119, 117, 75, 116, 61, 115])).
% 16.34/10.42 tff(129,plain,
% 16.34/10.42 ((~((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7))))) | (m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7)))),
% 16.34/10.42 inference(tautology,[status(thm)],[])).
% 16.34/10.42 tff(130,plain,
% 16.34/10.42 ((~((m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)) | elem(m_Ack(X0!7, Z!8), queue(host(X0!7))))) | (m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[129, 128])).
% 16.34/10.42 tff(131,plain,
% 16.34/10.42 (m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[130, 108])).
% 16.34/10.42 tff(132,plain,
% 16.34/10.42 (^[X1: $i, X2: $i, Y1: $i, Y2: $i] : refl(((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))) <=> ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))))),
% 16.34/10.42 inference(bind,[status(th)],[])).
% 16.34/10.42 tff(133,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))) <=> ![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))),
% 16.34/10.42 inference(quant_intro,[status(thm)],[132])).
% 16.34/10.42 tff(134,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))) <=> ![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))),
% 16.34/10.42 inference(rewrite,[status(thm)],[])).
% 16.34/10.42 tff(135,plain,
% 16.34/10.42 (^[X1: $i, X2: $i, Y1: $i, Y2: $i] : rewrite(((~(Y1 = Y2)) => (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))) <=> ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))))),
% 16.34/10.42 inference(bind,[status(th)],[])).
% 16.34/10.42 tff(136,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(Y1 = Y2)) => (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))) <=> ![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))),
% 16.34/10.42 inference(quant_intro,[status(thm)],[135])).
% 16.34/10.42 tff(137,axiom,(![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(Y1 = Y2)) => (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_32')).
% 16.34/10.42 tff(138,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[137, 136])).
% 16.34/10.42 tff(139,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[138, 134])).
% 16.34/10.42 tff(140,plain,(
% 16.34/10.42 ![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))),
% 16.34/10.42 inference(skolemize,[status(sab)],[139])).
% 16.34/10.42 tff(141,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[140, 133])).
% 16.34/10.42 tff(142,plain,
% 16.34/10.42 (((~![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))) | ((Z!8 = W!4) | (~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))))) <=> ((~![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))) | (Z!8 = W!4) | (~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))))),
% 16.34/10.42 inference(rewrite,[status(thm)],[])).
% 16.34/10.42 tff(143,plain,
% 16.34/10.42 ((~![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))) | ((Z!8 = W!4) | (~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))))),
% 16.34/10.42 inference(quant_inst,[status(thm)],[])).
% 16.34/10.42 tff(144,plain,
% 16.34/10.42 ((~![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))) | (Z!8 = W!4) | (~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[143, 142])).
% 16.34/10.42 tff(145,plain,
% 16.34/10.42 ((Z!8 = W!4) | (~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4)))),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[144, 141])).
% 16.34/10.42 tff(146,plain,
% 16.34/10.42 (Z!8 = W!4),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[145, 131])).
% 16.34/10.42 tff(147,plain,
% 16.34/10.42 (^[Pid: $i, Pid2: $i] : refl(((host(Pid) = host(Pid2)) | (~(Pid = Pid2))) <=> ((host(Pid) = host(Pid2)) | (~(Pid = Pid2))))),
% 16.34/10.42 inference(bind,[status(th)],[])).
% 16.34/10.42 tff(148,plain,
% 16.34/10.42 (![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2))) <=> ![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))),
% 16.34/10.42 inference(quant_intro,[status(thm)],[147])).
% 16.34/10.42 tff(149,plain,
% 16.34/10.42 (![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2))) <=> ![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))),
% 16.34/10.42 inference(rewrite,[status(thm)],[])).
% 16.34/10.42 tff(150,plain,
% 16.34/10.42 (^[Pid: $i, Pid2: $i] : rewrite(((~(host(Pid) = host(Pid2))) => (~(Pid = Pid2))) <=> ((host(Pid) = host(Pid2)) | (~(Pid = Pid2))))),
% 16.34/10.42 inference(bind,[status(th)],[])).
% 16.34/10.42 tff(151,plain,
% 16.34/10.42 (![Pid: $i, Pid2: $i] : ((~(host(Pid) = host(Pid2))) => (~(Pid = Pid2))) <=> ![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))),
% 16.34/10.42 inference(quant_intro,[status(thm)],[150])).
% 16.34/10.42 tff(152,axiom,(![Pid: $i, Pid2: $i] : ((~(host(Pid) = host(Pid2))) => (~(Pid = Pid2)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_33')).
% 16.34/10.42 tff(153,plain,
% 16.34/10.42 (![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[152, 151])).
% 16.34/10.42 tff(154,plain,
% 16.34/10.42 (![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[153, 149])).
% 16.34/10.42 tff(155,plain,(
% 16.34/10.42 ![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))),
% 16.34/10.42 inference(skolemize,[status(sab)],[154])).
% 16.34/10.42 tff(156,plain,
% 16.34/10.42 (![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[155, 148])).
% 16.34/10.42 tff(157,plain,
% 16.34/10.42 (((~![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))) | ((host(Z!8) = host(W!4)) | (~(Z!8 = W!4)))) <=> ((~![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))) | (host(Z!8) = host(W!4)) | (~(Z!8 = W!4)))),
% 16.34/10.42 inference(rewrite,[status(thm)],[])).
% 16.34/10.42 tff(158,plain,
% 16.34/10.42 ((~![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))) | ((host(Z!8) = host(W!4)) | (~(Z!8 = W!4)))),
% 16.34/10.42 inference(quant_inst,[status(thm)],[])).
% 16.34/10.42 tff(159,plain,
% 16.34/10.42 ((~![Pid: $i, Pid2: $i] : ((host(Pid) = host(Pid2)) | (~(Pid = Pid2)))) | (host(Z!8) = host(W!4)) | (~(Z!8 = W!4))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[158, 157])).
% 16.34/10.42 tff(160,plain,
% 16.34/10.42 ((host(Z!8) = host(W!4)) | (~(Z!8 = W!4))),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[159, 156])).
% 16.34/10.42 tff(161,plain,
% 16.34/10.42 (host(Z!8) = host(W!4)),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[160, 146])).
% 16.34/10.42 tff(162,plain,
% 16.34/10.42 (host(W!4) = host(Z!8)),
% 16.34/10.42 inference(symmetry,[status(thm)],[161])).
% 16.34/10.42 tff(163,plain,
% 16.34/10.42 ((host(W!4) = host(Y!6)) <=> (host(Z!8) = host(Y!6))),
% 16.34/10.42 inference(monotonicity,[status(thm)],[162])).
% 16.34/10.42 tff(164,plain,
% 16.34/10.42 ((host(W!4) = host(Y!6)) <=> (host(Y!6) = host(Z!8))),
% 16.34/10.42 inference(transitivity,[status(thm)],[163, 89])).
% 16.34/10.42 tff(165,plain,
% 16.34/10.42 ((~(host(W!4) = host(Y!6))) <=> (~(host(Y!6) = host(Z!8)))),
% 16.34/10.42 inference(monotonicity,[status(thm)],[164])).
% 16.34/10.42 tff(166,plain,
% 16.34/10.42 (~(host(W!4) = host(Y!6))),
% 16.34/10.42 inference(and_elim,[status(thm)],[17])).
% 16.34/10.42 tff(167,plain,
% 16.34/10.42 (~(host(Y!6) = host(Z!8))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[166, 165])).
% 16.34/10.42 tff(168,plain,
% 16.34/10.42 (~(nbr_proc = host(Y!6))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[167, 95])).
% 16.34/10.42 tff(169,plain,
% 16.34/10.42 ((~((~((~leq(nbr_proc, host(Y!6))) | (~leq(host(Y!6), nbr_proc)))) <=> (nbr_proc = host(Y!6)))) | ((~leq(nbr_proc, host(Y!6))) | (~leq(host(Y!6), nbr_proc))) | (nbr_proc = host(Y!6))),
% 16.34/10.42 inference(tautology,[status(thm)],[])).
% 16.34/10.42 tff(170,plain,
% 16.34/10.42 ((~leq(nbr_proc, host(Y!6))) | (~leq(host(Y!6), nbr_proc))),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[169, 168, 88])).
% 16.34/10.42 tff(171,plain,
% 16.34/10.42 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(Y!6), nbr_proc)),
% 16.34/10.42 inference(quant_inst,[status(thm)],[])).
% 16.34/10.42 tff(172,plain,
% 16.34/10.42 (leq(host(Y!6), nbr_proc)),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[171, 71])).
% 16.34/10.42 tff(173,plain,
% 16.34/10.42 ((~((~leq(nbr_proc, host(Y!6))) | (~leq(host(Y!6), nbr_proc)))) | (~leq(nbr_proc, host(Y!6))) | (~leq(host(Y!6), nbr_proc))),
% 16.34/10.42 inference(tautology,[status(thm)],[])).
% 16.34/10.42 tff(174,plain,
% 16.34/10.42 ((~((~leq(nbr_proc, host(Y!6))) | (~leq(host(Y!6), nbr_proc)))) | (~leq(nbr_proc, host(Y!6)))),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[173, 172])).
% 16.34/10.42 tff(175,plain,
% 16.34/10.42 (~leq(nbr_proc, host(Y!6))),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[174, 170])).
% 16.34/10.42 tff(176,plain,
% 16.34/10.42 (~leq(index(pendack, host(X!3)), host(Y!6))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[175, 86])).
% 16.34/10.42 tff(177,plain,
% 16.34/10.42 (index(status, host(X!3)) = index(status, host(X0!7))),
% 16.34/10.42 inference(monotonicity,[status(thm)],[81])).
% 16.34/10.42 tff(178,plain,
% 16.34/10.42 (index(status, host(X!3)) = elec_2),
% 16.34/10.42 inference(transitivity,[status(thm)],[177, 116])).
% 16.34/10.42 tff(179,plain,
% 16.34/10.42 (^[X1: $i, X2: $i, Y1: $i, Y2: $i] : refl(((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2)) <=> ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2)))),
% 16.34/10.42 inference(bind,[status(th)],[])).
% 16.34/10.42 tff(180,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2)) <=> ![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))),
% 16.34/10.42 inference(quant_intro,[status(thm)],[179])).
% 16.34/10.42 tff(181,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2)) <=> ![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))),
% 16.34/10.42 inference(rewrite,[status(thm)],[])).
% 16.34/10.42 tff(182,plain,
% 16.34/10.42 (^[X1: $i, X2: $i, Y1: $i, Y2: $i] : rewrite(((~(X1 = X2)) => (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))) <=> ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2)))),
% 16.34/10.42 inference(bind,[status(th)],[])).
% 16.34/10.42 tff(183,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(X1 = X2)) => (~(m_Ack(X1, Y1) = m_Ack(X2, Y2)))) <=> ![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))),
% 16.34/10.42 inference(quant_intro,[status(thm)],[182])).
% 16.34/10.42 tff(184,axiom,(![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(X1 = X2)) => (~(m_Ack(X1, Y1) = m_Ack(X2, Y2))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_31')).
% 16.34/10.42 tff(185,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[184, 183])).
% 16.34/10.42 tff(186,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[185, 181])).
% 16.34/10.42 tff(187,plain,(
% 16.34/10.42 ![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))),
% 16.34/10.42 inference(skolemize,[status(sab)],[186])).
% 16.34/10.42 tff(188,plain,
% 16.34/10.42 (![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[187, 180])).
% 16.34/10.42 tff(189,plain,
% 16.34/10.42 (((~![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))) | ((~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))) | (X0!7 = X!3))) <=> ((~![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))) | (~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))) | (X0!7 = X!3))),
% 16.34/10.42 inference(rewrite,[status(thm)],[])).
% 16.34/10.42 tff(190,plain,
% 16.34/10.42 ((~![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))) | ((~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))) | (X0!7 = X!3))),
% 16.34/10.42 inference(quant_inst,[status(thm)],[])).
% 16.34/10.42 tff(191,plain,
% 16.34/10.42 ((~![X1: $i, X2: $i, Y1: $i, Y2: $i] : ((~(m_Ack(X1, Y1) = m_Ack(X2, Y2))) | (X1 = X2))) | (~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))) | (X0!7 = X!3)),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[190, 189])).
% 16.34/10.42 tff(192,plain,
% 16.34/10.42 ((~(m_Ack(X0!7, Z!8) = m_Ack(X!3, W!4))) | (X0!7 = X!3)),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[191, 188])).
% 16.34/10.42 tff(193,plain,
% 16.34/10.42 (X0!7 = X!3),
% 16.34/10.42 inference(unit_resolution,[status(thm)],[192, 131])).
% 16.34/10.42 tff(194,plain,
% 16.34/10.42 (setIn(X0!7, alive) <=> setIn(X!3, alive)),
% 16.34/10.42 inference(monotonicity,[status(thm)],[193])).
% 16.34/10.42 tff(195,plain,
% 16.34/10.42 (setIn(X!3, alive)),
% 16.34/10.42 inference(modus_ponens,[status(thm)],[117, 194])).
% 16.34/10.42 tff(196,plain,
% 16.34/10.42 (^[Y: $i, Z: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z))))) <=> ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z))))))),
% 16.34/10.43 inference(bind,[status(th)],[])).
% 16.34/10.43 tff(197,plain,
% 16.34/10.43 (![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z))))) <=> ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))),
% 16.34/10.43 inference(quant_intro,[status(thm)],[196])).
% 16.34/10.43 tff(198,plain,
% 16.34/10.43 (^[Y: $i, Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)) <=> (~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))), ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) <=> (~(~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))))), rewrite((~(~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))) <=> ((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)))), ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) <=> ((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))), trans(monotonicity(rewrite(((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)) <=> (~((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Halt(Pid0), queue(host(Z))))))), ((~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Halt(Pid0), queue(host(Z))))))))), rewrite((~(~((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Halt(Pid0), queue(host(Z))))))) <=> ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Halt(Pid0), queue(host(Z)))))), ((~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Halt(Pid0), queue(host(Z))))))), (((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) <=> (((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))) | ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Halt(Pid0), queue(host(Z)))))))), rewrite((((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))) | ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) <=> ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))), (((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) <=> ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))))),
% 16.34/10.43 inference(bind,[status(th)],[])).
% 16.34/10.43 tff(199,plain,
% 16.34/10.43 (![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) <=> ![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))),
% 16.34/10.43 inference(quant_intro,[status(thm)],[198])).
% 16.34/10.43 tff(200,plain,
% 16.34/10.43 (![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2))))),
% 16.34/10.43 inference(and_elim,[status(thm)],[17])).
% 16.34/10.43 tff(201,plain,
% 16.34/10.43 (![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))),
% 16.34/10.43 inference(modus_ponens,[status(thm)],[200, 199])).
% 16.34/10.43 tff(202,plain,
% 16.34/10.43 (![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))),
% 16.34/10.43 inference(modus_ponens,[status(thm)],[201, 197])).
% 16.34/10.43 tff(203,plain,
% 16.34/10.43 (((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | ((~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~elem(m_Halt(X!3), queue(host(W!4)))) | leq(index(pendack, host(X!3)), host(Y!6)))) <=> ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~elem(m_Halt(X!3), queue(host(W!4)))) | leq(index(pendack, host(X!3)), host(Y!6)))),
% 16.34/10.43 inference(rewrite,[status(thm)],[])).
% 16.34/10.43 tff(204,plain,
% 16.34/10.43 (((~setIn(X!3, alive)) | leq(index(pendack, host(X!3)), host(Y!6)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~elem(m_Halt(X!3), queue(host(W!4))))) <=> ((~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~elem(m_Halt(X!3), queue(host(W!4)))) | leq(index(pendack, host(X!3)), host(Y!6)))),
% 16.34/10.43 inference(rewrite,[status(thm)],[])).
% 16.34/10.43 tff(205,plain,
% 16.34/10.43 (((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | ((~setIn(X!3, alive)) | leq(index(pendack, host(X!3)), host(Y!6)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~elem(m_Halt(X!3), queue(host(W!4)))))) <=> ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | ((~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~elem(m_Halt(X!3), queue(host(W!4)))) | leq(index(pendack, host(X!3)), host(Y!6))))),
% 16.34/10.44 inference(monotonicity,[status(thm)],[204])).
% 16.34/10.44 tff(206,plain,
% 16.34/10.44 (((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | ((~setIn(X!3, alive)) | leq(index(pendack, host(X!3)), host(Y!6)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~elem(m_Halt(X!3), queue(host(W!4)))))) <=> ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~elem(m_Halt(X!3), queue(host(W!4)))) | leq(index(pendack, host(X!3)), host(Y!6)))),
% 16.34/10.44 inference(transitivity,[status(thm)],[205, 203])).
% 16.34/10.44 tff(207,plain,
% 16.34/10.44 ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | ((~setIn(X!3, alive)) | leq(index(pendack, host(X!3)), host(Y!6)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~elem(m_Halt(X!3), queue(host(W!4)))))),
% 16.34/10.44 inference(quant_inst,[status(thm)],[])).
% 16.34/10.44 tff(208,plain,
% 16.34/10.44 ((~![Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Y)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~setIn(Y!6, alive)) | (~(index(ldr, host(Y!6)) = host(Y!6))) | (~(index(status, host(Y!6)) = norm)) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~elem(m_Halt(X!3), queue(host(W!4)))) | leq(index(pendack, host(X!3)), host(Y!6))),
% 16.34/10.44 inference(modus_ponens,[status(thm)],[207, 206])).
% 16.34/10.44 tff(209,plain,
% 16.34/10.44 ((~elem(m_Halt(X!3), queue(host(W!4)))) | leq(index(pendack, host(X!3)), host(Y!6))),
% 16.34/10.44 inference(unit_resolution,[status(thm)],[208, 121, 120, 119, 202, 195, 178])).
% 16.34/10.44 tff(210,plain,
% 16.34/10.44 ($false),
% 16.34/10.44 inference(unit_resolution,[status(thm)],[209, 176, 41])).
% 16.34/10.44 % SZS output end Proof
%------------------------------------------------------------------------------