%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV466+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 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV466+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:51:54 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 tff(elem_type, type, (
% 0.18/0.42 elem: ( $i * $i ) > $o)).
% 0.18/0.42 tff(cons_type, type, (
% 0.18/0.42 cons: ( $i * $i ) > $i)).
% 0.18/0.42 tff(tptp_fun_V_5_type, type, (
% 0.18/0.42 tptp_fun_V_5: $i)).
% 0.18/0.42 tff(m_Down_type, type, (
% 0.18/0.42 m_Down: $i > $i)).
% 0.18/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.18/0.42 tptp_fun_Y_3: $i)).
% 0.18/0.42 tff(queue_type, type, (
% 0.18/0.42 queue: $i > $i)).
% 0.18/0.42 tff(host_type, type, (
% 0.18/0.42 host: $i > $i)).
% 0.18/0.42 tff(tptp_fun_X_4_type, type, (
% 0.18/0.42 tptp_fun_X_4: $i)).
% 0.18/0.42 tff(s_type, type, (
% 0.18/0.42 s: $i > $i)).
% 0.18/0.42 tff(index_type, type, (
% 0.18/0.42 index: ( $i * $i ) > $i)).
% 0.18/0.42 tff(pendack_type, type, (
% 0.18/0.42 pendack: $i)).
% 0.18/0.42 tff(elec_2_type, type, (
% 0.18/0.42 elec_2: $i)).
% 0.18/0.42 tff(status_type, type, (
% 0.18/0.42 status: $i)).
% 0.18/0.42 tff(leq_type, type, (
% 0.18/0.42 leq: ( $i * $i ) > $o)).
% 0.18/0.42 tff(nbr_proc_type, type, (
% 0.18/0.42 nbr_proc: $i)).
% 0.18/0.42 tff(m_Ack_type, type, (
% 0.18/0.42 m_Ack: ( $i * $i ) > $i)).
% 0.18/0.42 tff(setIn_type, type, (
% 0.18/0.42 setIn: ( $i * $i ) > $o)).
% 0.18/0.42 tff(alive_type, type, (
% 0.18/0.42 alive: $i)).
% 0.18/0.42 tff(norm_type, type, (
% 0.18/0.42 norm: $i)).
% 0.18/0.42 tff(ldr_type, type, (
% 0.18/0.42 ldr: $i)).
% 0.18/0.42 tff(elec_1_type, type, (
% 0.18/0.42 elec_1: $i)).
% 0.18/0.42 tff(tptp_fun_V0_11_type, type, (
% 0.18/0.42 tptp_fun_V0_11: ( $i * $i ) > $i)).
% 0.18/0.42 tff(zero_type, type, (
% 0.18/0.42 zero: $i)).
% 0.18/0.42 tff(down_type, type, (
% 0.18/0.42 down: $i)).
% 0.18/0.42 tff(m_Halt_type, type, (
% 0.18/0.42 m_Halt: $i > $i)).
% 0.18/0.42 tff(elid_type, type, (
% 0.18/0.42 elid: $i)).
% 0.18/0.42 tff(m_Ldr_type, type, (
% 0.18/0.42 m_Ldr: $i > $i)).
% 0.18/0.42 tff(tptp_fun_Y0_8_type, type, (
% 0.18/0.42 tptp_fun_Y0_8: $i)).
% 0.18/0.42 tff(tptp_fun_Z_6_type, type, (
% 0.18/0.42 tptp_fun_Z_6: $i)).
% 0.18/0.42 tff(tptp_fun_X0_9_type, type, (
% 0.18/0.42 tptp_fun_X0_9: $i)).
% 0.18/0.42 tff(tptp_fun_W0_10_type, type, (
% 0.18/0.42 tptp_fun_W0_10: $i)).
% 0.18/0.42 tff(snoc_type, type, (
% 0.18/0.42 snoc: ( $i * $i ) > $i)).
% 0.18/0.42 tff(tptp_fun_V0_7_type, type, (
% 0.18/0.42 tptp_fun_V0_7: $i)).
% 0.18/0.42 tff(acks_type, type, (
% 0.18/0.42 acks: $i)).
% 0.18/0.42 tff(1,plain,
% 0.18/0.42 ((leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(2,plain,
% 0.18/0.42 ((![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) <=> (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(3,plain,
% 0.18/0.43 ((setIn(host(Z!6), index(acks, host(X!4))) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) <=> (setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(4,plain,
% 0.18/0.43 ((~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))) <=> (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(5,plain,
% 0.18/0.43 (((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))) <=> ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[4])).
% 0.18/0.43 tff(6,plain,
% 0.18/0.43 ((setIn(host(Z!6), index(acks, host(X!4))) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) <=> (setIn(host(Z!6), index(acks, host(X!4))) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[5])).
% 0.18/0.43 tff(7,plain,
% 0.18/0.43 ((setIn(host(Z!6), index(acks, host(X!4))) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) <=> (setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[6, 3])).
% 0.18/0.43 tff(8,plain,
% 0.18/0.44 ((leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (setIn(host(Z!6), index(acks, host(X!4))) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[7, 2])).
% 0.18/0.44 tff(9,plain,
% 0.18/0.44 ((leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (setIn(host(Z!6), index(acks, host(X!4))) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[8, 1])).
% 0.18/0.45 tff(10,plain,
% 0.18/0.45 ((~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))) <=> (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(11,plain,
% 0.18/0.45 ((~![V: $i, W: $i, X: $i, Y: $i] : ((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) => leq(host(Z), index(pendack, host(Pid0))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid20), queue(host(Z)))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Pid20)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = nbr_proc)) & (host(Pid0) = host(Pid30))) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Pid30) = index(pendack, host(Pid0)))) & (host(Pid20) = s(index(pendack, host(Pid0))))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => (leq(host(X), host(Y)) => (((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) => (leq(nbr_proc, index(pendack, host(X))) => ![Z: $i] : (setIn(host(Z), index(acks, host(X))) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((host(Z) = host(Y0)) => ((~(host(X) = host(Y0))) => (((((((setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0))))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X)))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X)))) & (index(status, host(Y0)) = elec_2)) & (host(W0) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~(setIn(V0, alive) & (host(X) = host(V0))))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(12,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : ((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) => leq(host(Z), index(pendack, host(Pid0))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid20), queue(host(Z)))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Pid20)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = nbr_proc)) & (host(Pid0) = host(Pid30))) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Pid30) = index(pendack, host(Pid0)))) & (host(Pid20) = s(index(pendack, host(Pid0))))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => (leq(host(X), host(Y)) => (((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) => (leq(nbr_proc, index(pendack, host(X))) => ![Z: $i] : (setIn(host(Z), index(acks, host(X))) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((host(Z) = host(Y0)) => ((~(host(X) = host(Y0))) => (((((((setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0))))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X)))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X)))) & (index(status, host(Y0)) = elec_2)) & (host(W0) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~(setIn(V0, alive) & (host(X) = host(V0))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.18/0.46 tff(13,plain,
% 0.18/0.46 (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.46 tff(14,plain,
% 0.18/0.46 (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.18/0.46 tff(15,plain,
% 0.18/0.46 (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.18/0.46 tff(16,plain,
% 0.18/0.46 (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : ((~setIn(host(Z), index(acks, host(X)))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.18/0.46 tff(17,plain,
% 0.18/0.46 (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & setIn(host(Z!6), index(acks, host(X!4))) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.18/0.47 tff(18,plain,
% 0.18/0.47 (queue(host(X!4)) = cons(m_Down(Y!3), V!5)),
% 0.18/0.47 inference(and_elim,[status(thm)],[17])).
% 0.18/0.47 tff(19,plain,
% 0.18/0.47 (cons(m_Down(Y!3), V!5) = queue(host(X!4))),
% 0.18/0.47 inference(symmetry,[status(thm)],[18])).
% 0.18/0.47 tff(20,plain,
% 0.18/0.47 (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> elem(m_Down(Y!3), queue(host(X!4)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[19])).
% 0.18/0.47 tff(21,plain,
% 0.18/0.47 (elem(m_Down(Y!3), queue(host(X!4))) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.18/0.47 inference(symmetry,[status(thm)],[20])).
% 0.18/0.47 tff(22,plain,
% 0.18/0.47 ((~elem(m_Down(Y!3), queue(host(X!4)))) <=> (~elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[21])).
% 0.18/0.47 tff(23,plain,
% 0.18/0.47 (host(X!4) = host(V0!7)),
% 0.18/0.47 inference(and_elim,[status(thm)],[17])).
% 0.18/0.47 tff(24,plain,
% 0.18/0.47 (host(V0!7) = host(X!4)),
% 0.18/0.47 inference(symmetry,[status(thm)],[23])).
% 0.18/0.47 tff(25,plain,
% 0.18/0.47 (^[X: $i, Y: $i] : refl((leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(26,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.47 tff(27,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(28,plain,
% 0.18/0.47 (^[X: $i, Y: $i] : rewrite((leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y))) <=> (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(29,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.18/0.47 tff(30,axiom,(![X: $i, Y: $i] : (leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_64')).
% 0.18/0.47 tff(31,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.47 tff(32,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.18/0.47 tff(33,plain,(
% 0.18/0.47 ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[32])).
% 0.18/0.47 tff(34,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.18/0.47 tff(35,plain,
% 0.18/0.47 ((~![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))) | (leq(host(V0!7), s(index(pendack, host(Y0!8)))) <=> (leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8))))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(36,plain,
% 0.18/0.47 (leq(host(V0!7), s(index(pendack, host(Y0!8)))) <=> (leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.18/0.47 tff(37,plain,
% 0.18/0.47 (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))),
% 0.18/0.47 inference(and_elim,[status(thm)],[17])).
% 0.18/0.47 tff(38,plain,
% 0.18/0.47 (setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8))))),
% 0.18/0.47 inference(or_elim,[status(thm)],[37])).
% 0.18/0.47 tff(39,plain,
% 0.18/0.47 (host(X0!9) = s(index(pendack, host(Y0!8)))),
% 0.18/0.47 inference(and_elim,[status(thm)],[38])).
% 0.18/0.47 tff(40,plain,
% 0.18/0.47 (s(index(pendack, host(Y0!8))) = host(X0!9)),
% 0.18/0.47 inference(symmetry,[status(thm)],[39])).
% 0.18/0.47 tff(41,plain,
% 0.18/0.47 (leq(host(V0!7), s(index(pendack, host(Y0!8)))) <=> leq(host(X!4), host(X0!9))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[24, 40])).
% 0.18/0.47 tff(42,plain,
% 0.18/0.47 (leq(host(X!4), host(X0!9)) <=> leq(host(V0!7), s(index(pendack, host(Y0!8))))),
% 0.18/0.47 inference(symmetry,[status(thm)],[41])).
% 0.18/0.47 tff(43,plain,
% 0.18/0.47 (^[X: $i, Y: $i] : refl((~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(44,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> ![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.47 tff(45,plain,
% 0.18/0.47 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, X)) <=> (~((~leq(X, Y)) | (~leq(Y, X))))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))), rewrite(((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))))), rewrite((~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(46,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[45])).
% 0.18/0.47 tff(47,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(48,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_61')).
% 0.18/0.47 tff(49,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.47 tff(50,plain,(
% 0.18/0.47 ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.18/0.47 inference(skolemize,[status(sab)],[49])).
% 0.18/0.47 tff(51,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.18/0.47 tff(52,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.18/0.47 tff(53,plain,
% 0.18/0.47 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8)))))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(54,plain,
% 0.18/0.47 (~(((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8)))))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.18/0.47 tff(55,plain,
% 0.18/0.47 (leq(s(index(pendack, host(Y0!8))), nbr_proc) <=> leq(host(X0!9), nbr_proc)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[40])).
% 0.18/0.47 tff(56,plain,
% 0.18/0.47 (leq(host(X0!9), nbr_proc) <=> leq(s(index(pendack, host(Y0!8))), nbr_proc)),
% 0.18/0.47 inference(symmetry,[status(thm)],[55])).
% 0.18/0.47 tff(57,plain,
% 0.18/0.47 (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(58,plain,
% 0.18/0.47 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.18/0.47 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.47 tff(59,plain,
% 0.18/0.47 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(60,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 0.18/0.47 tff(61,plain,
% 0.18/0.47 (![P: $i] : leq(host(P), nbr_proc)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.47 tff(62,plain,(
% 0.18/0.47 ![P: $i] : leq(host(P), nbr_proc)),
% 0.18/0.47 inference(skolemize,[status(sab)],[61])).
% 0.18/0.47 tff(63,plain,
% 0.18/0.47 (![P: $i] : leq(host(P), nbr_proc)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.47 tff(64,plain,
% 0.18/0.47 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X0!9), nbr_proc)),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(65,plain,
% 0.18/0.47 (leq(host(X0!9), nbr_proc)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.18/0.47 tff(66,plain,
% 0.18/0.47 (leq(s(index(pendack, host(Y0!8))), nbr_proc)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[65, 56])).
% 0.18/0.47 tff(67,plain,
% 0.18/0.47 (leq(nbr_proc, s(index(pendack, host(Y0!8))))),
% 0.18/0.47 inference(and_elim,[status(thm)],[38])).
% 0.18/0.47 tff(68,plain,
% 0.18/0.47 ((~((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8)))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(69,plain,
% 0.18/0.47 ((~((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.47 tff(70,plain,
% 0.18/0.47 (~((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[69, 66])).
% 0.18/0.47 tff(71,plain,
% 0.18/0.47 ((((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8)))))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc)) | ((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8)))))) | (s(index(pendack, host(Y0!8))) = nbr_proc)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(72,plain,
% 0.18/0.47 (s(index(pendack, host(Y0!8))) = nbr_proc),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[71, 70, 54])).
% 0.18/0.47 tff(73,plain,
% 0.18/0.47 (nbr_proc = s(index(pendack, host(Y0!8)))),
% 0.18/0.47 inference(symmetry,[status(thm)],[72])).
% 0.18/0.47 tff(74,plain,
% 0.18/0.47 (nbr_proc = host(X0!9)),
% 0.18/0.47 inference(transitivity,[status(thm)],[73, 40])).
% 0.18/0.47 tff(75,plain,
% 0.18/0.47 (leq(host(X!4), nbr_proc) <=> leq(host(X!4), host(X0!9))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[74])).
% 0.18/0.47 tff(76,plain,
% 0.18/0.47 (leq(host(X!4), nbr_proc) <=> leq(host(V0!7), s(index(pendack, host(Y0!8))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[75, 42])).
% 0.18/0.47 tff(77,plain,
% 0.18/0.47 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X!4), nbr_proc)),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(78,plain,
% 0.18/0.47 (leq(host(X!4), nbr_proc)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[77, 63])).
% 0.18/0.47 tff(79,plain,
% 0.18/0.47 (leq(host(V0!7), s(index(pendack, host(Y0!8))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[78, 76])).
% 0.18/0.47 tff(80,plain,
% 0.18/0.47 ((~(leq(host(V0!7), s(index(pendack, host(Y0!8)))) <=> (leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8))))))) | (~leq(host(V0!7), s(index(pendack, host(Y0!8))))) | (leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8)))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(81,plain,
% 0.18/0.47 ((~(leq(host(V0!7), s(index(pendack, host(Y0!8)))) <=> (leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8))))))) | (leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.18/0.47 tff(82,plain,
% 0.18/0.47 (leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[81, 36])).
% 0.18/0.47 tff(83,plain,
% 0.18/0.47 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(host(V0!7), index(pendack, host(Y0!8)))) | (~leq(index(pendack, host(Y0!8)), host(V0!7)))) <=> (host(V0!7) = index(pendack, host(Y0!8)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(84,plain,
% 0.18/0.47 (~(((~leq(host(V0!7), index(pendack, host(Y0!8)))) | (~leq(index(pendack, host(Y0!8)), host(V0!7)))) <=> (host(V0!7) = index(pendack, host(Y0!8))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[83, 52])).
% 0.18/0.47 tff(85,plain,
% 0.18/0.47 (host(W0!10) = index(pendack, host(Y0!8))),
% 0.18/0.47 inference(and_elim,[status(thm)],[38])).
% 0.18/0.47 tff(86,plain,
% 0.18/0.47 (index(pendack, host(Y0!8)) = host(W0!10)),
% 0.18/0.47 inference(symmetry,[status(thm)],[85])).
% 0.18/0.47 tff(87,plain,
% 0.18/0.47 ((host(V0!7) = index(pendack, host(Y0!8))) <=> (host(X!4) = host(W0!10))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[24, 86])).
% 0.18/0.47 tff(88,plain,
% 0.18/0.47 ((host(X!4) = host(W0!10)) <=> (host(V0!7) = index(pendack, host(Y0!8)))),
% 0.18/0.47 inference(symmetry,[status(thm)],[87])).
% 0.18/0.47 tff(89,plain,
% 0.18/0.47 ((~(host(X!4) = host(W0!10))) <=> (~(host(V0!7) = index(pendack, host(Y0!8))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[88])).
% 0.18/0.47 tff(90,plain,
% 0.18/0.47 (^[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))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(91,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.47 tff(92,plain,
% 0.18/0.47 (![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)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(93,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 0.18/0.47 tff(94,plain,
% 0.18/0.47 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.47 tff(95,plain,(
% 0.18/0.47 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[94])).
% 0.18/0.47 tff(96,plain,
% 0.18/0.47 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.18/0.47 tff(97,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(98,plain,
% 0.18/0.47 (elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.18/0.47 tff(99,plain,
% 0.18/0.47 (elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4)))),
% 0.18/0.47 inference(and_elim,[status(thm)],[38])).
% 0.18/0.47 tff(100,plain,
% 0.18/0.47 ((~(elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))))) | (~elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4)))) | ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(101,plain,
% 0.18/0.47 ((~(elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))))) | ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.18/0.47 tff(102,plain,
% 0.18/0.47 ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[101, 98])).
% 0.18/0.47 tff(103,plain,
% 0.18/0.47 (^[X: $i, Y: $i, Z: $i] : refl((~(m_Ack(X, Y) = m_Ldr(Z))) <=> (~(m_Ack(X, Y) = m_Ldr(Z))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(104,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.47 tff(105,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(106,axiom,(![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_14')).
% 0.18/0.47 tff(107,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.47 tff(108,plain,(
% 0.18/0.47 ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[107])).
% 0.18/0.47 tff(109,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.18/0.47 tff(110,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))) | (~(m_Ack(Y0!8, W0!10) = m_Ldr(X!4)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(111,plain,
% 0.18/0.47 (~(m_Ack(Y0!8, W0!10) = m_Ldr(X!4))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.18/0.47 tff(112,plain,
% 0.18/0.47 ((~((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))) | (m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(113,plain,
% 0.18/0.47 ((~((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.18/0.47 tff(114,plain,
% 0.18/0.47 (elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[113, 102])).
% 0.18/0.47 tff(115,plain,
% 0.18/0.47 (^[Z: $i, Pid20: $i, Pid0: $i] : refl(((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(116,plain,
% 0.18/0.47 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[115])).
% 0.18/0.47 tff(117,plain,
% 0.18/0.47 (^[Z: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)) <=> (~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2))))))), rewrite((~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2))))), (((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) <=> ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))))), rewrite(((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))), (((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(118,plain,
% 0.18/0.47 (![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[117])).
% 0.18/0.47 tff(119,plain,
% 0.18/0.47 (![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))),
% 0.18/0.47 inference(and_elim,[status(thm)],[17])).
% 0.18/0.47 tff(120,plain,
% 0.18/0.48 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.18/0.48 tff(121,plain,
% 0.18/0.48 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.18/0.48 tff(122,plain,
% 0.18/0.48 (index(status, host(X!4)) = elec_2),
% 0.18/0.48 inference(and_elim,[status(thm)],[17])).
% 0.18/0.48 tff(123,plain,
% 0.18/0.48 (index(status, host(Y0!8)) = elec_2),
% 0.18/0.48 inference(and_elim,[status(thm)],[38])).
% 0.18/0.48 tff(124,plain,
% 0.18/0.48 (setIn(Y0!8, alive)),
% 0.18/0.48 inference(and_elim,[status(thm)],[38])).
% 0.18/0.48 tff(125,plain,
% 0.18/0.48 (setIn(X!4, alive)),
% 0.18/0.48 inference(and_elim,[status(thm)],[17])).
% 0.18/0.48 tff(126,plain,
% 0.18/0.48 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) | ((~setIn(X!4, alive)) | (~(host(X!4) = host(W0!10))) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) | (~setIn(X!4, alive)) | (~(host(X!4) = host(W0!10))) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(127,plain,
% 0.18/0.48 (((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2))) <=> ((~setIn(X!4, alive)) | (~(host(X!4) = host(W0!10))) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(128,plain,
% 0.18/0.48 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) | ((~setIn(X!4, alive)) | (~(host(X!4) = host(W0!10))) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[127])).
% 0.18/0.48 tff(129,plain,
% 0.18/0.48 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) | (~setIn(X!4, alive)) | (~(host(X!4) = host(W0!10))) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[128, 126])).
% 0.18/0.48 tff(130,plain,
% 0.18/0.48 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(131,plain,
% 0.18/0.48 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~(index(status, host(Z)) = elec_2)))) | (~setIn(X!4, alive)) | (~(host(X!4) = host(W0!10))) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.48 tff(132,plain,
% 0.18/0.48 ((~(host(X!4) = host(W0!10))) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[131, 125, 124, 123, 122, 121])).
% 0.18/0.48 tff(133,plain,
% 0.18/0.48 (~(host(X!4) = host(W0!10))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[132, 114])).
% 0.18/0.48 tff(134,plain,
% 0.18/0.48 (~(host(V0!7) = index(pendack, host(Y0!8)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[133, 89])).
% 0.18/0.48 tff(135,plain,
% 0.18/0.48 ((((~leq(host(V0!7), index(pendack, host(Y0!8)))) | (~leq(index(pendack, host(Y0!8)), host(V0!7)))) <=> (host(V0!7) = index(pendack, host(Y0!8)))) | ((~leq(host(V0!7), index(pendack, host(Y0!8)))) | (~leq(index(pendack, host(Y0!8)), host(V0!7)))) | (host(V0!7) = index(pendack, host(Y0!8)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(136,plain,
% 0.18/0.48 ((~leq(host(V0!7), index(pendack, host(Y0!8)))) | (~leq(index(pendack, host(Y0!8)), host(V0!7)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[135, 134, 84])).
% 0.18/0.48 tff(137,plain,
% 0.18/0.48 (index(status, host(V0!7)) = index(status, host(X!4))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.48 tff(138,plain,
% 0.18/0.48 (index(status, host(V0!7)) = elec_2),
% 0.18/0.48 inference(transitivity,[status(thm)],[137, 122])).
% 0.18/0.48 tff(139,plain,
% 0.18/0.48 (host(Y!3) = index(pendack, host(X!4))),
% 0.18/0.48 inference(and_elim,[status(thm)],[17])).
% 0.18/0.48 tff(140,plain,
% 0.18/0.48 (index(pendack, host(X!4)) = host(Y!3)),
% 0.18/0.48 inference(symmetry,[status(thm)],[139])).
% 0.18/0.48 tff(141,plain,
% 0.18/0.48 (index(pendack, host(V0!7)) = index(pendack, host(X!4))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.48 tff(142,plain,
% 0.18/0.48 (index(pendack, host(V0!7)) = host(Y!3)),
% 0.18/0.48 inference(transitivity,[status(thm)],[141, 140])).
% 0.18/0.48 tff(143,plain,
% 0.18/0.48 (leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7))) <=> leq(index(pendack, host(Y0!8)), host(Y!3))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[142])).
% 0.18/0.48 tff(144,plain,
% 0.18/0.48 (leq(index(pendack, host(Y0!8)), host(Y!3)) <=> leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))),
% 0.18/0.48 inference(symmetry,[status(thm)],[143])).
% 0.18/0.48 tff(145,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(146,plain,
% 0.18/0.48 ((~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(147,plain,
% 0.18/0.48 ((((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc)) <=> (((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(148,plain,
% 0.18/0.48 ((~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[147])).
% 0.18/0.48 tff(149,plain,
% 0.18/0.48 ((~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[148, 146])).
% 0.18/0.48 tff(150,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[149])).
% 0.18/0.48 tff(151,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[150, 145])).
% 0.18/0.48 tff(152,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(153,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.18/0.48 tff(154,plain,
% 0.18/0.48 (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[153, 52])).
% 0.18/0.48 tff(155,plain,
% 0.18/0.48 (leq(index(pendack, host(X!4)), nbr_proc) <=> leq(host(Y!3), nbr_proc)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[140])).
% 0.18/0.48 tff(156,plain,
% 0.18/0.48 (leq(host(Y!3), nbr_proc) <=> leq(index(pendack, host(X!4)), nbr_proc)),
% 0.18/0.48 inference(symmetry,[status(thm)],[155])).
% 0.18/0.48 tff(157,plain,
% 0.18/0.48 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(Y!3), nbr_proc)),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(158,plain,
% 0.18/0.48 (leq(host(Y!3), nbr_proc)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[157, 63])).
% 0.18/0.48 tff(159,plain,
% 0.18/0.48 (leq(index(pendack, host(X!4)), nbr_proc)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[158, 156])).
% 0.18/0.48 tff(160,plain,
% 0.18/0.48 (leq(nbr_proc, index(pendack, host(X!4)))),
% 0.18/0.48 inference(and_elim,[status(thm)],[17])).
% 0.18/0.48 tff(161,plain,
% 0.18/0.48 ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) | (~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(162,plain,
% 0.18/0.48 ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) | (~leq(index(pendack, host(X!4)), nbr_proc))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.18/0.48 tff(163,plain,
% 0.18/0.48 (~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.18/0.48 tff(164,plain,
% 0.18/0.48 ((((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)) | ((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) | (index(pendack, host(X!4)) = nbr_proc)),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(165,plain,
% 0.18/0.48 (index(pendack, host(X!4)) = nbr_proc),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[164, 163, 154])).
% 0.18/0.48 tff(166,plain,
% 0.18/0.48 (nbr_proc = index(pendack, host(X!4))),
% 0.18/0.48 inference(symmetry,[status(thm)],[165])).
% 0.18/0.48 tff(167,plain,
% 0.18/0.48 (host(X0!9) = host(Y!3)),
% 0.18/0.48 inference(transitivity,[status(thm)],[39, 72, 166, 140])).
% 0.18/0.48 tff(168,plain,
% 0.18/0.48 (leq(host(W0!10), host(X0!9)) <=> leq(index(pendack, host(Y0!8)), host(Y!3))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[85, 167])).
% 0.18/0.48 tff(169,plain,
% 0.18/0.48 (leq(host(W0!10), host(X0!9)) <=> leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[168, 144])).
% 0.18/0.48 tff(170,plain,
% 0.18/0.48 (leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))) <=> leq(host(W0!10), host(X0!9))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[86, 40])).
% 0.18/0.48 tff(171,plain,
% 0.18/0.48 (^[X: $i] : refl((~leq(s(X), X)) <=> (~leq(s(X), X)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(172,plain,
% 0.18/0.48 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[171])).
% 0.18/0.48 tff(173,plain,
% 0.18/0.48 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(174,axiom,(![X: $i] : (~leq(s(X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_58')).
% 0.18/0.48 tff(175,plain,
% 0.18/0.48 (![X: $i] : (~leq(s(X), X))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.48 tff(176,plain,(
% 0.18/0.48 ![X: $i] : (~leq(s(X), X))),
% 0.18/0.48 inference(skolemize,[status(sab)],[175])).
% 0.18/0.48 tff(177,plain,
% 0.18/0.48 (![X: $i] : (~leq(s(X), X))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.18/0.48 tff(178,plain,
% 0.18/0.48 ((~![X: $i] : (~leq(s(X), X))) | (~leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(179,plain,
% 0.18/0.48 (~leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.18/0.48 tff(180,plain,
% 0.18/0.48 (^[X: $i, Y: $i] : refl((leq(Y, X) | leq(X, Y)) <=> (leq(Y, X) | leq(X, Y)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(181,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[180])).
% 0.18/0.48 tff(182,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(183,plain,
% 0.18/0.48 (^[X: $i, Y: $i] : rewrite((leq(X, Y) | leq(Y, X)) <=> (leq(Y, X) | leq(X, Y)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(184,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (leq(X, Y) | leq(Y, X)) <=> ![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[183])).
% 0.18/0.48 tff(185,axiom,(![X: $i, Y: $i] : (leq(X, Y) | leq(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_60')).
% 0.18/0.48 tff(186,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.18/0.48 tff(187,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.18/0.48 tff(188,plain,(
% 0.18/0.48 ![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.18/0.48 inference(skolemize,[status(sab)],[187])).
% 0.18/0.48 tff(189,plain,
% 0.18/0.48 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.18/0.48 tff(190,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | (leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))) | leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))))) <=> ((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))) | leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(191,plain,
% 0.18/0.48 ((leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))) | leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8)))) <=> (leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))) | leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(192,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | (leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))) | leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))))) <=> ((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | (leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))) | leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[191])).
% 0.18/0.48 tff(193,plain,
% 0.18/0.48 (((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | (leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))) | leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))))) <=> ((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))) | leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[192, 190])).
% 0.18/0.48 tff(194,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | (leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8)))) | leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(195,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | leq(s(index(pendack, host(Y0!8))), index(pendack, host(Y0!8))) | leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.18/0.48 tff(196,plain,
% 0.18/0.48 (leq(index(pendack, host(Y0!8)), s(index(pendack, host(Y0!8))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[195, 189, 179])).
% 0.18/0.48 tff(197,plain,
% 0.18/0.48 (leq(host(W0!10), host(X0!9))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[196, 170])).
% 0.18/0.48 tff(198,plain,
% 0.18/0.48 (leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[197, 169])).
% 0.18/0.48 tff(199,plain,
% 0.18/0.48 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))) <=> ![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(200,plain,
% 0.18/0.48 (^[Z: $i, Pid0: $i] : refl((leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(201,plain,
% 0.18/0.48 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))) <=> ![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[200])).
% 0.18/0.48 tff(202,plain,
% 0.18/0.48 (^[Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)) <=> (~(leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))), ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) <=> (~(~(leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))))), rewrite((~(~(leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))), ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))), (((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) <=> ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))))), rewrite(((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))), (((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(203,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) <=> ![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[202])).
% 0.18/0.49 tff(204,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))),
% 0.18/0.49 inference(and_elim,[status(thm)],[17])).
% 0.18/0.49 tff(205,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.18/0.49 tff(206,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.18/0.49 tff(207,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.18/0.49 tff(208,plain,
% 0.18/0.49 (setIn(V0!7, alive) & (host(X!4) = host(V0!7))),
% 0.18/0.49 inference(or_elim,[status(thm)],[37])).
% 0.18/0.49 tff(209,plain,
% 0.18/0.49 (setIn(V0!7, alive)),
% 0.18/0.49 inference(and_elim,[status(thm)],[208])).
% 0.18/0.49 tff(210,plain,
% 0.18/0.49 (((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(Y0!8), host(V0!7)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))))) <=> ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(Y0!8), host(V0!7)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(211,plain,
% 0.18/0.49 ((leq(host(Y0!8), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(Y0!8, alive)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))) | (~(index(status, host(Y0!8)) = elec_2)) | (~(index(status, host(V0!7)) = elec_2))) <=> ((~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(Y0!8), host(V0!7)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(212,plain,
% 0.18/0.49 (((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (leq(host(Y0!8), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(Y0!8, alive)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))) | (~(index(status, host(Y0!8)) = elec_2)) | (~(index(status, host(V0!7)) = elec_2)))) <=> ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(Y0!8), host(V0!7)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[211])).
% 0.18/0.49 tff(213,plain,
% 0.18/0.49 (((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (leq(host(Y0!8), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(Y0!8, alive)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))) | (~(index(status, host(Y0!8)) = elec_2)) | (~(index(status, host(V0!7)) = elec_2)))) <=> ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(Y0!8), host(V0!7)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[212, 210])).
% 0.18/0.49 tff(214,plain,
% 0.18/0.49 ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (leq(host(Y0!8), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(Y0!8, alive)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7)))) | (~(index(status, host(Y0!8)) = elec_2)) | (~(index(status, host(V0!7)) = elec_2)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(215,plain,
% 0.18/0.49 ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(Y0!8), host(V0!7)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.18/0.49 tff(216,plain,
% 0.18/0.49 ((~(index(status, host(V0!7)) = elec_2)) | leq(host(Y0!8), host(V0!7)) | (~leq(index(pendack, host(Y0!8)), index(pendack, host(V0!7))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[215, 209, 124, 123, 207])).
% 0.18/0.49 tff(217,plain,
% 0.18/0.49 (leq(host(Y0!8), host(V0!7))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[216, 198, 138])).
% 0.18/0.49 tff(218,plain,
% 0.18/0.49 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) <=> (host(V0!7) = host(Y0!8))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(219,plain,
% 0.18/0.49 (~(((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) <=> (host(V0!7) = host(Y0!8)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[218, 52])).
% 0.18/0.49 tff(220,plain,
% 0.18/0.49 ((host(V0!7) = host(Y0!8)) <=> (host(X!4) = host(Y0!8))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.49 tff(221,plain,
% 0.18/0.49 ((host(X!4) = host(Y0!8)) <=> (host(V0!7) = host(Y0!8))),
% 0.18/0.49 inference(symmetry,[status(thm)],[220])).
% 0.18/0.49 tff(222,plain,
% 0.18/0.49 ((~(host(X!4) = host(Y0!8))) <=> (~(host(V0!7) = host(Y0!8)))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[221])).
% 0.18/0.49 tff(223,plain,
% 0.18/0.49 (~(host(X!4) = host(Y0!8))),
% 0.18/0.49 inference(or_elim,[status(thm)],[37])).
% 0.18/0.49 tff(224,plain,
% 0.18/0.49 (~(host(V0!7) = host(Y0!8))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.18/0.49 tff(225,plain,
% 0.18/0.49 ((((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) <=> (host(V0!7) = host(Y0!8))) | ((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) | (host(V0!7) = host(Y0!8))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(226,plain,
% 0.18/0.49 ((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[225, 224, 219])).
% 0.18/0.49 tff(227,plain,
% 0.18/0.49 ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) | (~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(228,plain,
% 0.18/0.49 (~leq(host(V0!7), host(Y0!8))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[227, 226, 217])).
% 0.18/0.49 tff(229,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))) <=> ![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(230,plain,
% 0.18/0.49 (^[Z: $i, Pid0: $i] : refl((leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(231,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))) <=> ![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[230])).
% 0.18/0.49 tff(232,plain,
% 0.18/0.49 (^[Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)) <=> (~(leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))), ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) <=> (~(~(leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))))), rewrite((~(~(leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))), ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))))), (((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite(((leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))), (((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(233,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[232])).
% 0.18/0.49 tff(234,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 0.18/0.49 inference(and_elim,[status(thm)],[17])).
% 0.18/0.49 tff(235,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.18/0.49 tff(236,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.18/0.49 tff(237,plain,
% 0.18/0.49 (![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.18/0.49 tff(238,plain,
% 0.18/0.49 (((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(V0!7), host(Y0!8)) | leq(index(pendack, host(Y0!8)), host(V0!7)))) <=> ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(V0!7), host(Y0!8)) | leq(index(pendack, host(Y0!8)), host(V0!7)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(239,plain,
% 0.18/0.49 ((leq(host(V0!7), host(Y0!8)) | (~setIn(Y0!8, alive)) | (~setIn(V0!7, alive)) | leq(index(pendack, host(Y0!8)), host(V0!7)) | (~(index(status, host(V0!7)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2))) <=> ((~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(V0!7), host(Y0!8)) | leq(index(pendack, host(Y0!8)), host(V0!7)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(240,plain,
% 0.18/0.49 (((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (leq(host(V0!7), host(Y0!8)) | (~setIn(Y0!8, alive)) | (~setIn(V0!7, alive)) | leq(index(pendack, host(Y0!8)), host(V0!7)) | (~(index(status, host(V0!7)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))) <=> ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(V0!7), host(Y0!8)) | leq(index(pendack, host(Y0!8)), host(V0!7))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[239])).
% 0.18/0.49 tff(241,plain,
% 0.18/0.49 (((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (leq(host(V0!7), host(Y0!8)) | (~setIn(Y0!8, alive)) | (~setIn(V0!7, alive)) | leq(index(pendack, host(Y0!8)), host(V0!7)) | (~(index(status, host(V0!7)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))) <=> ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(V0!7), host(Y0!8)) | leq(index(pendack, host(Y0!8)), host(V0!7)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[240, 238])).
% 0.18/0.49 tff(242,plain,
% 0.18/0.49 ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (leq(host(V0!7), host(Y0!8)) | (~setIn(Y0!8, alive)) | (~setIn(V0!7, alive)) | leq(index(pendack, host(Y0!8)), host(V0!7)) | (~(index(status, host(V0!7)) = elec_2)) | (~(index(status, host(Y0!8)) = elec_2)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(243,plain,
% 0.18/0.50 ((~![Z: $i, Pid0: $i] : (leq(host(Z), host(Pid0)) | (~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | leq(host(V0!7), host(Y0!8)) | leq(index(pendack, host(Y0!8)), host(V0!7))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.18/0.50 tff(244,plain,
% 0.18/0.50 ((~(index(status, host(V0!7)) = elec_2)) | leq(host(V0!7), host(Y0!8)) | leq(index(pendack, host(Y0!8)), host(V0!7))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[243, 209, 124, 123, 237])).
% 0.18/0.50 tff(245,plain,
% 0.18/0.50 (leq(index(pendack, host(Y0!8)), host(V0!7))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[244, 228, 138])).
% 0.18/0.50 tff(246,plain,
% 0.18/0.50 ((~((~leq(host(V0!7), index(pendack, host(Y0!8)))) | (~leq(index(pendack, host(Y0!8)), host(V0!7))))) | (~leq(host(V0!7), index(pendack, host(Y0!8)))) | (~leq(index(pendack, host(Y0!8)), host(V0!7)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(247,plain,
% 0.18/0.50 (~leq(host(V0!7), index(pendack, host(Y0!8)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[246, 245, 136])).
% 0.18/0.50 tff(248,plain,
% 0.18/0.50 ((~(leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8)))))) | leq(host(V0!7), index(pendack, host(Y0!8))) | (host(V0!7) = s(index(pendack, host(Y0!8))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(249,plain,
% 0.18/0.50 (host(V0!7) = s(index(pendack, host(Y0!8)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[248, 247, 82])).
% 0.18/0.50 tff(250,plain,
% 0.18/0.50 (s(index(pendack, host(Y0!8))) = host(V0!7)),
% 0.18/0.50 inference(symmetry,[status(thm)],[249])).
% 0.18/0.50 tff(251,plain,
% 0.18/0.50 (host(X0!9) = host(X!4)),
% 0.18/0.50 inference(transitivity,[status(thm)],[39, 250, 24])).
% 0.18/0.50 tff(252,plain,
% 0.18/0.50 (queue(host(X0!9)) = queue(host(X!4))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[251])).
% 0.18/0.50 tff(253,plain,
% 0.18/0.50 (elem(m_Down(Y!3), queue(host(X0!9))) <=> elem(m_Down(Y!3), queue(host(X!4)))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[252])).
% 0.18/0.50 tff(254,plain,
% 0.18/0.50 ((~elem(m_Down(Y!3), queue(host(X0!9)))) <=> (~elem(m_Down(Y!3), queue(host(X!4))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[253])).
% 0.18/0.50 tff(255,plain,
% 0.18/0.50 (host(Y!3) = host(X0!9)),
% 0.18/0.50 inference(transitivity,[status(thm)],[139, 165, 73, 40])).
% 0.18/0.50 tff(256,plain,
% 0.18/0.50 (queue(host(Y!3)) = queue(host(X0!9))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[255])).
% 0.18/0.50 tff(257,plain,
% 0.18/0.50 (elem(m_Down(Y!3), queue(host(Y!3))) <=> elem(m_Down(Y!3), queue(host(X0!9)))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[256])).
% 0.18/0.50 tff(258,plain,
% 0.18/0.50 ((~elem(m_Down(Y!3), queue(host(Y!3)))) <=> (~elem(m_Down(Y!3), queue(host(X0!9))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[257])).
% 0.18/0.50 tff(259,plain,
% 0.18/0.50 (^[Z: $i, Pid0: $i] : refl(((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) <=> ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(260,plain,
% 0.18/0.50 (![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) <=> ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[259])).
% 0.18/0.50 tff(261,plain,
% 0.18/0.50 (![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))),
% 0.18/0.50 inference(and_elim,[status(thm)],[17])).
% 0.18/0.50 tff(262,plain,
% 0.18/0.50 (![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.18/0.50 tff(263,plain,
% 0.18/0.50 (((~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~elem(m_Down(Y!3), queue(host(Y!3))))) <=> ((~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~elem(m_Down(Y!3), queue(host(Y!3)))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(264,plain,
% 0.18/0.50 (($false | (~elem(m_Down(Y!3), queue(host(Y!3))))) <=> (~elem(m_Down(Y!3), queue(host(Y!3))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(265,plain,
% 0.18/0.50 ((~$true) <=> $false),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(266,plain,
% 0.18/0.50 ((host(Y!3) = host(Y!3)) <=> $true),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(267,plain,
% 0.18/0.50 ((~(host(Y!3) = host(Y!3))) <=> (~$true)),
% 0.18/0.50 inference(monotonicity,[status(thm)],[266])).
% 0.18/0.50 tff(268,plain,
% 0.18/0.50 ((~(host(Y!3) = host(Y!3))) <=> $false),
% 0.18/0.50 inference(transitivity,[status(thm)],[267, 265])).
% 0.18/0.50 tff(269,plain,
% 0.18/0.50 (((~(host(Y!3) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(Y!3))))) <=> ($false | (~elem(m_Down(Y!3), queue(host(Y!3)))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[268])).
% 0.18/0.50 tff(270,plain,
% 0.18/0.50 (((~(host(Y!3) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(Y!3))))) <=> (~elem(m_Down(Y!3), queue(host(Y!3))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[269, 264])).
% 0.18/0.50 tff(271,plain,
% 0.18/0.50 (((~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | ((~(host(Y!3) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(Y!3)))))) <=> ((~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~elem(m_Down(Y!3), queue(host(Y!3)))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[270])).
% 0.18/0.50 tff(272,plain,
% 0.18/0.50 (((~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | ((~(host(Y!3) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(Y!3)))))) <=> ((~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~elem(m_Down(Y!3), queue(host(Y!3)))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[271, 263])).
% 0.18/0.50 tff(273,plain,
% 0.18/0.50 ((~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | ((~(host(Y!3) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(Y!3)))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(274,plain,
% 0.18/0.50 ((~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~elem(m_Down(Y!3), queue(host(Y!3))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.18/0.50 tff(275,plain,
% 0.18/0.50 (~elem(m_Down(Y!3), queue(host(Y!3)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[274, 262])).
% 0.18/0.50 tff(276,plain,
% 0.18/0.50 (~elem(m_Down(Y!3), queue(host(X0!9)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[275, 258])).
% 0.18/0.50 tff(277,plain,
% 0.18/0.50 (~elem(m_Down(Y!3), queue(host(X!4)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[276, 254])).
% 0.18/0.50 tff(278,plain,
% 0.18/0.50 (~elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[277, 22])).
% 0.18/0.50 tff(279,plain,
% 0.18/0.50 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(280,plain,
% 0.18/0.50 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[279])).
% 0.18/0.50 tff(281,plain,
% 0.18/0.50 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(282,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 0.18/0.50 tff(283,plain,
% 0.18/0.50 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.18/0.50 tff(284,plain,(
% 0.18/0.50 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.50 inference(skolemize,[status(sab)],[283])).
% 0.18/0.50 tff(285,plain,
% 0.18/0.50 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.18/0.50 tff(286,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(287,plain,
% 0.18/0.50 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> $true) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(288,plain,
% 0.18/0.50 (($true | elem(m_Down(Y!3), V!5)) <=> $true),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(289,plain,
% 0.18/0.50 ((m_Down(Y!3) = m_Down(Y!3)) <=> $true),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(290,plain,
% 0.18/0.50 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> ($true | elem(m_Down(Y!3), V!5))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[289])).
% 0.18/0.50 tff(291,plain,
% 0.18/0.50 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> $true),
% 0.18/0.50 inference(transitivity,[status(thm)],[290, 288])).
% 0.18/0.50 tff(292,plain,
% 0.18/0.50 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5))) <=> (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> $true)),
% 0.18/0.50 inference(monotonicity,[status(thm)],[291])).
% 0.18/0.50 tff(293,plain,
% 0.18/0.50 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5))) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.18/0.50 inference(transitivity,[status(thm)],[292, 287])).
% 0.18/0.50 tff(294,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[293])).
% 0.18/0.50 tff(295,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[294, 286])).
% 0.18/0.50 tff(296,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(297,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.18/0.50 tff(298,plain,
% 0.18/0.50 (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[297, 285])).
% 0.18/0.50 tff(299,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[298, 278])).
% 0.18/0.50 % SZS output end Proof
% 0.18/0.50 % E exiting
%------------------------------------------------------------------------------