TSTP Solution File: SWV472+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV472+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 15:17:42 EDT 2022
% Result : Theorem 1.00s 0.88s
% Output : Proof 1.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV472+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 03:54:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.00/0.88 % SZS status Theorem
% 1.00/0.88 % SZS output start Proof
% 1.00/0.88 tff(leq_type, type, (
% 1.00/0.88 leq: ( $i * $i ) > $o)).
% 1.00/0.88 tff(tptp_fun_V0_11_type, type, (
% 1.00/0.88 tptp_fun_V0_11: ( $i * $i ) > $i)).
% 1.00/0.88 tff(tptp_fun_X0_9_type, type, (
% 1.00/0.88 tptp_fun_X0_9: $i)).
% 1.00/0.88 tff(tptp_fun_Y0_8_type, type, (
% 1.00/0.88 tptp_fun_Y0_8: $i)).
% 1.00/0.88 tff(s_type, type, (
% 1.00/0.88 s: $i > $i)).
% 1.00/0.88 tff(zero_type, type, (
% 1.00/0.88 zero: $i)).
% 1.00/0.88 tff(host_type, type, (
% 1.00/0.88 host: $i > $i)).
% 1.00/0.88 tff(setIn_type, type, (
% 1.00/0.88 setIn: ( $i * $i ) > $o)).
% 1.00/0.88 tff(index_type, type, (
% 1.00/0.88 index: ( $i * $i ) > $i)).
% 1.00/0.88 tff(down_type, type, (
% 1.00/0.88 down: $i)).
% 1.00/0.88 tff(elem_type, type, (
% 1.00/0.88 elem: ( $i * $i ) > $o)).
% 1.00/0.88 tff(queue_type, type, (
% 1.00/0.88 queue: $i > $i)).
% 1.00/0.88 tff(tptp_fun_W_5_type, type, (
% 1.00/0.88 tptp_fun_W_5: $i)).
% 1.00/0.88 tff(m_Down_type, type, (
% 1.00/0.88 m_Down: $i > $i)).
% 1.00/0.88 tff(tptp_fun_W0_10_type, type, (
% 1.00/0.88 tptp_fun_W0_10: $i)).
% 1.00/0.88 tff(cons_type, type, (
% 1.00/0.88 cons: ( $i * $i ) > $i)).
% 1.00/0.88 tff(tptp_fun_V_6_type, type, (
% 1.00/0.88 tptp_fun_V_6: $i)).
% 1.00/0.88 tff(m_Ack_type, type, (
% 1.00/0.88 m_Ack: ( $i * $i ) > $i)).
% 1.00/0.88 tff(tptp_fun_Y_3_type, type, (
% 1.00/0.88 tptp_fun_Y_3: $i)).
% 1.00/0.88 tff(tptp_fun_X_4_type, type, (
% 1.00/0.88 tptp_fun_X_4: $i)).
% 1.00/0.88 tff(elec_1_type, type, (
% 1.00/0.88 elec_1: $i)).
% 1.00/0.88 tff(status_type, type, (
% 1.00/0.88 status: $i)).
% 1.00/0.88 tff(nbr_proc_type, type, (
% 1.00/0.88 nbr_proc: $i)).
% 1.00/0.88 tff(alive_type, type, (
% 1.00/0.88 alive: $i)).
% 1.00/0.88 tff(elid_type, type, (
% 1.00/0.88 elid: $i)).
% 1.00/0.88 tff(wait_type, type, (
% 1.00/0.88 wait: $i)).
% 1.00/0.88 tff(ldr_type, type, (
% 1.00/0.88 ldr: $i)).
% 1.00/0.88 tff(norm_type, type, (
% 1.00/0.88 norm: $i)).
% 1.00/0.88 tff(elec_2_type, type, (
% 1.00/0.88 elec_2: $i)).
% 1.00/0.88 tff(m_NotNorm_type, type, (
% 1.00/0.88 m_NotNorm: $i > $i)).
% 1.00/0.88 tff(m_Ldr_type, type, (
% 1.00/0.88 m_Ldr: $i > $i)).
% 1.00/0.88 tff(pendack_type, type, (
% 1.00/0.88 pendack: $i)).
% 1.00/0.88 tff(tptp_fun_Z_7_type, type, (
% 1.00/0.88 tptp_fun_Z_7: $i)).
% 1.00/0.88 tff(snoc_type, type, (
% 1.00/0.88 snoc: ( $i * $i ) > $i)).
% 1.00/0.88 tff(m_Halt_type, type, (
% 1.00/0.88 m_Halt: $i > $i)).
% 1.00/0.88 tff(1,plain,
% 1.00/0.88 ((setIn(X!4, alive) & (~leq(nbr_proc, index(pendack, host(X!4)))) & (setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7))) & ((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & (~leq(nbr_proc, index(pendack, host(X!4)))) & setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7)) & (index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(2,plain,
% 1.00/0.89 ((![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] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6))) <=> (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(3,plain,
% 1.00/0.89 ((~(~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))))) <=> ((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(4,plain,
% 1.00/0.89 (((setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7))) <=> (setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7)))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(5,plain,
% 1.00/0.89 ((~(~(s(index(pendack, host(X!4))) = host(Z!7)))) <=> (s(index(pendack, host(X!4))) = host(Z!7))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(6,plain,
% 1.00/0.89 ((~(~(host(X!4) = host(Z!7)))) <=> (host(X!4) = host(Z!7))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(7,plain,
% 1.00/0.89 (((setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))) <=> (setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(8,plain,
% 1.00/0.89 ((![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) <=> (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(9,plain,
% 1.00/0.89 ((~(~(setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))))) <=> (setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))))),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(10,plain,
% 1.00/0.89 (((~(~(setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))) <=> ((setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)))),
% 1.00/0.89 inference(monotonicity,[status(thm)],[9, 8])).
% 1.00/0.89 tff(11,plain,
% 1.00/0.89 (((~(~(setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))) <=> (setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))),
% 1.00/0.89 inference(transitivity,[status(thm)],[10, 7])).
% 1.00/0.89 tff(12,plain,
% 1.00/0.89 ((((~(~(setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))) & (~(~(host(X!4) = host(Z!7)))) & (~(~(s(index(pendack, host(X!4))) = host(Z!7))))) <=> ((setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7)))),
% 1.00/0.89 inference(monotonicity,[status(thm)],[11, 6, 5])).
% 1.00/0.89 tff(13,plain,
% 1.00/0.89 ((((~(~(setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))) & (~(~(host(X!4) = host(Z!7)))) & (~(~(s(index(pendack, host(X!4))) = host(Z!7))))) <=> (setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7)))),
% 1.00/0.89 inference(transitivity,[status(thm)],[12, 4])).
% 1.00/0.89 tff(14,plain,
% 1.00/0.89 ((~(~setIn(X!4, alive))) <=> setIn(X!4, alive)),
% 1.00/0.89 inference(rewrite,[status(thm)],[])).
% 1.00/0.89 tff(15,plain,
% 1.00/0.89 (((~(~setIn(X!4, alive))) & (~leq(nbr_proc, index(pendack, host(X!4)))) & (((~(~(setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))) & (~(~(host(X!4) = host(Z!7)))) & (~(~(s(index(pendack, host(X!4))) = host(Z!7))))) & (~(~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & (~leq(nbr_proc, index(pendack, host(X!4)))) & (setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7))) & ((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6))))),
% 1.00/0.89 inference(monotonicity,[status(thm)],[14, 13, 3, 2])).
% 1.00/0.89 tff(16,plain,
% 1.00/0.89 (((~(~setIn(X!4, alive))) & (~leq(nbr_proc, index(pendack, host(X!4)))) & (((~(~(setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))) & (~(~(host(X!4) = host(Z!7)))) & (~(~(s(index(pendack, host(X!4))) = host(Z!7))))) & (~(~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4)))))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & (~leq(nbr_proc, index(pendack, host(X!4)))) & setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7)) & (index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))),
% 1.00/0.90 inference(transitivity,[status(thm)],[15, 1])).
% 1.00/0.90 tff(17,plain,
% 1.00/0.90 ((~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))) <=> (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V))))))),
% 1.00/0.90 inference(rewrite,[status(thm)],[])).
% 1.00/0.90 tff(18,plain,
% 1.00/0.90 ((~![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] : ((host(Pid0) = nbr_proc) => (~elem(m_NotNorm(Z), queue(host(Pid0)))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~elem(m_Down(Z), queue(host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~elem(m_Down(Z), queue(host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, 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))))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2)) & (host(Y) = index(pendack, host(X)))) => ((~leq(nbr_proc, index(pendack, host(X)))) => ![Z: $i] : ((s(index(pendack, host(X))) = host(Z)) => ((host(X) = host(Z)) => ![W0: $i, X0: $i, Y0: $i] : ((~(s(index(pendack, host(X))) = host(Y0))) => ((~(host(X) = host(Y0))) => (((((![V0: $i] : (((~leq(host(Y0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Y0))) | (V0 = host(X0)))) & elem(m_Down(X0), queue(host(Y0)))) & (host(Y0) = host(W0))) & (host(Y0) = nbr_proc)) & (index(status, host(Y0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))))))))))))) <=> (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V))))))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(19,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] : ((host(Pid0) = nbr_proc) => (~elem(m_NotNorm(Z), queue(host(Pid0)))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~elem(m_Down(Z), queue(host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~elem(m_Down(Z), queue(host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, 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))))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2)) & (host(Y) = index(pendack, host(X)))) => ((~leq(nbr_proc, index(pendack, host(X)))) => ![Z: $i] : ((s(index(pendack, host(X))) = host(Z)) => ((host(X) = host(Z)) => ![W0: $i, X0: $i, Y0: $i] : ((~(s(index(pendack, host(X))) = host(Y0))) => ((~(host(X) = host(Y0))) => (((((![V0: $i] : (((~leq(host(Y0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Y0))) | (V0 = host(X0)))) & elem(m_Down(X0), queue(host(Y0)))) & (host(Y0) = host(W0))) & (host(Y0) = nbr_proc)) & (index(status, host(Y0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 1.04/0.90 tff(20,plain,
% 1.04/0.90 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.04/0.90 tff(21,plain,
% 1.04/0.90 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[20, 17])).
% 1.04/0.90 tff(22,plain,
% 1.04/0.90 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[21, 17])).
% 1.04/0.90 tff(23,plain,
% 1.04/0.90 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[22, 17])).
% 1.04/0.90 tff(24,plain,
% 1.04/0.90 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[23, 17])).
% 1.04/0.90 tff(25,plain,
% 1.04/0.90 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[24, 17])).
% 1.04/0.90 tff(26,plain,
% 1.04/0.90 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i] : (![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), snoc(V, m_Halt(X))))) | (s(index(pendack, host(X))) = host(Y0)) | (host(X) = host(Y0)) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), queue(host(Y0))) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1)))) | (~(host(X) = host(Z))) | (~(s(index(pendack, host(X))) = host(Z)))) | (~((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, 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)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[25, 17])).
% 1.04/0.91 tff(27,plain,
% 1.04/0.91 (setIn(X!4, alive) & (~leq(nbr_proc, index(pendack, host(X!4)))) & setIn(Z!7, alive) & elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) & (~(s(index(pendack, host(X!4))) = host(Y0!8))) & (~(host(X!4) = host(Y0!8))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Z!7)) & (s(index(pendack, host(X!4))) = host(Z!7)) & (index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[26, 16])).
% 1.04/0.91 tff(28,plain,
% 1.04/0.91 (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(29,plain,
% 1.04/0.91 (index(status, host(X!4)) = elec_2),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(30,plain,
% 1.04/0.91 (((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2)) | (~(index(status, host(X!4)) = elec_2))),
% 1.04/0.91 inference(tautology,[status(thm)],[])).
% 1.04/0.91 tff(31,plain,
% 1.04/0.91 ((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2)),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.04/0.91 tff(32,plain,
% 1.04/0.91 (^[Z: $i] : refl(((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))) <=> ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(33,plain,
% 1.04/0.91 (![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))) <=> ![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[32])).
% 1.04/0.91 tff(34,plain,
% 1.04/0.91 (^[Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) <=> (~((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))), ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) <=> (~(~((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))))), rewrite((~(~((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))) <=> ((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))), ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) <=> ((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))))), (((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) <=> (((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))) | (index(elid, host(Z)) = Z)))), rewrite((((~setIn(Z, alive)) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)))) | (index(elid, host(Z)) = Z)) <=> ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))), (((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) <=> ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(35,plain,
% 1.04/0.91 (![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) <=> ![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[34])).
% 1.04/0.91 tff(36,plain,
% 1.04/0.91 (![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(37,plain,
% 1.04/0.91 (![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.04/0.91 tff(38,plain,
% 1.04/0.91 (![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[37, 33])).
% 1.04/0.91 tff(39,plain,
% 1.04/0.91 (setIn(X!4, alive)),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(40,plain,
% 1.04/0.91 (((~![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))) | ((~setIn(X!4, alive)) | (index(elid, host(X!4)) = X!4) | (~((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2))))) <=> ((~![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))) | (~setIn(X!4, alive)) | (index(elid, host(X!4)) = X!4) | (~((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(41,plain,
% 1.04/0.91 ((~![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))) | ((~setIn(X!4, alive)) | (index(elid, host(X!4)) = X!4) | (~((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2))))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(42,plain,
% 1.04/0.91 ((~![Z: $i] : ((~setIn(Z, alive)) | (index(elid, host(Z)) = Z) | (~((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2))))) | (~setIn(X!4, alive)) | (index(elid, host(X!4)) = X!4) | (~((index(status, host(X!4)) = elec_1) | (index(status, host(X!4)) = elec_2)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.04/0.91 tff(43,plain,
% 1.04/0.91 (index(elid, host(X!4)) = X!4),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[42, 39, 38, 31])).
% 1.04/0.91 tff(44,plain,
% 1.04/0.91 (index(elid, host(X!4)) = W!5),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(45,plain,
% 1.04/0.91 (W!5 = index(elid, host(X!4))),
% 1.04/0.91 inference(symmetry,[status(thm)],[44])).
% 1.04/0.91 tff(46,plain,
% 1.04/0.91 (W!5 = X!4),
% 1.04/0.91 inference(transitivity,[status(thm)],[45, 43])).
% 1.04/0.91 tff(47,plain,
% 1.04/0.91 (host(W!5) = host(X!4)),
% 1.04/0.91 inference(monotonicity,[status(thm)],[46])).
% 1.04/0.91 tff(48,plain,
% 1.04/0.91 (queue(host(W!5)) = queue(host(X!4))),
% 1.04/0.91 inference(monotonicity,[status(thm)],[47])).
% 1.04/0.91 tff(49,plain,
% 1.04/0.91 (queue(host(W!5)) = cons(m_Ack(W!5, Y!3), V!6)),
% 1.04/0.91 inference(transitivity,[status(thm)],[48, 28])).
% 1.04/0.91 tff(50,plain,
% 1.04/0.91 (elem(m_Down(W0!10), queue(host(W!5))) <=> elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6))),
% 1.04/0.91 inference(monotonicity,[status(thm)],[49])).
% 1.04/0.91 tff(51,plain,
% 1.04/0.91 (elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6)) <=> elem(m_Down(W0!10), queue(host(W!5)))),
% 1.04/0.91 inference(symmetry,[status(thm)],[50])).
% 1.04/0.91 tff(52,plain,
% 1.04/0.91 (^[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))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(53,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[52])).
% 1.04/0.91 tff(54,plain,
% 1.04/0.91 (![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)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(55,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')).
% 1.04/0.91 tff(56,plain,
% 1.04/0.91 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.04/0.91 tff(57,plain,(
% 1.04/0.91 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 1.04/0.91 inference(skolemize,[status(sab)],[56])).
% 1.04/0.91 tff(58,plain,
% 1.04/0.91 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[57, 53])).
% 1.04/0.91 tff(59,plain,
% 1.04/0.91 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6)) <=> ((m_Down(W0!10) = m_Ack(W!5, Y!3)) | elem(m_Down(W0!10), V!6)))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(60,plain,
% 1.04/0.91 (elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6)) <=> ((m_Down(W0!10) = m_Ack(W!5, Y!3)) | elem(m_Down(W0!10), V!6))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[59, 58])).
% 1.04/0.91 tff(61,plain,
% 1.04/0.91 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(62,plain,
% 1.04/0.91 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[61])).
% 1.04/0.91 tff(63,plain,
% 1.04/0.91 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(64,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 1.04/0.91 tff(65,plain,
% 1.04/0.91 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.04/0.91 tff(66,plain,(
% 1.04/0.91 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 1.04/0.91 inference(skolemize,[status(sab)],[65])).
% 1.04/0.91 tff(67,plain,
% 1.04/0.91 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.04/0.91 tff(68,plain,
% 1.04/0.91 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) <=> ((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6)))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(69,plain,
% 1.04/0.91 (elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) <=> ((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[68, 67])).
% 1.04/0.91 tff(70,plain,
% 1.04/0.91 (elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(71,plain,
% 1.04/0.91 ((~(elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) <=> ((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6)))) | (~elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4)))) | ((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6))),
% 1.04/0.91 inference(tautology,[status(thm)],[])).
% 1.04/0.91 tff(72,plain,
% 1.04/0.91 ((~(elem(m_Down(W0!10), snoc(V!6, m_Halt(X!4))) <=> ((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6)))) | ((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[71, 70])).
% 1.04/0.91 tff(73,plain,
% 1.04/0.91 ((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6)),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[72, 69])).
% 1.04/0.91 tff(74,plain,
% 1.04/0.91 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Halt(Y))) <=> (~(m_Down(X) = m_Halt(Y))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(75,plain,
% 1.04/0.91 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[74])).
% 1.04/0.91 tff(76,plain,
% 1.04/0.91 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(77,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_17')).
% 1.04/0.91 tff(78,plain,
% 1.04/0.91 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.04/0.91 tff(79,plain,(
% 1.04/0.91 ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 1.04/0.91 inference(skolemize,[status(sab)],[78])).
% 1.04/0.91 tff(80,plain,
% 1.04/0.91 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.04/0.91 tff(81,plain,
% 1.04/0.91 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))) | (~(m_Down(W0!10) = m_Halt(X!4)))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(82,plain,
% 1.04/0.91 (~(m_Down(W0!10) = m_Halt(X!4))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[81, 80])).
% 1.04/0.91 tff(83,plain,
% 1.04/0.91 ((~((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6))) | (m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6)),
% 1.04/0.91 inference(tautology,[status(thm)],[])).
% 1.04/0.91 tff(84,plain,
% 1.04/0.91 ((~((m_Down(W0!10) = m_Halt(X!4)) | elem(m_Down(W0!10), V!6))) | elem(m_Down(W0!10), V!6)),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[83, 82])).
% 1.04/0.91 tff(85,plain,
% 1.04/0.91 (elem(m_Down(W0!10), V!6)),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[84, 73])).
% 1.04/0.91 tff(86,plain,
% 1.04/0.91 (((m_Down(W0!10) = m_Ack(W!5, Y!3)) | elem(m_Down(W0!10), V!6)) | (~elem(m_Down(W0!10), V!6))),
% 1.04/0.91 inference(tautology,[status(thm)],[])).
% 1.04/0.91 tff(87,plain,
% 1.04/0.91 ((m_Down(W0!10) = m_Ack(W!5, Y!3)) | elem(m_Down(W0!10), V!6)),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[86, 85])).
% 1.04/0.91 tff(88,plain,
% 1.04/0.91 ((~(elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6)) <=> ((m_Down(W0!10) = m_Ack(W!5, Y!3)) | elem(m_Down(W0!10), V!6)))) | elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6)) | (~((m_Down(W0!10) = m_Ack(W!5, Y!3)) | elem(m_Down(W0!10), V!6)))),
% 1.04/0.91 inference(tautology,[status(thm)],[])).
% 1.04/0.91 tff(89,plain,
% 1.04/0.91 ((~(elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6)) <=> ((m_Down(W0!10) = m_Ack(W!5, Y!3)) | elem(m_Down(W0!10), V!6)))) | elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[88, 87])).
% 1.04/0.91 tff(90,plain,
% 1.04/0.91 (elem(m_Down(W0!10), cons(m_Ack(W!5, Y!3), V!6))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[89, 60])).
% 1.04/0.91 tff(91,plain,
% 1.04/0.91 (elem(m_Down(W0!10), queue(host(W!5)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[90, 51])).
% 1.04/0.91 tff(92,plain,
% 1.04/0.91 (setIn(W!5, alive) <=> setIn(X!4, alive)),
% 1.04/0.91 inference(monotonicity,[status(thm)],[46])).
% 1.04/0.91 tff(93,plain,
% 1.04/0.91 (setIn(X!4, alive) <=> setIn(W!5, alive)),
% 1.04/0.91 inference(symmetry,[status(thm)],[92])).
% 1.04/0.91 tff(94,plain,
% 1.04/0.91 (setIn(W!5, alive)),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[39, 93])).
% 1.04/0.91 tff(95,plain,
% 1.04/0.91 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : refl(((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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)))))) <=> ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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)))))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(96,plain,
% 1.04/0.91 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[95])).
% 1.04/0.91 tff(97,plain,
% 1.04/0.91 (^[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))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> (((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))))), rewrite((((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))))),
% 1.04/0.91 inference(bind,[status(th)],[])).
% 1.04/0.91 tff(98,plain,
% 1.04/0.91 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))),
% 1.04/0.91 inference(quant_intro,[status(thm)],[97])).
% 1.04/0.91 tff(99,plain,
% 1.04/0.91 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((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) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(100,plain,
% 1.04/0.91 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.04/0.91 tff(101,plain,
% 1.04/0.91 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[100, 96])).
% 1.04/0.91 tff(102,plain,
% 1.04/0.91 (index(status, host(Y0!8)) = elec_1),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(103,plain,
% 1.04/0.91 (host(Y0!8) = nbr_proc),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(104,plain,
% 1.04/0.91 (host(Y0!8) = host(W0!10)),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(105,plain,
% 1.04/0.91 (elem(m_Down(X0!9), queue(host(Y0!8)))),
% 1.04/0.91 inference(and_elim,[status(thm)],[27])).
% 1.04/0.91 tff(106,plain,
% 1.04/0.91 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))) | ((~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(107,plain,
% 1.04/0.91 (((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))) <=> ((~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(108,plain,
% 1.04/0.91 ((~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) <=> (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(109,plain,
% 1.04/0.91 (((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))) <=> ((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[108])).
% 1.04/0.92 tff(110,plain,
% 1.04/0.92 (((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))) <=> ((~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))))),
% 1.04/0.92 inference(transitivity,[status(thm)],[109, 107])).
% 1.04/0.92 tff(111,plain,
% 1.04/0.92 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))) | ((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))) | ((~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5))))))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[110])).
% 1.04/0.92 tff(112,plain,
% 1.04/0.92 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))) | ((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))))),
% 1.04/0.92 inference(transitivity,[status(thm)],[111, 106])).
% 1.04/0.92 tff(113,plain,
% 1.04/0.92 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))) | ((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(114,plain,
% 1.04/0.92 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(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))))))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) | (~setIn(W!5, alive)) | (~elem(m_Down(W0!10), queue(host(W!5))))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.04/0.92 tff(115,plain,
% 1.04/0.92 ((~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) | (~elem(m_Down(W0!10), queue(host(W!5))))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[114, 105, 104, 103, 102, 101, 94])).
% 1.04/0.92 tff(116,plain,
% 1.04/0.92 (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[115, 91])).
% 1.04/0.92 tff(117,plain,
% 1.04/0.92 (((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))) | leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))),
% 1.04/0.92 inference(tautology,[status(thm)],[])).
% 1.04/0.92 tff(118,plain,
% 1.04/0.92 (leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[117, 116])).
% 1.04/0.92 tff(119,plain,
% 1.04/0.92 (((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))) | (~leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)))),
% 1.04/0.92 inference(tautology,[status(thm)],[])).
% 1.04/0.92 tff(120,plain,
% 1.04/0.92 (~leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[119, 116])).
% 1.04/0.92 tff(121,plain,
% 1.04/0.92 (((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))) | (~setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))))),
% 1.04/0.92 inference(tautology,[status(thm)],[])).
% 1.04/0.92 tff(122,plain,
% 1.04/0.92 (~setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8)))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[121, 116])).
% 1.04/0.92 tff(123,plain,
% 1.04/0.92 (((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))) | (~(tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)))),
% 1.04/0.92 inference(tautology,[status(thm)],[])).
% 1.04/0.92 tff(124,plain,
% 1.04/0.92 (~(tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[123, 116])).
% 1.04/0.92 tff(125,plain,
% 1.04/0.92 (^[V0: $i] : refl(((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0))) <=> ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0))))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(126,plain,
% 1.04/0.92 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0))) <=> ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))),
% 1.04/0.92 inference(quant_intro,[status(thm)],[125])).
% 1.04/0.92 tff(127,plain,
% 1.04/0.92 (^[V0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(Y0!8), V0)) & leq(s(zero), V0)) <=> (~(leq(host(Y0!8), V0) | (~leq(s(zero), V0))))), ((~((~leq(host(Y0!8), V0)) & leq(s(zero), V0))) <=> (~(~(leq(host(Y0!8), V0) | (~leq(s(zero), V0))))))), rewrite((~(~(leq(host(Y0!8), V0) | (~leq(s(zero), V0))))) <=> (leq(host(Y0!8), V0) | (~leq(s(zero), V0)))), ((~((~leq(host(Y0!8), V0)) & leq(s(zero), V0))) <=> (leq(host(Y0!8), V0) | (~leq(s(zero), V0))))), (((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) <=> ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (leq(host(Y0!8), V0) | (~leq(s(zero), V0)))))), rewrite(((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) <=> ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))), (((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) <=> ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(128,plain,
% 1.04/0.92 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) <=> ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))),
% 1.04/0.92 inference(quant_intro,[status(thm)],[127])).
% 1.04/0.92 tff(129,plain,
% 1.04/0.92 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0))))),
% 1.04/0.92 inference(and_elim,[status(thm)],[27])).
% 1.04/0.92 tff(130,plain,
% 1.04/0.92 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.04/0.92 tff(131,plain,
% 1.04/0.92 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[130, 126])).
% 1.04/0.92 tff(132,plain,
% 1.04/0.92 (((~![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) | ((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) <=> ((~![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) | (tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(133,plain,
% 1.04/0.92 ((~![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) | ((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(134,plain,
% 1.04/0.92 ((~![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) | (tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.04/0.92 tff(135,plain,
% 1.04/0.92 ($false),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[134, 131, 124, 122, 120, 118])).
% 1.04/0.92 % SZS output end Proof
%------------------------------------------------------------------------------