TSTP Solution File: SWV467+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV467+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 15:17:41 EDT 2022
% Result : Theorem 2.61s 2.03s
% Output : Proof 2.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SWV467+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.16 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.37 % Computer : n014.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 4 03:50:15 EDT 2022
% 0.13/0.39 % CPUTime :
% 0.13/0.41 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.41 Usage: tptp [options] [-file:]file
% 0.13/0.41 -h, -? prints this message.
% 0.13/0.41 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.41 -m, -model generate model.
% 0.13/0.41 -p, -proof generate proof.
% 0.13/0.41 -c, -core generate unsat core of named formulas.
% 0.13/0.41 -st, -statistics display statistics.
% 0.13/0.41 -t:timeout set timeout (in second).
% 0.13/0.41 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.41 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.41 -<param>:<value> configuration parameter and value.
% 0.13/0.41 -o:<output-file> file to place output in.
% 2.61/2.03 % SZS status Theorem
% 2.61/2.03 % SZS output start Proof
% 2.61/2.03 tff(leq_type, type, (
% 2.61/2.03 leq: ( $i * $i ) > $o)).
% 2.61/2.03 tff(tptp_fun_V0_11_type, type, (
% 2.61/2.03 tptp_fun_V0_11: ( $i * $i ) > $i)).
% 2.61/2.03 tff(tptp_fun_Y_3_type, type, (
% 2.61/2.03 tptp_fun_Y_3: $i)).
% 2.61/2.03 tff(tptp_fun_X_4_type, type, (
% 2.61/2.03 tptp_fun_X_4: $i)).
% 2.61/2.03 tff(host_type, type, (
% 2.61/2.03 host: $i > $i)).
% 2.61/2.03 tff(setIn_type, type, (
% 2.61/2.03 setIn: ( $i * $i ) > $o)).
% 2.61/2.03 tff(index_type, type, (
% 2.61/2.03 index: ( $i * $i ) > $i)).
% 2.61/2.03 tff(down_type, type, (
% 2.61/2.03 down: $i)).
% 2.61/2.03 tff(s_type, type, (
% 2.61/2.03 s: $i > $i)).
% 2.61/2.03 tff(zero_type, type, (
% 2.61/2.03 zero: $i)).
% 2.61/2.03 tff(elem_type, type, (
% 2.61/2.03 elem: ( $i * $i ) > $o)).
% 2.61/2.03 tff(queue_type, type, (
% 2.61/2.03 queue: $i > $i)).
% 2.61/2.03 tff(m_Down_type, type, (
% 2.61/2.03 m_Down: $i > $i)).
% 2.61/2.03 tff(cons_type, type, (
% 2.61/2.03 cons: ( $i * $i ) > $i)).
% 2.61/2.03 tff(tptp_fun_V_5_type, type, (
% 2.61/2.03 tptp_fun_V_5: $i)).
% 2.61/2.03 tff(pendack_type, type, (
% 2.61/2.03 pendack: $i)).
% 2.61/2.03 tff(elec_2_type, type, (
% 2.61/2.03 elec_2: $i)).
% 2.61/2.03 tff(status_type, type, (
% 2.61/2.03 status: $i)).
% 2.61/2.03 tff(nbr_proc_type, type, (
% 2.61/2.03 nbr_proc: $i)).
% 2.61/2.03 tff(m_Ack_type, type, (
% 2.61/2.03 m_Ack: ( $i * $i ) > $i)).
% 2.61/2.03 tff(alive_type, type, (
% 2.61/2.03 alive: $i)).
% 2.61/2.03 tff(norm_type, type, (
% 2.61/2.03 norm: $i)).
% 2.61/2.03 tff(ldr_type, type, (
% 2.61/2.03 ldr: $i)).
% 2.61/2.03 tff(elec_1_type, type, (
% 2.61/2.03 elec_1: $i)).
% 2.61/2.03 tff(m_Halt_type, type, (
% 2.61/2.03 m_Halt: $i > $i)).
% 2.61/2.03 tff(elid_type, type, (
% 2.61/2.03 elid: $i)).
% 2.61/2.03 tff(m_Ldr_type, type, (
% 2.61/2.03 m_Ldr: $i > $i)).
% 2.61/2.03 tff(tptp_fun_Y0_8_type, type, (
% 2.61/2.03 tptp_fun_Y0_8: $i)).
% 2.61/2.03 tff(tptp_fun_X0_9_type, type, (
% 2.61/2.03 tptp_fun_X0_9: $i)).
% 2.61/2.03 tff(tptp_fun_W0_10_type, type, (
% 2.61/2.03 tptp_fun_W0_10: $i)).
% 2.61/2.03 tff(tptp_fun_V0_7_type, type, (
% 2.61/2.03 tptp_fun_V0_7: $i)).
% 2.61/2.03 tff(setEmpty_type, type, (
% 2.61/2.03 setEmpty: $i)).
% 2.61/2.03 tff(tptp_fun_Z_6_type, type, (
% 2.61/2.03 tptp_fun_Z_6: $i)).
% 2.61/2.03 tff(wait_type, type, (
% 2.61/2.03 wait: $i)).
% 2.61/2.03 tff(1,plain,
% 2.61/2.03 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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))) & ((~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8))))))))) & leq(nbr_proc, host(X!4)) & (![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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))) & (~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))) & leq(nbr_proc, host(X!4)) & ![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 2.61/2.03 inference(rewrite,[status(thm)],[])).
% 2.61/2.03 tff(2,plain,
% 2.61/2.03 ((![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) <=> (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 2.61/2.03 inference(rewrite,[status(thm)],[])).
% 2.61/2.03 tff(3,plain,
% 2.61/2.03 ((![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))),
% 2.61/2.03 inference(rewrite,[status(thm)],[])).
% 2.61/2.03 tff(4,plain,
% 2.61/2.03 ((~(~leq(nbr_proc, host(X!4)))) <=> leq(nbr_proc, host(X!4))),
% 2.61/2.03 inference(rewrite,[status(thm)],[])).
% 2.61/2.03 tff(5,plain,
% 2.61/2.03 (((~setIn(host(Z!6), setEmpty)) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))))) <=> ((~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))))),
% 2.61/2.04 inference(rewrite,[status(thm)],[])).
% 2.61/2.04 tff(6,plain,
% 2.61/2.04 (((~(~(host(X!4) = host(V0!7)))) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8))))))))) <=> ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))))),
% 2.61/2.04 inference(rewrite,[status(thm)],[])).
% 2.61/2.04 tff(7,plain,
% 2.61/2.04 (((~setIn(host(Z!6), setEmpty)) & ((~(~(host(X!4) = host(V0!7)))) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))))) <=> ((~setIn(host(Z!6), setEmpty)) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8))))))))))),
% 2.61/2.04 inference(monotonicity,[status(thm)],[6])).
% 2.61/2.04 tff(8,plain,
% 2.61/2.04 (((~setIn(host(Z!6), setEmpty)) & ((~(~(host(X!4) = host(V0!7)))) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))))) <=> ((~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))))),
% 2.61/2.04 inference(transitivity,[status(thm)],[7, 5])).
% 2.61/2.04 tff(9,plain,
% 2.61/2.04 ((~(~setIn(X!4, alive))) <=> setIn(X!4, alive)),
% 2.61/2.04 inference(rewrite,[status(thm)],[])).
% 2.61/2.04 tff(10,plain,
% 2.61/2.04 (((~leq(host(X!4), host(Y!3))) & (~(~setIn(X!4, alive))) & (~((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))) & ((~setIn(host(Z!6), setEmpty)) & ((~(~(host(X!4) = host(V0!7)))) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))))) & (~(~leq(nbr_proc, host(X!4)))) & (![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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))) & ((~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8))))))))) & leq(nbr_proc, host(X!4)) & (![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))))),
% 2.61/2.04 inference(monotonicity,[status(thm)],[9, 8, 4, 3, 2])).
% 2.61/2.04 tff(11,plain,
% 2.61/2.04 (((~leq(host(X!4), host(Y!3))) & (~(~setIn(X!4, alive))) & (~((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))) & ((~setIn(host(Z!6), setEmpty)) & ((~(~(host(X!4) = host(V0!7)))) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))))) & (~(~leq(nbr_proc, host(X!4)))) & (![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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))) & (~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))) & leq(nbr_proc, host(X!4)) & ![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 2.61/2.04 inference(transitivity,[status(thm)],[10, 1])).
% 2.61/2.04 tff(12,plain,
% 2.61/2.04 ((~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 2.61/2.05 inference(rewrite,[status(thm)],[])).
% 2.61/2.05 tff(13,plain,
% 2.61/2.05 ((~![V: $i, W: $i, X: $i, Y: $i] : ((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) => leq(host(Z), index(pendack, host(Pid0))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid20), queue(host(Z)))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Pid20)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = nbr_proc)) & (host(Pid0) = host(Pid30))) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Pid30) = index(pendack, host(Pid0)))) & (host(Pid20) = s(index(pendack, host(Pid0))))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(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] : ((~setIn(host(Z), setEmpty)) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((~(host(X) = host(Y0))) => (((((((setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0)))) & elem(m_Ack(Y0, W0), queue(host(Y0)))) & leq(nbr_proc, s(index(pendack, host(Y0))))) & (index(status, host(Y0)) = elec_2)) & (host(W0) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~(setIn(V0, alive) & (host(X) = host(V0))))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 2.61/2.05 inference(rewrite,[status(thm)],[])).
% 2.61/2.05 tff(14,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : ((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) => leq(host(Z), index(pendack, host(Pid0))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid20), queue(host(Z)))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Pid20)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = nbr_proc)) & (host(Pid0) = host(Pid30))) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Pid30) = index(pendack, host(Pid0)))) & (host(Pid20) = s(index(pendack, host(Pid0))))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(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] : ((~setIn(host(Z), setEmpty)) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((~(host(X) = host(Y0))) => (((((((setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0)))) & elem(m_Ack(Y0, W0), queue(host(Y0)))) & leq(nbr_proc, s(index(pendack, host(Y0))))) & (index(status, host(Y0)) = elec_2)) & (host(W0) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~(setIn(V0, alive) & (host(X) = host(V0))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 2.61/2.05 tff(15,plain,
% 2.61/2.05 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 2.61/2.06 inference(modus_ponens,[status(thm)],[14, 13])).
% 2.61/2.06 tff(16,plain,
% 2.61/2.06 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 2.61/2.06 inference(modus_ponens,[status(thm)],[15, 12])).
% 2.61/2.06 tff(17,plain,
% 2.61/2.06 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 2.61/2.06 inference(modus_ponens,[status(thm)],[16, 12])).
% 2.61/2.06 tff(18,plain,
% 2.61/2.06 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 2.61/2.06 inference(modus_ponens,[status(thm)],[17, 12])).
% 2.61/2.06 tff(19,plain,
% 2.61/2.06 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 2.61/2.06 inference(modus_ponens,[status(thm)],[18, 12])).
% 2.61/2.06 tff(20,plain,
% 2.61/2.06 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 2.61/2.06 inference(modus_ponens,[status(thm)],[19, 12])).
% 2.61/2.06 tff(21,plain,
% 2.61/2.06 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(setIn(Y0, alive) & elem(m_Down(X0), queue(host(Y0))) & elem(m_Ack(Y0, W0), queue(host(Y0))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0))))))))) | (~leq(nbr_proc, host(X))) | (~(![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 2.61/2.07 inference(modus_ponens,[status(thm)],[20, 12])).
% 2.61/2.07 tff(22,plain,
% 2.61/2.07 ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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))) & (~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))) & leq(nbr_proc, host(X!4)) & ![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, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))),
% 2.61/2.07 inference(modus_ponens,[status(thm)],[21, 11])).
% 2.61/2.07 tff(23,plain,
% 2.61/2.07 (queue(host(X!4)) = cons(m_Down(Y!3), V!5)),
% 2.61/2.07 inference(and_elim,[status(thm)],[22])).
% 2.61/2.07 tff(24,plain,
% 2.61/2.07 (elem(m_Down(Y!3), queue(host(X!4))) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 2.61/2.07 inference(monotonicity,[status(thm)],[23])).
% 2.61/2.07 tff(25,plain,
% 2.61/2.07 (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> elem(m_Down(Y!3), queue(host(X!4)))),
% 2.61/2.07 inference(symmetry,[status(thm)],[24])).
% 2.61/2.07 tff(26,assumption,(~elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))), introduced(assumption)).
% 2.61/2.07 tff(27,plain,
% 2.61/2.07 (^[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))))),
% 2.61/2.07 inference(bind,[status(th)],[])).
% 2.61/2.07 tff(28,plain,
% 2.61/2.07 (![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)))),
% 2.61/2.07 inference(quant_intro,[status(thm)],[27])).
% 2.61/2.07 tff(29,plain,
% 2.61/2.07 (![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)))),
% 2.61/2.07 inference(rewrite,[status(thm)],[])).
% 2.61/2.07 tff(30,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 2.61/2.07 tff(31,plain,
% 2.61/2.07 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 2.61/2.07 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.61/2.07 tff(32,plain,(
% 2.61/2.07 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 2.61/2.07 inference(skolemize,[status(sab)],[31])).
% 2.61/2.07 tff(33,plain,
% 2.61/2.07 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 2.61/2.07 inference(modus_ponens,[status(thm)],[32, 28])).
% 2.61/2.07 tff(34,plain,
% 2.61/2.07 (((~![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)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(35,plain,
% 2.71/2.07 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> $true) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(36,plain,
% 2.71/2.07 (($true | elem(m_Down(Y!3), V!5)) <=> $true),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(37,plain,
% 2.71/2.07 ((m_Down(Y!3) = m_Down(Y!3)) <=> $true),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(38,plain,
% 2.71/2.07 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> ($true | elem(m_Down(Y!3), V!5))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[37])).
% 2.71/2.07 tff(39,plain,
% 2.71/2.07 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> $true),
% 2.71/2.07 inference(transitivity,[status(thm)],[38, 36])).
% 2.71/2.07 tff(40,plain,
% 2.71/2.07 ((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)),
% 2.71/2.07 inference(monotonicity,[status(thm)],[39])).
% 2.71/2.07 tff(41,plain,
% 2.71/2.07 ((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))),
% 2.71/2.07 inference(transitivity,[status(thm)],[40, 35])).
% 2.71/2.07 tff(42,plain,
% 2.71/2.07 (((~![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)))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[41])).
% 2.71/2.07 tff(43,plain,
% 2.71/2.07 (((~![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)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[42, 34])).
% 2.71/2.07 tff(44,plain,
% 2.71/2.07 ((~![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)))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(45,plain,
% 2.71/2.07 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.71/2.07 tff(46,plain,
% 2.71/2.07 ($false),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[45, 33, 26])).
% 2.71/2.07 tff(47,plain,(elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))), inference(lemma,lemma(discharge,[]))).
% 2.71/2.07 tff(48,plain,
% 2.71/2.07 (elem(m_Down(Y!3), queue(host(X!4)))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[47, 25])).
% 2.71/2.07 tff(49,plain,
% 2.71/2.07 (^[X: $i, Y: $i] : refl(((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 2.71/2.07 inference(bind,[status(th)],[])).
% 2.71/2.07 tff(50,plain,
% 2.71/2.07 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 2.71/2.07 inference(quant_intro,[status(thm)],[49])).
% 2.71/2.07 tff(51,plain,
% 2.71/2.07 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 2.71/2.07 inference(bind,[status(th)],[])).
% 2.71/2.07 tff(52,plain,
% 2.71/2.07 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 2.71/2.07 inference(quant_intro,[status(thm)],[51])).
% 2.71/2.07 tff(53,plain,
% 2.71/2.07 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(54,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_61')).
% 2.71/2.07 tff(55,plain,
% 2.71/2.07 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[54, 53])).
% 2.71/2.07 tff(56,plain,(
% 2.71/2.07 ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 2.71/2.07 inference(skolemize,[status(sab)],[55])).
% 2.71/2.07 tff(57,plain,
% 2.71/2.07 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[56, 52])).
% 2.71/2.07 tff(58,plain,
% 2.71/2.07 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[57, 50])).
% 2.71/2.07 tff(59,plain,
% 2.71/2.07 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))) <=> (host(V0!7) = nbr_proc))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(60,plain,
% 2.71/2.07 ((~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))) <=> (host(V0!7) = nbr_proc)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[59, 58])).
% 2.71/2.07 tff(61,plain,
% 2.71/2.07 (host(X!4) = host(V0!7)),
% 2.71/2.07 inference(and_elim,[status(thm)],[22])).
% 2.71/2.07 tff(62,plain,
% 2.71/2.07 (host(V0!7) = host(X!4)),
% 2.71/2.07 inference(symmetry,[status(thm)],[61])).
% 2.71/2.07 tff(63,plain,
% 2.71/2.07 (leq(host(V0!7), nbr_proc) <=> leq(host(X!4), nbr_proc)),
% 2.71/2.07 inference(monotonicity,[status(thm)],[62])).
% 2.71/2.07 tff(64,plain,
% 2.71/2.07 (leq(host(X!4), nbr_proc) <=> leq(host(V0!7), nbr_proc)),
% 2.71/2.07 inference(symmetry,[status(thm)],[63])).
% 2.71/2.07 tff(65,plain,
% 2.71/2.07 (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 2.71/2.07 inference(bind,[status(th)],[])).
% 2.71/2.07 tff(66,plain,
% 2.71/2.07 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 2.71/2.07 inference(quant_intro,[status(thm)],[65])).
% 2.71/2.07 tff(67,plain,
% 2.71/2.07 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(68,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 2.71/2.07 tff(69,plain,
% 2.71/2.07 (![P: $i] : leq(host(P), nbr_proc)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[68, 67])).
% 2.71/2.07 tff(70,plain,(
% 2.71/2.07 ![P: $i] : leq(host(P), nbr_proc)),
% 2.71/2.07 inference(skolemize,[status(sab)],[69])).
% 2.71/2.07 tff(71,plain,
% 2.71/2.07 (![P: $i] : leq(host(P), nbr_proc)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[70, 66])).
% 2.71/2.07 tff(72,plain,
% 2.71/2.07 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X!4), nbr_proc)),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(73,plain,
% 2.71/2.07 (leq(host(X!4), nbr_proc)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[72, 71])).
% 2.71/2.07 tff(74,plain,
% 2.71/2.07 (leq(host(V0!7), nbr_proc)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[73, 64])).
% 2.71/2.07 tff(75,plain,
% 2.71/2.07 (leq(nbr_proc, host(V0!7)) <=> leq(nbr_proc, host(X!4))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[62])).
% 2.71/2.07 tff(76,plain,
% 2.71/2.07 (leq(nbr_proc, host(X!4)) <=> leq(nbr_proc, host(V0!7))),
% 2.71/2.07 inference(symmetry,[status(thm)],[75])).
% 2.71/2.07 tff(77,plain,
% 2.71/2.07 (leq(nbr_proc, host(X!4))),
% 2.71/2.07 inference(and_elim,[status(thm)],[22])).
% 2.71/2.07 tff(78,plain,
% 2.71/2.07 (leq(nbr_proc, host(V0!7))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[77, 76])).
% 2.71/2.07 tff(79,plain,
% 2.71/2.07 ((~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))) | (~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7)))),
% 2.71/2.07 inference(tautology,[status(thm)],[])).
% 2.71/2.07 tff(80,plain,
% 2.71/2.07 (~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[79, 78, 74])).
% 2.71/2.07 tff(81,plain,
% 2.71/2.07 ((~((~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))) <=> (host(V0!7) = nbr_proc))) | ((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7)))) | (host(V0!7) = nbr_proc)),
% 2.71/2.07 inference(tautology,[status(thm)],[])).
% 2.71/2.07 tff(82,plain,
% 2.71/2.07 (host(V0!7) = nbr_proc),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[81, 80, 60])).
% 2.71/2.07 tff(83,plain,
% 2.71/2.07 (host(X!4) = nbr_proc),
% 2.71/2.07 inference(transitivity,[status(thm)],[61, 82])).
% 2.71/2.07 tff(84,plain,
% 2.71/2.07 (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))))),
% 2.71/2.07 inference(and_elim,[status(thm)],[22])).
% 2.71/2.07 tff(85,plain,
% 2.71/2.07 (setIn(Y0!8, alive) & elem(m_Down(X0!9), queue(host(Y0!8))) & elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8))))),
% 2.71/2.07 inference(or_elim,[status(thm)],[84])).
% 2.71/2.07 tff(86,plain,
% 2.71/2.07 (host(X0!9) = s(index(pendack, host(Y0!8)))),
% 2.71/2.07 inference(and_elim,[status(thm)],[85])).
% 2.71/2.07 tff(87,plain,
% 2.71/2.07 (s(index(pendack, host(Y0!8))) = host(X0!9)),
% 2.71/2.07 inference(symmetry,[status(thm)],[86])).
% 2.71/2.07 tff(88,plain,
% 2.71/2.07 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc)))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(89,plain,
% 2.71/2.07 (((~((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc)) <=> ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc))),
% 2.71/2.07 inference(rewrite,[status(thm)],[])).
% 2.71/2.07 tff(90,plain,
% 2.71/2.07 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc)))),
% 2.71/2.07 inference(monotonicity,[status(thm)],[89])).
% 2.71/2.07 tff(91,plain,
% 2.71/2.07 (((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc))) <=> ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc)))),
% 2.71/2.07 inference(transitivity,[status(thm)],[90, 88])).
% 2.71/2.07 tff(92,plain,
% 2.71/2.07 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(s(index(pendack, host(Y0!8))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc))),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(93,plain,
% 2.71/2.07 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc))),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[92, 91])).
% 2.71/2.07 tff(94,plain,
% 2.71/2.07 ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[93, 58])).
% 2.71/2.07 tff(95,plain,
% 2.71/2.07 (leq(s(index(pendack, host(Y0!8))), nbr_proc) <=> leq(host(X0!9), nbr_proc)),
% 2.71/2.07 inference(monotonicity,[status(thm)],[87])).
% 2.71/2.07 tff(96,plain,
% 2.71/2.07 (leq(host(X0!9), nbr_proc) <=> leq(s(index(pendack, host(Y0!8))), nbr_proc)),
% 2.71/2.07 inference(symmetry,[status(thm)],[95])).
% 2.71/2.07 tff(97,plain,
% 2.71/2.07 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X0!9), nbr_proc)),
% 2.71/2.07 inference(quant_inst,[status(thm)],[])).
% 2.71/2.07 tff(98,plain,
% 2.71/2.07 (leq(host(X0!9), nbr_proc)),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[97, 71])).
% 2.71/2.07 tff(99,plain,
% 2.71/2.07 (leq(s(index(pendack, host(Y0!8))), nbr_proc)),
% 2.71/2.07 inference(modus_ponens,[status(thm)],[98, 96])).
% 2.71/2.07 tff(100,plain,
% 2.71/2.07 (leq(nbr_proc, s(index(pendack, host(Y0!8))))),
% 2.71/2.07 inference(and_elim,[status(thm)],[85])).
% 2.71/2.07 tff(101,plain,
% 2.71/2.07 ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc))),
% 2.71/2.07 inference(tautology,[status(thm)],[])).
% 2.71/2.07 tff(102,plain,
% 2.71/2.07 ((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc))),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[101, 100])).
% 2.71/2.07 tff(103,plain,
% 2.71/2.07 (~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[102, 99])).
% 2.71/2.07 tff(104,plain,
% 2.71/2.07 ((~((~((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc)))) <=> (s(index(pendack, host(Y0!8))) = nbr_proc))) | ((~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~leq(s(index(pendack, host(Y0!8))), nbr_proc))) | (s(index(pendack, host(Y0!8))) = nbr_proc)),
% 2.71/2.07 inference(tautology,[status(thm)],[])).
% 2.71/2.07 tff(105,plain,
% 2.71/2.07 (s(index(pendack, host(Y0!8))) = nbr_proc),
% 2.71/2.07 inference(unit_resolution,[status(thm)],[104, 103, 94])).
% 2.71/2.07 tff(106,plain,
% 2.71/2.07 (nbr_proc = s(index(pendack, host(Y0!8)))),
% 2.71/2.07 inference(symmetry,[status(thm)],[105])).
% 2.71/2.07 tff(107,plain,
% 2.71/2.07 (host(X!4) = host(X0!9)),
% 2.71/2.07 inference(transitivity,[status(thm)],[61, 82, 106, 87])).
% 2.71/2.07 tff(108,plain,
% 2.71/2.07 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : refl(((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) <=> ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))))),
% 2.71/2.07 inference(bind,[status(th)],[])).
% 2.71/2.07 tff(109,plain,
% 2.71/2.07 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))),
% 2.71/2.08 inference(quant_intro,[status(thm)],[108])).
% 2.71/2.08 tff(110,plain,
% 2.71/2.08 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z)))) <=> (~((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))))), ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) <=> (~(~((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))))))), rewrite((~(~((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))))) <=> ((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))))), ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) <=> ((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))))), rewrite((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) <=> (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))), (((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> (((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))))), rewrite((((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))), (((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))))),
% 2.71/2.08 inference(bind,[status(th)],[])).
% 2.71/2.08 tff(111,plain,
% 2.71/2.08 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))),
% 2.71/2.08 inference(quant_intro,[status(thm)],[110])).
% 2.71/2.08 tff(112,plain,
% 2.71/2.08 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))),
% 2.71/2.08 inference(and_elim,[status(thm)],[22])).
% 2.71/2.08 tff(113,plain,
% 2.71/2.08 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.71/2.08 tff(114,plain,
% 2.71/2.08 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[113, 109])).
% 2.71/2.08 tff(115,plain,
% 2.71/2.08 (index(status, host(X!4)) = elec_1),
% 2.71/2.08 inference(and_elim,[status(thm)],[22])).
% 2.71/2.08 tff(116,plain,
% 2.71/2.08 (elem(m_Down(X0!9), queue(host(Y0!8)))),
% 2.71/2.08 inference(and_elim,[status(thm)],[85])).
% 2.71/2.08 tff(117,plain,
% 2.71/2.08 (setIn(Y0!8, alive)),
% 2.71/2.08 inference(and_elim,[status(thm)],[85])).
% 2.71/2.08 tff(118,plain,
% 2.71/2.08 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(X!4)) = elec_1)) | (~(host(X!4) = host(X0!9))) | (~(host(X!4) = nbr_proc)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(X!4)) = elec_1)) | (~(host(X!4) = host(X0!9))) | (~(host(X!4) = nbr_proc)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(119,plain,
% 2.71/2.08 (((~elem(m_Down(Y!3), queue(host(X!4)))) | (~(host(X!4) = nbr_proc)) | (~(host(X!4) = host(X0!9))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))))) <=> ((~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(X!4)) = elec_1)) | (~(host(X!4) = host(X0!9))) | (~(host(X!4) = nbr_proc)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(120,plain,
% 2.71/2.08 ((~((tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))))) <=> (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))))),
% 2.71/2.08 inference(rewrite,[status(thm)],[])).
% 2.71/2.08 tff(121,plain,
% 2.71/2.08 (((~elem(m_Down(Y!3), queue(host(X!4)))) | (~(host(X!4) = nbr_proc)) | (~(host(X!4) = host(X0!9))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3)))))) <=> ((~elem(m_Down(Y!3), queue(host(X!4)))) | (~(host(X!4) = nbr_proc)) | (~(host(X!4) = host(X0!9))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))))),
% 2.71/2.08 inference(monotonicity,[status(thm)],[120])).
% 2.71/2.08 tff(122,plain,
% 2.71/2.08 (((~elem(m_Down(Y!3), queue(host(X!4)))) | (~(host(X!4) = nbr_proc)) | (~(host(X!4) = host(X0!9))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3)))))) <=> ((~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(X!4)) = elec_1)) | (~(host(X!4) = host(X0!9))) | (~(host(X!4) = nbr_proc)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))))),
% 2.71/2.08 inference(transitivity,[status(thm)],[121, 119])).
% 2.71/2.08 tff(123,plain,
% 2.71/2.08 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~elem(m_Down(Y!3), queue(host(X!4)))) | (~(host(X!4) = nbr_proc)) | (~(host(X!4) = host(X0!9))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(X!4)) = elec_1)) | (~(host(X!4) = host(X0!9))) | (~(host(X!4) = nbr_proc)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))))))),
% 2.71/2.08 inference(monotonicity,[status(thm)],[122])).
% 2.71/2.08 tff(124,plain,
% 2.71/2.08 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~elem(m_Down(Y!3), queue(host(X!4)))) | (~(host(X!4) = nbr_proc)) | (~(host(X!4) = host(X0!9))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(X!4)) = elec_1)) | (~(host(X!4) = host(X0!9))) | (~(host(X!4) = nbr_proc)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))))),
% 2.71/2.08 inference(transitivity,[status(thm)],[123, 118])).
% 2.71/2.08 tff(125,plain,
% 2.71/2.08 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~elem(m_Down(Y!3), queue(host(X!4)))) | (~(host(X!4) = nbr_proc)) | (~(host(X!4) = host(X0!9))) | (~(index(status, host(X!4)) = elec_1)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))))))),
% 2.71/2.08 inference(quant_inst,[status(thm)],[])).
% 2.71/2.08 tff(126,plain,
% 2.71/2.08 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(X!4)) = elec_1)) | (~(host(X!4) = host(X0!9))) | (~(host(X!4) = nbr_proc)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))))),
% 2.71/2.08 inference(modus_ponens,[status(thm)],[125, 124])).
% 2.71/2.08 tff(127,plain,
% 2.71/2.08 ((~elem(m_Down(Y!3), queue(host(X!4)))) | (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))))),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[126, 117, 116, 115, 114, 107, 83])).
% 2.71/2.08 tff(128,plain,
% 2.71/2.08 (~((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[127, 48])).
% 2.71/2.08 tff(129,plain,
% 2.71/2.08 (((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))) | (~leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))),
% 2.71/2.08 inference(tautology,[status(thm)],[])).
% 2.71/2.08 tff(130,plain,
% 2.71/2.08 (~leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[129, 128])).
% 2.71/2.08 tff(131,plain,
% 2.71/2.08 (((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))) | (~(tptp_fun_V0_11(X!4, Y!3) = host(Y!3)))),
% 2.71/2.08 inference(tautology,[status(thm)],[])).
% 2.71/2.08 tff(132,plain,
% 2.71/2.08 (~(tptp_fun_V0_11(X!4, Y!3) = host(Y!3))),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[131, 128])).
% 2.71/2.08 tff(133,plain,
% 2.71/2.08 (((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))) | (~setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))))),
% 2.71/2.08 inference(tautology,[status(thm)],[])).
% 2.71/2.08 tff(134,plain,
% 2.71/2.08 (~setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4)))),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[133, 128])).
% 2.71/2.08 tff(135,plain,
% 2.71/2.08 (((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))) | leq(s(zero), tptp_fun_V0_11(X!4, Y!3))),
% 2.71/2.08 inference(tautology,[status(thm)],[])).
% 2.71/2.08 tff(136,plain,
% 2.71/2.08 (leq(s(zero), tptp_fun_V0_11(X!4, Y!3))),
% 2.71/2.08 inference(unit_resolution,[status(thm)],[135, 128])).
% 2.71/2.08 tff(137,plain,
% 2.71/2.08 (^[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))))),
% 2.71/2.08 inference(bind,[status(th)],[])).
% 2.71/2.08 tff(138,plain,
% 2.71/2.08 (![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)))),
% 2.71/2.08 inference(quant_intro,[status(thm)],[137])).
% 2.71/2.08 tff(139,plain,
% 2.71/2.08 (^[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)))))),
% 2.71/2.09 inference(bind,[status(th)],[])).
% 2.71/2.09 tff(140,plain,
% 2.71/2.09 (![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)))),
% 2.71/2.09 inference(quant_intro,[status(thm)],[139])).
% 2.71/2.09 tff(141,plain,
% 2.71/2.09 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z))))),
% 2.71/2.09 inference(and_elim,[status(thm)],[22])).
% 2.71/2.09 tff(142,plain,
% 2.71/2.09 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[141, 140])).
% 2.71/2.09 tff(143,plain,
% 2.71/2.09 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[142, 138])).
% 2.71/2.09 tff(144,plain,
% 2.71/2.09 (((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | ((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(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)))) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(145,plain,
% 2.71/2.09 (((tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3)))) <=> ((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))),
% 2.71/2.09 inference(rewrite,[status(thm)],[])).
% 2.71/2.09 tff(146,plain,
% 2.71/2.09 (((~![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_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(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)))) | ((~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))))),
% 2.71/2.09 inference(monotonicity,[status(thm)],[145])).
% 2.71/2.09 tff(147,plain,
% 2.71/2.09 (((~![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_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(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)))) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)))),
% 2.71/2.09 inference(transitivity,[status(thm)],[146, 144])).
% 2.71/2.09 tff(148,plain,
% 2.71/2.09 ((~![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_11(X!4, Y!3) = host(Y!3)) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3)) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))))),
% 2.71/2.09 inference(quant_inst,[status(thm)],[])).
% 2.71/2.09 tff(149,plain,
% 2.71/2.09 ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | (~leq(s(zero), tptp_fun_V0_11(X!4, Y!3))) | setIn(tptp_fun_V0_11(X!4, Y!3), index(down, host(X!4))) | (tptp_fun_V0_11(X!4, Y!3) = host(Y!3)) | leq(host(X!4), tptp_fun_V0_11(X!4, Y!3))),
% 2.71/2.09 inference(modus_ponens,[status(thm)],[148, 147])).
% 2.71/2.09 tff(150,plain,
% 2.71/2.09 ($false),
% 2.71/2.09 inference(unit_resolution,[status(thm)],[149, 143, 136, 134, 132, 130])).
% 2.71/2.09 % SZS output end Proof
%------------------------------------------------------------------------------