%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV473+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:34:07 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV473+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 09:51:35 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(leq_type, type, (
% 0.20/0.40 leq: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_V0_11_type, type, (
% 0.20/0.40 tptp_fun_V0_11: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X0_9_type, type, (
% 0.20/0.40 tptp_fun_X0_9: $i)).
% 0.20/0.40 tff(tptp_fun_Y0_8_type, type, (
% 0.20/0.40 tptp_fun_Y0_8: $i)).
% 0.20/0.40 tff(s_type, type, (
% 0.20/0.40 s: $i > $i)).
% 0.20/0.40 tff(zero_type, type, (
% 0.20/0.40 zero: $i)).
% 0.20/0.40 tff(host_type, type, (
% 0.20/0.40 host: $i > $i)).
% 0.20/0.40 tff(setIn_type, type, (
% 0.20/0.40 setIn: ( $i * $i ) > $o)).
% 0.20/0.40 tff(index_type, type, (
% 0.20/0.40 index: ( $i * $i ) > $i)).
% 0.20/0.40 tff(down_type, type, (
% 0.20/0.40 down: $i)).
% 0.20/0.40 tff(elem_type, type, (
% 0.20/0.40 elem: ( $i * $i ) > $o)).
% 0.20/0.40 tff(queue_type, type, (
% 0.20/0.40 queue: $i > $i)).
% 0.20/0.40 tff(m_Down_type, type, (
% 0.20/0.40 m_Down: $i > $i)).
% 0.20/0.40 tff(tptp_fun_X_4_type, type, (
% 0.20/0.40 tptp_fun_X_4: $i)).
% 0.20/0.40 tff(cons_type, type, (
% 0.20/0.40 cons: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_V_6_type, type, (
% 0.20/0.40 tptp_fun_V_6: $i)).
% 0.20/0.40 tff(m_Ack_type, type, (
% 0.20/0.40 m_Ack: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.40 tptp_fun_Y_3: $i)).
% 0.20/0.40 tff(tptp_fun_W_5_type, type, (
% 0.20/0.40 tptp_fun_W_5: $i)).
% 0.20/0.40 tff(elec_1_type, type, (
% 0.20/0.40 elec_1: $i)).
% 0.20/0.40 tff(status_type, type, (
% 0.20/0.40 status: $i)).
% 0.20/0.40 tff(nbr_proc_type, type, (
% 0.20/0.40 nbr_proc: $i)).
% 0.20/0.40 tff(alive_type, type, (
% 0.20/0.40 alive: $i)).
% 0.20/0.40 tff(elid_type, type, (
% 0.20/0.40 elid: $i)).
% 0.20/0.40 tff(wait_type, type, (
% 0.20/0.40 wait: $i)).
% 0.20/0.40 tff(ldr_type, type, (
% 0.20/0.40 ldr: $i)).
% 0.20/0.40 tff(norm_type, type, (
% 0.20/0.40 norm: $i)).
% 0.20/0.40 tff(elec_2_type, type, (
% 0.20/0.40 elec_2: $i)).
% 0.20/0.40 tff(m_NotNorm_type, type, (
% 0.20/0.40 m_NotNorm: $i > $i)).
% 0.20/0.40 tff(m_Ldr_type, type, (
% 0.20/0.40 m_Ldr: $i > $i)).
% 0.20/0.40 tff(tptp_fun_W0_10_type, type, (
% 0.20/0.40 tptp_fun_W0_10: $i)).
% 0.20/0.40 tff(tptp_fun_Z_7_type, type, (
% 0.20/0.40 tptp_fun_Z_7: $i)).
% 0.20/0.40 tff(pendack_type, type, (
% 0.20/0.40 pendack: $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 ((setIn(X!4, alive) & (~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))) & ((~(host(X!4) = host(Z!7))) & setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & (~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))) & (~(host(X!4) = host(Z!7))) & setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8)) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6))) <=> (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (((~(host(X!4) = host(Z!7))) & (setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8)))) <=> ((~(host(X!4) = host(Z!7))) & setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (((setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7)))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Y0!8))) <=> (setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 ((![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) <=> (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (((setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7)))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Y0!8))) <=> ((setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7)))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Y0!8)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (((setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7)))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Y0!8))) <=> (setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (((~(host(X!4) = host(Z!7))) & ((setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7)))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Y0!8)))) <=> ((~(host(X!4) = host(Z!7))) & (setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (((~(host(X!4) = host(Z!7))) & ((setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7)))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Y0!8)))) <=> ((~(host(X!4) = host(Z!7))) & setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[8, 3])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ((setIn(X!4, alive) & (~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))) & ((~(host(X!4) = host(Z!7))) & ((setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7)))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Y0!8)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & (~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))) & ((~(host(X!4) = host(Z!7))) & setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[9, 2])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 ((setIn(X!4, alive) & (~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))) & ((~(host(X!4) = host(Z!7))) & ((setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7)))) & (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1)) & (host(X!4) = host(Y0!8)))) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))) <=> (setIn(X!4, alive) & (~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))) & (~(host(X!4) = host(Z!7))) & setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8)) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[10, 1])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 ((~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), V) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1))) | (~(host(X) = host(Y0))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))) <=> (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), V) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1))) | (~(host(X) = host(Y0))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Ack(W, Y), V))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ((~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((host(Pid0) = nbr_proc) => (~elem(m_NotNorm(Z), queue(host(Pid0)))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~elem(m_Down(Z), queue(host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~elem(m_Down(Z), queue(host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = nbr_proc)) & (host(Pid0) = host(Pid30))) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((~(((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2)) & (host(Y) = index(pendack, host(X))))) => ![Z: $i] : ((~(host(X) = host(Z))) => ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) => (((((![V0: $i] : (((~leq(host(Y0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Y0))) | (V0 = host(X0)))) & elem(m_Down(X0), V)) & (host(Y0) = host(W0))) & (host(Y0) = nbr_proc)) & (index(status, host(Y0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z)))))))))))) <=> (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), V) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1))) | (~(host(X) = host(Y0))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Ack(W, Y), V))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(14,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((host(Pid0) = nbr_proc) => (~elem(m_NotNorm(Z), queue(host(Pid0)))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~elem(m_Down(Z), queue(host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~elem(m_Down(Z), queue(host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = nbr_proc)) & (host(Pid0) = host(Pid30))) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((~(((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2)) & (host(Y) = index(pendack, host(X))))) => ![Z: $i] : ((~(host(X) = host(Z))) => ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) => (((((![V0: $i] : (((~leq(host(Y0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Y0))) | (V0 = host(X0)))) & elem(m_Down(X0), V)) & (host(Y0) = host(W0))) & (host(Y0) = nbr_proc)) & (index(status, host(Y0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), V) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1))) | (~(host(X) = host(Y0))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), V) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1))) | (~(host(X) = host(Y0))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), V) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1))) | (~(host(X) = host(Y0))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (~![V: $i, W: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2) & (host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((host(X) = host(Z)) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(Z, alive) & elem(m_Down(W0), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(X0)) | setIn(V0, index(down, host(Y0))) | (~((~leq(host(Y0), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0), V) & (host(Y0) = host(W0)) & (host(Y0) = nbr_proc) & (index(status, host(Y0)) = elec_1))) | (~(host(X) = host(Y0))))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Ack(W, Y), V)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (setIn(X!4, alive) & (~((index(elid, host(X!4)) = W!5) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))))) & (~(host(X!4) = host(Z!7))) & setIn(Z!7, alive) & elem(m_Down(W0!10), queue(host(Z!7))) & ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) & elem(m_Down(X0!9), V!6) & (host(Y0!8) = host(W0!10)) & (host(Y0!8) = nbr_proc) & (index(status, host(Y0!8)) = elec_1) & (host(X!4) = host(Y0!8)) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_NotNorm(Z), queue(host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Z), queue(host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (host(X!4) = host(Y0!8)),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (host(Y0!8) = host(X!4)),
% 0.20/0.44 inference(symmetry,[status(thm)],[20])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 (queue(host(Y0!8)) = queue(host(X!4))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (elem(m_Down(X0!9), queue(host(Y0!8))) <=> elem(m_Down(X0!9), queue(host(X!4)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (elem(m_Down(X0!9), queue(host(X!4))) <=> elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.20/0.44 inference(symmetry,[status(thm)],[23])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (queue(host(X!4)) = cons(m_Ack(W!5, Y!3), V!6)),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (cons(m_Ack(W!5, Y!3), V!6) = queue(host(X!4))),
% 0.20/0.44 inference(symmetry,[status(thm)],[25])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6)) <=> elem(m_Down(X0!9), queue(host(X!4)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (elem(m_Down(X0!9), queue(host(X!4))) <=> elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6))),
% 0.20/0.44 inference(symmetry,[status(thm)],[27])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 ((~elem(m_Down(X0!9), queue(host(X!4)))) <=> (~elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.44 tff(30,assumption,(~elem(m_Down(X0!9), queue(host(X!4)))), introduced(assumption)).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (~elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(35,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')).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.44 tff(37,plain,(
% 0.20/0.44 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[36])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6)) <=> ((m_Down(X0!9) = m_Ack(W!5, Y!3)) | elem(m_Down(X0!9), V!6)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6)) <=> ((m_Down(X0!9) = m_Ack(W!5, Y!3)) | elem(m_Down(X0!9), V!6))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (elem(m_Down(X0!9), V!6)),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (((m_Down(X0!9) = m_Ack(W!5, Y!3)) | elem(m_Down(X0!9), V!6)) | (~elem(m_Down(X0!9), V!6))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 ((m_Down(X0!9) = m_Ack(W!5, Y!3)) | elem(m_Down(X0!9), V!6)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 ((~(elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6)) <=> ((m_Down(X0!9) = m_Ack(W!5, Y!3)) | elem(m_Down(X0!9), V!6)))) | elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6)) | (~((m_Down(X0!9) = m_Ack(W!5, Y!3)) | elem(m_Down(X0!9), V!6)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~(elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6)) <=> ((m_Down(X0!9) = m_Ack(W!5, Y!3)) | elem(m_Down(X0!9), V!6)))) | elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (elem(m_Down(X0!9), cons(m_Ack(W!5, Y!3), V!6))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[45, 40])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[46, 31])).
% 0.20/0.44 tff(48,plain,(elem(m_Down(X0!9), queue(host(X!4)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[48, 24])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : refl(((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) <=> ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z)))) <=> (~((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))))), ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) <=> (~(~((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))))))), rewrite((~(~((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))))) <=> ((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))))), ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) <=> ((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))))), rewrite((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) <=> (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))), (((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> (((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))))), rewrite((((~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))), (((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(host(Pid0) = nbr_proc)) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (index(status, host(Y0!8)) = elec_1),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (host(Y0!8) = nbr_proc),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (host(Y0!8) = host(W0!10)),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (elem(m_Down(W0!10), queue(host(Z!7)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (setIn(Z!7, alive)),
% 0.20/0.44 inference(and_elim,[status(thm)],[19])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~setIn(Z!7, alive)) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = host(W0!10))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~(host(Y0!8) = nbr_proc)) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | (~setIn(Z!7, alive)) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = host(W0!10))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~(host(Y0!8) = nbr_proc)) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(Z!7, alive)) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))) <=> ((~setIn(Z!7, alive)) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = host(W0!10))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~(host(Y0!8) = nbr_proc)) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ((~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) <=> (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(Z!7, alive)) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))) <=> ((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(Z!7, alive)) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(Z!7, alive)) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))) <=> ((~setIn(Z!7, alive)) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = host(W0!10))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~(host(Y0!8) = nbr_proc)) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(Z!7, alive)) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~setIn(Z!7, alive)) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = host(W0!10))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~(host(Y0!8) = nbr_proc)) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(Z!7, alive)) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | (~setIn(Z!7, alive)) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = host(W0!10))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~(host(Y0!8) = nbr_proc)) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[67, 62])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.46 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | ((~(host(Y0!8) = nbr_proc)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(Y0!8) = host(W0!10))) | (~(index(status, host(Y0!8)) = elec_1)) | (~setIn(Z!7, alive)) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = nbr_proc)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20)) | (~leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))) | (~setIn(Z!7, alive)) | (~(index(status, host(Y0!8)) = elec_1)) | (~(host(Y0!8) = host(W0!10))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~elem(m_Down(W0!10), queue(host(Z!7)))) | (~(host(Y0!8) = nbr_proc)) | (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (~((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[70, 61, 60, 59, 58, 57, 56, 49])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))) | leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))) | (~leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (~leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))) | (~setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (~setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[76, 71])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))) | (~(tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (~(tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[78, 71])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (^[V0: $i] : refl(((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0))) <=> ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0))) <=> ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (^[V0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(Y0!8), V0)) & leq(s(zero), V0)) <=> (~(leq(host(Y0!8), V0) | (~leq(s(zero), V0))))), ((~((~leq(host(Y0!8), V0)) & leq(s(zero), V0))) <=> (~(~(leq(host(Y0!8), V0) | (~leq(s(zero), V0))))))), rewrite((~(~(leq(host(Y0!8), V0) | (~leq(s(zero), V0))))) <=> (leq(host(Y0!8), V0) | (~leq(s(zero), V0)))), ((~((~leq(host(Y0!8), V0)) & leq(s(zero), V0))) <=> (leq(host(Y0!8), V0) | (~leq(s(zero), V0))))), (((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) <=> ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (leq(host(Y0!8), V0) | (~leq(s(zero), V0)))))), rewrite(((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) <=> ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))), (((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) <=> ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0)))) <=> ![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V0)) & leq(s(zero), V0))))),
% 0.20/0.46 inference(and_elim,[status(thm)],[19])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (((~![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) | ((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))) <=> ((~![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) | (tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 ((~![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) | ((tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 ((~![V0: $i] : ((V0 = host(X0!9)) | setIn(V0, index(down, host(Y0!8))) | leq(host(Y0!8), V0) | (~leq(s(zero), V0)))) | (tptp_fun_V0_11(Y0!8, X0!9) = host(X0!9)) | setIn(tptp_fun_V0_11(Y0!8, X0!9), index(down, host(Y0!8))) | leq(host(Y0!8), tptp_fun_V0_11(Y0!8, X0!9)) | (~leq(s(zero), tptp_fun_V0_11(Y0!8, X0!9)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[89, 86, 79, 77, 75, 73])).
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------