%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV461+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 : Sat Jun 21 05:34:06 AM UTC 2025
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SWV461+1 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:52:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(host_type, type, (
% 0.19/0.41 host: $i > $i)).
% 0.19/0.41 tff(tptp_fun_Z0_6_type, type, (
% 0.19/0.41 tptp_fun_Z0_6: $i)).
% 0.19/0.41 tff(tptp_fun_V_4_type, type, (
% 0.19/0.41 tptp_fun_V_4: $i)).
% 0.19/0.41 tff(setIn_type, type, (
% 0.19/0.41 setIn: ( $i * $i ) > $o)).
% 0.19/0.41 tff(alive_type, type, (
% 0.19/0.41 alive: $i)).
% 0.19/0.41 tff(tptp_fun_X_5_type, type, (
% 0.19/0.41 tptp_fun_X_5: $i)).
% 0.19/0.41 tff(s_type, type, (
% 0.19/0.41 s: $i > $i)).
% 0.19/0.41 tff(index_type, type, (
% 0.19/0.41 index: ( $i * $i ) > $i)).
% 0.19/0.41 tff(pendack_type, type, (
% 0.19/0.41 pendack: $i)).
% 0.19/0.41 tff(elec_2_type, type, (
% 0.19/0.41 elec_2: $i)).
% 0.19/0.41 tff(status_type, type, (
% 0.19/0.41 status: $i)).
% 0.19/0.41 tff(leq_type, type, (
% 0.19/0.41 leq: ( $i * $i ) > $o)).
% 0.19/0.41 tff(nbr_proc_type, type, (
% 0.19/0.41 nbr_proc: $i)).
% 0.19/0.41 tff(elem_type, type, (
% 0.19/0.41 elem: ( $i * $i ) > $o)).
% 0.19/0.41 tff(queue_type, type, (
% 0.19/0.41 queue: $i > $i)).
% 0.19/0.41 tff(m_Ack_type, type, (
% 0.19/0.41 m_Ack: ( $i * $i ) > $i)).
% 0.19/0.41 tff(m_Down_type, type, (
% 0.19/0.41 m_Down: $i > $i)).
% 0.19/0.41 tff(norm_type, type, (
% 0.19/0.41 norm: $i)).
% 0.19/0.41 tff(ldr_type, type, (
% 0.19/0.41 ldr: $i)).
% 0.19/0.41 tff(elec_1_type, type, (
% 0.19/0.41 elec_1: $i)).
% 0.19/0.41 tff(tptp_fun_V0_9_type, type, (
% 0.19/0.41 tptp_fun_V0_9: ( $i * $i ) > $i)).
% 0.19/0.41 tff(zero_type, type, (
% 0.19/0.41 zero: $i)).
% 0.19/0.41 tff(down_type, type, (
% 0.19/0.41 down: $i)).
% 0.19/0.41 tff(m_Halt_type, type, (
% 0.19/0.41 m_Halt: $i > $i)).
% 0.19/0.41 tff(elid_type, type, (
% 0.19/0.41 elid: $i)).
% 0.19/0.41 tff(m_Ldr_type, type, (
% 0.19/0.41 m_Ldr: $i > $i)).
% 0.19/0.41 tff(tptp_fun_W_3_type, type, (
% 0.19/0.41 tptp_fun_W_3: $i)).
% 0.19/0.41 tff(q_nil_type, type, (
% 0.19/0.41 q_nil: $i)).
% 0.19/0.41 tff(pids_type, type, (
% 0.19/0.41 pids: $i)).
% 0.19/0.41 tff(tptp_fun_Z_7_type, type, (
% 0.19/0.41 tptp_fun_Z_7: $i)).
% 0.19/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.19/0.41 tptp_fun_Y_8: $i)).
% 0.19/0.41 tff(snoc_type, type, (
% 0.19/0.41 snoc: ( $i * $i ) > $i)).
% 0.19/0.41 tff(1,assumption,(X!5 = V!4), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (host(X!5) = host(V!4)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (host(V!4) = host(X!5)),
% 0.19/0.41 inference(symmetry,[status(thm)],[2])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (((~leq(nbr_proc, host(V!4))) & ((~(host(V!4) = host(X!5))) & (~((~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~(s(host(V!4)) = host(Z0!6)))))) & (host(V!4) = s(zero)) & (![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4))) & (queue(host(W!3)) = q_nil) & (![X: $i] : ((~setIn(X, alive)) | (~(host(W!3) = host(X)))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))) <=> ((~leq(nbr_proc, host(V!4))) & (~(host(V!4) = host(X!5))) & (~((~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~(s(host(V!4)) = host(Z0!6))))) & (host(V!4) = s(zero)) & ![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4)) & (queue(host(W!3)) = q_nil) & ![X: $i] : ((~setIn(X, alive)) | (~(host(W!3) = host(X)))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 ((![X: $i] : ((~(host(W!3) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | ((~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0)))))))) <=> (![X: $i] : ((~setIn(X, alive)) | (~(host(W!3) = host(X)))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 ((![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4))) <=> (![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (((~(host(V!4) = host(X!5))) & (~((host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (~(s(host(V!4)) = host(Z0!6)))))) <=> ((~(host(V!4) = host(X!5))) & (~((~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~(s(host(V!4)) = host(Z0!6))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (((~leq(nbr_proc, host(V!4))) & ((~(host(V!4) = host(X!5))) & (~((host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (~(s(host(V!4)) = host(Z0!6)))))) & (host(V!4) = s(zero)) & (![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4))) & (queue(host(W!3)) = q_nil) & (![X: $i] : ((~(host(W!3) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | ((~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))) <=> ((~leq(nbr_proc, host(V!4))) & ((~(host(V!4) = host(X!5))) & (~((~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~(s(host(V!4)) = host(Z0!6)))))) & (host(V!4) = s(zero)) & (![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4))) & (queue(host(W!3)) = q_nil) & (![X: $i] : ((~setIn(X, alive)) | (~(host(W!3) = host(X)))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0)))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[7, 6, 5])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (((~leq(nbr_proc, host(V!4))) & ((~(host(V!4) = host(X!5))) & (~((host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (~(s(host(V!4)) = host(Z0!6)))))) & (host(V!4) = s(zero)) & (![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4))) & (queue(host(W!3)) = q_nil) & (![X: $i] : ((~(host(W!3) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | ((~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))) <=> ((~leq(nbr_proc, host(V!4))) & (~(host(V!4) = host(X!5))) & (~((~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~(s(host(V!4)) = host(Z0!6))))) & (host(V!4) = s(zero)) & ![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4)) & (queue(host(W!3)) = q_nil) & ![X: $i] : ((~setIn(X, alive)) | (~(host(W!3) = host(X)))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[8, 4])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 ((~![V: $i, W: $i] : (leq(nbr_proc, host(V)) | ![X: $i] : ((host(V) = host(X)) | ![Y: $i, Z: $i, Z0: $i] : ((host(V) = host(Z0)) | (~((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0)))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V))) & (index(status, host(Z0)) = elec_2) & (host(Y) = index(pendack, host(Z0))) & (host(Z) = s(index(pendack, host(Z0)))))) | (~((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(s(host(V)) = host(Z0))))) | (~(host(V) = s(zero))) | (~(![X: $i] : ((~(host(W) = host(X))) | leq(X, V)) & (~setIn(V, pids)) & (host(W) = host(V)))) | (~(queue(host(W)) = q_nil)) | (~(![X: $i] : ((~(host(W) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~(![V0: $i] : ((V0 = host(Z)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid0) = host(Y)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))))) <=> (~![V: $i, W: $i] : (leq(nbr_proc, host(V)) | ![X: $i] : ((host(V) = host(X)) | ![Y: $i, Z: $i, Z0: $i] : ((host(V) = host(Z0)) | (~((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0)))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V))) & (index(status, host(Z0)) = elec_2) & (host(Y) = index(pendack, host(Z0))) & (host(Z) = s(index(pendack, host(Z0)))))) | (~((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(s(host(V)) = host(Z0))))) | (~(host(V) = s(zero))) | (~(![X: $i] : ((~(host(W) = host(X))) | leq(X, V)) & (~setIn(V, pids)) & (host(W) = host(V)))) | (~(queue(host(W)) = q_nil)) | (~(![X: $i] : ((~(host(W) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~(![V0: $i] : ((V0 = host(Z)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid0) = host(Y)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0)))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 ((~![V: $i, W: $i] : ((((((((((((((((![X: $i] : ((host(W) = host(X)) => (~setIn(X, alive))) & ![X: $i, Y: $i] : (elem(m_Ldr(Y), queue(host(X))) => (~leq(host(X), host(Y))))) & ![X: $i, Y: $i] : (elem(m_Down(Y), queue(host(X))) => (~(host(Y) = host(X))))) & ![X: $i, Y: $i] : (elem(m_Halt(Y), queue(host(X))) => (~leq(host(X), host(Y))))) & ![X: $i, Y: $i, Z: $i] : (elem(m_Ack(Z, X), queue(host(Y))) => (~leq(host(X), host(Z))))) & ![X: $i, Y: $i] : (((~(Y = X)) & (host(Y) = host(X))) => ((~setIn(X, alive)) | (~setIn(Y, alive))))) & ![X: $i, Y: $i] : ((setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y)))) => leq(host(X), index(pendack, host(Y))))) & ![X: $i, Y: $i] : ((setIn(Y, alive) & (index(status, host(Y)) = elec_1)) => (~elem(m_Ack(Y, X), queue(host(Y)))))) & ![X: $i] : ((((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive)) => (index(elid, host(X)) = X))) & ![X: $i, Y: $i, Z: $i] : (((setIn(Z, alive) & elem(m_Down(Y), queue(host(Z)))) & (host(Y) = host(X))) => (~((setIn(X, alive) & (index(ldr, host(X)) = host(X))) & (index(status, host(X)) = norm))))) & ![X: $i, Y: $i, Z: $i] : (((((setIn(X, alive) & setIn(Z, alive)) & (host(Z) = host(Y))) & (index(status, host(X)) = elec_2)) & (index(status, host(Z)) = elec_2)) => (~elem(m_Ack(X, Y), queue(host(X)))))) & ![X: $i, Y: $i] : ((((((~leq(host(X), host(Y))) & setIn(X, alive)) & setIn(Y, alive)) & (index(status, host(X)) = elec_2)) & (index(status, host(Y)) = elec_2)) => leq(index(pendack, host(Y)), host(X)))) & ![X: $i, Y: $i] : ((((((~leq(host(X), host(Y))) & setIn(X, alive)) & setIn(Y, alive)) & (index(status, host(X)) = elec_2)) & (index(status, host(Y)) = elec_2)) => (~leq(index(pendack, host(X)), index(pendack, host(Y)))))) & ![X: $i, Y: $i, Z: $i] : (((((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive)) & elem(m_Halt(Z), queue(host(Y)))) & (index(status, host(Z)) = elec_2)) => (~((setIn(X, alive) & (index(ldr, host(X)) = host(X))) & (index(status, host(X)) = norm))))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Z)))) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid0) = host(Y))) & (host(Pid0) = nbr_proc)) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0)))) & elem(m_Ack(Pid0, Y), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Y) = index(pendack, host(Pid0)))) & (host(Z) = s(index(pendack, host(Pid0))))) => (~((setIn(X, alive) & (index(ldr, host(X)) = host(X))) & (index(status, host(X)) = norm))))) => ((queue(host(W)) = q_nil) => (((![X: $i] : ((host(W) = host(X)) => leq(X, V)) & (~setIn(V, pids))) & (host(W) = host(V))) => ((host(V) = s(zero)) => ((~leq(nbr_proc, host(V))) => ![X: $i] : ((~(host(V) = host(X))) => ![Y: $i, Z: $i, Z0: $i] : ((s(host(V)) = host(Z0)) => ((~(host(V) = host(Z0))) => ((((((((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0))))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V)))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V)))) & (index(status, host(Z0)) = elec_2)) & (host(Y) = index(pendack, host(Z0)))) & (host(Z) = s(index(pendack, host(Z0))))) => (~(((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X))) & (index(status, host(X)) = norm))))))))))))) <=> (~![V: $i, W: $i] : (leq(nbr_proc, host(V)) | ![X: $i] : ((host(V) = host(X)) | ![Y: $i, Z: $i, Z0: $i] : ((host(V) = host(Z0)) | (~((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0)))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V))) & (index(status, host(Z0)) = elec_2) & (host(Y) = index(pendack, host(Z0))) & (host(Z) = s(index(pendack, host(Z0)))))) | (~((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(s(host(V)) = host(Z0))))) | (~(host(V) = s(zero))) | (~(![X: $i] : ((~(host(W) = host(X))) | leq(X, V)) & (~setIn(V, pids)) & (host(W) = host(V)))) | (~(queue(host(W)) = q_nil)) | (~(![X: $i] : ((~(host(W) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~(![V0: $i] : ((V0 = host(Z)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid0) = host(Y)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0)))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(12,axiom,(~![V: $i, W: $i] : ((((((((((((((((![X: $i] : ((host(W) = host(X)) => (~setIn(X, alive))) & ![X: $i, Y: $i] : (elem(m_Ldr(Y), queue(host(X))) => (~leq(host(X), host(Y))))) & ![X: $i, Y: $i] : (elem(m_Down(Y), queue(host(X))) => (~(host(Y) = host(X))))) & ![X: $i, Y: $i] : (elem(m_Halt(Y), queue(host(X))) => (~leq(host(X), host(Y))))) & ![X: $i, Y: $i, Z: $i] : (elem(m_Ack(Z, X), queue(host(Y))) => (~leq(host(X), host(Z))))) & ![X: $i, Y: $i] : (((~(Y = X)) & (host(Y) = host(X))) => ((~setIn(X, alive)) | (~setIn(Y, alive))))) & ![X: $i, Y: $i] : ((setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y)))) => leq(host(X), index(pendack, host(Y))))) & ![X: $i, Y: $i] : ((setIn(Y, alive) & (index(status, host(Y)) = elec_1)) => (~elem(m_Ack(Y, X), queue(host(Y)))))) & ![X: $i] : ((((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive)) => (index(elid, host(X)) = X))) & ![X: $i, Y: $i, Z: $i] : (((setIn(Z, alive) & elem(m_Down(Y), queue(host(Z)))) & (host(Y) = host(X))) => (~((setIn(X, alive) & (index(ldr, host(X)) = host(X))) & (index(status, host(X)) = norm))))) & ![X: $i, Y: $i, Z: $i] : (((((setIn(X, alive) & setIn(Z, alive)) & (host(Z) = host(Y))) & (index(status, host(X)) = elec_2)) & (index(status, host(Z)) = elec_2)) => (~elem(m_Ack(X, Y), queue(host(X)))))) & ![X: $i, Y: $i] : ((((((~leq(host(X), host(Y))) & setIn(X, alive)) & setIn(Y, alive)) & (index(status, host(X)) = elec_2)) & (index(status, host(Y)) = elec_2)) => leq(index(pendack, host(Y)), host(X)))) & ![X: $i, Y: $i] : ((((((~leq(host(X), host(Y))) & setIn(X, alive)) & setIn(Y, alive)) & (index(status, host(X)) = elec_2)) & (index(status, host(Y)) = elec_2)) => (~leq(index(pendack, host(X)), index(pendack, host(Y)))))) & ![X: $i, Y: $i, Z: $i] : (((((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive)) & elem(m_Halt(Z), queue(host(Y)))) & (index(status, host(Z)) = elec_2)) => (~((setIn(X, alive) & (index(ldr, host(X)) = host(X))) & (index(status, host(X)) = norm))))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Z)))) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid0) = host(Y))) & (host(Pid0) = nbr_proc)) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0)))) & elem(m_Ack(Pid0, Y), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Y) = index(pendack, host(Pid0)))) & (host(Z) = s(index(pendack, host(Pid0))))) => (~((setIn(X, alive) & (index(ldr, host(X)) = host(X))) & (index(status, host(X)) = norm))))) => ((queue(host(W)) = q_nil) => (((![X: $i] : ((host(W) = host(X)) => leq(X, V)) & (~setIn(V, pids))) & (host(W) = host(V))) => ((host(V) = s(zero)) => ((~leq(nbr_proc, host(V))) => ![X: $i] : ((~(host(V) = host(X))) => ![Y: $i, Z: $i, Z0: $i] : ((s(host(V)) = host(Z0)) => ((~(host(V) = host(Z0))) => ((((((((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0))))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V)))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V)))) & (index(status, host(Z0)) = elec_2)) & (host(Y) = index(pendack, host(Z0)))) & (host(Z) = s(index(pendack, host(Z0))))) => (~(((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X))) & (index(status, host(X)) = norm))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (~![V: $i, W: $i] : (leq(nbr_proc, host(V)) | ![X: $i] : ((host(V) = host(X)) | ![Y: $i, Z: $i, Z0: $i] : ((host(V) = host(Z0)) | (~((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0)))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V))) & (index(status, host(Z0)) = elec_2) & (host(Y) = index(pendack, host(Z0))) & (host(Z) = s(index(pendack, host(Z0)))))) | (~((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(s(host(V)) = host(Z0))))) | (~(host(V) = s(zero))) | (~(![X: $i] : ((~(host(W) = host(X))) | leq(X, V)) & (~setIn(V, pids)) & (host(W) = host(V)))) | (~(queue(host(W)) = q_nil)) | (~(![X: $i] : ((~(host(W) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~(![V0: $i] : ((V0 = host(Z)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid0) = host(Y)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (~![V: $i, W: $i] : (leq(nbr_proc, host(V)) | ![X: $i] : ((host(V) = host(X)) | ![Y: $i, Z: $i, Z0: $i] : ((host(V) = host(Z0)) | (~((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0)))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V))) & (index(status, host(Z0)) = elec_2) & (host(Y) = index(pendack, host(Z0))) & (host(Z) = s(index(pendack, host(Z0)))))) | (~((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(s(host(V)) = host(Z0))))) | (~(host(V) = s(zero))) | (~(![X: $i] : ((~(host(W) = host(X))) | leq(X, V)) & (~setIn(V, pids)) & (host(W) = host(V)))) | (~(queue(host(W)) = q_nil)) | (~(![X: $i] : ((~(host(W) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~(![V0: $i] : ((V0 = host(Z)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid0) = host(Y)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 (~![V: $i, W: $i] : (leq(nbr_proc, host(V)) | ![X: $i] : ((host(V) = host(X)) | ![Y: $i, Z: $i, Z0: $i] : ((host(V) = host(Z0)) | (~((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0)))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V))) & (index(status, host(Z0)) = elec_2) & (host(Y) = index(pendack, host(Z0))) & (host(Z) = s(index(pendack, host(Z0)))))) | (~((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(s(host(V)) = host(Z0))))) | (~(host(V) = s(zero))) | (~(![X: $i] : ((~(host(W) = host(X))) | leq(X, V)) & (~setIn(V, pids)) & (host(W) = host(V)))) | (~(queue(host(W)) = q_nil)) | (~(![X: $i] : ((~(host(W) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~(![V0: $i] : ((V0 = host(Z)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid0) = host(Y)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (~![V: $i, W: $i] : (leq(nbr_proc, host(V)) | ![X: $i] : ((host(V) = host(X)) | ![Y: $i, Z: $i, Z0: $i] : ((host(V) = host(Z0)) | (~((setIn(Z0, alive) | (Z0 = V)) & leq(nbr_proc, s(index(pendack, host(Z0)))) & elem(m_Down(Z), snoc(queue(host(Z0)), m_Halt(V))) & elem(m_Ack(Z0, Y), snoc(queue(host(Z0)), m_Halt(V))) & (index(status, host(Z0)) = elec_2) & (host(Y) = index(pendack, host(Z0))) & (host(Z) = s(index(pendack, host(Z0)))))) | (~((setIn(X, alive) | (X = V)) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(s(host(V)) = host(Z0))))) | (~(host(V) = s(zero))) | (~(![X: $i] : ((~(host(W) = host(X))) | leq(X, V)) & (~setIn(V, pids)) & (host(W) = host(V)))) | (~(queue(host(W)) = q_nil)) | (~(![X: $i] : ((~(host(W) = host(X))) | (~setIn(X, alive))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~(![V0: $i] : ((V0 = host(Z)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid0) = host(Y)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 ((~leq(nbr_proc, host(V!4))) & (~(host(V!4) = host(X!5))) & (~((~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~(s(host(V!4)) = host(Z0!6))))) & (host(V!4) = s(zero)) & ![X: $i] : ((~(host(W!3) = host(X))) | leq(X, V!4)) & (~setIn(V!4, pids)) & (host(W!3) = host(V!4)) & (queue(host(W!3)) = q_nil) & ![X: $i] : ((~setIn(X, alive)) | (~(host(W!3) = host(X)))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Ldr(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~(host(Y) = host(X))) | (~elem(m_Down(Y), queue(host(X))))) & ![X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~elem(m_Halt(Y), queue(host(X))))) & ![X: $i, Y: $i, Z: $i] : ((~leq(host(X), host(Z))) | (~elem(m_Ack(Z, X), queue(host(Y))))) & ![X: $i, Y: $i] : ((~setIn(Y, alive)) | (~setIn(X, alive)) | (~((~(Y = X)) & (host(Y) = host(X))))) & ![X: $i, Y: $i] : ((~(setIn(Y, alive) & elem(m_Ack(Y, X), queue(host(Y))))) | leq(host(X), index(pendack, host(Y)))) & ![X: $i, Y: $i] : ((~elem(m_Ack(Y, X), queue(host(Y)))) | (~(setIn(Y, alive) & (index(status, host(Y)) = elec_1)))) & ![X: $i] : ((~(((index(status, host(X)) = elec_1) | (index(status, host(X)) = elec_2)) & setIn(X, alive))) | (index(elid, host(X)) = X)) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Down(Y), queue(host(Z))) & (host(Y) = host(X)))) | (~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)))) & ![X: $i, Y: $i, Z: $i] : ((~elem(m_Ack(X, Y), queue(host(X)))) | (~(setIn(X, alive) & setIn(Z, alive) & (host(Z) = host(Y)) & (index(status, host(X)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i] : ((~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2))) | leq(index(pendack, host(Y)), host(X))) & ![X: $i, Y: $i] : ((~leq(index(pendack, host(X)), index(pendack, host(Y)))) | (~((~leq(host(X), host(Y))) & setIn(X, alive) & setIn(Y, alive) & (index(status, host(X)) = elec_2) & (index(status, host(Y)) = elec_2)))) & ![X: $i, Y: $i, Z: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~((~leq(index(pendack, host(Z)), host(X))) & setIn(Z, alive) & elem(m_Halt(Z), queue(host(Y))) & (index(status, host(Z)) = elec_2)))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & elem(m_Down(Y), queue(host(X))))) | (~((tptp_fun_V0_9(Pid0, Z) = host(Z)) | setIn(tptp_fun_V0_9(Pid0, Z), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Z))) & leq(s(zero), tptp_fun_V0_9(Pid0, Z)))))) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(host(Pid0) = host(Y))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 (~(host(V!4) = host(X!5))),
% 0.19/0.46 inference(and_elim,[status(thm)],[17])).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[18, 3])).
% 0.19/0.46 tff(20,plain,(~(X!5 = V!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 (~((~((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm))) | (host(V!4) = host(Z0!6)) | (~((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6)))))) | (~(s(host(V!4)) = host(Z0!6))))),
% 0.19/0.46 inference(and_elim,[status(thm)],[17])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 ((setIn(X!5, alive) | (X!5 = V!4)) & (index(ldr, host(X!5)) = host(X!5)) & (index(status, host(X!5)) = norm)),
% 0.19/0.46 inference(or_elim,[status(thm)],[21])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (setIn(X!5, alive) | (X!5 = V!4)),
% 0.19/0.46 inference(and_elim,[status(thm)],[22])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (setIn(X!5, alive)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(28,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.46 tff(30,plain,(
% 0.19/0.46 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[29])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) <=> ((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) <=> ((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 ((setIn(Z0!6, alive) | (Z0!6 = V!4)) & leq(nbr_proc, s(index(pendack, host(Z0!6)))) & elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) & elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) & (index(status, host(Z0!6)) = elec_2) & (host(Y!8) = index(pendack, host(Z0!6))) & (host(Z!7) = s(index(pendack, host(Z0!6))))),
% 0.19/0.46 inference(or_elim,[status(thm)],[21])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[34])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 ((~(elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) <=> ((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6)))))) | (~elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4)))) | ((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 ((~(elem(m_Down(Z!7), snoc(queue(host(Z0!6)), m_Halt(V!4))) <=> ((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6)))))) | ((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 ((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[37, 33])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Halt(Y))) <=> (~(m_Down(X) = m_Halt(Y))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(42,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_17')).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.46 tff(44,plain,(
% 0.19/0.46 ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[43])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))) | (~(m_Down(Z!7) = m_Halt(V!4)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 (~(m_Down(Z!7) = m_Halt(V!4))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 ((~((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6))))) | (m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 ((~((m_Down(Z!7) = m_Halt(V!4)) | elem(m_Down(Z!7), queue(host(Z0!6))))) | elem(m_Down(Z!7), queue(host(Z0!6)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (elem(m_Down(Z!7), queue(host(Z0!6)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[49, 38])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) <=> ((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 (elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) <=> ((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[51, 31])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[34])).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 ((~(elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) <=> ((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))))) | (~elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4)))) | ((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 ((~(elem(m_Ack(Z0!6, Y!8), snoc(queue(host(Z0!6)), m_Halt(V!4))) <=> ((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))))) | ((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 ((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 (^[X: $i, Y: $i, Z: $i] : refl((~(m_Ack(X, Y) = m_Halt(Z))) <=> (~(m_Ack(X, Y) = m_Halt(Z))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(60,axiom,(![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_11')).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.47 tff(62,plain,(
% 0.19/0.47 ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[61])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))) | (~(m_Ack(Z0!6, Y!8) = m_Halt(V!4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (~(m_Ack(Z0!6, Y!8) = m_Halt(V!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 ((~((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6))))) | (m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 ((~((m_Ack(Z0!6, Y!8) = m_Halt(V!4)) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6))))) | elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 (elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[67, 56])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 (^[X: $i, Y: $i, Z: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0)))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0)))))) <=> ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (^[X: $i, Y: $i, Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm)) <=> (~((~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm))))), ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) <=> (~(~((~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm))))))), rewrite((~(~((~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm))))) <=> ((~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)))), ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) <=> ((~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm))))), trans(monotonicity(rewrite((setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))) <=> (~((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0)))))))), ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0)))))) <=> (~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0)))))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0)))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))), ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0)))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0)))))))), (((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))) <=> (((~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm))) | ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))))), rewrite((((~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm))) | ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))), (((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0))))))) <=> ![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~(setIn(X, alive) & (index(ldr, host(X)) = host(X)) & (index(status, host(X)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & elem(m_Ack(Pid0, Y), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Y) = index(pendack, host(Pid0))) & (host(Z) = s(index(pendack, host(Pid0)))))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[17])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 (host(Z!7) = s(index(pendack, host(Z0!6)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[34])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 (host(Y!8) = index(pendack, host(Z0!6))),
% 0.19/0.47 inference(and_elim,[status(thm)],[34])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (index(status, host(Z0!6)) = elec_2),
% 0.19/0.47 inference(and_elim,[status(thm)],[34])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (leq(nbr_proc, s(index(pendack, host(Z0!6))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[34])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 (index(status, host(X!5)) = norm),
% 0.19/0.47 inference(and_elim,[status(thm)],[22])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (index(ldr, host(X!5)) = host(X!5)),
% 0.19/0.47 inference(and_elim,[status(thm)],[22])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) | ((~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~setIn(Z0!6, alive)) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6))))))) <=> ((~![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) | (~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~setIn(Z0!6, alive)) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (((~setIn(Z0!6, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6)))))) <=> ((~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~setIn(Z0!6, alive)) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) | ((~setIn(Z0!6, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6))))))) <=> ((~![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) | ((~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~setIn(Z0!6, alive)) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) | ((~setIn(Z0!6, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6))))))) <=> ((~![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) | (~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~setIn(Z0!6, alive)) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) | ((~setIn(Z0!6, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Z), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(X, alive)) | (~(index(ldr, host(X)) = host(X))) | (~(index(status, host(X)) = norm)) | (~elem(m_Ack(Pid0, Y), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Y) = index(pendack, host(Pid0)))) | (~(host(Z) = s(index(pendack, host(Pid0))))))) | (~elem(m_Ack(Z0!6, Y!8), queue(host(Z0!6)))) | (~setIn(Z0!6, alive)) | (~(index(status, host(Z0!6)) = elec_2)) | (~setIn(X!5, alive)) | (~elem(m_Down(Z!7), queue(host(Z0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Z0!6))))) | (~(index(ldr, host(X!5)) = host(X!5))) | (~(index(status, host(X!5)) = norm)) | (~(host(Y!8) = index(pendack, host(Z0!6)))) | (~(host(Z!7) = s(index(pendack, host(Z0!6)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 ((~setIn(Z0!6, alive)) | (~setIn(X!5, alive))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[87, 81, 80, 79, 78, 77, 76, 75, 68, 50])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 (~setIn(Z0!6, alive)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[88, 24])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (setIn(Z0!6, alive) | (Z0!6 = V!4)),
% 0.19/0.48 inference(and_elim,[status(thm)],[34])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (Z0!6 = V!4),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (host(Z0!6) = host(V!4)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (host(V!4) = host(Z0!6)),
% 0.19/0.48 inference(symmetry,[status(thm)],[92])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 (~(host(V!4) = host(Z0!6))),
% 0.19/0.48 inference(or_elim,[status(thm)],[21])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------