%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV458+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:34:06 AM UTC 2025
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV458+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n014.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 09:51:54 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 tff(leq_type, type, (
% 0.19/0.49 leq: ( $i * $i ) > $o)).
% 0.19/0.49 tff(tptp_fun_V0_9_type, type, (
% 0.19/0.49 tptp_fun_V0_9: ( $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.49 tptp_fun_Y_3: $i)).
% 0.19/0.49 tff(tptp_fun_X_4_type, type, (
% 0.19/0.49 tptp_fun_X_4: $i)).
% 0.19/0.49 tff(s_type, type, (
% 0.19/0.49 s: $i > $i)).
% 0.19/0.49 tff(zero_type, type, (
% 0.19/0.49 zero: $i)).
% 0.19/0.49 tff(host_type, type, (
% 0.19/0.49 host: $i > $i)).
% 0.19/0.49 tff(setIn_type, type, (
% 0.19/0.49 setIn: ( $i * $i ) > $o)).
% 0.19/0.49 tff(index_type, type, (
% 0.19/0.49 index: ( $i * $i ) > $i)).
% 0.19/0.49 tff(down_type, type, (
% 0.19/0.49 down: $i)).
% 0.19/0.49 tff(elem_type, type, (
% 0.19/0.49 elem: ( $i * $i ) > $o)).
% 0.19/0.49 tff(queue_type, type, (
% 0.19/0.49 queue: $i > $i)).
% 0.19/0.49 tff(m_Down_type, type, (
% 0.19/0.49 m_Down: $i > $i)).
% 0.19/0.49 tff(cons_type, type, (
% 0.19/0.49 cons: ( $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_V_5_type, type, (
% 0.19/0.49 tptp_fun_V_5: $i)).
% 0.19/0.49 tff(elec_1_type, type, (
% 0.19/0.49 elec_1: $i)).
% 0.19/0.49 tff(status_type, type, (
% 0.19/0.49 status: $i)).
% 0.19/0.49 tff(norm_type, type, (
% 0.19/0.49 norm: $i)).
% 0.19/0.49 tff(ldr_type, type, (
% 0.19/0.49 ldr: $i)).
% 0.19/0.49 tff(alive_type, type, (
% 0.19/0.49 alive: $i)).
% 0.19/0.49 tff(elec_2_type, type, (
% 0.19/0.49 elec_2: $i)).
% 0.19/0.49 tff(m_Halt_type, type, (
% 0.19/0.49 m_Halt: $i > $i)).
% 0.19/0.49 tff(pendack_type, type, (
% 0.19/0.49 pendack: $i)).
% 0.19/0.49 tff(m_Ack_type, type, (
% 0.19/0.49 m_Ack: ( $i * $i ) > $i)).
% 0.19/0.49 tff(elid_type, type, (
% 0.19/0.49 elid: $i)).
% 0.19/0.49 tff(m_Ldr_type, type, (
% 0.19/0.49 m_Ldr: $i > $i)).
% 0.19/0.49 tff(nbr_proc_type, type, (
% 0.19/0.49 nbr_proc: $i)).
% 0.19/0.49 tff(tptp_fun_W0_7_type, type, (
% 0.19/0.49 tptp_fun_W0_7: $i)).
% 0.19/0.49 tff(tptp_fun_X0_8_type, type, (
% 0.19/0.49 tptp_fun_X0_8: $i)).
% 0.19/0.49 tff(snoc_type, type, (
% 0.19/0.49 snoc: ( $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_Z_6_type, type, (
% 0.19/0.49 tptp_fun_Z_6: $i)).
% 0.19/0.49 tff(wait_type, type, (
% 0.19/0.49 wait: $i)).
% 0.19/0.49 tff(1,plain,
% 0.19/0.49 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((~(host(X!4) = host(Z!6))) & (~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (~(host(X!4) = host(Z!6))) & (~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 ((![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) <=> (![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 ((![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) <=> (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(4,plain,
% 0.19/0.50 (((~(host(X!4) = host(Z!6))) & ((~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)))) <=> ((~(host(X!4) = host(Z!6))) & (~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 ((~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) <=> (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 (((~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7))) <=> ((~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.50 tff(7,plain,
% 0.19/0.50 (((~(host(X!4) = host(Z!6))) & ((~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)))) <=> ((~(host(X!4) = host(Z!6))) & ((~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[6])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (((~(host(X!4) = host(Z!6))) & ((~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)))) <=> ((~(host(X!4) = host(Z!6))) & (~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[7, 4])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((~(host(X!4) = host(Z!6))) & ((~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((~(host(X!4) = host(Z!6))) & (~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[8, 3, 2])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((~(host(X!4) = host(Z!6))) & ((~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (~(host(X!4) = host(Z!6))) & (~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[9, 1])).
% 0.19/0.51 tff(11,plain,
% 0.19/0.51 ((~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i] : ((host(X) = host(W0)) | ![X0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(s(host(X)), host(Z))) & setIn(X0, alive) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X))))) | (~(host(X) = host(X0)))) | (~(s(host(X)) = host(W0))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i] : ((host(X) = host(W0)) | ![X0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(s(host(X)), host(Z))) & setIn(X0, alive) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X))))) | (~(host(X) = host(X0)))) | (~(s(host(X)) = host(W0))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(12,plain,
% 0.19/0.51 ((~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((((((((![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![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] : ((((~setIn(Z, alive)) & leq(Pid0, Z)) & (host(Pid0) = host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((setIn(Z, alive) & setIn(Pid0, alive)) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm)) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (Pid0 = Z))) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & (~leq(host(Pid0), host(Z)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))))) => ((![Z: $i] : (((~leq(host(X), Z)) & leq(s(zero), Z)) => (setIn(Z, index(down, host(X))) | (Z = host(Y)))) & (index(status, host(X)) = elec_1)) => ((~leq(nbr_proc, host(X))) => ![Z: $i] : ((~(host(X) = host(Z))) => ![W0: $i] : ((s(host(X)) = host(W0)) => ((~(host(X) = host(W0))) => ![X0: $i] : ((host(X) = host(X0)) => ((((~leq(s(host(X)), host(Z))) & setIn(X0, alive)) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X)))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i] : ((host(X) = host(W0)) | ![X0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(s(host(X)), host(Z))) & setIn(X0, alive) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X))))) | (~(host(X) = host(X0)))) | (~(s(host(X)) = host(W0))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(13,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((((((((![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![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] : ((((~setIn(Z, alive)) & leq(Pid0, Z)) & (host(Pid0) = host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((setIn(Z, alive) & setIn(Pid0, alive)) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm)) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (Pid0 = Z))) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & (~leq(host(Pid0), host(Z)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))))) => ((![Z: $i] : (((~leq(host(X), Z)) & leq(s(zero), Z)) => (setIn(Z, index(down, host(X))) | (Z = host(Y)))) & (index(status, host(X)) = elec_1)) => ((~leq(nbr_proc, host(X))) => ![Z: $i] : ((~(host(X) = host(Z))) => ![W0: $i] : ((s(host(X)) = host(W0)) => ((~(host(X) = host(W0))) => ![X0: $i] : ((host(X) = host(X0)) => ((((~leq(s(host(X)), host(Z))) & setIn(X0, alive)) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X)))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.36/0.52 tff(14,plain,
% 0.36/0.52 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i] : ((host(X) = host(W0)) | ![X0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(s(host(X)), host(Z))) & setIn(X0, alive) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X))))) | (~(host(X) = host(X0)))) | (~(s(host(X)) = host(W0))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.36/0.52 tff(15,plain,
% 0.36/0.52 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i] : ((host(X) = host(W0)) | ![X0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(s(host(X)), host(Z))) & setIn(X0, alive) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X))))) | (~(host(X) = host(X0)))) | (~(s(host(X)) = host(W0))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.36/0.52 tff(16,plain,
% 0.36/0.52 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i] : ((host(X) = host(W0)) | ![X0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(s(host(X)), host(Z))) & setIn(X0, alive) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X))))) | (~(host(X) = host(X0)))) | (~(s(host(X)) = host(W0))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.36/0.52 tff(17,plain,
% 0.36/0.52 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i] : ((host(X) = host(W0)) | ![X0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(s(host(X)), host(Z))) & setIn(X0, alive) & elem(m_Halt(X0), snoc(queue(host(W0)), m_Halt(X))))) | (~(host(X) = host(X0)))) | (~(s(host(X)) = host(W0))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.36/0.53 tff(18,plain,
% 0.36/0.53 ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (~(host(X!4) = host(Z!6))) & (~(host(X!4) = host(W0!7))) & (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))) & (s(host(X!4)) = host(W0!7)) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i] : leq(index(pendack, host(Z)), nbr_proc) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(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)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, 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(Pid0, alive) & elem(m_Ack(Pid0, 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] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, 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, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.36/0.53 tff(19,plain,
% 0.36/0.53 (queue(host(X!4)) = cons(m_Down(Y!3), V!5)),
% 0.36/0.53 inference(and_elim,[status(thm)],[18])).
% 0.36/0.53 tff(20,plain,
% 0.36/0.53 (cons(m_Down(Y!3), V!5) = queue(host(X!4))),
% 0.36/0.53 inference(symmetry,[status(thm)],[19])).
% 0.36/0.53 tff(21,plain,
% 0.36/0.53 (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> elem(m_Down(Y!3), queue(host(X!4)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[20])).
% 0.36/0.53 tff(22,plain,
% 0.36/0.53 (elem(m_Down(Y!3), queue(host(X!4))) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.36/0.53 inference(symmetry,[status(thm)],[21])).
% 0.36/0.53 tff(23,plain,
% 0.36/0.53 ((~elem(m_Down(Y!3), queue(host(X!4)))) <=> (~elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[22])).
% 0.36/0.53 tff(24,assumption,(~elem(m_Down(Y!3), queue(host(X!4)))), introduced(assumption)).
% 0.36/0.53 tff(25,plain,
% 0.36/0.53 (~elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.36/0.53 tff(26,plain,
% 0.36/0.53 (^[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))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(27,plain,
% 0.36/0.53 (![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)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[26])).
% 0.36/0.53 tff(28,plain,
% 0.36/0.53 (![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)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(29,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 0.36/0.53 tff(30,plain,
% 0.36/0.53 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.36/0.53 tff(31,plain,(
% 0.36/0.53 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.36/0.53 inference(skolemize,[status(sab)],[30])).
% 0.36/0.53 tff(32,plain,
% 0.36/0.53 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.36/0.53 tff(33,plain,
% 0.36/0.53 (((~![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)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(34,plain,
% 0.36/0.53 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> $true) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(35,plain,
% 0.36/0.53 (($true | elem(m_Down(Y!3), V!5)) <=> $true),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(36,plain,
% 0.36/0.53 ((m_Down(Y!3) = m_Down(Y!3)) <=> $true),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(37,plain,
% 0.36/0.53 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> ($true | elem(m_Down(Y!3), V!5))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[36])).
% 0.36/0.53 tff(38,plain,
% 0.36/0.53 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> $true),
% 0.36/0.53 inference(transitivity,[status(thm)],[37, 35])).
% 0.36/0.53 tff(39,plain,
% 0.36/0.53 ((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)),
% 0.36/0.53 inference(monotonicity,[status(thm)],[38])).
% 0.36/0.53 tff(40,plain,
% 0.36/0.53 ((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))),
% 0.36/0.53 inference(transitivity,[status(thm)],[39, 34])).
% 0.36/0.53 tff(41,plain,
% 0.36/0.53 (((~![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)))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[40])).
% 0.38/0.53 tff(42,plain,
% 0.38/0.53 (((~![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)))),
% 0.38/0.53 inference(transitivity,[status(thm)],[41, 33])).
% 0.38/0.53 tff(43,plain,
% 0.38/0.53 ((~![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)))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(44,plain,
% 0.38/0.53 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.38/0.53 tff(45,plain,
% 0.38/0.53 (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[44, 32])).
% 0.38/0.53 tff(46,plain,
% 0.38/0.53 ($false),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[45, 25])).
% 0.38/0.53 tff(47,plain,(elem(m_Down(Y!3), queue(host(X!4)))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.53 tff(48,plain,
% 0.38/0.53 (~((~(setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm))) | (~((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4))))) | (~(host(X!4) = host(X0!8))))),
% 0.38/0.53 inference(and_elim,[status(thm)],[18])).
% 0.38/0.53 tff(49,plain,
% 0.38/0.53 (host(X!4) = host(X0!8)),
% 0.38/0.53 inference(or_elim,[status(thm)],[48])).
% 0.38/0.53 tff(50,plain,
% 0.38/0.53 (host(X0!8) = host(X!4)),
% 0.38/0.53 inference(symmetry,[status(thm)],[49])).
% 0.38/0.53 tff(51,plain,
% 0.38/0.53 (leq(host(X0!8), host(Z!6)) <=> leq(host(X!4), host(Z!6))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[50])).
% 0.38/0.53 tff(52,plain,
% 0.38/0.53 ((~leq(host(X0!8), host(Z!6))) <=> (~leq(host(X!4), host(Z!6)))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[51])).
% 0.38/0.53 tff(53,plain,
% 0.38/0.53 (^[X: $i, Y: $i] : refl((~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(54,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> ![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[53])).
% 0.38/0.53 tff(55,plain,
% 0.38/0.53 (^[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)))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(56,plain,
% 0.38/0.53 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[55])).
% 0.38/0.53 tff(57,plain,
% 0.38/0.53 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(58,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_61')).
% 0.38/0.53 tff(59,plain,
% 0.38/0.53 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.38/0.53 tff(60,plain,(
% 0.38/0.53 ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.38/0.53 inference(skolemize,[status(sab)],[59])).
% 0.38/0.53 tff(61,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.38/0.53 tff(62,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.38/0.53 tff(63,plain,
% 0.38/0.53 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(host(Z!6), host(X0!8))) | (~leq(host(X0!8), host(Z!6)))) <=> (host(Z!6) = host(X0!8))))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(64,plain,
% 0.38/0.53 (~(((~leq(host(Z!6), host(X0!8))) | (~leq(host(X0!8), host(Z!6)))) <=> (host(Z!6) = host(X0!8)))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.38/0.53 tff(65,plain,
% 0.38/0.53 ((host(Z!6) = host(X!4)) <=> (host(X!4) = host(Z!6))),
% 0.38/0.53 inference(commutativity,[status(thm)],[])).
% 0.38/0.53 tff(66,plain,
% 0.38/0.53 ((host(Z!6) = host(X0!8)) <=> (host(Z!6) = host(X!4))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[50])).
% 0.38/0.53 tff(67,plain,
% 0.38/0.53 ((host(Z!6) = host(X0!8)) <=> (host(X!4) = host(Z!6))),
% 0.38/0.53 inference(transitivity,[status(thm)],[66, 65])).
% 0.38/0.53 tff(68,plain,
% 0.38/0.53 ((host(X!4) = host(Z!6)) <=> (host(Z!6) = host(X0!8))),
% 0.38/0.53 inference(symmetry,[status(thm)],[67])).
% 0.38/0.53 tff(69,plain,
% 0.38/0.53 ((~(host(X!4) = host(Z!6))) <=> (~(host(Z!6) = host(X0!8)))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[68])).
% 0.38/0.53 tff(70,plain,
% 0.38/0.53 (~(host(X!4) = host(Z!6))),
% 0.38/0.53 inference(and_elim,[status(thm)],[18])).
% 0.38/0.53 tff(71,plain,
% 0.38/0.53 (~(host(Z!6) = host(X0!8))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.38/0.53 tff(72,plain,
% 0.38/0.53 ((((~leq(host(Z!6), host(X0!8))) | (~leq(host(X0!8), host(Z!6)))) <=> (host(Z!6) = host(X0!8))) | ((~leq(host(Z!6), host(X0!8))) | (~leq(host(X0!8), host(Z!6)))) | (host(Z!6) = host(X0!8))),
% 0.38/0.53 inference(tautology,[status(thm)],[])).
% 0.38/0.53 tff(73,plain,
% 0.38/0.53 ((~leq(host(Z!6), host(X0!8))) | (~leq(host(X0!8), host(Z!6)))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[72, 71, 64])).
% 0.38/0.53 tff(74,plain,
% 0.38/0.53 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> leq(s(X), s(Y))) <=> (leq(X, Y) <=> leq(s(X), s(Y))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(75,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y))) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[74])).
% 0.38/0.53 tff(76,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y))) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(77,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_63')).
% 0.38/0.53 tff(78,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.38/0.53 tff(79,plain,(
% 0.38/0.53 ![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))),
% 0.38/0.53 inference(skolemize,[status(sab)],[78])).
% 0.38/0.53 tff(80,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.38/0.53 tff(81,plain,
% 0.38/0.53 ((~![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))) | (leq(host(Z!6), host(X0!8)) <=> leq(s(host(Z!6)), s(host(X0!8))))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(82,plain,
% 0.38/0.53 (leq(host(Z!6), host(X0!8)) <=> leq(s(host(Z!6)), s(host(X0!8)))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.38/0.53 tff(83,plain,
% 0.38/0.53 (s(host(X0!8)) = s(host(X!4))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[50])).
% 0.38/0.53 tff(84,plain,
% 0.38/0.53 (s(host(X!4)) = s(host(X0!8))),
% 0.38/0.53 inference(symmetry,[status(thm)],[83])).
% 0.38/0.53 tff(85,plain,
% 0.38/0.53 (s(host(X!4)) = host(W0!7)),
% 0.38/0.53 inference(and_elim,[status(thm)],[18])).
% 0.38/0.53 tff(86,plain,
% 0.38/0.53 (host(W0!7) = s(host(X!4))),
% 0.38/0.53 inference(symmetry,[status(thm)],[85])).
% 0.38/0.53 tff(87,plain,
% 0.38/0.53 (host(W0!7) = s(host(X0!8))),
% 0.38/0.53 inference(transitivity,[status(thm)],[86, 84])).
% 0.38/0.53 tff(88,plain,
% 0.38/0.53 (leq(s(host(Z!6)), host(W0!7)) <=> leq(s(host(Z!6)), s(host(X0!8)))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[87])).
% 0.38/0.53 tff(89,plain,
% 0.38/0.53 (^[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)))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(90,plain,
% 0.38/0.53 (![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))))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[89])).
% 0.38/0.53 tff(91,plain,
% 0.38/0.53 (![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))))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(92,plain,
% 0.38/0.53 (^[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)))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(93,plain,
% 0.38/0.53 (![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))))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[92])).
% 0.38/0.53 tff(94,axiom,(![X: $i, Y: $i] : (leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_64')).
% 0.38/0.53 tff(95,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.38/0.53 tff(96,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.38/0.53 tff(97,plain,(
% 0.38/0.53 ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.38/0.53 inference(skolemize,[status(sab)],[96])).
% 0.38/0.53 tff(98,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.38/0.53 tff(99,plain,
% 0.38/0.53 ((~![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))) | (leq(s(host(Z!6)), s(host(W0!7))) <=> (leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7)))))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(100,plain,
% 0.38/0.53 (leq(s(host(Z!6)), s(host(W0!7))) <=> (leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7))))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.38/0.53 tff(101,plain,
% 0.38/0.53 ((~![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))) | (leq(host(Z!6), host(W0!7)) <=> leq(s(host(Z!6)), s(host(W0!7))))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(102,plain,
% 0.38/0.53 (leq(host(Z!6), host(W0!7)) <=> leq(s(host(Z!6)), s(host(W0!7)))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[101, 80])).
% 0.38/0.53 tff(103,plain,
% 0.38/0.53 (leq(host(W0!7), host(Z!6)) <=> leq(s(host(X!4)), host(Z!6))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[86])).
% 0.38/0.53 tff(104,plain,
% 0.38/0.53 (leq(s(host(X!4)), host(Z!6)) <=> leq(host(W0!7), host(Z!6))),
% 0.38/0.53 inference(symmetry,[status(thm)],[103])).
% 0.38/0.53 tff(105,plain,
% 0.38/0.53 ((~leq(s(host(X!4)), host(Z!6))) <=> (~leq(host(W0!7), host(Z!6)))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[104])).
% 0.38/0.53 tff(106,plain,
% 0.38/0.53 ((~leq(s(host(X!4)), host(Z!6))) & setIn(X0!8, alive) & elem(m_Halt(X0!8), snoc(queue(host(W0!7)), m_Halt(X!4)))),
% 0.38/0.53 inference(or_elim,[status(thm)],[48])).
% 0.38/0.53 tff(107,plain,
% 0.38/0.53 (~leq(s(host(X!4)), host(Z!6))),
% 0.38/0.53 inference(and_elim,[status(thm)],[106])).
% 0.38/0.53 tff(108,plain,
% 0.38/0.53 (~leq(host(W0!7), host(Z!6))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[107, 105])).
% 0.38/0.53 tff(109,plain,
% 0.38/0.53 (^[X: $i, Y: $i] : refl((leq(Y, X) | leq(X, Y)) <=> (leq(Y, X) | leq(X, Y)))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(110,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[109])).
% 0.38/0.53 tff(111,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(112,plain,
% 0.38/0.53 (^[X: $i, Y: $i] : rewrite((leq(X, Y) | leq(Y, X)) <=> (leq(Y, X) | leq(X, Y)))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(113,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(X, Y) | leq(Y, X)) <=> ![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[112])).
% 0.38/0.53 tff(114,axiom,(![X: $i, Y: $i] : (leq(X, Y) | leq(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_60')).
% 0.38/0.53 tff(115,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.38/0.53 tff(116,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.38/0.53 tff(117,plain,(
% 0.38/0.53 ![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.38/0.53 inference(skolemize,[status(sab)],[116])).
% 0.38/0.53 tff(118,plain,
% 0.38/0.53 (![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.38/0.53 tff(119,plain,
% 0.38/0.53 (((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | (leq(host(Z!6), host(W0!7)) | leq(host(W0!7), host(Z!6)))) <=> ((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | leq(host(Z!6), host(W0!7)) | leq(host(W0!7), host(Z!6)))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(120,plain,
% 0.38/0.53 ((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | (leq(host(Z!6), host(W0!7)) | leq(host(W0!7), host(Z!6)))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(121,plain,
% 0.38/0.53 ((~![X: $i, Y: $i] : (leq(Y, X) | leq(X, Y))) | leq(host(Z!6), host(W0!7)) | leq(host(W0!7), host(Z!6))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.38/0.53 tff(122,plain,
% 0.38/0.53 (leq(host(Z!6), host(W0!7)) | leq(host(W0!7), host(Z!6))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.38/0.53 tff(123,plain,
% 0.38/0.53 (leq(host(Z!6), host(W0!7))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[122, 108])).
% 0.38/0.53 tff(124,plain,
% 0.38/0.53 ((~(leq(host(Z!6), host(W0!7)) <=> leq(s(host(Z!6)), s(host(W0!7))))) | (~leq(host(Z!6), host(W0!7))) | leq(s(host(Z!6)), s(host(W0!7)))),
% 0.38/0.53 inference(tautology,[status(thm)],[])).
% 0.38/0.53 tff(125,plain,
% 0.38/0.53 (leq(s(host(Z!6)), s(host(W0!7)))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[124, 123, 102])).
% 0.38/0.53 tff(126,plain,
% 0.38/0.53 ((~(leq(s(host(Z!6)), s(host(W0!7))) <=> (leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7)))))) | (~leq(s(host(Z!6)), s(host(W0!7)))) | (leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7))))),
% 0.38/0.53 inference(tautology,[status(thm)],[])).
% 0.38/0.53 tff(127,plain,
% 0.38/0.53 ((~(leq(s(host(Z!6)), s(host(W0!7))) <=> (leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7)))))) | (leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7))))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.38/0.53 tff(128,plain,
% 0.38/0.53 (leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7)))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[127, 100])).
% 0.38/0.53 tff(129,plain,
% 0.38/0.53 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7)))))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7))))))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(130,plain,
% 0.38/0.53 ((~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7))))) <=> (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7)))))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(131,plain,
% 0.38/0.53 ((((~leq(s(host(Z!6)), s(host(W0!7)))) | (~leq(s(host(W0!7)), s(host(Z!6))))) <=> (s(host(Z!6)) = s(host(W0!7)))) <=> (((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7))))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(132,plain,
% 0.38/0.53 ((~(((~leq(s(host(Z!6)), s(host(W0!7)))) | (~leq(s(host(W0!7)), s(host(Z!6))))) <=> (s(host(Z!6)) = s(host(W0!7))))) <=> (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7)))))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[131])).
% 0.38/0.53 tff(133,plain,
% 0.38/0.53 ((~(((~leq(s(host(Z!6)), s(host(W0!7)))) | (~leq(s(host(W0!7)), s(host(Z!6))))) <=> (s(host(Z!6)) = s(host(W0!7))))) <=> (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7)))))),
% 0.38/0.53 inference(transitivity,[status(thm)],[132, 130])).
% 0.38/0.53 tff(134,plain,
% 0.38/0.53 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(Z!6)), s(host(W0!7)))) | (~leq(s(host(W0!7)), s(host(Z!6))))) <=> (s(host(Z!6)) = s(host(W0!7)))))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7))))))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[133])).
% 0.38/0.53 tff(135,plain,
% 0.38/0.53 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(Z!6)), s(host(W0!7)))) | (~leq(s(host(W0!7)), s(host(Z!6))))) <=> (s(host(Z!6)) = s(host(W0!7)))))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[134, 129])).
% 0.38/0.54 tff(136,plain,
% 0.38/0.54 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(Z!6)), s(host(W0!7)))) | (~leq(s(host(W0!7)), s(host(Z!6))))) <=> (s(host(Z!6)) = s(host(W0!7)))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(137,plain,
% 0.38/0.54 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7)))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.38/0.54 tff(138,plain,
% 0.38/0.54 (~(((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[137, 62])).
% 0.38/0.54 tff(139,plain,
% 0.38/0.54 ((~![X: $i, Y: $i] : (leq(X, Y) <=> leq(s(X), s(Y)))) | (leq(host(W0!7), host(Z!6)) <=> leq(s(host(W0!7)), s(host(Z!6))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(140,plain,
% 0.38/0.54 (leq(host(W0!7), host(Z!6)) <=> leq(s(host(W0!7)), s(host(Z!6)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[139, 80])).
% 0.38/0.54 tff(141,plain,
% 0.38/0.54 ((~(leq(host(W0!7), host(Z!6)) <=> leq(s(host(W0!7)), s(host(Z!6))))) | leq(host(W0!7), host(Z!6)) | (~leq(s(host(W0!7)), s(host(Z!6))))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(142,plain,
% 0.38/0.54 ((~(leq(host(W0!7), host(Z!6)) <=> leq(s(host(W0!7)), s(host(Z!6))))) | (~leq(s(host(W0!7)), s(host(Z!6))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[141, 108])).
% 0.38/0.54 tff(143,plain,
% 0.38/0.54 (~leq(s(host(W0!7)), s(host(Z!6)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[142, 140])).
% 0.38/0.54 tff(144,plain,
% 0.38/0.54 (((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) | leq(s(host(W0!7)), s(host(Z!6)))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(145,plain,
% 0.38/0.54 ((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.38/0.54 tff(146,plain,
% 0.38/0.54 ((((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7)))) | (~((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7)))))) | (~(s(host(Z!6)) = s(host(W0!7))))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(147,plain,
% 0.38/0.54 ((((~leq(s(host(W0!7)), s(host(Z!6)))) | (~leq(s(host(Z!6)), s(host(W0!7))))) <=> (s(host(Z!6)) = s(host(W0!7)))) | (~(s(host(Z!6)) = s(host(W0!7))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.38/0.54 tff(148,plain,
% 0.38/0.54 (~(s(host(Z!6)) = s(host(W0!7)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[147, 138])).
% 0.38/0.54 tff(149,plain,
% 0.38/0.54 ((~(leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7))))) | leq(s(host(Z!6)), host(W0!7)) | (s(host(Z!6)) = s(host(W0!7)))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(150,plain,
% 0.38/0.54 (leq(s(host(Z!6)), host(W0!7))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[149, 148, 128])).
% 0.38/0.54 tff(151,plain,
% 0.38/0.54 (leq(s(host(Z!6)), s(host(X0!8)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[150, 88])).
% 0.38/0.54 tff(152,plain,
% 0.38/0.54 ((~(leq(host(Z!6), host(X0!8)) <=> leq(s(host(Z!6)), s(host(X0!8))))) | leq(host(Z!6), host(X0!8)) | (~leq(s(host(Z!6)), s(host(X0!8))))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(153,plain,
% 0.38/0.54 (leq(host(Z!6), host(X0!8))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[152, 151, 82])).
% 0.38/0.54 tff(154,plain,
% 0.38/0.54 ((~((~leq(host(Z!6), host(X0!8))) | (~leq(host(X0!8), host(Z!6))))) | (~leq(host(Z!6), host(X0!8))) | (~leq(host(X0!8), host(Z!6)))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(155,plain,
% 0.38/0.54 (~leq(host(X0!8), host(Z!6))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[154, 153, 73])).
% 0.38/0.54 tff(156,plain,
% 0.38/0.54 (~leq(host(X!4), host(Z!6))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[155, 52])).
% 0.38/0.54 tff(157,plain,
% 0.38/0.54 (^[Z: $i, Pid20: $i, Pid0: $i] : refl((leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) <=> (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(158,plain,
% 0.38/0.54 (![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[157])).
% 0.38/0.54 tff(159,plain,
% 0.38/0.54 (^[Z: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)) <=> (~((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))))), ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) <=> (~(~((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))))))), rewrite((~(~((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))))) <=> ((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)))), ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) <=> ((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))))), rewrite((~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) <=> (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))), ((leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) <=> (leq(host(Pid0), host(Z)) | ((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))))), rewrite((leq(host(Pid0), host(Z)) | ((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) <=> (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))), ((leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) <=> (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(160,plain,
% 0.38/0.54 (![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[159])).
% 0.38/0.54 tff(161,plain,
% 0.38/0.54 (![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))),
% 0.38/0.54 inference(and_elim,[status(thm)],[18])).
% 0.38/0.54 tff(162,plain,
% 0.38/0.54 (![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.38/0.54 tff(163,plain,
% 0.38/0.54 (![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.38/0.54 tff(164,plain,
% 0.38/0.54 (index(status, host(X!4)) = elec_1),
% 0.38/0.54 inference(and_elim,[status(thm)],[18])).
% 0.38/0.54 tff(165,plain,
% 0.38/0.54 (setIn(Z!6, alive) & (index(ldr, host(Z!6)) = host(Z!6)) & (index(status, host(Z!6)) = norm)),
% 0.38/0.54 inference(or_elim,[status(thm)],[48])).
% 0.38/0.54 tff(166,plain,
% 0.38/0.54 (index(status, host(Z!6)) = norm),
% 0.38/0.54 inference(and_elim,[status(thm)],[165])).
% 0.38/0.54 tff(167,plain,
% 0.38/0.54 (index(ldr, host(Z!6)) = host(Z!6)),
% 0.38/0.54 inference(and_elim,[status(thm)],[165])).
% 0.38/0.54 tff(168,plain,
% 0.38/0.54 (setIn(Z!6, alive)),
% 0.38/0.54 inference(and_elim,[status(thm)],[165])).
% 0.38/0.54 tff(169,plain,
% 0.38/0.54 (((~![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))) | ((~(index(status, host(X!4)) = elec_1)) | leq(host(X!4), host(Z!6)) | (~setIn(Z!6, alive)) | (~(index(status, host(Z!6)) = norm)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))) | (~(index(status, host(X!4)) = elec_1)) | leq(host(X!4), host(Z!6)) | (~setIn(Z!6, alive)) | (~(index(status, host(Z!6)) = norm)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(170,plain,
% 0.38/0.54 ((leq(host(X!4), host(Z!6)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Z!6, alive)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~(index(status, host(Z!6)) = norm)) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))))) <=> ((~(index(status, host(X!4)) = elec_1)) | leq(host(X!4), host(Z!6)) | (~setIn(Z!6, alive)) | (~(index(status, host(Z!6)) = norm)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(171,plain,
% 0.38/0.54 ((~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))) <=> (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(172,plain,
% 0.38/0.54 ((leq(host(X!4), host(Z!6)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Z!6, alive)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~(index(status, host(Z!6)) = norm)) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))))) <=> (leq(host(X!4), host(Z!6)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Z!6, alive)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~(index(status, host(Z!6)) = norm)) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[171])).
% 0.38/0.54 tff(173,plain,
% 0.38/0.54 ((leq(host(X!4), host(Z!6)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Z!6, alive)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~(index(status, host(Z!6)) = norm)) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))))) <=> ((~(index(status, host(X!4)) = elec_1)) | leq(host(X!4), host(Z!6)) | (~setIn(Z!6, alive)) | (~(index(status, host(Z!6)) = norm)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[172, 170])).
% 0.38/0.54 tff(174,plain,
% 0.38/0.54 (((~![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))) | (leq(host(X!4), host(Z!6)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Z!6, alive)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~(index(status, host(Z!6)) = norm)) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))) | ((~(index(status, host(X!4)) = elec_1)) | leq(host(X!4), host(Z!6)) | (~setIn(Z!6, alive)) | (~(index(status, host(Z!6)) = norm)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[173])).
% 0.38/0.54 tff(175,plain,
% 0.38/0.54 (((~![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))) | (leq(host(X!4), host(Z!6)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Z!6, alive)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~(index(status, host(Z!6)) = norm)) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))) | (~(index(status, host(X!4)) = elec_1)) | leq(host(X!4), host(Z!6)) | (~setIn(Z!6, alive)) | (~(index(status, host(Z!6)) = norm)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[174, 169])).
% 0.38/0.54 tff(176,plain,
% 0.38/0.54 ((~![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))) | (leq(host(X!4), host(Z!6)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Z!6, alive)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~(index(status, host(Z!6)) = norm)) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(177,plain,
% 0.38/0.54 ((~![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_9(Pid0, Pid20))))))) | (~(index(status, host(X!4)) = elec_1)) | leq(host(X!4), host(Z!6)) | (~setIn(Z!6, alive)) | (~(index(status, host(Z!6)) = norm)) | (~(index(ldr, host(Z!6)) = host(Z!6))) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.38/0.54 tff(178,plain,
% 0.38/0.54 (~((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[177, 168, 167, 166, 164, 163, 156, 47])).
% 0.38/0.54 tff(179,plain,
% 0.38/0.54 (((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))) | leq(s(zero), tptp_fun_V0_9(X!4, Y!3))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(180,plain,
% 0.38/0.54 (leq(s(zero), tptp_fun_V0_9(X!4, Y!3))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.38/0.54 tff(181,plain,
% 0.38/0.54 (((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))) | (~leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(182,plain,
% 0.38/0.54 (~leq(host(X!4), tptp_fun_V0_9(X!4, Y!3))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.38/0.54 tff(183,plain,
% 0.38/0.54 (((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))) | (~setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(184,plain,
% 0.38/0.54 (~setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[183, 178])).
% 0.38/0.54 tff(185,plain,
% 0.38/0.54 (((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))) | (~(tptp_fun_V0_9(X!4, Y!3) = host(Y!3)))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(186,plain,
% 0.38/0.55 (~(tptp_fun_V0_9(X!4, Y!3) = host(Y!3))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[185, 178])).
% 0.38/0.55 tff(187,plain,
% 0.38/0.55 (^[Z: $i] : refl(((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(188,plain,
% 0.38/0.55 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))) <=> ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[187])).
% 0.38/0.55 tff(189,plain,
% 0.38/0.55 (^[Z: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(X!4), Z)) & leq(s(zero), Z)) <=> (~(leq(host(X!4), Z) | (~leq(s(zero), Z))))), ((~((~leq(host(X!4), Z)) & leq(s(zero), Z))) <=> (~(~(leq(host(X!4), Z) | (~leq(s(zero), Z))))))), rewrite((~(~(leq(host(X!4), Z) | (~leq(s(zero), Z))))) <=> (leq(host(X!4), Z) | (~leq(s(zero), Z)))), ((~((~leq(host(X!4), Z)) & leq(s(zero), Z))) <=> (leq(host(X!4), Z) | (~leq(s(zero), Z))))), (((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (leq(host(X!4), Z) | (~leq(s(zero), Z)))))), rewrite(((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (leq(host(X!4), Z) | (~leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))), (((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(190,plain,
% 0.38/0.55 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[189])).
% 0.38/0.55 tff(191,plain,
% 0.38/0.55 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z))))),
% 0.38/0.55 inference(and_elim,[status(thm)],[18])).
% 0.38/0.55 tff(192,plain,
% 0.38/0.55 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.38/0.55 tff(193,plain,
% 0.38/0.55 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.38/0.55 tff(194,plain,
% 0.38/0.55 (((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | ((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))) <=> ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | (tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(195,plain,
% 0.38/0.55 ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | ((tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3))))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(196,plain,
% 0.38/0.55 ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | (tptp_fun_V0_9(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_9(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_9(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_9(X!4, Y!3)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.38/0.55 tff(197,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[196, 193, 186, 184, 182, 180])).
% 0.38/0.55 % SZS output end Proof
% 0.38/0.55 % E exiting
%------------------------------------------------------------------------------