TSTP Solution File: SWV468+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV468+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:17:41 EDT 2022
% Result : Theorem 0.87s 0.81s
% Output : Proof 0.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV468+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 03:42:27 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.87/0.81 % SZS status Theorem
% 0.87/0.81 % SZS output start Proof
% 0.87/0.81 tff(elem_type, type, (
% 0.87/0.81 elem: ( $i * $i ) > $o)).
% 0.87/0.81 tff(queue_type, type, (
% 0.87/0.81 queue: $i > $i)).
% 0.87/0.81 tff(host_type, type, (
% 0.87/0.81 host: $i > $i)).
% 0.87/0.81 tff(tptp_fun_X_4_type, type, (
% 0.87/0.81 tptp_fun_X_4: $i)).
% 0.87/0.81 tff(m_Down_type, type, (
% 0.87/0.81 m_Down: $i > $i)).
% 0.87/0.81 tff(tptp_fun_Y_3_type, type, (
% 0.87/0.81 tptp_fun_Y_3: $i)).
% 0.87/0.81 tff(cons_type, type, (
% 0.87/0.81 cons: ( $i * $i ) > $i)).
% 0.87/0.81 tff(tptp_fun_V_5_type, type, (
% 0.87/0.81 tptp_fun_V_5: $i)).
% 0.87/0.81 tff(elec_1_type, type, (
% 0.87/0.81 elec_1: $i)).
% 0.87/0.81 tff(index_type, type, (
% 0.87/0.81 index: ( $i * $i ) > $i)).
% 0.87/0.81 tff(status_type, type, (
% 0.87/0.81 status: $i)).
% 0.87/0.81 tff(leq_type, type, (
% 0.87/0.81 leq: ( $i * $i ) > $o)).
% 0.87/0.81 tff(tptp_fun_V0_9_type, type, (
% 0.87/0.81 tptp_fun_V0_9: ( $i * $i ) > $i)).
% 0.87/0.81 tff(s_type, type, (
% 0.87/0.81 s: $i > $i)).
% 0.87/0.81 tff(zero_type, type, (
% 0.87/0.81 zero: $i)).
% 0.87/0.81 tff(setIn_type, type, (
% 0.87/0.81 setIn: ( $i * $i ) > $o)).
% 0.87/0.81 tff(down_type, type, (
% 0.87/0.81 down: $i)).
% 0.87/0.81 tff(norm_type, type, (
% 0.87/0.81 norm: $i)).
% 0.87/0.81 tff(ldr_type, type, (
% 0.87/0.81 ldr: $i)).
% 0.87/0.81 tff(alive_type, type, (
% 0.87/0.81 alive: $i)).
% 0.87/0.81 tff(elec_2_type, type, (
% 0.87/0.81 elec_2: $i)).
% 0.87/0.81 tff(pendack_type, type, (
% 0.87/0.81 pendack: $i)).
% 0.87/0.81 tff(m_Ack_type, type, (
% 0.87/0.81 m_Ack: ( $i * $i ) > $i)).
% 0.87/0.81 tff(elid_type, type, (
% 0.87/0.81 elid: $i)).
% 0.87/0.81 tff(m_Ldr_type, type, (
% 0.87/0.81 m_Ldr: $i > $i)).
% 0.87/0.81 tff(nbr_proc_type, type, (
% 0.87/0.81 nbr_proc: $i)).
% 0.87/0.81 tff(tptp_fun_W0_8_type, type, (
% 0.87/0.81 tptp_fun_W0_8: $i)).
% 0.87/0.81 tff(tptp_fun_V0_7_type, type, (
% 0.87/0.81 tptp_fun_V0_7: $i)).
% 0.87/0.81 tff(setEmpty_type, type, (
% 0.87/0.81 setEmpty: $i)).
% 0.87/0.81 tff(tptp_fun_Z_6_type, type, (
% 0.87/0.81 tptp_fun_Z_6: $i)).
% 0.87/0.81 tff(wait_type, type, (
% 0.87/0.81 wait: $i)).
% 0.87/0.81 tff(1,plain,
% 0.87/0.81 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2)))))) & leq(nbr_proc, host(X!4)) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))) & leq(nbr_proc, host(X!4)) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.87/0.82 inference(rewrite,[status(thm)],[])).
% 0.87/0.82 tff(2,plain,
% 0.87/0.82 ((![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~(~leq(host(Pid0), host(Z)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) <=> (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.87/0.82 inference(rewrite,[status(thm)],[])).
% 0.87/0.82 tff(3,plain,
% 0.87/0.82 ((![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) <=> (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1))),
% 0.87/0.82 inference(rewrite,[status(thm)],[])).
% 0.87/0.82 tff(4,plain,
% 0.87/0.82 ((~(~leq(nbr_proc, host(X!4)))) <=> leq(nbr_proc, host(X!4))),
% 0.87/0.82 inference(rewrite,[status(thm)],[])).
% 0.87/0.82 tff(5,plain,
% 0.87/0.82 (((~setIn(host(Z!6), setEmpty)) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))))) <=> ((~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))))),
% 0.87/0.82 inference(rewrite,[status(thm)],[])).
% 0.87/0.82 tff(6,plain,
% 0.87/0.82 (((~(~(host(X!4) = host(V0!7)))) & (~((host(X!4) = host(W0!8)) | (~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2)))))) <=> ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))))),
% 0.87/0.82 inference(rewrite,[status(thm)],[])).
% 0.87/0.82 tff(7,plain,
% 0.87/0.82 (((~setIn(host(Z!6), setEmpty)) & ((~(~(host(X!4) = host(V0!7)))) & (~((host(X!4) = host(W0!8)) | (~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))))) <=> ((~setIn(host(Z!6), setEmpty)) & ((host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2)))))))),
% 0.87/0.82 inference(monotonicity,[status(thm)],[6])).
% 0.87/0.82 tff(8,plain,
% 0.87/0.82 (((~setIn(host(Z!6), setEmpty)) & ((~(~(host(X!4) = host(V0!7)))) & (~((host(X!4) = host(W0!8)) | (~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))))) <=> ((~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))))),
% 0.87/0.82 inference(transitivity,[status(thm)],[7, 5])).
% 0.87/0.82 tff(9,plain,
% 0.87/0.82 ((~(~setIn(X!4, alive))) <=> setIn(X!4, alive)),
% 0.87/0.82 inference(rewrite,[status(thm)],[])).
% 0.87/0.82 tff(10,plain,
% 0.87/0.82 (((~leq(host(X!4), host(Y!3))) & (~(~setIn(X!4, alive))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((~setIn(host(Z!6), setEmpty)) & ((~(~(host(X!4) = host(V0!7)))) & (~((host(X!4) = host(W0!8)) | (~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))))) & (~(~leq(nbr_proc, host(X!4)))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~(~leq(host(Pid0), host(Z)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2)))))) & leq(nbr_proc, host(X!4)) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))))),
% 0.87/0.83 inference(monotonicity,[status(thm)],[9, 8, 4, 3, 2])).
% 0.87/0.83 tff(11,plain,
% 0.87/0.83 (((~leq(host(X!4), host(Y!3))) & (~(~setIn(X!4, alive))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((~setIn(host(Z!6), setEmpty)) & ((~(~(host(X!4) = host(V0!7)))) & (~((host(X!4) = host(W0!8)) | (~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))))) & (~(~leq(nbr_proc, host(X!4)))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | ((~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~(~leq(host(Pid0), host(Z)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))) & leq(nbr_proc, host(X!4)) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.87/0.83 inference(transitivity,[status(thm)],[10, 1])).
% 0.87/0.83 tff(12,plain,
% 0.87/0.83 ((~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(13,plain,
% 0.87/0.84 ((~![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] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid0), queue(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, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~leq(host(Pid0), host(Z))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Down(Pid20), queue(host(Z)))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid20), queue(host(Z)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & (host(Pid20) = host(Pid0))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))))) & ![Z: $i, Pid0: $i] : ((((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & (~leq(host(Pid0), host(Z)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))))) => ((![Z: $i] : (((~leq(host(X), Z)) & leq(s(zero), Z)) => (setIn(Z, index(down, host(X))) | (Z = host(Y)))) & (index(status, host(X)) = elec_1)) => (leq(nbr_proc, host(X)) => ![Z: $i] : ((~setIn(host(Z), setEmpty)) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i] : ((~(host(X) = host(W0))) => ((((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive)) & (index(status, host(W0)) = elec_2)) => (~(setIn(V0, alive) & (host(X) = host(V0))))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.87/0.84 inference(rewrite,[status(thm)],[])).
% 0.87/0.84 tff(14,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid0), queue(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, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~leq(host(Pid0), host(Z))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Down(Pid20), queue(host(Z)))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid20), queue(host(Z)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & (host(Pid20) = host(Pid0))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))))) & ![Z: $i, Pid0: $i] : ((((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & (~leq(host(Pid0), host(Z)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))))) => ((![Z: $i] : (((~leq(host(X), Z)) & leq(s(zero), Z)) => (setIn(Z, index(down, host(X))) | (Z = host(Y)))) & (index(status, host(X)) = elec_1)) => (leq(nbr_proc, host(X)) => ![Z: $i] : ((~setIn(host(Z), setEmpty)) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i] : ((~(host(X) = host(W0))) => ((((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive)) & (index(status, host(W0)) = elec_2)) => (~(setIn(V0, alive) & (host(X) = host(V0))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.87/0.84 tff(15,plain,
% 0.87/0.84 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.87/0.85 tff(16,plain,
% 0.87/0.85 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.87/0.85 tff(17,plain,
% 0.87/0.85 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.87/0.85 tff(18,plain,
% 0.87/0.85 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.87/0.85 tff(19,plain,
% 0.87/0.85 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.87/0.85 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.87/0.85 tff(20,plain,
% 0.87/0.85 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.87/0.86 tff(21,plain,
% 0.87/0.86 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : (setIn(host(Z), setEmpty) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i] : ((host(X) = host(W0)) | (~(setIn(V0, alive) & (host(X) = host(V0)))) | (~((~leq(index(pendack, host(W0)), host(V0))) & setIn(W0, alive) & (index(status, host(W0)) = elec_2)))))) | (~leq(nbr_proc, host(X))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & (~leq(host(Pid0), host(Z))) & elem(m_Down(Pid20), queue(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.87/0.86 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.87/0.86 tff(22,plain,
% 0.87/0.86 ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (~setIn(host(Z!6), setEmpty)) & (host(X!4) = host(V0!7)) & (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))) & leq(nbr_proc, host(X!4)) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (leq(host(Pid0), host(Z)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((tptp_fun_V0_9(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_9(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_9(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_9(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.99/0.86 tff(23,plain,
% 0.99/0.86 (queue(host(X!4)) = cons(m_Down(Y!3), V!5)),
% 0.99/0.86 inference(and_elim,[status(thm)],[22])).
% 0.99/0.86 tff(24,plain,
% 0.99/0.86 (elem(m_Down(Y!3), queue(host(X!4))) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.99/0.86 inference(monotonicity,[status(thm)],[23])).
% 0.99/0.86 tff(25,plain,
% 0.99/0.86 (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> elem(m_Down(Y!3), queue(host(X!4)))),
% 0.99/0.86 inference(symmetry,[status(thm)],[24])).
% 0.99/0.86 tff(26,plain,
% 0.99/0.86 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))))),
% 0.99/0.86 inference(bind,[status(th)],[])).
% 0.99/0.86 tff(27,plain,
% 0.99/0.86 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.99/0.86 inference(quant_intro,[status(thm)],[26])).
% 0.99/0.86 tff(28,plain,
% 0.99/0.86 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.99/0.86 inference(rewrite,[status(thm)],[])).
% 0.99/0.86 tff(29,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 0.99/0.86 tff(30,plain,
% 0.99/0.86 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.99/0.86 tff(31,plain,(
% 0.99/0.86 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.99/0.86 inference(skolemize,[status(sab)],[30])).
% 0.99/0.86 tff(32,plain,
% 0.99/0.86 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.99/0.86 tff(33,plain,
% 0.99/0.86 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 0.99/0.86 inference(rewrite,[status(thm)],[])).
% 0.99/0.86 tff(34,plain,
% 0.99/0.86 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> $true) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.99/0.86 inference(rewrite,[status(thm)],[])).
% 0.99/0.86 tff(35,plain,
% 0.99/0.86 (($true | elem(m_Down(Y!3), V!5)) <=> $true),
% 0.99/0.86 inference(rewrite,[status(thm)],[])).
% 0.99/0.86 tff(36,plain,
% 0.99/0.86 ((m_Down(Y!3) = m_Down(Y!3)) <=> $true),
% 0.99/0.86 inference(rewrite,[status(thm)],[])).
% 0.99/0.86 tff(37,plain,
% 0.99/0.86 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> ($true | elem(m_Down(Y!3), V!5))),
% 0.99/0.86 inference(monotonicity,[status(thm)],[36])).
% 0.99/0.86 tff(38,plain,
% 0.99/0.86 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> $true),
% 0.99/0.86 inference(transitivity,[status(thm)],[37, 35])).
% 0.99/0.86 tff(39,plain,
% 0.99/0.86 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5))) <=> (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> $true)),
% 0.99/0.86 inference(monotonicity,[status(thm)],[38])).
% 0.99/0.86 tff(40,plain,
% 0.99/0.86 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5))) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.99/0.86 inference(transitivity,[status(thm)],[39, 34])).
% 0.99/0.86 tff(41,plain,
% 0.99/0.86 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 0.99/0.86 inference(monotonicity,[status(thm)],[40])).
% 0.99/0.86 tff(42,plain,
% 0.99/0.86 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 0.99/0.86 inference(transitivity,[status(thm)],[41, 33])).
% 0.99/0.86 tff(43,plain,
% 0.99/0.86 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))),
% 0.99/0.86 inference(quant_inst,[status(thm)],[])).
% 0.99/0.86 tff(44,plain,
% 0.99/0.86 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.99/0.86 tff(45,plain,
% 0.99/0.86 (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 0.99/0.86 inference(unit_resolution,[status(thm)],[44, 32])).
% 0.99/0.86 tff(46,plain,
% 0.99/0.86 (elem(m_Down(Y!3), queue(host(X!4)))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[45, 25])).
% 0.99/0.86 tff(47,plain,
% 0.99/0.86 (host(X!4) = host(V0!7)),
% 0.99/0.86 inference(and_elim,[status(thm)],[22])).
% 0.99/0.86 tff(48,plain,
% 0.99/0.86 (leq(index(pendack, host(W0!8)), host(X!4)) <=> leq(index(pendack, host(W0!8)), host(V0!7))),
% 0.99/0.86 inference(monotonicity,[status(thm)],[47])).
% 0.99/0.86 tff(49,plain,
% 0.99/0.86 (leq(index(pendack, host(W0!8)), host(V0!7)) <=> leq(index(pendack, host(W0!8)), host(X!4))),
% 0.99/0.86 inference(symmetry,[status(thm)],[48])).
% 0.99/0.86 tff(50,plain,
% 0.99/0.86 ((~leq(index(pendack, host(W0!8)), host(V0!7))) <=> (~leq(index(pendack, host(W0!8)), host(X!4)))),
% 0.99/0.86 inference(monotonicity,[status(thm)],[49])).
% 0.99/0.86 tff(51,plain,
% 0.99/0.86 (~((~(setIn(V0!7, alive) & (host(X!4) = host(V0!7)))) | (host(X!4) = host(W0!8)) | (~((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2))))),
% 0.99/0.86 inference(and_elim,[status(thm)],[22])).
% 0.99/0.86 tff(52,plain,
% 0.99/0.86 ((~leq(index(pendack, host(W0!8)), host(V0!7))) & setIn(W0!8, alive) & (index(status, host(W0!8)) = elec_2)),
% 0.99/0.86 inference(or_elim,[status(thm)],[51])).
% 0.99/0.86 tff(53,plain,
% 0.99/0.86 (~leq(index(pendack, host(W0!8)), host(V0!7))),
% 0.99/0.86 inference(and_elim,[status(thm)],[52])).
% 0.99/0.86 tff(54,plain,
% 0.99/0.86 (~leq(index(pendack, host(W0!8)), host(X!4))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.99/0.86 tff(55,plain,
% 0.99/0.86 (host(V0!7) = host(X!4)),
% 0.99/0.86 inference(symmetry,[status(thm)],[47])).
% 0.99/0.86 tff(56,plain,
% 0.99/0.86 (^[X: $i, Y: $i] : refl(((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 0.99/0.86 inference(bind,[status(th)],[])).
% 0.99/0.86 tff(57,plain,
% 0.99/0.86 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.99/0.86 inference(quant_intro,[status(thm)],[56])).
% 0.99/0.86 tff(58,plain,
% 0.99/0.86 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))),
% 0.99/0.86 inference(bind,[status(th)],[])).
% 0.99/0.86 tff(59,plain,
% 0.99/0.86 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.99/0.86 inference(quant_intro,[status(thm)],[58])).
% 0.99/0.86 tff(60,plain,
% 0.99/0.86 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.99/0.86 inference(rewrite,[status(thm)],[])).
% 0.99/0.86 tff(61,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_61')).
% 0.99/0.86 tff(62,plain,
% 0.99/0.86 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.99/0.86 tff(63,plain,(
% 0.99/0.86 ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.99/0.86 inference(skolemize,[status(sab)],[62])).
% 0.99/0.86 tff(64,plain,
% 0.99/0.86 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.99/0.86 tff(65,plain,
% 0.99/0.86 (![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.99/0.86 tff(66,plain,
% 0.99/0.86 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))) <=> (host(V0!7) = nbr_proc))),
% 0.99/0.86 inference(quant_inst,[status(thm)],[])).
% 0.99/0.86 tff(67,plain,
% 0.99/0.86 ((~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))) <=> (host(V0!7) = nbr_proc)),
% 0.99/0.86 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.99/0.86 tff(68,plain,
% 0.99/0.86 (leq(host(V0!7), nbr_proc) <=> leq(host(X!4), nbr_proc)),
% 0.99/0.86 inference(monotonicity,[status(thm)],[55])).
% 0.99/0.86 tff(69,plain,
% 0.99/0.86 (leq(host(X!4), nbr_proc) <=> leq(host(V0!7), nbr_proc)),
% 0.99/0.86 inference(symmetry,[status(thm)],[68])).
% 0.99/0.86 tff(70,plain,
% 0.99/0.86 (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 0.99/0.86 inference(bind,[status(th)],[])).
% 0.99/0.86 tff(71,plain,
% 0.99/0.86 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.99/0.86 inference(quant_intro,[status(thm)],[70])).
% 0.99/0.86 tff(72,plain,
% 0.99/0.86 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.99/0.86 inference(rewrite,[status(thm)],[])).
% 0.99/0.86 tff(73,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 0.99/0.86 tff(74,plain,
% 0.99/0.86 (![P: $i] : leq(host(P), nbr_proc)),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.99/0.86 tff(75,plain,(
% 0.99/0.86 ![P: $i] : leq(host(P), nbr_proc)),
% 0.99/0.86 inference(skolemize,[status(sab)],[74])).
% 0.99/0.86 tff(76,plain,
% 0.99/0.86 (![P: $i] : leq(host(P), nbr_proc)),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.99/0.86 tff(77,plain,
% 0.99/0.86 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X!4), nbr_proc)),
% 0.99/0.86 inference(quant_inst,[status(thm)],[])).
% 0.99/0.86 tff(78,plain,
% 0.99/0.86 (leq(host(X!4), nbr_proc)),
% 0.99/0.86 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.99/0.86 tff(79,plain,
% 0.99/0.86 (leq(host(V0!7), nbr_proc)),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[78, 69])).
% 0.99/0.86 tff(80,plain,
% 0.99/0.86 (leq(nbr_proc, host(V0!7)) <=> leq(nbr_proc, host(X!4))),
% 0.99/0.86 inference(monotonicity,[status(thm)],[55])).
% 0.99/0.86 tff(81,plain,
% 0.99/0.86 (leq(nbr_proc, host(X!4)) <=> leq(nbr_proc, host(V0!7))),
% 0.99/0.86 inference(symmetry,[status(thm)],[80])).
% 0.99/0.86 tff(82,plain,
% 0.99/0.86 (leq(nbr_proc, host(X!4))),
% 0.99/0.86 inference(and_elim,[status(thm)],[22])).
% 0.99/0.86 tff(83,plain,
% 0.99/0.86 (leq(nbr_proc, host(V0!7))),
% 0.99/0.86 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.99/0.87 tff(84,plain,
% 0.99/0.87 ((~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))) | (~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7)))),
% 0.99/0.87 inference(tautology,[status(thm)],[])).
% 0.99/0.87 tff(85,plain,
% 0.99/0.87 (~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[84, 83, 79])).
% 0.99/0.87 tff(86,plain,
% 0.99/0.87 ((~((~((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7))))) <=> (host(V0!7) = nbr_proc))) | ((~leq(host(V0!7), nbr_proc)) | (~leq(nbr_proc, host(V0!7)))) | (host(V0!7) = nbr_proc)),
% 0.99/0.87 inference(tautology,[status(thm)],[])).
% 0.99/0.87 tff(87,plain,
% 0.99/0.87 (host(V0!7) = nbr_proc),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[86, 85, 67])).
% 0.99/0.87 tff(88,plain,
% 0.99/0.87 (nbr_proc = host(V0!7)),
% 0.99/0.87 inference(symmetry,[status(thm)],[87])).
% 0.99/0.87 tff(89,plain,
% 0.99/0.87 (nbr_proc = host(X!4)),
% 0.99/0.87 inference(transitivity,[status(thm)],[88, 55])).
% 0.99/0.87 tff(90,plain,
% 0.99/0.87 (leq(nbr_proc, host(W0!8)) <=> leq(host(X!4), host(W0!8))),
% 0.99/0.87 inference(monotonicity,[status(thm)],[89])).
% 0.99/0.87 tff(91,plain,
% 0.99/0.87 ((~leq(nbr_proc, host(W0!8))) <=> (~leq(host(X!4), host(W0!8)))),
% 0.99/0.87 inference(monotonicity,[status(thm)],[90])).
% 0.99/0.87 tff(92,plain,
% 0.99/0.87 ((~![X: $i, Y: $i] : ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y))) | ((~((~leq(nbr_proc, host(W0!8))) | (~leq(host(W0!8), nbr_proc)))) <=> (nbr_proc = host(W0!8)))),
% 0.99/0.87 inference(quant_inst,[status(thm)],[])).
% 0.99/0.87 tff(93,plain,
% 0.99/0.87 ((~((~leq(nbr_proc, host(W0!8))) | (~leq(host(W0!8), nbr_proc)))) <=> (nbr_proc = host(W0!8))),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[92, 65])).
% 0.99/0.87 tff(94,plain,
% 0.99/0.87 ((nbr_proc = host(W0!8)) <=> (host(X!4) = host(W0!8))),
% 0.99/0.87 inference(monotonicity,[status(thm)],[89])).
% 0.99/0.87 tff(95,plain,
% 0.99/0.87 ((host(X!4) = host(W0!8)) <=> (nbr_proc = host(W0!8))),
% 0.99/0.87 inference(symmetry,[status(thm)],[94])).
% 0.99/0.87 tff(96,plain,
% 0.99/0.87 ((~(host(X!4) = host(W0!8))) <=> (~(nbr_proc = host(W0!8)))),
% 0.99/0.87 inference(monotonicity,[status(thm)],[95])).
% 0.99/0.87 tff(97,plain,
% 0.99/0.87 (~(host(X!4) = host(W0!8))),
% 0.99/0.87 inference(or_elim,[status(thm)],[51])).
% 0.99/0.87 tff(98,plain,
% 0.99/0.87 (~(nbr_proc = host(W0!8))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.99/0.87 tff(99,plain,
% 0.99/0.87 ((~((~((~leq(nbr_proc, host(W0!8))) | (~leq(host(W0!8), nbr_proc)))) <=> (nbr_proc = host(W0!8)))) | ((~leq(nbr_proc, host(W0!8))) | (~leq(host(W0!8), nbr_proc))) | (nbr_proc = host(W0!8))),
% 0.99/0.87 inference(tautology,[status(thm)],[])).
% 0.99/0.87 tff(100,plain,
% 0.99/0.87 ((~leq(nbr_proc, host(W0!8))) | (~leq(host(W0!8), nbr_proc))),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[99, 98, 93])).
% 0.99/0.87 tff(101,plain,
% 0.99/0.87 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(W0!8), nbr_proc)),
% 0.99/0.87 inference(quant_inst,[status(thm)],[])).
% 0.99/0.87 tff(102,plain,
% 0.99/0.87 (leq(host(W0!8), nbr_proc)),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[101, 76])).
% 0.99/0.87 tff(103,plain,
% 0.99/0.87 ((~((~leq(nbr_proc, host(W0!8))) | (~leq(host(W0!8), nbr_proc)))) | (~leq(nbr_proc, host(W0!8))) | (~leq(host(W0!8), nbr_proc))),
% 0.99/0.87 inference(tautology,[status(thm)],[])).
% 0.99/0.87 tff(104,plain,
% 0.99/0.87 ((~((~leq(nbr_proc, host(W0!8))) | (~leq(host(W0!8), nbr_proc)))) | (~leq(nbr_proc, host(W0!8)))),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.99/0.87 tff(105,plain,
% 0.99/0.87 (~leq(nbr_proc, host(W0!8))),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[104, 100])).
% 0.99/0.87 tff(106,plain,
% 0.99/0.87 (~leq(host(X!4), host(W0!8))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[105, 91])).
% 0.99/0.87 tff(107,plain,
% 0.99/0.87 (index(down, host(V0!7)) = index(down, host(X!4))),
% 0.99/0.87 inference(monotonicity,[status(thm)],[55])).
% 0.99/0.87 tff(108,plain,
% 0.99/0.87 (setIn(host(W0!8), index(down, host(V0!7))) <=> setIn(host(W0!8), index(down, host(X!4)))),
% 0.99/0.87 inference(monotonicity,[status(thm)],[107])).
% 0.99/0.87 tff(109,plain,
% 0.99/0.87 ((~setIn(host(W0!8), index(down, host(V0!7)))) <=> (~setIn(host(W0!8), index(down, host(X!4))))),
% 0.99/0.87 inference(monotonicity,[status(thm)],[108])).
% 0.99/0.87 tff(110,plain,
% 0.99/0.87 (^[Z: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))),
% 0.99/0.87 inference(bind,[status(th)],[])).
% 0.99/0.87 tff(111,plain,
% 0.99/0.87 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))),
% 0.99/0.87 inference(quant_intro,[status(thm)],[110])).
% 0.99/0.87 tff(112,plain,
% 0.99/0.87 (^[Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2)) <=> (~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite((((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))))),
% 0.99/0.87 inference(bind,[status(th)],[])).
% 0.99/0.87 tff(113,plain,
% 0.99/0.87 (![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))),
% 0.99/0.87 inference(quant_intro,[status(thm)],[112])).
% 0.99/0.87 tff(114,plain,
% 0.99/0.87 (![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 0.99/0.87 inference(and_elim,[status(thm)],[22])).
% 0.99/0.87 tff(115,plain,
% 0.99/0.87 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.99/0.87 tff(116,plain,
% 0.99/0.87 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.99/0.87 tff(117,plain,
% 0.99/0.87 (index(status, host(W0!8)) = elec_2),
% 0.99/0.87 inference(and_elim,[status(thm)],[52])).
% 0.99/0.87 tff(118,plain,
% 0.99/0.87 (setIn(W0!8, alive)),
% 0.99/0.87 inference(and_elim,[status(thm)],[52])).
% 0.99/0.87 tff(119,plain,
% 0.99/0.87 (setIn(V0!7, alive) & (host(X!4) = host(V0!7))),
% 0.99/0.87 inference(or_elim,[status(thm)],[51])).
% 0.99/0.87 tff(120,plain,
% 0.99/0.87 (setIn(V0!7, alive)),
% 0.99/0.87 inference(and_elim,[status(thm)],[119])).
% 0.99/0.87 tff(121,plain,
% 0.99/0.87 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | (leq(index(pendack, host(W0!8)), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7)))))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | leq(index(pendack, host(W0!8)), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7)))))),
% 0.99/0.87 inference(rewrite,[status(thm)],[])).
% 0.99/0.87 tff(122,plain,
% 0.99/0.87 (((~setIn(W0!8, alive)) | (~setIn(V0!7, alive)) | leq(index(pendack, host(W0!8)), host(V0!7)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7))))) <=> (leq(index(pendack, host(W0!8)), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7)))))),
% 0.99/0.87 inference(rewrite,[status(thm)],[])).
% 0.99/0.87 tff(123,plain,
% 0.99/0.87 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | ((~setIn(W0!8, alive)) | (~setIn(V0!7, alive)) | leq(index(pendack, host(W0!8)), host(V0!7)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7)))))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | (leq(index(pendack, host(W0!8)), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7))))))),
% 0.99/0.87 inference(monotonicity,[status(thm)],[122])).
% 0.99/0.87 tff(124,plain,
% 0.99/0.87 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | ((~setIn(W0!8, alive)) | (~setIn(V0!7, alive)) | leq(index(pendack, host(W0!8)), host(V0!7)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7)))))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | leq(index(pendack, host(W0!8)), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7)))))),
% 0.99/0.87 inference(transitivity,[status(thm)],[123, 121])).
% 0.99/0.87 tff(125,plain,
% 0.99/0.87 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | ((~setIn(W0!8, alive)) | (~setIn(V0!7, alive)) | leq(index(pendack, host(W0!8)), host(V0!7)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7)))))),
% 0.99/0.87 inference(quant_inst,[status(thm)],[])).
% 0.99/0.87 tff(126,plain,
% 0.99/0.87 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | leq(index(pendack, host(W0!8)), host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(host(W0!8), index(down, host(V0!7))))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.99/0.87 tff(127,plain,
% 0.99/0.87 (~setIn(host(W0!8), index(down, host(V0!7)))),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[126, 120, 53, 118, 117, 116])).
% 0.99/0.87 tff(128,plain,
% 0.99/0.87 (~setIn(host(W0!8), index(down, host(X!4)))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[127, 109])).
% 0.99/0.87 tff(129,plain,
% 0.99/0.87 (^[P: $i] : refl(leq(s(zero), host(P)) <=> leq(s(zero), host(P)))),
% 0.99/0.87 inference(bind,[status(th)],[])).
% 0.99/0.87 tff(130,plain,
% 0.99/0.87 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.99/0.87 inference(quant_intro,[status(thm)],[129])).
% 0.99/0.87 tff(131,plain,
% 0.99/0.87 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.99/0.87 inference(rewrite,[status(thm)],[])).
% 0.99/0.87 tff(132,axiom,(![P: $i] : leq(s(zero), host(P))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_02')).
% 0.99/0.87 tff(133,plain,
% 0.99/0.87 (![P: $i] : leq(s(zero), host(P))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.99/0.87 tff(134,plain,(
% 0.99/0.87 ![P: $i] : leq(s(zero), host(P))),
% 0.99/0.87 inference(skolemize,[status(sab)],[133])).
% 0.99/0.87 tff(135,plain,
% 0.99/0.87 (![P: $i] : leq(s(zero), host(P))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.99/0.87 tff(136,plain,
% 0.99/0.87 ((~![P: $i] : leq(s(zero), host(P))) | leq(s(zero), host(W0!8))),
% 0.99/0.87 inference(quant_inst,[status(thm)],[])).
% 0.99/0.87 tff(137,plain,
% 0.99/0.87 (leq(s(zero), host(W0!8))),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.99/0.87 tff(138,plain,
% 0.99/0.87 (^[Z: $i] : refl(((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))))),
% 0.99/0.87 inference(bind,[status(th)],[])).
% 0.99/0.87 tff(139,plain,
% 0.99/0.87 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))) <=> ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 0.99/0.87 inference(quant_intro,[status(thm)],[138])).
% 0.99/0.87 tff(140,plain,
% 0.99/0.87 (^[Z: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(X!4), Z)) & leq(s(zero), Z)) <=> (~(leq(host(X!4), Z) | (~leq(s(zero), Z))))), ((~((~leq(host(X!4), Z)) & leq(s(zero), Z))) <=> (~(~(leq(host(X!4), Z) | (~leq(s(zero), Z))))))), rewrite((~(~(leq(host(X!4), Z) | (~leq(s(zero), Z))))) <=> (leq(host(X!4), Z) | (~leq(s(zero), Z)))), ((~((~leq(host(X!4), Z)) & leq(s(zero), Z))) <=> (leq(host(X!4), Z) | (~leq(s(zero), Z))))), (((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (leq(host(X!4), Z) | (~leq(s(zero), Z)))))), rewrite(((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (leq(host(X!4), Z) | (~leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))), (((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))))),
% 0.99/0.87 inference(bind,[status(th)],[])).
% 0.99/0.87 tff(141,plain,
% 0.99/0.87 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 0.99/0.87 inference(quant_intro,[status(thm)],[140])).
% 0.99/0.87 tff(142,plain,
% 0.99/0.87 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z))))),
% 0.99/0.87 inference(and_elim,[status(thm)],[22])).
% 0.99/0.87 tff(143,plain,
% 0.99/0.87 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.99/0.87 tff(144,plain,
% 0.99/0.87 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.99/0.87 tff(145,plain,
% 0.99/0.87 (((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | ((host(W0!8) = host(Y!3)) | setIn(host(W0!8), index(down, host(X!4))) | leq(host(X!4), host(W0!8)) | (~leq(s(zero), host(W0!8))))) <=> ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | (host(W0!8) = host(Y!3)) | setIn(host(W0!8), index(down, host(X!4))) | leq(host(X!4), host(W0!8)) | (~leq(s(zero), host(W0!8))))),
% 0.99/0.87 inference(rewrite,[status(thm)],[])).
% 0.99/0.87 tff(146,plain,
% 0.99/0.87 ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | ((host(W0!8) = host(Y!3)) | setIn(host(W0!8), index(down, host(X!4))) | leq(host(X!4), host(W0!8)) | (~leq(s(zero), host(W0!8))))),
% 0.99/0.87 inference(quant_inst,[status(thm)],[])).
% 0.99/0.87 tff(147,plain,
% 0.99/0.87 ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | (host(W0!8) = host(Y!3)) | setIn(host(W0!8), index(down, host(X!4))) | leq(host(X!4), host(W0!8)) | (~leq(s(zero), host(W0!8)))),
% 0.99/0.87 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.99/0.87 tff(148,plain,
% 0.99/0.87 ((host(W0!8) = host(Y!3)) | leq(host(X!4), host(W0!8))),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[147, 144, 137, 128])).
% 0.99/0.87 tff(149,plain,
% 0.99/0.87 (host(W0!8) = host(Y!3)),
% 0.99/0.87 inference(unit_resolution,[status(thm)],[148, 106])).
% 0.99/0.87 tff(150,plain,
% 0.99/0.87 (^[Z: $i, Pid20: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))))),
% 0.99/0.87 inference(bind,[status(th)],[])).
% 0.99/0.87 tff(151,plain,
% 0.99/0.87 (![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))),
% 0.99/0.87 inference(quant_intro,[status(thm)],[150])).
% 0.99/0.87 tff(152,plain,
% 0.99/0.87 (^[Z: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)) <=> (~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite((((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))))),
% 0.99/0.88 inference(bind,[status(th)],[])).
% 0.99/0.88 tff(153,plain,
% 0.99/0.88 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))),
% 0.99/0.88 inference(quant_intro,[status(thm)],[152])).
% 0.99/0.88 tff(154,plain,
% 0.99/0.88 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 0.99/0.88 inference(and_elim,[status(thm)],[22])).
% 0.99/0.88 tff(155,plain,
% 0.99/0.88 (![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))),
% 0.99/0.88 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.99/0.88 tff(156,plain,
% 0.99/0.88 (![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))),
% 0.99/0.88 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.99/0.88 tff(157,plain,
% 0.99/0.88 (setIn(X!4, alive)),
% 0.99/0.88 inference(and_elim,[status(thm)],[22])).
% 0.99/0.88 tff(158,plain,
% 0.99/0.88 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))) | ((~setIn(X!4, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~(host(W0!8) = host(Y!3))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~elem(m_Down(Y!3), queue(host(X!4)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))) | (~setIn(X!4, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~(host(W0!8) = host(Y!3))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~elem(m_Down(Y!3), queue(host(X!4)))))),
% 0.99/0.88 inference(rewrite,[status(thm)],[])).
% 0.99/0.88 tff(159,plain,
% 0.99/0.88 (((~setIn(W0!8, alive)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~(host(W0!8) = host(Y!3))) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(X!4, alive))) <=> ((~setIn(X!4, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~(host(W0!8) = host(Y!3))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~elem(m_Down(Y!3), queue(host(X!4)))))),
% 0.99/0.88 inference(rewrite,[status(thm)],[])).
% 0.99/0.88 tff(160,plain,
% 0.99/0.88 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))) | ((~setIn(W0!8, alive)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~(host(W0!8) = host(Y!3))) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(X!4, alive)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))) | ((~setIn(X!4, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~(host(W0!8) = host(Y!3))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~elem(m_Down(Y!3), queue(host(X!4))))))),
% 0.99/0.88 inference(monotonicity,[status(thm)],[159])).
% 0.99/0.88 tff(161,plain,
% 0.99/0.88 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))) | ((~setIn(W0!8, alive)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~(host(W0!8) = host(Y!3))) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(X!4, alive)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))) | (~setIn(X!4, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~(host(W0!8) = host(Y!3))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~elem(m_Down(Y!3), queue(host(X!4)))))),
% 0.99/0.88 inference(transitivity,[status(thm)],[160, 158])).
% 0.99/0.88 tff(162,plain,
% 0.99/0.88 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))) | ((~setIn(W0!8, alive)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~(host(W0!8) = host(Y!3))) | (~(index(status, host(W0!8)) = elec_2)) | (~setIn(X!4, alive)))),
% 0.99/0.88 inference(quant_inst,[status(thm)],[])).
% 0.99/0.88 tff(163,plain,
% 0.99/0.88 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(host(Pid0) = host(Pid20))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)))) | (~setIn(X!4, alive)) | (~setIn(W0!8, alive)) | (~(index(status, host(W0!8)) = elec_2)) | (~(host(W0!8) = host(Y!3))) | leq(index(pendack, host(W0!8)), host(X!4)) | (~elem(m_Down(Y!3), queue(host(X!4))))),
% 0.99/0.88 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.99/0.88 tff(164,plain,
% 0.99/0.88 ($false),
% 0.99/0.88 inference(unit_resolution,[status(thm)],[163, 157, 118, 117, 156, 149, 54, 46])).
% 0.99/0.88 % SZS output end Proof
%------------------------------------------------------------------------------