%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV478+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 15:17:43 EDT 2022

% Result   : Theorem 0.18s 0.43s
% Output   : Proof 0.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV478+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33  % Computer : n005.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Sun Sep  4 03:52:33 EDT 2022
% 0.11/0.34  % CPUTime  : 
% 0.11/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34  Usage: tptp [options] [-file:]file
% 0.11/0.34    -h, -?       prints this message.
% 0.11/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.11/0.34    -m, -model   generate model.
% 0.11/0.34    -p, -proof   generate proof.
% 0.11/0.34    -c, -core    generate unsat core of named formulas.
% 0.11/0.34    -st, -statistics display statistics.
% 0.11/0.34    -t:timeout   set timeout (in second).
% 0.11/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.11/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34    -<param>:<value> configuration parameter and value.
% 0.11/0.34    -o:<output-file> file to place output in.
% 0.18/0.43  % SZS status Theorem
% 0.18/0.43  % SZS output start Proof
% 0.18/0.43  tff(host_type, type, (
% 0.18/0.43     host: $i > $i)).
% 0.18/0.43  tff(tptp_fun_V0_7_type, type, (
% 0.18/0.43     tptp_fun_V0_7: $i)).
% 0.18/0.43  tff(tptp_fun_Y0_8_type, type, (
% 0.18/0.43     tptp_fun_Y0_8: $i)).
% 0.18/0.43  tff(leq_type, type, (
% 0.18/0.43     leq: ( $i * $i ) > $o)).
% 0.18/0.43  tff(s_type, type, (
% 0.18/0.43     s: $i > $i)).
% 0.18/0.43  tff(nbr_proc_type, type, (
% 0.18/0.43     nbr_proc: $i)).
% 0.18/0.43  tff(tptp_fun_X_4_type, type, (
% 0.18/0.43     tptp_fun_X_4: $i)).
% 0.18/0.43  tff(tptp_fun_W0_10_type, type, (
% 0.18/0.43     tptp_fun_W0_10: $i)).
% 0.18/0.43  tff(cons_type, type, (
% 0.18/0.43     cons: ( $i * $i ) > $i)).
% 0.18/0.43  tff(tptp_fun_V_5_type, type, (
% 0.18/0.43     tptp_fun_V_5: $i)).
% 0.18/0.43  tff(m_Down_type, type, (
% 0.18/0.43     m_Down: $i > $i)).
% 0.18/0.43  tff(tptp_fun_Y_3_type, type, (
% 0.18/0.43     tptp_fun_Y_3: $i)).
% 0.18/0.43  tff(queue_type, type, (
% 0.18/0.43     queue: $i > $i)).
% 0.18/0.43  tff(elem_type, type, (
% 0.18/0.43     elem: ( $i * $i ) > $o)).
% 0.18/0.43  tff(elec_1_type, type, (
% 0.18/0.43     elec_1: $i)).
% 0.18/0.43  tff(index_type, type, (
% 0.18/0.43     index: ( $i * $i ) > $i)).
% 0.18/0.43  tff(status_type, type, (
% 0.18/0.43     status: $i)).
% 0.18/0.43  tff(tptp_fun_V0_11_type, type, (
% 0.18/0.43     tptp_fun_V0_11: ( $i * $i ) > $i)).
% 0.18/0.43  tff(zero_type, type, (
% 0.18/0.43     zero: $i)).
% 0.18/0.43  tff(setIn_type, type, (
% 0.18/0.43     setIn: ( $i * $i ) > $o)).
% 0.18/0.43  tff(down_type, type, (
% 0.18/0.43     down: $i)).
% 0.18/0.43  tff(norm_type, type, (
% 0.18/0.43     norm: $i)).
% 0.18/0.43  tff(ldr_type, type, (
% 0.18/0.43     ldr: $i)).
% 0.18/0.43  tff(alive_type, type, (
% 0.18/0.43     alive: $i)).
% 0.18/0.43  tff(elec_2_type, type, (
% 0.18/0.43     elec_2: $i)).
% 0.18/0.43  tff(m_Ack_type, type, (
% 0.18/0.43     m_Ack: ( $i * $i ) > $i)).
% 0.18/0.43  tff(elid_type, type, (
% 0.18/0.43     elid: $i)).
% 0.18/0.43  tff(wait_type, type, (
% 0.18/0.43     wait: $i)).
% 0.18/0.43  tff(pendack_type, type, (
% 0.18/0.43     pendack: $i)).
% 0.18/0.43  tff(m_Ldr_type, type, (
% 0.18/0.43     m_Ldr: $i > $i)).
% 0.18/0.43  tff(tptp_fun_Z_6_type, type, (
% 0.18/0.43     tptp_fun_Z_6: $i)).
% 0.18/0.43  tff(snoc_type, type, (
% 0.18/0.43     snoc: ( $i * $i ) > $i)).
% 0.18/0.43  tff(tptp_fun_X0_9_type, type, (
% 0.18/0.43     tptp_fun_X0_9: $i)).
% 0.18/0.43  tff(acks_type, type, (
% 0.18/0.43     acks: $i)).
% 0.18/0.43  tff(1,plain,
% 0.18/0.43      (^[X: $i, Y: $i] : refl((leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))))),
% 0.18/0.43      inference(bind,[status(th)],[])).
% 0.18/0.43  tff(2,plain,
% 0.18/0.43      (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.43      inference(quant_intro,[status(thm)],[1])).
% 0.18/0.43  tff(3,plain,
% 0.18/0.43      (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.43      inference(rewrite,[status(thm)],[])).
% 0.18/0.43  tff(4,plain,
% 0.18/0.43      (^[X: $i, Y: $i] : rewrite((leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y))) <=> (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))))),
% 0.18/0.43      inference(bind,[status(th)],[])).
% 0.18/0.43  tff(5,plain,
% 0.18/0.43      (![X: $i, Y: $i] : (leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.43      inference(quant_intro,[status(thm)],[4])).
% 0.18/0.43  tff(6,axiom,(![X: $i, Y: $i] : (leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_64')).
% 0.18/0.43  tff(7,plain,
% 0.18/0.43      (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.43  tff(8,plain,
% 0.18/0.43      (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.43  tff(9,plain,(
% 0.18/0.43      ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.43      inference(skolemize,[status(sab)],[8])).
% 0.18/0.43  tff(10,plain,
% 0.18/0.43      (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.43  tff(11,plain,
% 0.18/0.43      ((~![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))) | (leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))))),
% 0.18/0.43      inference(quant_inst,[status(thm)],[])).
% 0.18/0.43  tff(12,plain,
% 0.18/0.43      (leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))),
% 0.18/0.43      inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.43  tff(13,plain,
% 0.18/0.43      (^[X: $i, Y: $i] : refl(((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 0.18/0.43      inference(bind,[status(th)],[])).
% 0.18/0.43  tff(14,plain,
% 0.18/0.43      (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.18/0.43      inference(quant_intro,[status(thm)],[13])).
% 0.18/0.43  tff(15,plain,
% 0.18/0.43      (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 0.18/0.43      inference(bind,[status(th)],[])).
% 0.18/0.43  tff(16,plain,
% 0.18/0.43      (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.18/0.43      inference(quant_intro,[status(thm)],[15])).
% 0.18/0.43  tff(17,plain,
% 0.18/0.43      (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.18/0.43      inference(rewrite,[status(thm)],[])).
% 0.18/0.43  tff(18,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_61')).
% 0.18/0.43  tff(19,plain,
% 0.18/0.43      (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.43  tff(20,plain,(
% 0.18/0.43      ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.18/0.43      inference(skolemize,[status(sab)],[19])).
% 0.18/0.43  tff(21,plain,
% 0.18/0.43      (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[20, 16])).
% 0.18/0.43  tff(22,plain,
% 0.18/0.43      (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.18/0.43      inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.43  tff(23,plain,
% 0.18/0.43      ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8)))))) <=> (s(host(Y0!8)) = nbr_proc))),
% 0.18/0.43      inference(quant_inst,[status(thm)],[])).
% 0.18/0.43  tff(24,plain,
% 0.18/0.43      ((~((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8)))))) <=> (s(host(Y0!8)) = nbr_proc)),
% 0.18/0.43      inference(unit_resolution,[status(thm)],[23, 22])).
% 0.18/0.43  tff(25,plain,
% 0.18/0.43      ((leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.18/0.44      inference(rewrite,[status(thm)],[])).
% 0.18/0.44  tff(26,plain,
% 0.18/0.44      ((![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Pid0, alive)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) <=> (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.18/0.44      inference(rewrite,[status(thm)],[])).
% 0.18/0.44  tff(27,plain,
% 0.18/0.44      ((~(~((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))))) <=> ((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))),
% 0.18/0.44      inference(rewrite,[status(thm)],[])).
% 0.18/0.44  tff(28,plain,
% 0.18/0.44      ((~(~leq(nbr_proc, index(pendack, host(X!4))))) <=> leq(nbr_proc, index(pendack, host(X!4)))),
% 0.18/0.44      inference(rewrite,[status(thm)],[])).
% 0.18/0.44  tff(29,plain,
% 0.18/0.44      ((setIn(host(Z!6), index(acks, host(X!4))) & ((host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)))) <=> (setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(30,plain,
% 0.18/0.45      (((host(X!4) = host(V0!7)) & ((~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)))) <=> ((host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(31,plain,
% 0.18/0.45      (((~(host(X!4) = host(Y0!8))) & (setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (host(Z!6) = host(Y0!8))) <=> ((~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(32,plain,
% 0.18/0.45      ((~(~(host(Z!6) = host(Y0!8)))) <=> (host(Z!6) = host(Y0!8))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(33,plain,
% 0.18/0.45      ((![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) <=> (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(34,plain,
% 0.18/0.45      ((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) <=> (setIn(V0!7, alive) & (host(X!4) = host(V0!7)))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(35,plain,
% 0.18/0.45      (((~(host(X!4) = host(Y0!8))) & (~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (~(~(host(Z!6) = host(Y0!8))))) <=> ((~(host(X!4) = host(Y0!8))) & (setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (host(Z!6) = host(Y0!8)))),
% 0.18/0.45      inference(monotonicity,[status(thm)],[34, 33, 32])).
% 0.18/0.45  tff(36,plain,
% 0.18/0.45      (((~(host(X!4) = host(Y0!8))) & (~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (~(~(host(Z!6) = host(Y0!8))))) <=> ((~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)))),
% 0.18/0.45      inference(transitivity,[status(thm)],[35, 31])).
% 0.18/0.45  tff(37,plain,
% 0.18/0.45      ((~(~(host(X!4) = host(V0!7)))) <=> (host(X!4) = host(V0!7))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(38,plain,
% 0.18/0.45      (((~(~(host(X!4) = host(V0!7)))) & ((~(host(X!4) = host(Y0!8))) & (~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (~(~(host(Z!6) = host(Y0!8)))))) <=> ((host(X!4) = host(V0!7)) & ((~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8))))),
% 0.18/0.45      inference(monotonicity,[status(thm)],[37, 36])).
% 0.18/0.45  tff(39,plain,
% 0.18/0.45      (((~(~(host(X!4) = host(V0!7)))) & ((~(host(X!4) = host(Y0!8))) & (~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (~(~(host(Z!6) = host(Y0!8)))))) <=> ((host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)))),
% 0.18/0.45      inference(transitivity,[status(thm)],[38, 30])).
% 0.18/0.45  tff(40,plain,
% 0.18/0.45      ((~(~setIn(host(Z!6), index(acks, host(X!4))))) <=> setIn(host(Z!6), index(acks, host(X!4)))),
% 0.18/0.45      inference(rewrite,[status(thm)],[])).
% 0.18/0.45  tff(41,plain,
% 0.18/0.45      (((~(~setIn(host(Z!6), index(acks, host(X!4))))) & ((~(~(host(X!4) = host(V0!7)))) & ((~(host(X!4) = host(Y0!8))) & (~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (~(~(host(Z!6) = host(Y0!8))))))) <=> (setIn(host(Z!6), index(acks, host(X!4))) & ((host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8))))),
% 0.18/0.46      inference(monotonicity,[status(thm)],[40, 39])).
% 0.18/0.46  tff(42,plain,
% 0.18/0.46      (((~(~setIn(host(Z!6), index(acks, host(X!4))))) & ((~(~(host(X!4) = host(V0!7)))) & ((~(host(X!4) = host(Y0!8))) & (~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (~(~(host(Z!6) = host(Y0!8))))))) <=> (setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)))),
% 0.18/0.46      inference(transitivity,[status(thm)],[41, 29])).
% 0.18/0.46  tff(43,plain,
% 0.18/0.46      ((~(~setIn(X!4, alive))) <=> setIn(X!4, alive)),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(44,plain,
% 0.18/0.46      ((~(~leq(host(X!4), host(Y!3)))) <=> leq(host(X!4), host(Y!3))),
% 0.18/0.46      inference(rewrite,[status(thm)],[])).
% 0.18/0.46  tff(45,plain,
% 0.18/0.46      (((~(~leq(host(X!4), host(Y!3)))) & (~(~setIn(X!4, alive))) & ((~(~setIn(host(Z!6), index(acks, host(X!4))))) & ((~(~(host(X!4) = host(V0!7)))) & ((~(host(X!4) = host(Y0!8))) & (~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (~(~(host(Z!6) = host(Y0!8))))))) & (~(~leq(nbr_proc, index(pendack, host(X!4))))) & (~(~((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Pid0, alive)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))))),
% 0.18/0.46      inference(monotonicity,[status(thm)],[44, 43, 42, 28, 27, 26])).
% 0.18/0.46  tff(46,plain,
% 0.18/0.46      (((~(~leq(host(X!4), host(Y!3)))) & (~(~setIn(X!4, alive))) & ((~(~setIn(host(Z!6), index(acks, host(X!4))))) & ((~(~(host(X!4) = host(V0!7)))) & ((~(host(X!4) = host(Y0!8))) & (~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & (~(~(host(Z!6) = host(Y0!8))))))) & (~(~leq(nbr_proc, index(pendack, host(X!4))))) & (~(~((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Pid0, alive)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.18/0.47      inference(transitivity,[status(thm)],[45, 25])).
% 0.18/0.47  tff(47,plain,
% 0.18/0.47      ((~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))) <=> (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.18/0.48      inference(rewrite,[status(thm)],[])).
% 0.18/0.48  tff(48,plain,
% 0.18/0.48      ((~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & (host(Pid20) = host(Pid0))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))))) & ![Z: $i, Pid0: $i] : ((((((setIn(Z, alive) & setIn(Pid0, alive)) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm)) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (Pid0 = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & setIn(Z, alive)) & leq(host(Z), host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid30) = host(Pid0))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Z, Pid30), queue(host(Z)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & setIn(Pid0, alive)) & leq(nbr_proc, s(host(Pid0)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Down(Pid30), queue(host(Pid0)))) & (host(Pid30) = s(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => (leq(host(X), host(Y)) => (((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) => (leq(nbr_proc, index(pendack, host(X))) => ![Z: $i] : (setIn(host(Z), index(acks, host(X))) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((host(Z) = host(Y0)) => ((~(host(X) = host(Y0))) => (((((((![V1: $i] : (((~leq(host(Y0), V1)) & leq(s(zero), V1)) => (setIn(V1, index(down, host(Y0))) | (V1 = host(X0)))) & setIn(Y0, alive)) & leq(nbr_proc, s(host(Y0)))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X)))) & (host(W0) = s(host(Y0)))) & (index(status, host(Y0)) = elec_1)) => (~(setIn(V0, alive) & (host(X) = host(V0))))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.18/0.48      inference(rewrite,[status(thm)],[])).
% 0.18/0.48  tff(49,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & (host(Pid20) = host(Pid0))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))))) & ![Z: $i, Pid0: $i] : ((((((setIn(Z, alive) & setIn(Pid0, alive)) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm)) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (Pid0 = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & setIn(Z, alive)) & leq(host(Z), host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid30) = host(Pid0))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Z, Pid30), queue(host(Z)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & setIn(Pid0, alive)) & leq(nbr_proc, s(host(Pid0)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Down(Pid30), queue(host(Pid0)))) & (host(Pid30) = s(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => (leq(host(X), host(Y)) => (((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) => (leq(nbr_proc, index(pendack, host(X))) => ![Z: $i] : (setIn(host(Z), index(acks, host(X))) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((host(Z) = host(Y0)) => ((~(host(X) = host(Y0))) => (((((((![V1: $i] : (((~leq(host(Y0), V1)) & leq(s(zero), V1)) => (setIn(V1, index(down, host(Y0))) | (V1 = host(X0)))) & setIn(Y0, alive)) & leq(nbr_proc, s(host(Y0)))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X)))) & (host(W0) = s(host(Y0)))) & (index(status, host(Y0)) = elec_1)) => (~(setIn(V0, alive) & (host(X) = host(V0))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.18/0.49  tff(50,plain,
% 0.18/0.49      (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.49      inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.49  tff(51,plain,
% 0.18/0.49      (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.50      inference(modus_ponens,[status(thm)],[50, 47])).
% 0.18/0.50  tff(52,plain,
% 0.18/0.50      (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.50      inference(modus_ponens,[status(thm)],[51, 47])).
% 0.18/0.50  tff(53,plain,
% 0.18/0.50      (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.50      inference(modus_ponens,[status(thm)],[52, 47])).
% 0.18/0.50  tff(54,plain,
% 0.18/0.50      (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.51      inference(modus_ponens,[status(thm)],[53, 47])).
% 0.18/0.51  tff(55,plain,
% 0.18/0.51      (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.51      inference(modus_ponens,[status(thm)],[54, 47])).
% 0.18/0.51  tff(56,plain,
% 0.18/0.51      (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.52      inference(modus_ponens,[status(thm)],[55, 47])).
% 0.18/0.52  tff(57,plain,
% 0.18/0.52      (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & setIn(V0!7, alive) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & (host(Z!6) = host(Y0!8)) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))),
% 0.37/0.52      inference(modus_ponens,[status(thm)],[56, 46])).
% 0.37/0.52  tff(58,plain,
% 0.37/0.52      (host(W0!10) = s(host(Y0!8))),
% 0.37/0.52      inference(and_elim,[status(thm)],[57])).
% 0.37/0.52  tff(59,plain,
% 0.37/0.52      (s(host(Y0!8)) = host(W0!10)),
% 0.37/0.52      inference(symmetry,[status(thm)],[58])).
% 0.37/0.52  tff(60,plain,
% 0.37/0.52      (leq(s(host(Y0!8)), nbr_proc) <=> leq(host(W0!10), nbr_proc)),
% 0.37/0.52      inference(monotonicity,[status(thm)],[59])).
% 0.37/0.52  tff(61,plain,
% 0.37/0.52      (leq(host(W0!10), nbr_proc) <=> leq(s(host(Y0!8)), nbr_proc)),
% 0.37/0.52      inference(symmetry,[status(thm)],[60])).
% 0.37/0.52  tff(62,plain,
% 0.37/0.52      (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 0.37/0.52      inference(bind,[status(th)],[])).
% 0.37/0.52  tff(63,plain,
% 0.37/0.52      (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.37/0.52      inference(quant_intro,[status(thm)],[62])).
% 0.37/0.52  tff(64,plain,
% 0.37/0.52      (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.37/0.52      inference(rewrite,[status(thm)],[])).
% 0.37/0.52  tff(65,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 0.37/0.52  tff(66,plain,
% 0.37/0.52      (![P: $i] : leq(host(P), nbr_proc)),
% 0.37/0.52      inference(modus_ponens,[status(thm)],[65, 64])).
% 0.37/0.52  tff(67,plain,(
% 0.37/0.52      ![P: $i] : leq(host(P), nbr_proc)),
% 0.37/0.52      inference(skolemize,[status(sab)],[66])).
% 0.37/0.52  tff(68,plain,
% 0.37/0.52      (![P: $i] : leq(host(P), nbr_proc)),
% 0.37/0.52      inference(modus_ponens,[status(thm)],[67, 63])).
% 0.37/0.52  tff(69,plain,
% 0.37/0.52      ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(W0!10), nbr_proc)),
% 0.37/0.52      inference(quant_inst,[status(thm)],[])).
% 0.37/0.52  tff(70,plain,
% 0.37/0.52      (leq(host(W0!10), nbr_proc)),
% 0.37/0.52      inference(unit_resolution,[status(thm)],[69, 68])).
% 0.37/0.52  tff(71,plain,
% 0.37/0.52      (leq(s(host(Y0!8)), nbr_proc)),
% 0.37/0.52      inference(modus_ponens,[status(thm)],[70, 61])).
% 0.37/0.52  tff(72,plain,
% 0.37/0.52      (leq(nbr_proc, s(host(Y0!8)))),
% 0.37/0.52      inference(and_elim,[status(thm)],[57])).
% 0.37/0.52  tff(73,plain,
% 0.37/0.52      ((~((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8)))))) | (~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8))))),
% 0.37/0.52      inference(tautology,[status(thm)],[])).
% 0.37/0.52  tff(74,plain,
% 0.37/0.52      ((~((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8)))))) | (~leq(s(host(Y0!8)), nbr_proc))),
% 0.37/0.52      inference(unit_resolution,[status(thm)],[73, 72])).
% 0.37/0.52  tff(75,plain,
% 0.37/0.52      (~((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8)))))),
% 0.37/0.52      inference(unit_resolution,[status(thm)],[74, 71])).
% 0.37/0.52  tff(76,plain,
% 0.37/0.52      ((~((~((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8)))))) <=> (s(host(Y0!8)) = nbr_proc))) | ((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8))))) | (s(host(Y0!8)) = nbr_proc)),
% 0.37/0.52      inference(tautology,[status(thm)],[])).
% 0.37/0.52  tff(77,plain,
% 0.37/0.52      (s(host(Y0!8)) = nbr_proc),
% 0.37/0.52      inference(unit_resolution,[status(thm)],[76, 75, 24])).
% 0.37/0.52  tff(78,plain,
% 0.37/0.52      (host(X!4) = host(V0!7)),
% 0.37/0.52      inference(and_elim,[status(thm)],[57])).
% 0.37/0.52  tff(79,plain,
% 0.37/0.52      (host(V0!7) = host(X!4)),
% 0.37/0.52      inference(symmetry,[status(thm)],[78])).
% 0.37/0.52  tff(80,plain,
% 0.37/0.52      (leq(host(V0!7), s(host(Y0!8))) <=> leq(host(X!4), nbr_proc)),
% 0.37/0.52      inference(monotonicity,[status(thm)],[79, 77])).
% 0.37/0.52  tff(81,plain,
% 0.37/0.52      (leq(host(X!4), nbr_proc) <=> leq(host(V0!7), s(host(Y0!8)))),
% 0.37/0.52      inference(symmetry,[status(thm)],[80])).
% 0.37/0.52  tff(82,plain,
% 0.37/0.52      ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X!4), nbr_proc)),
% 0.37/0.52      inference(quant_inst,[status(thm)],[])).
% 0.37/0.52  tff(83,plain,
% 0.37/0.52      (leq(host(X!4), nbr_proc)),
% 0.37/0.52      inference(unit_resolution,[status(thm)],[82, 68])).
% 0.37/0.52  tff(84,plain,
% 0.37/0.52      (leq(host(V0!7), s(host(Y0!8)))),
% 0.37/0.52      inference(modus_ponens,[status(thm)],[83, 81])).
% 0.37/0.52  tff(85,plain,
% 0.37/0.52      ((~(leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))))) | (~leq(host(V0!7), s(host(Y0!8)))) | (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))),
% 0.37/0.52      inference(tautology,[status(thm)],[])).
% 0.37/0.52  tff(86,plain,
% 0.37/0.52      ((~(leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))))) | (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))),
% 0.37/0.52      inference(unit_resolution,[status(thm)],[85, 84])).
% 0.37/0.52  tff(87,plain,
% 0.37/0.52      (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))),
% 0.37/0.52      inference(unit_resolution,[status(thm)],[86, 12])).
% 0.37/0.52  tff(88,plain,
% 0.37/0.52      ((host(V0!7) = s(host(Y0!8))) <=> (host(X!4) = host(W0!10))),
% 0.37/0.52      inference(monotonicity,[status(thm)],[79, 59])).
% 0.37/0.52  tff(89,plain,
% 0.37/0.52      ((host(X!4) = host(W0!10)) <=> (host(V0!7) = s(host(Y0!8)))),
% 0.37/0.52      inference(symmetry,[status(thm)],[88])).
% 0.37/0.52  tff(90,plain,
% 0.37/0.52      ((~(host(X!4) = host(W0!10))) <=> (~(host(V0!7) = s(host(Y0!8))))),
% 0.37/0.52      inference(monotonicity,[status(thm)],[89])).
% 0.37/0.52  tff(91,plain,
% 0.37/0.52      (nbr_proc = s(host(Y0!8))),
% 0.37/0.52      inference(symmetry,[status(thm)],[77])).
% 0.37/0.52  tff(92,plain,
% 0.37/0.52      (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.37/0.52      inference(rewrite,[status(thm)],[])).
% 0.37/0.52  tff(93,plain,
% 0.37/0.52      (((~((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4)))))) <=> (index(pendack, host(X!4)) = nbr_proc)) <=> ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc))),
% 0.37/0.52      inference(rewrite,[status(thm)],[])).
% 0.37/0.52  tff(94,plain,
% 0.37/0.52      (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4)))))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.37/0.52      inference(monotonicity,[status(thm)],[93])).
% 0.37/0.52  tff(95,plain,
% 0.37/0.52      (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4)))))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.37/0.52      inference(transitivity,[status(thm)],[94, 92])).
% 0.37/0.52  tff(96,plain,
% 0.37/0.52      ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4)))))) <=> (index(pendack, host(X!4)) = nbr_proc))),
% 0.37/0.52      inference(quant_inst,[status(thm)],[])).
% 0.37/0.52  tff(97,plain,
% 0.37/0.52      ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc))),
% 0.37/0.52      inference(modus_ponens,[status(thm)],[96, 95])).
% 0.37/0.52  tff(98,plain,
% 0.37/0.52      ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc)),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[97, 22])).
% 0.37/0.53  tff(99,plain,
% 0.37/0.53      (host(Y!3) = index(pendack, host(X!4))),
% 0.37/0.53      inference(and_elim,[status(thm)],[57])).
% 0.37/0.53  tff(100,plain,
% 0.37/0.53      (index(pendack, host(X!4)) = host(Y!3)),
% 0.37/0.53      inference(symmetry,[status(thm)],[99])).
% 0.37/0.53  tff(101,plain,
% 0.37/0.53      (leq(index(pendack, host(X!4)), nbr_proc) <=> leq(host(Y!3), nbr_proc)),
% 0.37/0.53      inference(monotonicity,[status(thm)],[100])).
% 0.37/0.53  tff(102,plain,
% 0.37/0.53      (leq(host(Y!3), nbr_proc) <=> leq(index(pendack, host(X!4)), nbr_proc)),
% 0.37/0.53      inference(symmetry,[status(thm)],[101])).
% 0.37/0.53  tff(103,plain,
% 0.37/0.53      ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(Y!3), nbr_proc)),
% 0.37/0.53      inference(quant_inst,[status(thm)],[])).
% 0.37/0.53  tff(104,plain,
% 0.37/0.53      (leq(host(Y!3), nbr_proc)),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[103, 68])).
% 0.37/0.53  tff(105,plain,
% 0.37/0.53      (leq(index(pendack, host(X!4)), nbr_proc)),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[104, 102])).
% 0.37/0.53  tff(106,plain,
% 0.37/0.53      (leq(nbr_proc, index(pendack, host(X!4)))),
% 0.37/0.53      inference(and_elim,[status(thm)],[57])).
% 0.37/0.53  tff(107,plain,
% 0.37/0.53      ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) | (~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))),
% 0.37/0.53      inference(tautology,[status(thm)],[])).
% 0.37/0.53  tff(108,plain,
% 0.37/0.53      ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) | (~leq(index(pendack, host(X!4)), nbr_proc))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[107, 106])).
% 0.37/0.53  tff(109,plain,
% 0.37/0.53      (~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[108, 105])).
% 0.37/0.53  tff(110,plain,
% 0.37/0.53      ((~((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc))) | ((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) | (index(pendack, host(X!4)) = nbr_proc)),
% 0.37/0.53      inference(tautology,[status(thm)],[])).
% 0.37/0.53  tff(111,plain,
% 0.37/0.53      (index(pendack, host(X!4)) = nbr_proc),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[110, 109, 98])).
% 0.37/0.53  tff(112,plain,
% 0.37/0.53      (index(pendack, host(X!4)) = s(host(Y0!8))),
% 0.37/0.53      inference(transitivity,[status(thm)],[111, 91])).
% 0.37/0.53  tff(113,plain,
% 0.37/0.53      (leq(index(pendack, host(X!4)), host(Y0!8)) <=> leq(s(host(Y0!8)), host(Y0!8))),
% 0.37/0.53      inference(monotonicity,[status(thm)],[112])).
% 0.37/0.53  tff(114,plain,
% 0.37/0.53      (leq(s(host(Y0!8)), host(Y0!8)) <=> leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.37/0.53      inference(symmetry,[status(thm)],[113])).
% 0.37/0.53  tff(115,plain,
% 0.37/0.53      ((~leq(s(host(Y0!8)), host(Y0!8))) <=> (~leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.37/0.53      inference(monotonicity,[status(thm)],[114])).
% 0.37/0.53  tff(116,plain,
% 0.37/0.53      (^[X: $i] : refl((~leq(s(X), X)) <=> (~leq(s(X), X)))),
% 0.37/0.53      inference(bind,[status(th)],[])).
% 0.37/0.53  tff(117,plain,
% 0.37/0.53      (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.37/0.53      inference(quant_intro,[status(thm)],[116])).
% 0.37/0.53  tff(118,plain,
% 0.37/0.53      (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.37/0.53      inference(rewrite,[status(thm)],[])).
% 0.37/0.53  tff(119,axiom,(![X: $i] : (~leq(s(X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_58')).
% 0.37/0.53  tff(120,plain,
% 0.37/0.53      (![X: $i] : (~leq(s(X), X))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[119, 118])).
% 0.37/0.53  tff(121,plain,(
% 0.37/0.53      ![X: $i] : (~leq(s(X), X))),
% 0.37/0.53      inference(skolemize,[status(sab)],[120])).
% 0.37/0.53  tff(122,plain,
% 0.37/0.53      (![X: $i] : (~leq(s(X), X))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[121, 117])).
% 0.37/0.53  tff(123,plain,
% 0.37/0.53      ((~![X: $i] : (~leq(s(X), X))) | (~leq(s(host(Y0!8)), host(Y0!8)))),
% 0.37/0.53      inference(quant_inst,[status(thm)],[])).
% 0.37/0.53  tff(124,plain,
% 0.37/0.53      (~leq(s(host(Y0!8)), host(Y0!8))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[123, 122])).
% 0.37/0.53  tff(125,plain,
% 0.37/0.53      (~leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[124, 115])).
% 0.37/0.53  tff(126,plain,
% 0.37/0.53      (^[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))))),
% 0.37/0.53      inference(bind,[status(th)],[])).
% 0.37/0.53  tff(127,plain,
% 0.37/0.53      (![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)))),
% 0.37/0.53      inference(quant_intro,[status(thm)],[126])).
% 0.37/0.53  tff(128,plain,
% 0.37/0.53      (![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)))),
% 0.37/0.53      inference(rewrite,[status(thm)],[])).
% 0.37/0.53  tff(129,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 0.37/0.53  tff(130,plain,
% 0.37/0.53      (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[129, 128])).
% 0.37/0.53  tff(131,plain,(
% 0.37/0.53      ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.37/0.53      inference(skolemize,[status(sab)],[130])).
% 0.37/0.53  tff(132,plain,
% 0.37/0.53      (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[131, 127])).
% 0.37/0.53  tff(133,plain,
% 0.37/0.53      ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8)))))),
% 0.37/0.53      inference(quant_inst,[status(thm)],[])).
% 0.37/0.53  tff(134,plain,
% 0.37/0.53      (elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8))))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[133, 132])).
% 0.37/0.53  tff(135,plain,
% 0.37/0.53      (elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4)))),
% 0.37/0.53      inference(and_elim,[status(thm)],[57])).
% 0.37/0.53  tff(136,plain,
% 0.37/0.53      ((~(elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8)))))) | (~elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4)))) | ((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8))))),
% 0.37/0.53      inference(tautology,[status(thm)],[])).
% 0.37/0.53  tff(137,plain,
% 0.37/0.53      ((~(elem(m_Down(W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8)))))) | ((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8))))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[136, 135])).
% 0.37/0.53  tff(138,plain,
% 0.37/0.53      ((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8)))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[137, 134])).
% 0.37/0.53  tff(139,plain,
% 0.37/0.53      (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Ldr(Y))) <=> (~(m_Down(X) = m_Ldr(Y))))),
% 0.37/0.53      inference(bind,[status(th)],[])).
% 0.37/0.53  tff(140,plain,
% 0.37/0.53      (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.37/0.53      inference(quant_intro,[status(thm)],[139])).
% 0.37/0.53  tff(141,plain,
% 0.37/0.53      (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.37/0.53      inference(rewrite,[status(thm)],[])).
% 0.37/0.53  tff(142,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_18')).
% 0.37/0.53  tff(143,plain,
% 0.37/0.53      (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[142, 141])).
% 0.37/0.53  tff(144,plain,(
% 0.37/0.53      ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.37/0.53      inference(skolemize,[status(sab)],[143])).
% 0.37/0.53  tff(145,plain,
% 0.37/0.53      (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[144, 140])).
% 0.37/0.53  tff(146,plain,
% 0.37/0.53      ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))) | (~(m_Down(W0!10) = m_Ldr(X!4)))),
% 0.37/0.53      inference(quant_inst,[status(thm)],[])).
% 0.37/0.53  tff(147,plain,
% 0.37/0.53      (~(m_Down(W0!10) = m_Ldr(X!4))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[146, 145])).
% 0.37/0.53  tff(148,plain,
% 0.37/0.53      ((~((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8))))) | (m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8)))),
% 0.37/0.53      inference(tautology,[status(thm)],[])).
% 0.37/0.53  tff(149,plain,
% 0.37/0.53      ((~((m_Down(W0!10) = m_Ldr(X!4)) | elem(m_Down(W0!10), queue(host(Y0!8))))) | elem(m_Down(W0!10), queue(host(Y0!8)))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[148, 147])).
% 0.37/0.53  tff(150,plain,
% 0.37/0.53      (elem(m_Down(W0!10), queue(host(Y0!8)))),
% 0.37/0.53      inference(unit_resolution,[status(thm)],[149, 138])).
% 0.37/0.53  tff(151,plain,
% 0.37/0.53      (^[Z: $i, Pid20: $i, Pid0: $i] : refl(((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))),
% 0.37/0.53      inference(bind,[status(th)],[])).
% 0.37/0.53  tff(152,plain,
% 0.37/0.53      (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))),
% 0.37/0.53      inference(quant_intro,[status(thm)],[151])).
% 0.37/0.53  tff(153,plain,
% 0.37/0.53      (^[Z: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)) <=> (~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))))), rewrite((~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite((((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))))),
% 0.37/0.53      inference(bind,[status(th)],[])).
% 0.37/0.53  tff(154,plain,
% 0.37/0.53      (![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))),
% 0.37/0.53      inference(quant_intro,[status(thm)],[153])).
% 0.37/0.53  tff(155,plain,
% 0.37/0.53      (![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 0.37/0.53      inference(and_elim,[status(thm)],[57])).
% 0.37/0.53  tff(156,plain,
% 0.37/0.53      (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[155, 154])).
% 0.37/0.53  tff(157,plain,
% 0.37/0.53      (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))),
% 0.37/0.53      inference(modus_ponens,[status(thm)],[156, 152])).
% 0.37/0.53  tff(158,plain,
% 0.37/0.53      (index(status, host(X!4)) = elec_2),
% 0.37/0.53      inference(and_elim,[status(thm)],[57])).
% 0.37/0.53  tff(159,plain,
% 0.37/0.53      (setIn(Y0!8, alive)),
% 0.37/0.53      inference(and_elim,[status(thm)],[57])).
% 0.37/0.53  tff(160,plain,
% 0.37/0.53      (setIn(X!4, alive)),
% 0.37/0.53      inference(and_elim,[status(thm)],[57])).
% 0.37/0.53  tff(161,plain,
% 0.37/0.53      (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))) | leq(index(pendack, host(X!4)), host(Y0!8)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))) | leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.37/0.53      inference(rewrite,[status(thm)],[])).
% 0.37/0.53  tff(162,plain,
% 0.37/0.53      (((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8))))) <=> ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))) | leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.37/0.53      inference(rewrite,[status(thm)],[])).
% 0.37/0.53  tff(163,plain,
% 0.37/0.53      (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))) | leq(index(pendack, host(X!4)), host(Y0!8))))),
% 0.37/0.53      inference(monotonicity,[status(thm)],[162])).
% 0.37/0.53  tff(164,plain,
% 0.37/0.53      (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))) | leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.39/0.54      inference(transitivity,[status(thm)],[163, 161])).
% 0.39/0.54  tff(165,plain,
% 0.39/0.54      ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))),
% 0.39/0.54      inference(quant_inst,[status(thm)],[])).
% 0.39/0.54  tff(166,plain,
% 0.39/0.54      ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))) | leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.39/0.54      inference(modus_ponens,[status(thm)],[165, 164])).
% 0.39/0.54  tff(167,plain,
% 0.39/0.54      ((~(host(X!4) = host(W0!10))) | leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.39/0.54      inference(unit_resolution,[status(thm)],[166, 160, 159, 158, 157, 150])).
% 0.39/0.54  tff(168,plain,
% 0.39/0.54      (~(host(X!4) = host(W0!10))),
% 0.39/0.54      inference(unit_resolution,[status(thm)],[167, 125])).
% 0.39/0.54  tff(169,plain,
% 0.39/0.54      (~(host(V0!7) = s(host(Y0!8)))),
% 0.39/0.54      inference(modus_ponens,[status(thm)],[168, 90])).
% 0.39/0.54  tff(170,plain,
% 0.39/0.54      ((~(leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))) | leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))),
% 0.39/0.54      inference(tautology,[status(thm)],[])).
% 0.39/0.54  tff(171,plain,
% 0.39/0.54      (leq(host(V0!7), host(Y0!8))),
% 0.39/0.54      inference(unit_resolution,[status(thm)],[170, 169, 87])).
% 0.39/0.54  tff(172,plain,
% 0.39/0.54      (leq(s(zero), host(V0!7)) <=> leq(s(zero), host(X!4))),
% 0.39/0.54      inference(monotonicity,[status(thm)],[79])).
% 0.39/0.54  tff(173,plain,
% 0.39/0.54      (leq(s(zero), host(X!4)) <=> leq(s(zero), host(V0!7))),
% 0.39/0.54      inference(symmetry,[status(thm)],[172])).
% 0.39/0.54  tff(174,plain,
% 0.39/0.54      (^[P: $i] : refl(leq(s(zero), host(P)) <=> leq(s(zero), host(P)))),
% 0.39/0.54      inference(bind,[status(th)],[])).
% 0.39/0.54  tff(175,plain,
% 0.39/0.54      (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.39/0.54      inference(quant_intro,[status(thm)],[174])).
% 0.39/0.54  tff(176,plain,
% 0.39/0.54      (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.39/0.54      inference(rewrite,[status(thm)],[])).
% 0.39/0.54  tff(177,axiom,(![P: $i] : leq(s(zero), host(P))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_02')).
% 0.39/0.54  tff(178,plain,
% 0.39/0.54      (![P: $i] : leq(s(zero), host(P))),
% 0.39/0.54      inference(modus_ponens,[status(thm)],[177, 176])).
% 0.39/0.54  tff(179,plain,(
% 0.39/0.54      ![P: $i] : leq(s(zero), host(P))),
% 0.39/0.54      inference(skolemize,[status(sab)],[178])).
% 0.39/0.54  tff(180,plain,
% 0.39/0.54      (![P: $i] : leq(s(zero), host(P))),
% 0.39/0.54      inference(modus_ponens,[status(thm)],[179, 175])).
% 0.39/0.54  tff(181,plain,
% 0.39/0.54      ((~![P: $i] : leq(s(zero), host(P))) | leq(s(zero), host(X!4))),
% 0.39/0.54      inference(quant_inst,[status(thm)],[])).
% 0.39/0.54  tff(182,plain,
% 0.39/0.54      (leq(s(zero), host(X!4))),
% 0.39/0.54      inference(unit_resolution,[status(thm)],[181, 180])).
% 0.39/0.54  tff(183,plain,
% 0.39/0.54      (leq(s(zero), host(V0!7))),
% 0.39/0.54      inference(modus_ponens,[status(thm)],[182, 173])).
% 0.39/0.54  tff(184,plain,
% 0.39/0.54      (setIn(host(X!4), index(down, host(Y0!8))) <=> setIn(host(V0!7), index(down, host(Y0!8)))),
% 0.39/0.54      inference(monotonicity,[status(thm)],[78])).
% 0.39/0.54  tff(185,plain,
% 0.39/0.54      ((~setIn(host(X!4), index(down, host(Y0!8)))) <=> (~setIn(host(V0!7), index(down, host(Y0!8))))),
% 0.39/0.54      inference(monotonicity,[status(thm)],[184])).
% 0.39/0.54  tff(186,plain,
% 0.39/0.54      (^[Z: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))),
% 0.39/0.54      inference(bind,[status(th)],[])).
% 0.39/0.54  tff(187,plain,
% 0.39/0.54      (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.39/0.54      inference(quant_intro,[status(thm)],[186])).
% 0.39/0.54  tff(188,plain,
% 0.39/0.54      (^[Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2)) <=> (~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite((((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))))),
% 0.39/0.54      inference(bind,[status(th)],[])).
% 0.39/0.54  tff(189,plain,
% 0.39/0.54      (![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.39/0.54      inference(quant_intro,[status(thm)],[188])).
% 0.39/0.54  tff(190,plain,
% 0.39/0.54      (![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 0.39/0.54      inference(and_elim,[status(thm)],[57])).
% 0.39/0.54  tff(191,plain,
% 0.39/0.54      (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.39/0.54      inference(modus_ponens,[status(thm)],[190, 189])).
% 0.39/0.54  tff(192,plain,
% 0.39/0.54      (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.39/0.54      inference(modus_ponens,[status(thm)],[191, 187])).
% 0.39/0.54  tff(193,plain,
% 0.39/0.54      (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8)))))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8)))))),
% 0.39/0.54      inference(rewrite,[status(thm)],[])).
% 0.39/0.54  tff(194,plain,
% 0.39/0.54      (((~setIn(X!4, alive)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8)))) | (~(index(status, host(X!4)) = elec_2))) <=> ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8)))))),
% 0.39/0.54      inference(rewrite,[status(thm)],[])).
% 0.39/0.54  tff(195,plain,
% 0.39/0.54      (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(X!4, alive)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8)))) | (~(index(status, host(X!4)) = elec_2)))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8))))))),
% 0.39/0.54      inference(monotonicity,[status(thm)],[194])).
% 0.39/0.54  tff(196,plain,
% 0.39/0.54      (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(X!4, alive)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8)))) | (~(index(status, host(X!4)) = elec_2)))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8)))))),
% 0.39/0.54      inference(transitivity,[status(thm)],[195, 193])).
% 0.39/0.54  tff(197,plain,
% 0.39/0.54      ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(X!4, alive)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8)))) | (~(index(status, host(X!4)) = elec_2)))),
% 0.39/0.54      inference(quant_inst,[status(thm)],[])).
% 0.39/0.54  tff(198,plain,
% 0.39/0.54      ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8))))),
% 0.39/0.55      inference(modus_ponens,[status(thm)],[197, 196])).
% 0.39/0.55  tff(199,plain,
% 0.39/0.55      (leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8))))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[198, 160, 159, 158, 192])).
% 0.39/0.55  tff(200,plain,
% 0.39/0.55      (~setIn(host(X!4), index(down, host(Y0!8)))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[199, 125])).
% 0.39/0.55  tff(201,plain,
% 0.39/0.55      (~setIn(host(V0!7), index(down, host(Y0!8)))),
% 0.39/0.55      inference(modus_ponens,[status(thm)],[200, 185])).
% 0.39/0.55  tff(202,plain,
% 0.39/0.55      ((host(X!4) = host(X0!9)) <=> (host(V0!7) = host(X0!9))),
% 0.39/0.55      inference(monotonicity,[status(thm)],[78])).
% 0.39/0.55  tff(203,plain,
% 0.39/0.55      ((~(host(X!4) = host(X0!9))) <=> (~(host(V0!7) = host(X0!9)))),
% 0.39/0.55      inference(monotonicity,[status(thm)],[202])).
% 0.39/0.55  tff(204,plain,
% 0.39/0.55      ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))))),
% 0.39/0.55      inference(quant_inst,[status(thm)],[])).
% 0.39/0.55  tff(205,plain,
% 0.39/0.55      (elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[204, 132])).
% 0.39/0.55  tff(206,plain,
% 0.39/0.55      (elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4)))),
% 0.39/0.55      inference(and_elim,[status(thm)],[57])).
% 0.39/0.55  tff(207,plain,
% 0.39/0.55      ((~(elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))))) | (~elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4)))) | ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))),
% 0.39/0.55      inference(tautology,[status(thm)],[])).
% 0.39/0.55  tff(208,plain,
% 0.39/0.55      ((~(elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))))) | ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[207, 206])).
% 0.39/0.55  tff(209,plain,
% 0.39/0.55      ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[208, 205])).
% 0.39/0.55  tff(210,plain,
% 0.39/0.55      ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))) | (~(m_Down(X0!9) = m_Ldr(X!4)))),
% 0.39/0.55      inference(quant_inst,[status(thm)],[])).
% 0.39/0.55  tff(211,plain,
% 0.39/0.55      (~(m_Down(X0!9) = m_Ldr(X!4))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[210, 145])).
% 0.39/0.55  tff(212,plain,
% 0.39/0.55      ((~((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))) | (m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.39/0.55      inference(tautology,[status(thm)],[])).
% 0.39/0.55  tff(213,plain,
% 0.39/0.55      ((~((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))) | elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[212, 211])).
% 0.39/0.55  tff(214,plain,
% 0.39/0.55      (elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[213, 209])).
% 0.39/0.55  tff(215,plain,
% 0.39/0.55      (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))) | leq(index(pendack, host(X!4)), host(Y0!8)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))) | leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.39/0.55      inference(rewrite,[status(thm)],[])).
% 0.39/0.55  tff(216,plain,
% 0.39/0.55      (((~(host(X!4) = host(X0!9))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8))))) <=> ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))) | leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.39/0.55      inference(rewrite,[status(thm)],[])).
% 0.39/0.55  tff(217,plain,
% 0.39/0.55      (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(X0!9))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))) | leq(index(pendack, host(X!4)), host(Y0!8))))),
% 0.39/0.55      inference(monotonicity,[status(thm)],[216])).
% 0.39/0.55  tff(218,plain,
% 0.39/0.55      (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(X0!9))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))) | leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.39/0.55      inference(transitivity,[status(thm)],[217, 215])).
% 0.39/0.55  tff(219,plain,
% 0.39/0.55      ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(X0!9))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))))),
% 0.39/0.55      inference(quant_inst,[status(thm)],[])).
% 0.39/0.55  tff(220,plain,
% 0.39/0.55      ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))) | leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.39/0.55      inference(modus_ponens,[status(thm)],[219, 218])).
% 0.39/0.55  tff(221,plain,
% 0.39/0.55      ((~(host(X!4) = host(X0!9))) | leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[220, 160, 159, 158, 157, 214])).
% 0.39/0.55  tff(222,plain,
% 0.39/0.55      (~(host(X!4) = host(X0!9))),
% 0.39/0.55      inference(unit_resolution,[status(thm)],[221, 125])).
% 0.39/0.55  tff(223,plain,
% 0.39/0.55      (~(host(V0!7) = host(X0!9))),
% 0.39/0.55      inference(modus_ponens,[status(thm)],[222, 203])).
% 0.39/0.55  tff(224,plain,
% 0.39/0.55      (^[V1: $i] : refl(((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1))) <=> ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1))))),
% 0.39/0.55      inference(bind,[status(th)],[])).
% 0.39/0.55  tff(225,plain,
% 0.39/0.55      (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1))) <=> ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.39/0.55      inference(quant_intro,[status(thm)],[224])).
% 0.39/0.55  tff(226,plain,
% 0.39/0.55      (^[V1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(Y0!8), V1)) & leq(s(zero), V1)) <=> (~(leq(host(Y0!8), V1) | (~leq(s(zero), V1))))), ((~((~leq(host(Y0!8), V1)) & leq(s(zero), V1))) <=> (~(~(leq(host(Y0!8), V1) | (~leq(s(zero), V1))))))), rewrite((~(~(leq(host(Y0!8), V1) | (~leq(s(zero), V1))))) <=> (leq(host(Y0!8), V1) | (~leq(s(zero), V1)))), ((~((~leq(host(Y0!8), V1)) & leq(s(zero), V1))) <=> (leq(host(Y0!8), V1) | (~leq(s(zero), V1))))), (((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) <=> ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (leq(host(Y0!8), V1) | (~leq(s(zero), V1)))))), rewrite(((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) <=> ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))), (((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) <=> ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))))),
% 0.39/0.55      inference(bind,[status(th)],[])).
% 0.39/0.55  tff(227,plain,
% 0.39/0.55      (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) <=> ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.39/0.55      inference(quant_intro,[status(thm)],[226])).
% 0.39/0.55  tff(228,plain,
% 0.39/0.55      (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1))))),
% 0.39/0.55      inference(and_elim,[status(thm)],[57])).
% 0.39/0.55  tff(229,plain,
% 0.39/0.55      (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.39/0.55      inference(modus_ponens,[status(thm)],[228, 227])).
% 0.39/0.55  tff(230,plain,
% 0.39/0.55      (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.39/0.55      inference(modus_ponens,[status(thm)],[229, 225])).
% 0.39/0.55  tff(231,plain,
% 0.39/0.55      (((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | (leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | (~leq(s(zero), host(V0!7))))) <=> ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | (~leq(s(zero), host(V0!7))))),
% 0.39/0.55      inference(rewrite,[status(thm)],[])).
% 0.39/0.55  tff(232,plain,
% 0.39/0.55      (((host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (~leq(s(zero), host(V0!7)))) <=> (leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | (~leq(s(zero), host(V0!7))))),
% 0.39/0.55      inference(rewrite,[status(thm)],[])).
% 0.39/0.55  tff(233,plain,
% 0.39/0.55      (((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | ((host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (~leq(s(zero), host(V0!7))))) <=> ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | (leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | (~leq(s(zero), host(V0!7)))))),
% 0.39/0.55      inference(monotonicity,[status(thm)],[232])).
% 0.39/0.55  tff(234,plain,
% 0.39/0.55      (((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | ((host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (~leq(s(zero), host(V0!7))))) <=> ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | (~leq(s(zero), host(V0!7))))),
% 0.39/0.56      inference(transitivity,[status(thm)],[233, 231])).
% 0.39/0.56  tff(235,plain,
% 0.39/0.56      ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | ((host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (~leq(s(zero), host(V0!7))))),
% 0.39/0.56      inference(quant_inst,[status(thm)],[])).
% 0.39/0.56  tff(236,plain,
% 0.39/0.56      ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | (~leq(s(zero), host(V0!7)))),
% 0.39/0.56      inference(modus_ponens,[status(thm)],[235, 234])).
% 0.39/0.56  tff(237,plain,
% 0.39/0.56      (leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | (~leq(s(zero), host(V0!7)))),
% 0.39/0.56      inference(unit_resolution,[status(thm)],[236, 230])).
% 0.39/0.56  tff(238,plain,
% 0.39/0.56      (leq(host(Y0!8), host(V0!7))),
% 0.39/0.56      inference(unit_resolution,[status(thm)],[237, 223, 201, 183])).
% 0.39/0.56  tff(239,plain,
% 0.39/0.56      ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) | (~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))),
% 0.39/0.56      inference(tautology,[status(thm)],[])).
% 0.39/0.56  tff(240,plain,
% 0.39/0.56      (~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))),
% 0.39/0.56      inference(unit_resolution,[status(thm)],[239, 238, 171])).
% 0.39/0.56  tff(241,plain,
% 0.39/0.56      ((host(Y0!8) = host(X!4)) <=> (host(X!4) = host(Y0!8))),
% 0.39/0.56      inference(commutativity,[status(thm)],[])).
% 0.39/0.56  tff(242,plain,
% 0.39/0.56      ((host(Y0!8) = host(V0!7)) <=> (host(Y0!8) = host(X!4))),
% 0.39/0.56      inference(monotonicity,[status(thm)],[79])).
% 0.39/0.56  tff(243,plain,
% 0.39/0.56      ((host(Y0!8) = host(V0!7)) <=> (host(X!4) = host(Y0!8))),
% 0.39/0.56      inference(transitivity,[status(thm)],[242, 241])).
% 0.39/0.56  tff(244,plain,
% 0.39/0.56      ((host(X!4) = host(Y0!8)) <=> (host(Y0!8) = host(V0!7))),
% 0.39/0.56      inference(symmetry,[status(thm)],[243])).
% 0.39/0.56  tff(245,plain,
% 0.39/0.56      ((~(host(X!4) = host(Y0!8))) <=> (~(host(Y0!8) = host(V0!7)))),
% 0.39/0.56      inference(monotonicity,[status(thm)],[244])).
% 0.39/0.56  tff(246,plain,
% 0.39/0.56      (~(host(X!4) = host(Y0!8))),
% 0.39/0.56      inference(and_elim,[status(thm)],[57])).
% 0.39/0.56  tff(247,plain,
% 0.39/0.56      (~(host(Y0!8) = host(V0!7))),
% 0.39/0.56      inference(modus_ponens,[status(thm)],[246, 245])).
% 0.39/0.56  tff(248,plain,
% 0.39/0.56      ((~((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7)))) | ((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) | (host(Y0!8) = host(V0!7))),
% 0.39/0.56      inference(tautology,[status(thm)],[])).
% 0.39/0.56  tff(249,plain,
% 0.39/0.56      (~((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7)))),
% 0.39/0.56      inference(unit_resolution,[status(thm)],[248, 247, 240])).
% 0.39/0.56  tff(250,plain,
% 0.39/0.56      (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7)))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7))))),
% 0.39/0.56      inference(rewrite,[status(thm)],[])).
% 0.39/0.56  tff(251,plain,
% 0.39/0.56      (((~((~leq(host(Y0!8), host(V0!7))) | (~leq(host(V0!7), host(Y0!8))))) <=> (host(Y0!8) = host(V0!7))) <=> ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7)))),
% 0.39/0.56      inference(rewrite,[status(thm)],[])).
% 0.39/0.56  tff(252,plain,
% 0.39/0.56      (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(Y0!8), host(V0!7))) | (~leq(host(V0!7), host(Y0!8))))) <=> (host(Y0!8) = host(V0!7)))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7))))),
% 0.39/0.56      inference(monotonicity,[status(thm)],[251])).
% 0.39/0.56  tff(253,plain,
% 0.39/0.56      (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(Y0!8), host(V0!7))) | (~leq(host(V0!7), host(Y0!8))))) <=> (host(Y0!8) = host(V0!7)))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7))))),
% 0.39/0.57      inference(transitivity,[status(thm)],[252, 250])).
% 0.39/0.57  tff(254,plain,
% 0.39/0.57      ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(Y0!8), host(V0!7))) | (~leq(host(V0!7), host(Y0!8))))) <=> (host(Y0!8) = host(V0!7)))),
% 0.39/0.57      inference(quant_inst,[status(thm)],[])).
% 0.39/0.57  tff(255,plain,
% 0.39/0.57      ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7)))),
% 0.39/0.57      inference(modus_ponens,[status(thm)],[254, 253])).
% 0.39/0.57  tff(256,plain,
% 0.39/0.57      ($false),
% 0.39/0.57      inference(unit_resolution,[status(thm)],[255, 22, 249])).
% 0.39/0.57  % SZS output end Proof
%------------------------------------------------------------------------------