TSTP Solution File: SWV480+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV480+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 15:17:44 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV480+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 03:50:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(host_type, type, (
% 0.19/0.43 host: $i > $i)).
% 0.19/0.43 tff(tptp_fun_V0_7_type, type, (
% 0.19/0.43 tptp_fun_V0_7: $i)).
% 0.19/0.43 tff(tptp_fun_Y0_8_type, type, (
% 0.19/0.43 tptp_fun_Y0_8: $i)).
% 0.19/0.43 tff(leq_type, type, (
% 0.19/0.43 leq: ( $i * $i ) > $o)).
% 0.19/0.43 tff(s_type, type, (
% 0.19/0.43 s: $i > $i)).
% 0.19/0.43 tff(nbr_proc_type, type, (
% 0.19/0.43 nbr_proc: $i)).
% 0.19/0.43 tff(tptp_fun_X_4_type, type, (
% 0.19/0.43 tptp_fun_X_4: $i)).
% 0.19/0.43 tff(tptp_fun_W0_10_type, type, (
% 0.19/0.43 tptp_fun_W0_10: $i)).
% 0.19/0.43 tff(cons_type, type, (
% 0.19/0.43 cons: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_V_5_type, type, (
% 0.19/0.43 tptp_fun_V_5: $i)).
% 0.19/0.43 tff(m_Down_type, type, (
% 0.19/0.43 m_Down: $i > $i)).
% 0.19/0.43 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.43 tptp_fun_Y_3: $i)).
% 0.19/0.43 tff(queue_type, type, (
% 0.19/0.43 queue: $i > $i)).
% 0.19/0.43 tff(elem_type, type, (
% 0.19/0.43 elem: ( $i * $i ) > $o)).
% 0.19/0.43 tff(elec_1_type, type, (
% 0.19/0.43 elec_1: $i)).
% 0.19/0.43 tff(index_type, type, (
% 0.19/0.43 index: ( $i * $i ) > $i)).
% 0.19/0.43 tff(status_type, type, (
% 0.19/0.43 status: $i)).
% 0.19/0.43 tff(tptp_fun_V0_11_type, type, (
% 0.19/0.43 tptp_fun_V0_11: ( $i * $i ) > $i)).
% 0.19/0.43 tff(zero_type, type, (
% 0.19/0.43 zero: $i)).
% 0.19/0.43 tff(setIn_type, type, (
% 0.19/0.43 setIn: ( $i * $i ) > $o)).
% 0.19/0.43 tff(down_type, type, (
% 0.19/0.43 down: $i)).
% 0.19/0.43 tff(norm_type, type, (
% 0.19/0.43 norm: $i)).
% 0.19/0.43 tff(ldr_type, type, (
% 0.19/0.43 ldr: $i)).
% 0.19/0.43 tff(alive_type, type, (
% 0.19/0.43 alive: $i)).
% 0.19/0.43 tff(elec_2_type, type, (
% 0.19/0.43 elec_2: $i)).
% 0.19/0.43 tff(m_Ack_type, type, (
% 0.19/0.43 m_Ack: ( $i * $i ) > $i)).
% 0.19/0.43 tff(elid_type, type, (
% 0.19/0.43 elid: $i)).
% 0.19/0.43 tff(wait_type, type, (
% 0.19/0.43 wait: $i)).
% 0.19/0.43 tff(pendack_type, type, (
% 0.19/0.43 pendack: $i)).
% 0.19/0.43 tff(m_Ldr_type, type, (
% 0.19/0.43 m_Ldr: $i > $i)).
% 0.19/0.43 tff(tptp_fun_X0_9_type, type, (
% 0.19/0.43 tptp_fun_X0_9: $i)).
% 0.19/0.43 tff(acks_type, type, (
% 0.19/0.43 acks: $i)).
% 0.19/0.43 tff(tptp_fun_Z_6_type, type, (
% 0.19/0.43 tptp_fun_Z_6: $i)).
% 0.19/0.43 tff(1,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.43 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')).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.43 tff(9,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[8])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 ((~![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)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl(((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 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')).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.44 tff(20,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.19/0.44 inference(skolemize,[status(sab)],[19])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) <=> (s(host(Y0!8)) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) <=> (s(host(Y0!8)) = nbr_proc)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 (((~((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8)))))) <=> (s(host(Y0!8)) = nbr_proc)) <=> ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) <=> (s(host(Y0!8)) = nbr_proc))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (((~![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))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) <=> (s(host(Y0!8)) = nbr_proc)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (((~![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))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) <=> (s(host(Y0!8)) = nbr_proc)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[25, 23])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 ((~![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))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) <=> (s(host(Y0!8)) = nbr_proc))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) <=> (s(host(Y0!8)) = nbr_proc)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 ((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)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & 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)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & 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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 ((![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 ((~(~((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))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 ((~(~leq(nbr_proc, index(pendack, host(X!4))))) <=> leq(nbr_proc, index(pendack, host(X!4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (((~setIn(host(Z!6), index(acks, host(X!4)))) & ((host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> ((~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (((host(X!4) = host(V0!7)) & (setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> ((host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> (setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 ((![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 ((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) <=> (setIn(V0!7, alive) & (host(X!4) = host(V0!7)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> ((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[38, 37])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> (setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.46 inference(transitivity,[status(thm)],[39, 36])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 ((~(~(host(X!4) = host(V0!7)))) <=> (host(X!4) = host(V0!7))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (((~(~(host(X!4) = host(V0!7)))) & ((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))) <=> ((host(X!4) = host(V0!7)) & (setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[41, 40])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (((~(~(host(X!4) = host(V0!7)))) & ((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))) <=> ((host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.46 inference(transitivity,[status(thm)],[42, 35])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (((~setIn(host(Z!6), index(acks, host(X!4)))) & ((~(~(host(X!4) = host(V0!7)))) & ((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))))) <=> ((~setIn(host(Z!6), index(acks, host(X!4)))) & ((host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (((~setIn(host(Z!6), index(acks, host(X!4)))) & ((~(~(host(X!4) = host(V0!7)))) & ((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))))) <=> ((~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.46 inference(transitivity,[status(thm)],[44, 34])).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 ((~(~setIn(X!4, alive))) <=> setIn(X!4, alive)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 ((~(~leq(host(X!4), host(Y!3)))) <=> leq(host(X!4), host(Y!3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 (((~(~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)))) & ((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))))) & (~(~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)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & 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))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[47, 46, 45, 33, 32, 31])).
% 0.19/0.46 tff(49,plain,
% 0.19/0.46 (((~(~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)))) & ((~(~(setIn(V0!7, alive) & (host(X!4) = host(V0!7))))) & (~(host(X!4) = host(Y0!8))) & (![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))))) & (~(~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)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & 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)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[48, 30])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 ((~![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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 ((~![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(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), queue(host(Y0)))) & elem(m_Down(X0), queue(host(Y0)))) & (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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(52,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(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), queue(host(Y0)))) & elem(m_Down(X0), queue(host(Y0)))) & (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')).
% 0.19/0.48 tff(53,plain,
% 0.19/0.48 (~![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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 (~![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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.19/0.49 tff(55,plain,
% 0.19/0.49 (~![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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 (~![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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[55, 50])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (~![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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[56, 50])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 (~![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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.49 tff(59,plain,
% 0.19/0.49 (~![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] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![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), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[58, 50])).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 (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)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![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), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & 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))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.19/0.50 tff(61,plain,
% 0.19/0.50 (host(W0!10) = s(host(Y0!8))),
% 0.19/0.50 inference(and_elim,[status(thm)],[60])).
% 0.19/0.50 tff(62,plain,
% 0.19/0.50 (s(host(Y0!8)) = host(W0!10)),
% 0.19/0.50 inference(symmetry,[status(thm)],[61])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 (leq(s(host(Y0!8)), nbr_proc) <=> leq(host(W0!10), nbr_proc)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.50 tff(64,plain,
% 0.19/0.50 (leq(host(W0!10), nbr_proc) <=> leq(s(host(Y0!8)), nbr_proc)),
% 0.19/0.50 inference(symmetry,[status(thm)],[63])).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(68,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 (![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.50 tff(70,plain,(
% 0.19/0.50 ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.50 inference(skolemize,[status(sab)],[69])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(W0!10), nbr_proc)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 (leq(host(W0!10), nbr_proc)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 (leq(s(host(Y0!8)), nbr_proc)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[73, 64])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (leq(nbr_proc, s(host(Y0!8)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[60])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) | (~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) | (~leq(s(host(Y0!8)), nbr_proc))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.50 tff(78,plain,
% 0.19/0.50 (~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.19/0.50 tff(79,plain,
% 0.19/0.50 ((~((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) <=> (s(host(Y0!8)) = nbr_proc))) | ((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) | (s(host(Y0!8)) = nbr_proc)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(80,plain,
% 0.19/0.50 (s(host(Y0!8)) = nbr_proc),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[79, 78, 29])).
% 0.19/0.50 tff(81,plain,
% 0.19/0.50 (host(X!4) = host(V0!7)),
% 0.19/0.50 inference(and_elim,[status(thm)],[60])).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (host(V0!7) = host(X!4)),
% 0.19/0.50 inference(symmetry,[status(thm)],[81])).
% 0.19/0.50 tff(83,plain,
% 0.19/0.50 (leq(host(V0!7), s(host(Y0!8))) <=> leq(host(X!4), nbr_proc)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[82, 80])).
% 0.19/0.50 tff(84,plain,
% 0.19/0.50 (leq(host(X!4), nbr_proc) <=> leq(host(V0!7), s(host(Y0!8)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[83])).
% 0.19/0.50 tff(85,plain,
% 0.19/0.50 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X!4), nbr_proc)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(86,plain,
% 0.19/0.50 (leq(host(X!4), nbr_proc)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[85, 71])).
% 0.19/0.50 tff(87,plain,
% 0.19/0.50 (leq(host(V0!7), s(host(Y0!8)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[86, 84])).
% 0.19/0.50 tff(88,plain,
% 0.19/0.50 ((~(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))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(89,plain,
% 0.19/0.50 ((~(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))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.50 tff(90,plain,
% 0.19/0.50 (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[89, 12])).
% 0.19/0.50 tff(91,plain,
% 0.19/0.50 ((host(V0!7) = s(host(Y0!8))) <=> (host(X!4) = host(W0!10))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[82, 62])).
% 0.19/0.50 tff(92,plain,
% 0.19/0.50 ((host(X!4) = host(W0!10)) <=> (host(V0!7) = s(host(Y0!8)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[91])).
% 0.19/0.50 tff(93,plain,
% 0.19/0.50 ((~(host(X!4) = host(W0!10))) <=> (~(host(V0!7) = s(host(Y0!8))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.50 tff(94,plain,
% 0.19/0.50 (nbr_proc = s(host(Y0!8))),
% 0.19/0.50 inference(symmetry,[status(thm)],[80])).
% 0.19/0.50 tff(95,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(96,plain,
% 0.19/0.50 (((~((~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))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(97,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[96])).
% 0.19/0.50 tff(98,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[97, 95])).
% 0.19/0.50 tff(99,plain,
% 0.19/0.50 ((~![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))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(100,plain,
% 0.19/0.50 ((~![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))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.50 tff(101,plain,
% 0.19/0.50 ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[100, 22])).
% 0.19/0.50 tff(102,plain,
% 0.19/0.50 (host(Y!3) = index(pendack, host(X!4))),
% 0.19/0.50 inference(and_elim,[status(thm)],[60])).
% 0.19/0.50 tff(103,plain,
% 0.19/0.50 (index(pendack, host(X!4)) = host(Y!3)),
% 0.19/0.50 inference(symmetry,[status(thm)],[102])).
% 0.19/0.50 tff(104,plain,
% 0.19/0.50 (leq(index(pendack, host(X!4)), nbr_proc) <=> leq(host(Y!3), nbr_proc)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.50 tff(105,plain,
% 0.19/0.50 (leq(host(Y!3), nbr_proc) <=> leq(index(pendack, host(X!4)), nbr_proc)),
% 0.19/0.50 inference(symmetry,[status(thm)],[104])).
% 0.19/0.50 tff(106,plain,
% 0.19/0.50 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(Y!3), nbr_proc)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(107,plain,
% 0.19/0.50 (leq(host(Y!3), nbr_proc)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[106, 71])).
% 0.19/0.50 tff(108,plain,
% 0.19/0.50 (leq(index(pendack, host(X!4)), nbr_proc)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[107, 105])).
% 0.19/0.50 tff(109,plain,
% 0.19/0.50 (leq(nbr_proc, index(pendack, host(X!4)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[60])).
% 0.19/0.50 tff(110,plain,
% 0.19/0.50 ((~((~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))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(111,plain,
% 0.19/0.50 ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) | (~leq(index(pendack, host(X!4)), nbr_proc))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.50 tff(112,plain,
% 0.19/0.50 (~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.19/0.50 tff(113,plain,
% 0.19/0.50 ((~((~((~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)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(114,plain,
% 0.19/0.50 (index(pendack, host(X!4)) = nbr_proc),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[113, 112, 101])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 (index(pendack, host(X!4)) = s(host(Y0!8))),
% 0.19/0.50 inference(transitivity,[status(thm)],[114, 94])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 (leq(index(pendack, host(X!4)), host(Y0!8)) <=> leq(s(host(Y0!8)), host(Y0!8))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 (leq(s(host(Y0!8)), host(Y0!8)) <=> leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.19/0.50 inference(symmetry,[status(thm)],[116])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 ((~leq(s(host(Y0!8)), host(Y0!8))) <=> (~leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 (^[X: $i] : refl((~leq(s(X), X)) <=> (~leq(s(X), X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(122,axiom,(![X: $i] : (~leq(s(X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_58')).
% 0.19/0.50 tff(123,plain,
% 0.19/0.50 (![X: $i] : (~leq(s(X), X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.50 tff(124,plain,(
% 0.19/0.50 ![X: $i] : (~leq(s(X), X))),
% 0.19/0.50 inference(skolemize,[status(sab)],[123])).
% 0.19/0.50 tff(125,plain,
% 0.19/0.50 (![X: $i] : (~leq(s(X), X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.19/0.50 tff(126,plain,
% 0.19/0.50 ((~![X: $i] : (~leq(s(X), X))) | (~leq(s(host(Y0!8)), host(Y0!8)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(127,plain,
% 0.19/0.50 (~leq(s(host(Y0!8)), host(Y0!8))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.50 tff(128,plain,
% 0.19/0.50 (~leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[127, 118])).
% 0.19/0.50 tff(129,plain,
% 0.19/0.50 (^[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))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(130,plain,
% 0.19/0.50 (![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)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.50 tff(131,plain,
% 0.19/0.50 (^[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)))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(132,plain,
% 0.19/0.50 (![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)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.50 tff(133,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[60])).
% 0.19/0.50 tff(134,plain,
% 0.19/0.50 (![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)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 (![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)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.19/0.50 tff(136,plain,
% 0.19/0.50 (index(status, host(X!4)) = elec_2),
% 0.19/0.50 inference(and_elim,[status(thm)],[60])).
% 0.19/0.51 tff(137,plain,
% 0.19/0.51 (elem(m_Down(W0!10), queue(host(Y0!8)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[60])).
% 0.19/0.51 tff(138,plain,
% 0.19/0.51 (setIn(Y0!8, alive)),
% 0.19/0.51 inference(and_elim,[status(thm)],[60])).
% 0.19/0.51 tff(139,plain,
% 0.19/0.51 (setIn(X!4, alive)),
% 0.19/0.51 inference(and_elim,[status(thm)],[60])).
% 0.19/0.51 tff(140,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(141,plain,
% 0.19/0.51 (((~(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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(142,plain,
% 0.19/0.51 (((~![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))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[141])).
% 0.19/0.51 tff(143,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[142, 140])).
% 0.19/0.51 tff(144,plain,
% 0.19/0.51 ((~![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)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(145,plain,
% 0.19/0.51 ((~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.51 tff(146,plain,
% 0.19/0.51 ((~(host(X!4) = host(W0!10))) | leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[145, 139, 138, 137, 136, 135])).
% 0.19/0.51 tff(147,plain,
% 0.19/0.51 (~(host(X!4) = host(W0!10))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[146, 128])).
% 0.19/0.51 tff(148,plain,
% 0.19/0.51 (~(host(V0!7) = s(host(Y0!8)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[147, 93])).
% 0.19/0.51 tff(149,plain,
% 0.19/0.51 ((~(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)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(150,plain,
% 0.19/0.51 (leq(host(V0!7), host(Y0!8))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[149, 148, 90])).
% 0.19/0.51 tff(151,plain,
% 0.19/0.51 (leq(s(zero), host(V0!7)) <=> leq(s(zero), host(X!4))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.51 tff(152,plain,
% 0.19/0.51 (leq(s(zero), host(X!4)) <=> leq(s(zero), host(V0!7))),
% 0.19/0.51 inference(symmetry,[status(thm)],[151])).
% 0.19/0.51 tff(153,plain,
% 0.19/0.51 (^[P: $i] : refl(leq(s(zero), host(P)) <=> leq(s(zero), host(P)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(154,plain,
% 0.19/0.51 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.51 tff(155,plain,
% 0.19/0.51 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(156,axiom,(![P: $i] : leq(s(zero), host(P))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_02')).
% 0.19/0.51 tff(157,plain,
% 0.19/0.51 (![P: $i] : leq(s(zero), host(P))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.51 tff(158,plain,(
% 0.19/0.51 ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.51 inference(skolemize,[status(sab)],[157])).
% 0.19/0.51 tff(159,plain,
% 0.19/0.51 (![P: $i] : leq(s(zero), host(P))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.19/0.51 tff(160,plain,
% 0.19/0.51 ((~![P: $i] : leq(s(zero), host(P))) | leq(s(zero), host(X!4))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(161,plain,
% 0.19/0.51 (leq(s(zero), host(X!4))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.51 tff(162,plain,
% 0.19/0.51 (leq(s(zero), host(V0!7))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[161, 152])).
% 0.19/0.51 tff(163,plain,
% 0.19/0.51 (setIn(host(X!4), index(down, host(Y0!8))) <=> setIn(host(V0!7), index(down, host(Y0!8)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.51 tff(164,plain,
% 0.19/0.51 ((~setIn(host(X!4), index(down, host(Y0!8)))) <=> (~setIn(host(V0!7), index(down, host(Y0!8))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[163])).
% 0.19/0.51 tff(165,plain,
% 0.19/0.51 (^[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))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(166,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[165])).
% 0.19/0.51 tff(167,plain,
% 0.19/0.51 (^[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)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(168,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[167])).
% 0.19/0.51 tff(169,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[60])).
% 0.19/0.51 tff(170,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.51 tff(171,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.19/0.51 tff(172,plain,
% 0.19/0.51 (((~![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)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(173,plain,
% 0.19/0.51 (((~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)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(174,plain,
% 0.19/0.51 (((~![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))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[173])).
% 0.19/0.51 tff(175,plain,
% 0.19/0.51 (((~![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)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[174, 172])).
% 0.19/0.51 tff(176,plain,
% 0.19/0.51 ((~![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)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(177,plain,
% 0.19/0.51 ((~![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))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.51 tff(178,plain,
% 0.19/0.51 (leq(index(pendack, host(X!4)), host(Y0!8)) | (~setIn(host(X!4), index(down, host(Y0!8))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[177, 139, 138, 136, 171])).
% 0.19/0.51 tff(179,plain,
% 0.19/0.51 (~setIn(host(X!4), index(down, host(Y0!8)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[178, 128])).
% 0.19/0.51 tff(180,plain,
% 0.19/0.51 (~setIn(host(V0!7), index(down, host(Y0!8)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[179, 164])).
% 0.19/0.51 tff(181,plain,
% 0.19/0.51 ((host(X!4) = host(X0!9)) <=> (host(V0!7) = host(X0!9))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.51 tff(182,plain,
% 0.19/0.51 ((~(host(X!4) = host(X0!9))) <=> (~(host(V0!7) = host(X0!9)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[181])).
% 0.19/0.51 tff(183,plain,
% 0.19/0.51 (elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[60])).
% 0.19/0.51 tff(184,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(185,plain,
% 0.19/0.51 (((~(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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(186,plain,
% 0.19/0.51 (((~![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))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[185])).
% 0.19/0.51 tff(187,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[186, 184])).
% 0.19/0.51 tff(188,plain,
% 0.19/0.51 ((~![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)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(189,plain,
% 0.19/0.51 ((~![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))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.19/0.52 tff(190,plain,
% 0.19/0.52 ((~(host(X!4) = host(X0!9))) | leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[189, 139, 138, 183, 136, 135])).
% 0.19/0.52 tff(191,plain,
% 0.19/0.52 (~(host(X!4) = host(X0!9))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[190, 128])).
% 0.19/0.52 tff(192,plain,
% 0.19/0.52 (~(host(V0!7) = host(X0!9))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[191, 182])).
% 0.19/0.52 tff(193,plain,
% 0.19/0.52 (^[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))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(194,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.52 tff(195,plain,
% 0.19/0.52 (^[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)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(196,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[195])).
% 0.19/0.52 tff(197,plain,
% 0.19/0.52 (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1))))),
% 0.19/0.52 inference(and_elim,[status(thm)],[60])).
% 0.19/0.52 tff(198,plain,
% 0.19/0.52 (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.52 tff(199,plain,
% 0.19/0.52 (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.19/0.52 tff(200,plain,
% 0.19/0.52 (((~![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))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(201,plain,
% 0.19/0.52 (((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))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(202,plain,
% 0.19/0.52 (((~![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)))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[201])).
% 0.19/0.52 tff(203,plain,
% 0.19/0.52 (((~![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))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[202, 200])).
% 0.19/0.52 tff(204,plain,
% 0.19/0.52 ((~![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))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(205,plain,
% 0.19/0.52 ((~![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)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.52 tff(206,plain,
% 0.19/0.52 (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)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[205, 199])).
% 0.19/0.52 tff(207,plain,
% 0.19/0.52 (leq(host(Y0!8), host(V0!7))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[206, 192, 180, 162])).
% 0.19/0.52 tff(208,plain,
% 0.19/0.52 ((~((~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)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(209,plain,
% 0.19/0.52 (~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[208, 207, 150])).
% 0.19/0.52 tff(210,plain,
% 0.19/0.52 ((host(Y0!8) = host(X!4)) <=> (host(X!4) = host(Y0!8))),
% 0.19/0.52 inference(commutativity,[status(thm)],[])).
% 0.19/0.52 tff(211,plain,
% 0.19/0.52 ((host(Y0!8) = host(V0!7)) <=> (host(Y0!8) = host(X!4))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.52 tff(212,plain,
% 0.19/0.52 ((host(Y0!8) = host(V0!7)) <=> (host(X!4) = host(Y0!8))),
% 0.19/0.52 inference(transitivity,[status(thm)],[211, 210])).
% 0.19/0.52 tff(213,plain,
% 0.19/0.52 ((host(X!4) = host(Y0!8)) <=> (host(Y0!8) = host(V0!7))),
% 0.19/0.52 inference(symmetry,[status(thm)],[212])).
% 0.19/0.52 tff(214,plain,
% 0.19/0.52 ((~(host(X!4) = host(Y0!8))) <=> (~(host(Y0!8) = host(V0!7)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[213])).
% 0.19/0.52 tff(215,plain,
% 0.19/0.52 (~(host(X!4) = host(Y0!8))),
% 0.19/0.52 inference(and_elim,[status(thm)],[60])).
% 0.19/0.52 tff(216,plain,
% 0.19/0.52 (~(host(Y0!8) = host(V0!7))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.19/0.52 tff(217,plain,
% 0.19/0.52 ((~((~((~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))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(218,plain,
% 0.19/0.52 (~((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[217, 216, 209])).
% 0.19/0.52 tff(219,plain,
% 0.19/0.52 (((~![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))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(220,plain,
% 0.19/0.52 (((~((~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)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(221,plain,
% 0.19/0.52 (((~![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))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[220])).
% 0.19/0.52 tff(222,plain,
% 0.19/0.52 (((~![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))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[221, 219])).
% 0.19/0.52 tff(223,plain,
% 0.19/0.52 ((~![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)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(224,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) <=> (host(Y0!8) = host(V0!7)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.19/0.52 tff(225,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[224, 22, 218])).
% 0.19/0.52 % SZS output end Proof
%------------------------------------------------------------------------------