TSTP Solution File: SWV475+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV475+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:17:43 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV475+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 04:14:53 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.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(host_type, type, (
% 0.19/0.44 host: $i > $i)).
% 0.19/0.44 tff(tptp_fun_V0_8_type, type, (
% 0.19/0.44 tptp_fun_V0_8: $i)).
% 0.19/0.44 tff(tptp_fun_Y0_9_type, type, (
% 0.19/0.44 tptp_fun_Y0_9: $i)).
% 0.19/0.44 tff(leq_type, type, (
% 0.19/0.44 leq: ( $i * $i ) > $o)).
% 0.19/0.44 tff(s_type, type, (
% 0.19/0.44 s: $i > $i)).
% 0.19/0.44 tff(nbr_proc_type, type, (
% 0.19/0.44 nbr_proc: $i)).
% 0.19/0.44 tff(tptp_fun_X_4_type, type, (
% 0.19/0.44 tptp_fun_X_4: $i)).
% 0.19/0.44 tff(tptp_fun_W0_11_type, type, (
% 0.19/0.44 tptp_fun_W0_11: $i)).
% 0.19/0.44 tff(cons_type, type, (
% 0.19/0.44 cons: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_V_6_type, type, (
% 0.19/0.44 tptp_fun_V_6: $i)).
% 0.19/0.44 tff(m_Ack_type, type, (
% 0.19/0.44 m_Ack: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.44 tptp_fun_Y_3: $i)).
% 0.19/0.44 tff(tptp_fun_W_5_type, type, (
% 0.19/0.44 tptp_fun_W_5: $i)).
% 0.19/0.44 tff(queue_type, type, (
% 0.19/0.44 queue: $i > $i)).
% 0.19/0.44 tff(elem_type, type, (
% 0.19/0.44 elem: ( $i * $i ) > $o)).
% 0.19/0.44 tff(m_Down_type, type, (
% 0.19/0.44 m_Down: $i > $i)).
% 0.19/0.44 tff(elec_1_type, type, (
% 0.19/0.44 elec_1: $i)).
% 0.19/0.44 tff(index_type, type, (
% 0.19/0.44 index: ( $i * $i ) > $i)).
% 0.19/0.44 tff(status_type, type, (
% 0.19/0.44 status: $i)).
% 0.19/0.44 tff(tptp_fun_V0_12_type, type, (
% 0.19/0.44 tptp_fun_V0_12: ( $i * $i ) > $i)).
% 0.19/0.44 tff(zero_type, type, (
% 0.19/0.44 zero: $i)).
% 0.19/0.44 tff(setIn_type, type, (
% 0.19/0.44 setIn: ( $i * $i ) > $o)).
% 0.19/0.44 tff(down_type, type, (
% 0.19/0.44 down: $i)).
% 0.19/0.44 tff(norm_type, type, (
% 0.19/0.44 norm: $i)).
% 0.19/0.44 tff(ldr_type, type, (
% 0.19/0.44 ldr: $i)).
% 0.19/0.44 tff(alive_type, type, (
% 0.19/0.44 alive: $i)).
% 0.19/0.44 tff(elec_2_type, type, (
% 0.19/0.44 elec_2: $i)).
% 0.19/0.44 tff(elid_type, type, (
% 0.19/0.44 elid: $i)).
% 0.19/0.44 tff(wait_type, type, (
% 0.19/0.44 wait: $i)).
% 0.19/0.44 tff(pendack_type, type, (
% 0.19/0.44 pendack: $i)).
% 0.19/0.44 tff(m_Ldr_type, type, (
% 0.19/0.44 m_Ldr: $i > $i)).
% 0.19/0.44 tff(tptp_fun_Z_7_type, type, (
% 0.19/0.44 tptp_fun_Z_7: $i)).
% 0.19/0.44 tff(snoc_type, type, (
% 0.19/0.44 snoc: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_X0_10_type, type, (
% 0.19/0.44 tptp_fun_X0_10: $i)).
% 0.19/0.44 tff(acks_type, type, (
% 0.19/0.44 acks: $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.44 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')).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.44 tff(9,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[8])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))) | (leq(host(V0!8), s(host(Y0!9))) <=> (leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (leq(host(V0!8), s(host(Y0!9))) <=> (leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : refl(((~((~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(14,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)],[13])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (^[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(s(host(Y0!9)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!9)))))) <=> (s(host(Y0!9)) = nbr_proc))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 ((~((~leq(s(host(Y0!9)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!9)))))) <=> (s(host(Y0!9)) = nbr_proc)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 ((setIn(X!4, alive) & (((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & (host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(elid, host(X!4)) = W!5) & (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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & ((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & (host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)) & leq(nbr_proc, index(pendack, host(X!4))) & (index(elid, host(X!4)) = W!5) & (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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(26,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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6))) <=> (![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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 ((~(~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))))) <=> ((index(elid, host(X!4)) = W!5) & (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(28,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(29,plain,
% 0.19/0.45 ((((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & ((host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)))) <=> (((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & (host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (((host(X!4) = host(V0!8)) & ((~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & (host(X!4) = host(V0!8)) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)))) <=> ((host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (((~(host(X!4) = host(Y0!9))) & (setIn(V0!8, alive) & (host(X!4) = host(V0!8))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (host(Z!7) = host(Y0!9))) <=> ((~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & (host(X!4) = host(V0!8)) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 ((~(~(host(Z!7) = host(Y0!9)))) <=> (host(Z!7) = host(Y0!9))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 ((![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) <=> (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 ((~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) <=> (setIn(V0!8, alive) & (host(X!4) = host(V0!8)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (((~(host(X!4) = host(Y0!9))) & (~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (~(~(host(Z!7) = host(Y0!9))))) <=> ((~(host(X!4) = host(Y0!9))) & (setIn(V0!8, alive) & (host(X!4) = host(V0!8))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (host(Z!7) = host(Y0!9)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[34, 33, 32])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (((~(host(X!4) = host(Y0!9))) & (~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (~(~(host(Z!7) = host(Y0!9))))) <=> ((~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & (host(X!4) = host(V0!8)) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[35, 31])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 ((~(~(host(X!4) = host(V0!8)))) <=> (host(X!4) = host(V0!8))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (((~(~(host(X!4) = host(V0!8)))) & ((~(host(X!4) = host(Y0!9))) & (~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (~(~(host(Z!7) = host(Y0!9)))))) <=> ((host(X!4) = host(V0!8)) & ((~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & (host(X!4) = host(V0!8)) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[37, 36])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (((~(~(host(X!4) = host(V0!8)))) & ((~(host(X!4) = host(Y0!9))) & (~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (~(~(host(Z!7) = host(Y0!9)))))) <=> ((host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[38, 30])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 ((~(~((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))))) <=> ((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (((~(~((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))))) & ((~(~(host(X!4) = host(V0!8)))) & ((~(host(X!4) = host(Y0!9))) & (~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (~(~(host(Z!7) = host(Y0!9))))))) <=> (((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & ((host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[40, 39])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (((~(~((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))))) & ((~(~(host(X!4) = host(V0!8)))) & ((~(host(X!4) = host(Y0!9))) & (~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (~(~(host(Z!7) = host(Y0!9))))))) <=> (((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & (host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[41, 29])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 ((~(~setIn(X!4, alive))) <=> setIn(X!4, alive)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (((~(~setIn(X!4, alive))) & ((~(~((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))))) & ((~(~(host(X!4) = host(V0!8)))) & ((~(host(X!4) = host(Y0!9))) & (~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (~(~(host(Z!7) = host(Y0!9))))))) & (~(~leq(nbr_proc, index(pendack, host(X!4))))) & (~(~((index(elid, host(X!4)) = W!5) & (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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & (((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & (host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(elid, host(X!4)) = W!5) & (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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[43, 42, 28, 27, 26])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (((~(~setIn(X!4, alive))) & ((~(~((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))))) & ((~(~(host(X!4) = host(V0!8)))) & ((~(host(X!4) = host(Y0!9))) & (~(~(setIn(V0!8, alive) & (host(X!4) = host(V0!8))))) & (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1)) & (~(~(host(Z!7) = host(Y0!9))))))) & (~(~leq(nbr_proc, index(pendack, host(X!4))))) & (~(~((index(elid, host(X!4)) = W!5) & (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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & ((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & (host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)) & leq(nbr_proc, index(pendack, host(X!4))) & (index(elid, host(X!4)) = W!5) & (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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[44, 25])).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 ((~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V)))))) <=> (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(47,plain,
% 0.19/0.48 ((~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & (host(Pid20) = host(Pid0))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))))) & ![Z: $i, Pid0: $i] : ((((((setIn(Z, alive) & setIn(Pid0, alive)) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm)) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (Pid0 = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & setIn(Z, alive)) & leq(host(Z), host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid30) = host(Pid0))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Z, Pid30), queue(host(Z)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & setIn(Pid0, alive)) & leq(nbr_proc, s(host(Pid0)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Down(Pid30), queue(host(Pid0)))) & (host(Pid30) = s(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((((index(elid, host(X)) = W) & (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))) | (host(Z) = host(Y))) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((host(Z) = host(Y0)) => ((~(host(X) = host(Y0))) => (((((((![V1: $i] : (((~leq(host(Y0), V1)) & leq(s(zero), V1)) => (setIn(V1, index(down, host(Y0))) | (V1 = host(X0)))) & setIn(Y0, alive)) & leq(nbr_proc, s(host(Y0)))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X)))) & (host(W0) = s(host(Y0)))) & (index(status, host(Y0)) = elec_1)) => (~(setIn(V0, alive) & (host(X) = host(V0)))))))))))))) <=> (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(48,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_Ack(W, Y), V))) => (setIn(X, alive) => ((((index(elid, host(X)) = W) & (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))) | (host(Z) = host(Y))) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((host(Z) = host(Y0)) => ((~(host(X) = host(Y0))) => (((((((![V1: $i] : (((~leq(host(Y0), V1)) & leq(s(zero), V1)) => (setIn(V1, index(down, host(Y0))) | (V1 = host(X0)))) & setIn(Y0, alive)) & leq(nbr_proc, s(host(Y0)))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X)))) & (host(W0) = s(host(Y0)))) & (index(status, host(Y0)) = elec_1)) => (~(setIn(V0, alive) & (host(X) = host(V0)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.19/0.49 tff(51,plain,
% 0.19/0.49 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[52, 46])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.50 tff(55,plain,
% 0.19/0.50 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(elid, host(X)) = W) & (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_Ack(W, Y), V)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[54, 46])).
% 0.19/0.51 tff(56,plain,
% 0.19/0.51 (setIn(X!4, alive) & ((host(Z!7) = host(Y!3)) | setIn(host(Z!7), index(acks, host(X!4)))) & (host(X!4) = host(V0!8)) & (~(host(X!4) = host(Y0!9))) & setIn(V0!8, alive) & ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) & setIn(Y0!9, alive) & leq(nbr_proc, s(host(Y0!9))) & elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) & (host(W0!11) = s(host(Y0!9))) & (index(status, host(Y0!9)) = elec_1) & (host(Z!7) = host(Y0!9)) & leq(nbr_proc, index(pendack, host(X!4))) & (index(elid, host(X!4)) = W!5) & (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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_12(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_12(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_12(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_12(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_Ack(W!5, Y!3), V!6))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.19/0.51 tff(57,plain,
% 0.19/0.51 (host(W0!11) = s(host(Y0!9))),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.51 tff(58,plain,
% 0.19/0.51 (s(host(Y0!9)) = host(W0!11)),
% 0.19/0.51 inference(symmetry,[status(thm)],[57])).
% 0.19/0.51 tff(59,plain,
% 0.19/0.51 (leq(s(host(Y0!9)), nbr_proc) <=> leq(host(W0!11), nbr_proc)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.51 tff(60,plain,
% 0.19/0.51 (leq(host(W0!11), nbr_proc) <=> leq(s(host(Y0!9)), nbr_proc)),
% 0.19/0.51 inference(symmetry,[status(thm)],[59])).
% 0.19/0.51 tff(61,plain,
% 0.19/0.51 (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(62,plain,
% 0.19/0.51 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.51 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.51 tff(63,plain,
% 0.19/0.51 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(64,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 0.19/0.51 tff(65,plain,
% 0.19/0.51 (![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.51 tff(66,plain,(
% 0.19/0.51 ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.51 inference(skolemize,[status(sab)],[65])).
% 0.19/0.51 tff(67,plain,
% 0.19/0.51 (![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.51 tff(68,plain,
% 0.19/0.51 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(W0!11), nbr_proc)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(69,plain,
% 0.19/0.51 (leq(host(W0!11), nbr_proc)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.51 tff(70,plain,
% 0.19/0.51 (leq(s(host(Y0!9)), nbr_proc)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[69, 60])).
% 0.19/0.51 tff(71,plain,
% 0.19/0.51 (leq(nbr_proc, s(host(Y0!9)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.51 tff(72,plain,
% 0.19/0.51 ((~((~leq(s(host(Y0!9)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!9)))))) | (~leq(s(host(Y0!9)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!9))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(73,plain,
% 0.19/0.51 ((~((~leq(s(host(Y0!9)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!9)))))) | (~leq(s(host(Y0!9)), nbr_proc))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.51 tff(74,plain,
% 0.19/0.51 (~((~leq(s(host(Y0!9)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!9)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.19/0.51 tff(75,plain,
% 0.19/0.51 ((~((~((~leq(s(host(Y0!9)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!9)))))) <=> (s(host(Y0!9)) = nbr_proc))) | ((~leq(s(host(Y0!9)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!9))))) | (s(host(Y0!9)) = nbr_proc)),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(76,plain,
% 0.19/0.51 (s(host(Y0!9)) = nbr_proc),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[75, 74, 24])).
% 0.19/0.51 tff(77,plain,
% 0.19/0.51 (host(X!4) = host(V0!8)),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.51 tff(78,plain,
% 0.19/0.51 (host(V0!8) = host(X!4)),
% 0.19/0.51 inference(symmetry,[status(thm)],[77])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 (leq(host(V0!8), s(host(Y0!9))) <=> leq(host(X!4), nbr_proc)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[78, 76])).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 (leq(host(X!4), nbr_proc) <=> leq(host(V0!8), s(host(Y0!9)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[79])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X!4), nbr_proc)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 (leq(host(X!4), nbr_proc)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[81, 67])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (leq(host(V0!8), s(host(Y0!9)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[82, 80])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 ((~(leq(host(V0!8), s(host(Y0!9))) <=> (leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9)))))) | (~leq(host(V0!8), s(host(Y0!9)))) | (leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(85,plain,
% 0.19/0.51 ((~(leq(host(V0!8), s(host(Y0!9))) <=> (leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9)))))) | (leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.51 tff(86,plain,
% 0.19/0.51 (leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[85, 12])).
% 0.19/0.51 tff(87,plain,
% 0.19/0.51 ((host(V0!8) = s(host(Y0!9))) <=> (host(X!4) = host(W0!11))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[78, 58])).
% 0.19/0.51 tff(88,plain,
% 0.19/0.51 ((host(X!4) = host(W0!11)) <=> (host(V0!8) = s(host(Y0!9)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[87])).
% 0.19/0.51 tff(89,plain,
% 0.19/0.51 (index(status, host(X!4)) = elec_2),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.51 tff(90,plain,
% 0.19/0.51 (((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2)) | (~(index(status, host(X!4)) = elec_2))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(91,plain,
% 0.19/0.51 ((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.19/0.51 tff(92,plain,
% 0.19/0.51 (^[Z: $i] : refl(((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))) <=> ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(93,plain,
% 0.19/0.51 (![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))) <=> ![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.51 tff(94,plain,
% 0.19/0.51 (^[Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) <=> (~((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))), ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) <=> (~(~((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))))), rewrite((~(~((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))) <=> ((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))), ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) <=> ((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))), (((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) <=> (((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))) | (index(elid, host(Z)) = Z)))), rewrite((((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))) | (index(elid, host(Z)) = Z)) <=> ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))), (((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) <=> ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(95,plain,
% 0.19/0.51 (![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) <=> ![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.51 tff(96,plain,
% 0.19/0.51 (![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.51 tff(97,plain,
% 0.19/0.51 (![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.51 tff(98,plain,
% 0.19/0.51 (![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.51 tff(99,plain,
% 0.19/0.51 (setIn(X!4, alive)),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.51 tff(100,plain,
% 0.19/0.51 (((~![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))) | ((~setIn(X!4, alive)) | (index(elid, host(X!4)) = X!4) | (~((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2))))) <=> ((~![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))) | (~setIn(X!4, alive)) | (index(elid, host(X!4)) = X!4) | (~((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(101,plain,
% 0.19/0.51 ((~![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))) | ((~setIn(X!4, alive)) | (index(elid, host(X!4)) = X!4) | (~((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(102,plain,
% 0.19/0.51 ((~![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))) | (~setIn(X!4, alive)) | (index(elid, host(X!4)) = X!4) | (~((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.51 tff(103,plain,
% 0.19/0.51 (index(elid, host(X!4)) = X!4),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[102, 99, 98, 91])).
% 0.19/0.51 tff(104,plain,
% 0.19/0.51 (index(elid, host(X!4)) = W!5),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.51 tff(105,plain,
% 0.19/0.51 (W!5 = index(elid, host(X!4))),
% 0.19/0.51 inference(symmetry,[status(thm)],[104])).
% 0.19/0.51 tff(106,plain,
% 0.19/0.51 (W!5 = X!4),
% 0.19/0.51 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.51 tff(107,plain,
% 0.19/0.51 (host(W!5) = host(X!4)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.51 tff(108,plain,
% 0.19/0.51 ((host(W!5) = host(W0!11)) <=> (host(X!4) = host(W0!11))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.51 tff(109,plain,
% 0.19/0.51 ((host(W!5) = host(W0!11)) <=> (host(V0!8) = s(host(Y0!9)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[108, 88])).
% 0.19/0.51 tff(110,plain,
% 0.19/0.51 ((~(host(W!5) = host(W0!11))) <=> (~(host(V0!8) = s(host(Y0!9))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.51 tff(111,plain,
% 0.19/0.51 (index(status, host(W!5)) = index(status, host(X!4))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.51 tff(112,plain,
% 0.19/0.51 (index(status, host(W!5)) = elec_2),
% 0.19/0.51 inference(transitivity,[status(thm)],[111, 89])).
% 0.19/0.51 tff(113,plain,
% 0.19/0.51 (nbr_proc = s(host(Y0!9))),
% 0.19/0.51 inference(symmetry,[status(thm)],[76])).
% 0.19/0.51 tff(114,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(115,plain,
% 0.19/0.51 (((~((~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))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(116,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.51 tff(117,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[116, 114])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 ((~![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))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(119,plain,
% 0.19/0.51 ((~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[119, 22])).
% 0.19/0.51 tff(121,plain,
% 0.19/0.51 (host(Y!3) = index(pendack, host(X!4))),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.51 tff(122,plain,
% 0.19/0.51 (index(pendack, host(X!4)) = host(Y!3)),
% 0.19/0.51 inference(symmetry,[status(thm)],[121])).
% 0.19/0.51 tff(123,plain,
% 0.19/0.51 (leq(index(pendack, host(X!4)), nbr_proc) <=> leq(host(Y!3), nbr_proc)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.51 tff(124,plain,
% 0.19/0.51 (leq(host(Y!3), nbr_proc) <=> leq(index(pendack, host(X!4)), nbr_proc)),
% 0.19/0.51 inference(symmetry,[status(thm)],[123])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(Y!3), nbr_proc)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 (leq(host(Y!3), nbr_proc)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[125, 67])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 (leq(index(pendack, host(X!4)), nbr_proc)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[126, 124])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 (leq(nbr_proc, index(pendack, host(X!4)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[56])).
% 0.19/0.52 tff(129,plain,
% 0.19/0.52 ((~((~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))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(130,plain,
% 0.19/0.52 ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) | (~leq(index(pendack, host(X!4)), nbr_proc))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.19/0.52 tff(131,plain,
% 0.19/0.52 (~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.19/0.52 tff(132,plain,
% 0.19/0.52 ((~((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) <=> (index(pendack, host(X!4)) = nbr_proc))) | ((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) | (index(pendack, host(X!4)) = nbr_proc)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(133,plain,
% 0.19/0.52 (index(pendack, host(X!4)) = nbr_proc),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[132, 131, 120])).
% 0.19/0.52 tff(134,plain,
% 0.19/0.52 (index(pendack, host(W!5)) = index(pendack, host(X!4))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.52 tff(135,plain,
% 0.19/0.52 (index(pendack, host(W!5)) = s(host(Y0!9))),
% 0.19/0.52 inference(transitivity,[status(thm)],[134, 133, 113])).
% 0.19/0.52 tff(136,plain,
% 0.19/0.52 (leq(index(pendack, host(W!5)), host(Y0!9)) <=> leq(s(host(Y0!9)), host(Y0!9))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 (leq(s(host(Y0!9)), host(Y0!9)) <=> leq(index(pendack, host(W!5)), host(Y0!9))),
% 0.19/0.52 inference(symmetry,[status(thm)],[136])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 ((~leq(s(host(Y0!9)), host(Y0!9))) <=> (~leq(index(pendack, host(W!5)), host(Y0!9)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.52 tff(139,plain,
% 0.19/0.52 (^[X: $i] : refl((~leq(s(X), X)) <=> (~leq(s(X), X)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(140,plain,
% 0.19/0.52 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[139])).
% 0.19/0.52 tff(141,plain,
% 0.19/0.52 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(142,axiom,(![X: $i] : (~leq(s(X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_58')).
% 0.19/0.52 tff(143,plain,
% 0.19/0.52 (![X: $i] : (~leq(s(X), X))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.52 tff(144,plain,(
% 0.19/0.52 ![X: $i] : (~leq(s(X), X))),
% 0.19/0.52 inference(skolemize,[status(sab)],[143])).
% 0.19/0.52 tff(145,plain,
% 0.19/0.52 (![X: $i] : (~leq(s(X), X))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.19/0.52 tff(146,plain,
% 0.19/0.52 ((~![X: $i] : (~leq(s(X), X))) | (~leq(s(host(Y0!9)), host(Y0!9)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(147,plain,
% 0.19/0.52 (~leq(s(host(Y0!9)), host(Y0!9))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.19/0.52 tff(148,plain,
% 0.19/0.52 (~leq(index(pendack, host(W!5)), host(Y0!9))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[147, 138])).
% 0.19/0.52 tff(149,plain,
% 0.19/0.52 (setIn(W!5, alive) <=> setIn(X!4, alive)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.52 tff(150,plain,
% 0.19/0.52 (setIn(X!4, alive) <=> setIn(W!5, alive)),
% 0.19/0.52 inference(symmetry,[status(thm)],[149])).
% 0.19/0.52 tff(151,plain,
% 0.19/0.52 (setIn(W!5, alive)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[99, 150])).
% 0.19/0.52 tff(152,plain,
% 0.19/0.52 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(153,plain,
% 0.19/0.52 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[152])).
% 0.19/0.52 tff(154,plain,
% 0.19/0.52 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(155,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 0.19/0.52 tff(156,plain,
% 0.19/0.52 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.52 tff(157,plain,(
% 0.19/0.52 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[156])).
% 0.19/0.52 tff(158,plain,
% 0.19/0.52 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.19/0.52 tff(159,plain,
% 0.19/0.52 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) <=> ((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9)))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(160,plain,
% 0.19/0.52 (elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) <=> ((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.52 tff(161,plain,
% 0.19/0.52 (elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[56])).
% 0.19/0.52 tff(162,plain,
% 0.19/0.52 ((~(elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) <=> ((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9)))))) | (~elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4)))) | ((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(163,plain,
% 0.19/0.52 ((~(elem(m_Down(W0!11), snoc(queue(host(Y0!9)), m_Ldr(X!4))) <=> ((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9)))))) | ((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.19/0.52 tff(164,plain,
% 0.19/0.52 ((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[163, 160])).
% 0.19/0.52 tff(165,plain,
% 0.19/0.52 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Ldr(Y))) <=> (~(m_Down(X) = m_Ldr(Y))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(166,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[165])).
% 0.19/0.52 tff(167,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(168,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_18')).
% 0.19/0.52 tff(169,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.52 tff(170,plain,(
% 0.19/0.52 ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[169])).
% 0.19/0.52 tff(171,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.19/0.52 tff(172,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))) | (~(m_Down(W0!11) = m_Ldr(X!4)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(173,plain,
% 0.19/0.52 (~(m_Down(W0!11) = m_Ldr(X!4))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.19/0.52 tff(174,plain,
% 0.19/0.52 ((~((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9))))) | (m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(175,plain,
% 0.19/0.52 ((~((m_Down(W0!11) = m_Ldr(X!4)) | elem(m_Down(W0!11), queue(host(Y0!9))))) | elem(m_Down(W0!11), queue(host(Y0!9)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.19/0.52 tff(176,plain,
% 0.19/0.52 (elem(m_Down(W0!11), queue(host(Y0!9)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[175, 164])).
% 0.19/0.52 tff(177,plain,
% 0.19/0.52 (^[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))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(178,plain,
% 0.19/0.52 (![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)))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[177])).
% 0.19/0.52 tff(179,plain,
% 0.19/0.52 (^[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)))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(180,plain,
% 0.19/0.52 (![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)))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.52 tff(181,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[56])).
% 0.19/0.52 tff(182,plain,
% 0.19/0.52 (![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)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.52 tff(183,plain,
% 0.19/0.52 (![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)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.19/0.52 tff(184,plain,
% 0.19/0.52 (setIn(Y0!9, alive)),
% 0.19/0.52 inference(and_elim,[status(thm)],[56])).
% 0.19/0.52 tff(185,plain,
% 0.19/0.52 (((~![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(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(W0!11))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)))) <=> ((~![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(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(W0!11))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(186,plain,
% 0.19/0.52 (((~(host(W!5) = host(W0!11))) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)) | (~setIn(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9))))) <=> ((~setIn(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(W0!11))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(187,plain,
% 0.19/0.52 (((~![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(W!5) = host(W0!11))) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)) | (~setIn(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))))) <=> ((~![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(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(W0!11))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[186])).
% 0.19/0.52 tff(188,plain,
% 0.19/0.52 (((~![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(W!5) = host(W0!11))) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)) | (~setIn(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))))) <=> ((~![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(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(W0!11))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[187, 185])).
% 0.19/0.52 tff(189,plain,
% 0.19/0.52 ((~![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(W!5) = host(W0!11))) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)) | (~setIn(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(190,plain,
% 0.19/0.52 ((~![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(Y0!9, alive)) | (~elem(m_Down(W0!11), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(W0!11))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.52 tff(191,plain,
% 0.19/0.52 ((~(host(W!5) = host(W0!11))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[190, 184, 183, 176, 151])).
% 0.19/0.52 tff(192,plain,
% 0.19/0.52 (~(host(W!5) = host(W0!11))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[191, 148, 112])).
% 0.19/0.52 tff(193,plain,
% 0.19/0.52 (~(host(V0!8) = s(host(Y0!9)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[192, 110])).
% 0.19/0.52 tff(194,plain,
% 0.19/0.52 ((~(leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9))))) | leq(host(V0!8), host(Y0!9)) | (host(V0!8) = s(host(Y0!9)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(195,plain,
% 0.19/0.52 (leq(host(V0!8), host(Y0!9))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[194, 193, 86])).
% 0.19/0.52 tff(196,plain,
% 0.19/0.52 (leq(s(zero), host(V0!8)) <=> leq(s(zero), host(X!4))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.52 tff(197,plain,
% 0.19/0.52 (leq(s(zero), host(X!4)) <=> leq(s(zero), host(V0!8))),
% 0.19/0.52 inference(symmetry,[status(thm)],[196])).
% 0.19/0.52 tff(198,plain,
% 0.19/0.52 (^[P: $i] : refl(leq(s(zero), host(P)) <=> leq(s(zero), host(P)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(199,plain,
% 0.19/0.52 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[198])).
% 0.19/0.52 tff(200,plain,
% 0.19/0.52 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(201,axiom,(![P: $i] : leq(s(zero), host(P))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_02')).
% 0.19/0.52 tff(202,plain,
% 0.19/0.52 (![P: $i] : leq(s(zero), host(P))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.52 tff(203,plain,(
% 0.19/0.52 ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.52 inference(skolemize,[status(sab)],[202])).
% 0.19/0.52 tff(204,plain,
% 0.19/0.52 (![P: $i] : leq(s(zero), host(P))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.19/0.52 tff(205,plain,
% 0.19/0.52 ((~![P: $i] : leq(s(zero), host(P))) | leq(s(zero), host(X!4))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(206,plain,
% 0.19/0.52 (leq(s(zero), host(X!4))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.19/0.52 tff(207,plain,
% 0.19/0.52 (leq(s(zero), host(V0!8))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[206, 197])).
% 0.19/0.52 tff(208,plain,
% 0.19/0.52 (host(W!5) = host(V0!8)),
% 0.19/0.52 inference(transitivity,[status(thm)],[107, 77])).
% 0.19/0.52 tff(209,plain,
% 0.19/0.52 (setIn(host(W!5), index(down, host(Y0!9))) <=> setIn(host(V0!8), index(down, host(Y0!9)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.52 tff(210,plain,
% 0.19/0.52 ((~setIn(host(W!5), index(down, host(Y0!9)))) <=> (~setIn(host(V0!8), index(down, host(Y0!9))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[209])).
% 0.19/0.52 tff(211,plain,
% 0.19/0.52 (^[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))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(212,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[211])).
% 0.19/0.53 tff(213,plain,
% 0.19/0.53 (^[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)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(214,plain,
% 0.19/0.53 (![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)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[213])).
% 0.19/0.53 tff(215,plain,
% 0.19/0.53 (![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)))),
% 0.19/0.53 inference(and_elim,[status(thm)],[56])).
% 0.19/0.53 tff(216,plain,
% 0.19/0.53 (![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)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.19/0.53 tff(217,plain,
% 0.19/0.53 (![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)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.19/0.53 tff(218,plain,
% 0.19/0.53 (((~![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(Y0!9, alive)) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = 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(Y0!9, alive)) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(219,plain,
% 0.19/0.53 (((~setIn(W!5, alive)) | (~setIn(Y0!9, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = elec_2))) <=> ((~setIn(Y0!9, alive)) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(220,plain,
% 0.19/0.53 (((~![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(W!5, alive)) | (~setIn(Y0!9, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = 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(Y0!9, alive)) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = elec_2))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.53 tff(221,plain,
% 0.19/0.53 (((~![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(W!5, alive)) | (~setIn(Y0!9, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = 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(Y0!9, alive)) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[220, 218])).
% 0.19/0.53 tff(222,plain,
% 0.19/0.53 ((~![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(W!5, alive)) | (~setIn(Y0!9, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(223,plain,
% 0.19/0.53 ((~![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(Y0!9, alive)) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = elec_2))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.53 tff(224,plain,
% 0.19/0.53 (leq(index(pendack, host(W!5)), host(Y0!9)) | (~setIn(host(W!5), index(down, host(Y0!9)))) | (~(index(status, host(W!5)) = elec_2))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[223, 184, 217, 151])).
% 0.19/0.53 tff(225,plain,
% 0.19/0.53 (~setIn(host(W!5), index(down, host(Y0!9)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[224, 148, 112])).
% 0.19/0.53 tff(226,plain,
% 0.19/0.53 (~setIn(host(V0!8), index(down, host(Y0!9)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[225, 210])).
% 0.19/0.53 tff(227,plain,
% 0.19/0.53 ((host(W!5) = host(X0!10)) <=> (host(V0!8) = host(X0!10))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.53 tff(228,plain,
% 0.19/0.53 ((~(host(W!5) = host(X0!10))) <=> (~(host(V0!8) = host(X0!10)))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[227])).
% 0.19/0.53 tff(229,plain,
% 0.19/0.53 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) <=> ((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(230,plain,
% 0.19/0.53 (elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) <=> ((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[229, 158])).
% 0.19/0.53 tff(231,plain,
% 0.19/0.53 (elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4)))),
% 0.19/0.53 inference(and_elim,[status(thm)],[56])).
% 0.19/0.53 tff(232,plain,
% 0.19/0.53 ((~(elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) <=> ((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9)))))) | (~elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4)))) | ((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(233,plain,
% 0.19/0.53 ((~(elem(m_Down(X0!10), snoc(queue(host(Y0!9)), m_Ldr(X!4))) <=> ((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9)))))) | ((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.19/0.53 tff(234,plain,
% 0.19/0.53 ((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[233, 230])).
% 0.19/0.53 tff(235,plain,
% 0.19/0.53 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))) | (~(m_Down(X0!10) = m_Ldr(X!4)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(236,plain,
% 0.19/0.53 (~(m_Down(X0!10) = m_Ldr(X!4))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[235, 171])).
% 0.19/0.53 tff(237,plain,
% 0.19/0.53 ((~((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9))))) | (m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(238,plain,
% 0.19/0.53 ((~((m_Down(X0!10) = m_Ldr(X!4)) | elem(m_Down(X0!10), queue(host(Y0!9))))) | elem(m_Down(X0!10), queue(host(Y0!9)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.19/0.53 tff(239,plain,
% 0.19/0.53 (elem(m_Down(X0!10), queue(host(Y0!9)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[238, 234])).
% 0.19/0.53 tff(240,plain,
% 0.19/0.53 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(X0!10))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)))) <=> ((~![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(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(X0!10))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(241,plain,
% 0.19/0.53 (((~(host(W!5) = host(X0!10))) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)) | (~setIn(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9))))) <=> ((~setIn(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(X0!10))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(242,plain,
% 0.19/0.53 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(W!5) = host(X0!10))) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)) | (~setIn(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))))) <=> ((~![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(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(X0!10))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[241])).
% 0.19/0.53 tff(243,plain,
% 0.19/0.53 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(W!5) = host(X0!10))) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)) | (~setIn(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))))) <=> ((~![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(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(X0!10))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[242, 240])).
% 0.19/0.53 tff(244,plain,
% 0.19/0.53 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(W!5) = host(X0!10))) | (~setIn(W!5, alive)) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2)) | (~setIn(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(245,plain,
% 0.19/0.53 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(Y0!9, alive)) | (~elem(m_Down(X0!10), queue(host(Y0!9)))) | (~setIn(W!5, alive)) | (~(host(W!5) = host(X0!10))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.19/0.53 tff(246,plain,
% 0.19/0.53 ((~(host(W!5) = host(X0!10))) | leq(index(pendack, host(W!5)), host(Y0!9)) | (~(index(status, host(W!5)) = elec_2))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[245, 184, 183, 239, 151])).
% 0.19/0.53 tff(247,plain,
% 0.19/0.53 (~(host(W!5) = host(X0!10))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[246, 148, 112])).
% 0.19/0.53 tff(248,plain,
% 0.19/0.53 (~(host(V0!8) = host(X0!10))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[247, 228])).
% 0.19/0.53 tff(249,plain,
% 0.19/0.53 (^[V1: $i] : refl(((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1))) <=> ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(250,plain,
% 0.19/0.53 (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1))) <=> ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[249])).
% 0.19/0.53 tff(251,plain,
% 0.19/0.53 (^[V1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(Y0!9), V1)) & leq(s(zero), V1)) <=> (~(leq(host(Y0!9), V1) | (~leq(s(zero), V1))))), ((~((~leq(host(Y0!9), V1)) & leq(s(zero), V1))) <=> (~(~(leq(host(Y0!9), V1) | (~leq(s(zero), V1))))))), rewrite((~(~(leq(host(Y0!9), V1) | (~leq(s(zero), V1))))) <=> (leq(host(Y0!9), V1) | (~leq(s(zero), V1)))), ((~((~leq(host(Y0!9), V1)) & leq(s(zero), V1))) <=> (leq(host(Y0!9), V1) | (~leq(s(zero), V1))))), (((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) <=> ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (leq(host(Y0!9), V1) | (~leq(s(zero), V1)))))), rewrite(((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) <=> ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))), (((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) <=> ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(252,plain,
% 0.19/0.53 (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1)))) <=> ![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[251])).
% 0.19/0.53 tff(253,plain,
% 0.19/0.53 (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | (~((~leq(host(Y0!9), V1)) & leq(s(zero), V1))))),
% 0.19/0.53 inference(and_elim,[status(thm)],[56])).
% 0.19/0.53 tff(254,plain,
% 0.19/0.53 (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.53 tff(255,plain,
% 0.19/0.53 (![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.19/0.53 tff(256,plain,
% 0.19/0.53 (((~![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) | (leq(host(Y0!9), host(V0!8)) | (host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | (~leq(s(zero), host(V0!8))))) <=> ((~![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) | leq(host(Y0!9), host(V0!8)) | (host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | (~leq(s(zero), host(V0!8))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(257,plain,
% 0.19/0.53 (((host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | leq(host(Y0!9), host(V0!8)) | (~leq(s(zero), host(V0!8)))) <=> (leq(host(Y0!9), host(V0!8)) | (host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | (~leq(s(zero), host(V0!8))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(258,plain,
% 0.19/0.53 (((~![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) | ((host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | leq(host(Y0!9), host(V0!8)) | (~leq(s(zero), host(V0!8))))) <=> ((~![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) | (leq(host(Y0!9), host(V0!8)) | (host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | (~leq(s(zero), host(V0!8)))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[257])).
% 0.19/0.53 tff(259,plain,
% 0.19/0.53 (((~![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) | ((host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | leq(host(Y0!9), host(V0!8)) | (~leq(s(zero), host(V0!8))))) <=> ((~![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) | leq(host(Y0!9), host(V0!8)) | (host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | (~leq(s(zero), host(V0!8))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[258, 256])).
% 0.19/0.53 tff(260,plain,
% 0.19/0.53 ((~![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) | ((host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | leq(host(Y0!9), host(V0!8)) | (~leq(s(zero), host(V0!8))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(261,plain,
% 0.19/0.54 ((~![V1: $i] : ((V1 = host(X0!10)) | setIn(V1, index(down, host(Y0!9))) | leq(host(Y0!9), V1) | (~leq(s(zero), V1)))) | leq(host(Y0!9), host(V0!8)) | (host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | (~leq(s(zero), host(V0!8)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.19/0.54 tff(262,plain,
% 0.19/0.54 (leq(host(Y0!9), host(V0!8)) | (host(V0!8) = host(X0!10)) | setIn(host(V0!8), index(down, host(Y0!9))) | (~leq(s(zero), host(V0!8)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[261, 255])).
% 0.19/0.54 tff(263,plain,
% 0.19/0.54 (leq(host(Y0!9), host(V0!8))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[262, 248, 226, 207])).
% 0.19/0.54 tff(264,plain,
% 0.19/0.54 ((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) | (~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(265,plain,
% 0.19/0.54 (~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[264, 263, 195])).
% 0.19/0.54 tff(266,plain,
% 0.19/0.54 ((host(Y0!9) = host(X!4)) <=> (host(X!4) = host(Y0!9))),
% 0.19/0.54 inference(commutativity,[status(thm)],[])).
% 0.19/0.54 tff(267,plain,
% 0.19/0.54 ((host(Y0!9) = host(V0!8)) <=> (host(Y0!9) = host(X!4))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.54 tff(268,plain,
% 0.19/0.54 ((host(Y0!9) = host(V0!8)) <=> (host(X!4) = host(Y0!9))),
% 0.19/0.54 inference(transitivity,[status(thm)],[267, 266])).
% 0.19/0.54 tff(269,plain,
% 0.19/0.54 ((host(X!4) = host(Y0!9)) <=> (host(Y0!9) = host(V0!8))),
% 0.19/0.54 inference(symmetry,[status(thm)],[268])).
% 0.19/0.54 tff(270,plain,
% 0.19/0.54 ((~(host(X!4) = host(Y0!9))) <=> (~(host(Y0!9) = host(V0!8)))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[269])).
% 0.19/0.54 tff(271,plain,
% 0.19/0.54 (~(host(X!4) = host(Y0!9))),
% 0.19/0.54 inference(and_elim,[status(thm)],[56])).
% 0.19/0.54 tff(272,plain,
% 0.19/0.54 (~(host(Y0!9) = host(V0!8))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.19/0.54 tff(273,plain,
% 0.19/0.54 ((~((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) <=> (host(Y0!9) = host(V0!8)))) | ((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8)))) | (host(Y0!9) = host(V0!8))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(274,plain,
% 0.19/0.54 (~((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) <=> (host(Y0!9) = host(V0!8)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[273, 272, 265])).
% 0.19/0.54 tff(275,plain,
% 0.19/0.54 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) <=> (host(Y0!9) = host(V0!8)))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) <=> (host(Y0!9) = host(V0!8))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(276,plain,
% 0.19/0.54 (((~((~leq(host(Y0!9), host(V0!8))) | (~leq(host(V0!8), host(Y0!9))))) <=> (host(Y0!9) = host(V0!8))) <=> ((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) <=> (host(Y0!9) = host(V0!8)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(277,plain,
% 0.19/0.54 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(Y0!9), host(V0!8))) | (~leq(host(V0!8), host(Y0!9))))) <=> (host(Y0!9) = host(V0!8)))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) <=> (host(Y0!9) = host(V0!8))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[276])).
% 0.19/0.54 tff(278,plain,
% 0.19/0.54 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(Y0!9), host(V0!8))) | (~leq(host(V0!8), host(Y0!9))))) <=> (host(Y0!9) = host(V0!8)))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) <=> (host(Y0!9) = host(V0!8))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[277, 275])).
% 0.19/0.54 tff(279,plain,
% 0.19/0.54 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(Y0!9), host(V0!8))) | (~leq(host(V0!8), host(Y0!9))))) <=> (host(Y0!9) = host(V0!8)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(280,plain,
% 0.19/0.54 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!8), host(Y0!9))) | (~leq(host(Y0!9), host(V0!8))))) <=> (host(Y0!9) = host(V0!8)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.19/0.54 tff(281,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[280, 22, 274])).
% 0.19/0.54 % SZS output end Proof
%------------------------------------------------------------------------------