%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV465+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:34:06 AM UTC 2025
% Result : Theorem 3.82s 4.06s
% Output : Proof 3.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV465+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:51:57 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.82/4.06 % SZS status Theorem
% 3.82/4.06 % SZS output start Proof
% 3.82/4.06 tff(s_type, type, (
% 3.82/4.06 s: $i > $i)).
% 3.82/4.06 tff(index_type, type, (
% 3.82/4.06 index: ( $i * $i ) > $i)).
% 3.82/4.06 tff(host_type, type, (
% 3.82/4.06 host: $i > $i)).
% 3.82/4.06 tff(tptp_fun_X_3_type, type, (
% 3.82/4.06 tptp_fun_X_3: $i)).
% 3.82/4.06 tff(pendack_type, type, (
% 3.82/4.06 pendack: $i)).
% 3.82/4.06 tff(tptp_fun_Y_0_type, type, (
% 3.82/4.06 tptp_fun_Y_0: $i > $i)).
% 3.82/4.06 tff(m_Down_type, type, (
% 3.82/4.06 m_Down: $i > $i)).
% 3.82/4.06 tff(tptp_fun_X0_7_type, type, (
% 3.82/4.06 tptp_fun_X0_7: $i)).
% 3.82/4.06 tff(tptp_fun_Y0_6_type, type, (
% 3.82/4.06 tptp_fun_Y0_6: $i)).
% 3.82/4.06 tff(tptp_fun_W_4_type, type, (
% 3.82/4.06 tptp_fun_W_4: $i)).
% 3.82/4.06 tff(tptp_fun_Z_8_type, type, (
% 3.82/4.06 tptp_fun_Z_8: $i)).
% 3.82/4.06 tff(elec_2_type, type, (
% 3.82/4.06 elec_2: $i)).
% 3.82/4.06 tff(status_type, type, (
% 3.82/4.06 status: $i)).
% 3.82/4.06 tff(leq_type, type, (
% 3.82/4.06 leq: ( $i * $i ) > $o)).
% 3.82/4.06 tff(nbr_proc_type, type, (
% 3.82/4.06 nbr_proc: $i)).
% 3.82/4.06 tff(elem_type, type, (
% 3.82/4.06 elem: ( $i * $i ) > $o)).
% 3.82/4.06 tff(snoc_type, type, (
% 3.82/4.06 snoc: ( $i * $i ) > $i)).
% 3.82/4.06 tff(m_NotNorm_type, type, (
% 3.82/4.06 m_NotNorm: $i > $i)).
% 3.82/4.06 tff(tptp_fun_V_5_type, type, (
% 3.82/4.06 tptp_fun_V_5: $i)).
% 3.82/4.06 tff(m_Ack_type, type, (
% 3.82/4.06 m_Ack: ( $i * $i ) > $i)).
% 3.82/4.06 tff(setIn_type, type, (
% 3.82/4.06 setIn: ( $i * $i ) > $o)).
% 3.82/4.06 tff(alive_type, type, (
% 3.82/4.06 alive: $i)).
% 3.82/4.06 tff(norm_type, type, (
% 3.82/4.06 norm: $i)).
% 3.82/4.06 tff(tptp_fun_Y_9_type, type, (
% 3.82/4.06 tptp_fun_Y_9: $i)).
% 3.82/4.06 tff(ldr_type, type, (
% 3.82/4.06 ldr: $i)).
% 3.82/4.06 tff(cons_type, type, (
% 3.82/4.06 cons: ( $i * $i ) > $i)).
% 3.82/4.06 tff(m_NormQ_type, type, (
% 3.82/4.06 m_NormQ: $i > $i)).
% 3.82/4.06 tff(queue_type, type, (
% 3.82/4.06 queue: $i > $i)).
% 3.82/4.06 tff(elec_1_type, type, (
% 3.82/4.06 elec_1: $i)).
% 3.82/4.06 tff(tptp_fun_V0_10_type, type, (
% 3.82/4.06 tptp_fun_V0_10: ( $i * $i ) > $i)).
% 3.82/4.06 tff(zero_type, type, (
% 3.82/4.06 zero: $i)).
% 3.82/4.06 tff(down_type, type, (
% 3.82/4.06 down: $i)).
% 3.82/4.06 tff(m_Halt_type, type, (
% 3.82/4.06 m_Halt: $i > $i)).
% 3.82/4.06 tff(elid_type, type, (
% 3.82/4.06 elid: $i)).
% 3.82/4.06 tff(m_Ldr_type, type, (
% 3.82/4.06 m_Ldr: $i > $i)).
% 3.82/4.06 tff(pidElem_type, type, (
% 3.82/4.06 pidElem: $i > $o)).
% 3.82/4.06 tff(1,plain,
% 3.82/4.06 ((setIn(X!3, alive) & (~(index(status, host(X!3)) = norm)) & (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))) & (![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5)))) <=> (setIn(X!3, alive) & (~(index(status, host(X!3)) = norm)) & (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5)))),
% 3.82/4.06 inference(rewrite,[status(thm)],[])).
% 3.82/4.06 tff(2,plain,
% 3.82/4.06 ((![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | ((~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5))) <=> (![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5)))),
% 3.82/4.06 inference(rewrite,[status(thm)],[])).
% 3.82/4.06 tff(3,plain,
% 3.82/4.06 ((~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))) <=> (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6)))))),
% 3.82/4.06 inference(rewrite,[status(thm)],[])).
% 3.82/4.06 tff(4,plain,
% 3.82/4.06 ((setIn(X!3, alive) & (~(index(status, host(X!3)) = norm)) & (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))) & (![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | ((~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5)))) <=> (setIn(X!3, alive) & (~(index(status, host(X!3)) = norm)) & (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))) & (![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5))))),
% 3.82/4.07 inference(monotonicity,[status(thm)],[3, 2])).
% 3.82/4.07 tff(5,plain,
% 3.82/4.07 ((setIn(X!3, alive) & (~(index(status, host(X!3)) = norm)) & (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))) & (![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | ((~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5)))) <=> (setIn(X!3, alive) & (~(index(status, host(X!3)) = norm)) & (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5)))),
% 3.82/4.07 inference(transitivity,[status(thm)],[4, 1])).
% 3.82/4.07 tff(6,plain,
% 3.82/4.07 ((~![V: $i, W: $i, X: $i] : ((~setIn(X, alive)) | (index(status, host(X)) = norm) | ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(Z) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(X) = host(Y0))) | (~(host(W) = host(Y0)))) | (~(![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~(![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) = host(Z)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_NormQ(W), V)))))) <=> (~![V: $i, W: $i, X: $i] : ((~setIn(X, alive)) | (index(status, host(X)) = norm) | ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(Z) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(X) = host(Y0))) | (~(host(W) = host(Y0)))) | (~(![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~(![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) = host(Z)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_NormQ(W), V))))))),
% 3.82/4.07 inference(rewrite,[status(thm)],[])).
% 3.82/4.07 tff(7,plain,
% 3.82/4.07 ((~![V: $i, W: $i, X: $i] : ((((((((((((((((![Y: $i, Z: $i] : (elem(m_Ldr(Z), queue(host(Y))) => (~leq(host(Y), host(Z)))) & ![Y: $i, Z: $i] : (elem(m_Down(Z), queue(host(Y))) => (~(host(Z) = host(Y))))) & ![Y: $i, Z: $i] : (elem(m_Halt(Z), queue(host(Y))) => (~leq(host(Y), host(Z))))) & ![Y: $i, Z: $i, Pid0: $i] : (elem(m_Ack(Pid0, Y), queue(host(Z))) => (~leq(host(Y), host(Pid0))))) & ![Y: $i, Z: $i] : (((~(Z = Y)) & (host(Z) = host(Y))) => ((~setIn(Y, alive)) | (~setIn(Z, alive))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z)))) => leq(host(Y), index(pendack, host(Z))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & (index(status, host(Z)) = elec_1)) => (~elem(m_Ack(Z, Y), queue(host(Z)))))) & ![Y: $i] : ((((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive)) => (index(elid, host(Y)) = Y))) & ![Y: $i, Z: $i] : ((((((~leq(host(Y), host(Z))) & setIn(Y, alive)) & setIn(Z, alive)) & (index(status, host(Y)) = elec_2)) & (index(status, host(Z)) = elec_2)) => leq(index(pendack, host(Z)), host(Y)))) & ![Y: $i, Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Z) = host(Y))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & ![Y: $i, Z: $i, Pid0: $i] : (((((setIn(Y, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Y)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Y, Z), queue(host(Y)))))) & ![Y: $i, Z: $i] : ((((((~leq(host(Y), host(Z))) & setIn(Y, alive)) & setIn(Z, alive)) & (index(status, host(Y)) = elec_2)) & (index(status, host(Z)) = elec_2)) => (~leq(index(pendack, host(Y)), index(pendack, host(Z)))))) & ![Y: $i, Z: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Z)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & ![Y: $i, 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)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = host(Z))) & (host(Pid0) = nbr_proc)) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Z) = index(pendack, host(Pid0)))) & (host(Pid20) = s(index(pendack, host(Pid0))))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & (queue(host(X)) = cons(m_NormQ(W), V))) => (setIn(X, alive) => ((~(index(status, host(X)) = norm)) => ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((host(W) = host(Y0)) => ((host(X) = host(Y0)) => (((((((setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W)))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W)))) & leq(nbr_proc, s(index(pendack, host(Y0))))) & (index(status, host(Y0)) = elec_2)) & (host(Z) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm)))))))))) <=> (~![V: $i, W: $i, X: $i] : ((~setIn(X, alive)) | (index(status, host(X)) = norm) | ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(Z) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(X) = host(Y0))) | (~(host(W) = host(Y0)))) | (~(![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~(![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) = host(Z)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_NormQ(W), V))))))),
% 3.82/4.08 inference(rewrite,[status(thm)],[])).
% 3.82/4.08 tff(8,axiom,(~![V: $i, W: $i, X: $i] : ((((((((((((((((![Y: $i, Z: $i] : (elem(m_Ldr(Z), queue(host(Y))) => (~leq(host(Y), host(Z)))) & ![Y: $i, Z: $i] : (elem(m_Down(Z), queue(host(Y))) => (~(host(Z) = host(Y))))) & ![Y: $i, Z: $i] : (elem(m_Halt(Z), queue(host(Y))) => (~leq(host(Y), host(Z))))) & ![Y: $i, Z: $i, Pid0: $i] : (elem(m_Ack(Pid0, Y), queue(host(Z))) => (~leq(host(Y), host(Pid0))))) & ![Y: $i, Z: $i] : (((~(Z = Y)) & (host(Z) = host(Y))) => ((~setIn(Y, alive)) | (~setIn(Z, alive))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z)))) => leq(host(Y), index(pendack, host(Z))))) & ![Y: $i, Z: $i] : ((setIn(Z, alive) & (index(status, host(Z)) = elec_1)) => (~elem(m_Ack(Z, Y), queue(host(Z)))))) & ![Y: $i] : ((((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive)) => (index(elid, host(Y)) = Y))) & ![Y: $i, Z: $i] : ((((((~leq(host(Y), host(Z))) & setIn(Y, alive)) & setIn(Z, alive)) & (index(status, host(Y)) = elec_2)) & (index(status, host(Z)) = elec_2)) => leq(index(pendack, host(Z)), host(Y)))) & ![Y: $i, Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Z) = host(Y))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & ![Y: $i, Z: $i, Pid0: $i] : (((((setIn(Y, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Z))) & (index(status, host(Y)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Y, Z), queue(host(Y)))))) & ![Y: $i, Z: $i] : ((((((~leq(host(Y), host(Z))) & setIn(Y, alive)) & setIn(Z, alive)) & (index(status, host(Y)) = elec_2)) & (index(status, host(Z)) = elec_2)) => (~leq(index(pendack, host(Y)), index(pendack, host(Z)))))) & ![Y: $i, Z: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Z)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & ![Y: $i, 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)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = host(Z))) & (host(Pid0) = nbr_proc)) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Z) = index(pendack, host(Pid0)))) & (host(Pid20) = s(index(pendack, host(Pid0))))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm))))) & (queue(host(X)) = cons(m_NormQ(W), V))) => (setIn(X, alive) => ((~(index(status, host(X)) = norm)) => ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((host(W) = host(Y0)) => ((host(X) = host(Y0)) => (((((((setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W)))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W)))) & leq(nbr_proc, s(index(pendack, host(Y0))))) & (index(status, host(Y0)) = elec_2)) & (host(Z) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y))) & (index(status, host(Y)) = norm)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 3.82/4.08 tff(9,plain,
% 3.82/4.08 (~![V: $i, W: $i, X: $i] : ((~setIn(X, alive)) | (index(status, host(X)) = norm) | ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(Z) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(X) = host(Y0))) | (~(host(W) = host(Y0)))) | (~(![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~(![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) = host(Z)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_NormQ(W), V)))))),
% 3.82/4.08 inference(modus_ponens,[status(thm)],[8, 7])).
% 3.82/4.08 tff(10,plain,
% 3.82/4.08 (~![V: $i, W: $i, X: $i] : ((~setIn(X, alive)) | (index(status, host(X)) = norm) | ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(Z) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(X) = host(Y0))) | (~(host(W) = host(Y0)))) | (~(![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~(![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) = host(Z)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_NormQ(W), V)))))),
% 3.82/4.08 inference(modus_ponens,[status(thm)],[9, 6])).
% 3.82/4.08 tff(11,plain,
% 3.82/4.08 (~![V: $i, W: $i, X: $i] : ((~setIn(X, alive)) | (index(status, host(X)) = norm) | ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(Z) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(X) = host(Y0))) | (~(host(W) = host(Y0)))) | (~(![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~(![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) = host(Z)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_NormQ(W), V)))))),
% 3.82/4.08 inference(modus_ponens,[status(thm)],[10, 6])).
% 3.82/4.08 tff(12,plain,
% 3.82/4.08 (~![V: $i, W: $i, X: $i] : ((~setIn(X, alive)) | (index(status, host(X)) = norm) | ![Y: $i, Z: $i, X0: $i, Y0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Y0, alive) & elem(m_Down(X0), snoc(V, m_NotNorm(W))) & elem(m_Ack(Y0, Z), snoc(V, m_NotNorm(W))) & leq(nbr_proc, s(index(pendack, host(Y0)))) & (index(status, host(Y0)) = elec_2) & (host(Z) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(X) = host(Y0))) | (~(host(W) = host(Y0)))) | (~(![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~(![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) = host(Z)) & (host(Pid0) = nbr_proc) & (index(status, host(Pid0)) = elec_1)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X)) = cons(m_NormQ(W), V)))))),
% 3.93/4.08 inference(modus_ponens,[status(thm)],[11, 6])).
% 3.93/4.08 tff(13,plain,
% 3.93/4.08 (setIn(X!3, alive) & (~(index(status, host(X!3)) = norm)) & (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Ldr(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~elem(m_Down(Z), queue(host(Y))))) & ![Y: $i, Z: $i] : ((~leq(host(Y), host(Z))) | (~elem(m_Halt(Z), queue(host(Y))))) & ![Y: $i, Z: $i, Pid0: $i] : ((~leq(host(Y), host(Pid0))) | (~elem(m_Ack(Pid0, Y), queue(host(Z))))) & ![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) & ![Y: $i, Z: $i] : ((~(setIn(Z, alive) & elem(m_Ack(Z, Y), queue(host(Z))))) | leq(host(Y), index(pendack, host(Z)))) & ![Y: $i, Z: $i] : ((~elem(m_Ack(Z, Y), queue(host(Z)))) | (~(setIn(Z, alive) & (index(status, host(Z)) = elec_1)))) & ![Y: $i] : ((~(((index(status, host(Y)) = elec_1) | (index(status, host(Y)) = elec_2)) & setIn(Y, alive))) | (index(elid, host(Y)) = Y)) & ![Y: $i, Z: $i] : ((~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2))) | leq(index(pendack, host(Z)), host(Y))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Z) = host(Y)))) | (~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~elem(m_Ack(Y, Z), queue(host(Y)))) | (~(setIn(Y, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Z)) & (index(status, host(Y)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i] : ((~leq(index(pendack, host(Y)), index(pendack, host(Z)))) | (~((~leq(host(Y), host(Z))) & setIn(Y, alive) & setIn(Z, alive) & (index(status, host(Y)) = elec_2) & (index(status, host(Z)) = elec_2)))) & ![Y: $i, Z: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Y))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Z))) & (index(status, host(Pid0)) = elec_2)))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & elem(m_Down(Z), queue(host(Y))))) | (~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = host(Z))) | (~(host(Pid0) = nbr_proc)) | (~(index(status, host(Pid0)) = elec_1))) & ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (queue(host(X!3)) = cons(m_NormQ(W!4), V!5))),
% 3.93/4.08 inference(modus_ponens,[status(thm)],[12, 5])).
% 3.93/4.08 tff(14,plain,
% 3.93/4.08 (~((~(setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm))) | (~(setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(host(X!3) = host(Y0!6))) | (~(host(W!4) = host(Y0!6))))),
% 3.93/4.08 inference(and_elim,[status(thm)],[13])).
% 3.93/4.08 tff(15,plain,
% 3.93/4.08 (host(X!3) = host(Y0!6)),
% 3.93/4.08 inference(or_elim,[status(thm)],[14])).
% 3.93/4.08 tff(16,plain,
% 3.93/4.08 (index(pendack, host(X!3)) = index(pendack, host(Y0!6))),
% 3.93/4.08 inference(monotonicity,[status(thm)],[15])).
% 3.93/4.08 tff(17,plain,
% 3.93/4.08 (s(index(pendack, host(X!3))) = s(index(pendack, host(Y0!6)))),
% 3.93/4.08 inference(monotonicity,[status(thm)],[16])).
% 3.93/4.08 tff(18,plain,
% 3.93/4.08 (s(index(pendack, host(Y0!6))) = s(index(pendack, host(X!3)))),
% 3.93/4.08 inference(symmetry,[status(thm)],[17])).
% 3.93/4.08 tff(19,plain,
% 3.93/4.08 (setIn(Y0!6, alive) & elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) & elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & (index(status, host(Y0!6)) = elec_2) & (host(Z!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6))))),
% 3.93/4.08 inference(or_elim,[status(thm)],[14])).
% 3.93/4.08 tff(20,plain,
% 3.93/4.08 (host(X0!7) = s(index(pendack, host(Y0!6)))),
% 3.93/4.08 inference(and_elim,[status(thm)],[19])).
% 3.93/4.08 tff(21,plain,
% 3.93/4.08 (^[X: $i, Y: $i] : refl(((X = Y) <=> (m_Down(X) = m_Down(Y))) <=> ((X = Y) <=> (m_Down(X) = m_Down(Y))))),
% 3.93/4.08 inference(bind,[status(th)],[])).
% 3.93/4.08 tff(22,plain,
% 3.93/4.08 (![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y))) <=> ![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y)))),
% 3.93/4.08 inference(quant_intro,[status(thm)],[21])).
% 3.93/4.08 tff(23,plain,
% 3.93/4.08 (![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y))) <=> ![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y)))),
% 3.93/4.08 inference(rewrite,[status(thm)],[])).
% 3.93/4.08 tff(24,plain,
% 3.93/4.08 (^[X: $i, Y: $i] : rewrite(((~(X = Y)) <=> (~(m_Down(X) = m_Down(Y)))) <=> ((X = Y) <=> (m_Down(X) = m_Down(Y))))),
% 3.93/4.08 inference(bind,[status(th)],[])).
% 3.93/4.08 tff(25,plain,
% 3.93/4.08 (![X: $i, Y: $i] : ((~(X = Y)) <=> (~(m_Down(X) = m_Down(Y)))) <=> ![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y)))),
% 3.93/4.08 inference(quant_intro,[status(thm)],[24])).
% 3.93/4.08 tff(26,axiom,(![X: $i, Y: $i] : ((~(X = Y)) <=> (~(m_Down(X) = m_Down(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_30')).
% 3.93/4.08 tff(27,plain,
% 3.93/4.08 (![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y)))),
% 3.93/4.08 inference(modus_ponens,[status(thm)],[26, 25])).
% 3.93/4.08 tff(28,plain,
% 3.93/4.08 (![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y)))),
% 3.93/4.08 inference(modus_ponens,[status(thm)],[27, 23])).
% 3.93/4.08 tff(29,plain,(
% 3.93/4.08 ![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y)))),
% 3.93/4.08 inference(skolemize,[status(sab)],[28])).
% 3.93/4.08 tff(30,plain,
% 3.93/4.08 (![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y)))),
% 3.93/4.08 inference(modus_ponens,[status(thm)],[29, 22])).
% 3.93/4.08 tff(31,plain,
% 3.93/4.08 ((~![X: $i, Y: $i] : ((X = Y) <=> (m_Down(X) = m_Down(Y)))) | ((X0!7 = tptp_fun_Y_0(m_Down(X0!7))) <=> (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))))),
% 3.93/4.08 inference(quant_inst,[status(thm)],[])).
% 3.93/4.08 tff(32,plain,
% 3.93/4.08 ((X0!7 = tptp_fun_Y_0(m_Down(X0!7))) <=> (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7))))),
% 3.93/4.08 inference(unit_resolution,[status(thm)],[31, 30])).
% 3.93/4.08 tff(33,assumption,(m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))), introduced(assumption)).
% 3.93/4.08 tff(34,plain,
% 3.93/4.08 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Halt(Y))) <=> (~(m_Down(X) = m_Halt(Y))))),
% 3.93/4.08 inference(bind,[status(th)],[])).
% 3.93/4.08 tff(35,plain,
% 3.93/4.08 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 3.93/4.08 inference(quant_intro,[status(thm)],[34])).
% 3.93/4.08 tff(36,plain,
% 3.93/4.08 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 3.93/4.08 inference(rewrite,[status(thm)],[])).
% 3.93/4.08 tff(37,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_17')).
% 3.93/4.08 tff(38,plain,
% 3.93/4.08 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 3.93/4.08 inference(modus_ponens,[status(thm)],[37, 36])).
% 3.93/4.08 tff(39,plain,(
% 3.93/4.08 ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 3.93/4.08 inference(skolemize,[status(sab)],[38])).
% 3.93/4.08 tff(40,plain,
% 3.93/4.08 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 3.93/4.08 inference(modus_ponens,[status(thm)],[39, 35])).
% 3.93/4.08 tff(41,plain,
% 3.93/4.08 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))) | (~(m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))),
% 3.93/4.08 inference(quant_inst,[status(thm)],[])).
% 3.93/4.08 tff(42,plain,
% 3.93/4.08 ($false),
% 3.93/4.08 inference(unit_resolution,[status(thm)],[41, 40, 33])).
% 3.93/4.08 tff(43,plain,(~(m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7))))), inference(lemma,lemma(discharge,[]))).
% 3.93/4.08 tff(44,plain,
% 3.93/4.08 (((~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))) | $false) <=> (~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(45,plain,
% 3.93/4.09 ((~$true) <=> $false),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(46,plain,
% 3.93/4.09 (($true | (m_Down(X0!7) = m_Halt(X0!7))) <=> $true),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(47,plain,
% 3.93/4.09 ((m_Down(X0!7) = m_Down(X0!7)) <=> $true),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(48,plain,
% 3.93/4.09 (((m_Down(X0!7) = m_Down(X0!7)) | (m_Down(X0!7) = m_Halt(X0!7))) <=> ($true | (m_Down(X0!7) = m_Halt(X0!7)))),
% 3.93/4.09 inference(monotonicity,[status(thm)],[47])).
% 3.93/4.09 tff(49,plain,
% 3.93/4.09 (((m_Down(X0!7) = m_Down(X0!7)) | (m_Down(X0!7) = m_Halt(X0!7))) <=> $true),
% 3.93/4.09 inference(transitivity,[status(thm)],[48, 46])).
% 3.93/4.09 tff(50,plain,
% 3.93/4.09 ((~((m_Down(X0!7) = m_Down(X0!7)) | (m_Down(X0!7) = m_Halt(X0!7)))) <=> (~$true)),
% 3.93/4.09 inference(monotonicity,[status(thm)],[49])).
% 3.93/4.09 tff(51,plain,
% 3.93/4.09 ((~((m_Down(X0!7) = m_Down(X0!7)) | (m_Down(X0!7) = m_Halt(X0!7)))) <=> $false),
% 3.93/4.09 inference(transitivity,[status(thm)],[50, 45])).
% 3.93/4.09 tff(52,plain,
% 3.93/4.09 (((~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))) | (~((m_Down(X0!7) = m_Down(X0!7)) | (m_Down(X0!7) = m_Halt(X0!7))))) <=> ((~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))) | $false)),
% 3.93/4.09 inference(monotonicity,[status(thm)],[51])).
% 3.93/4.09 tff(53,plain,
% 3.93/4.09 (((~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))) | (~((m_Down(X0!7) = m_Down(X0!7)) | (m_Down(X0!7) = m_Halt(X0!7))))) <=> (~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))),
% 3.93/4.09 inference(transitivity,[status(thm)],[52, 44])).
% 3.93/4.09 tff(54,plain,
% 3.93/4.09 ((~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))) | (~((m_Down(X0!7) = m_Down(X0!7)) | (m_Down(X0!7) = m_Halt(X0!7))))),
% 3.93/4.09 inference(quant_inst,[status(thm)],[])).
% 3.93/4.09 tff(55,plain,
% 3.93/4.09 (~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[54, 53])).
% 3.93/4.09 tff(56,assumption,(![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))), introduced(assumption)).
% 3.93/4.09 tff(57,plain,
% 3.93/4.09 ($false),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[56, 55])).
% 3.93/4.09 tff(58,plain,(~![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))), inference(lemma,lemma(discharge,[]))).
% 3.93/4.09 tff(59,plain,
% 3.93/4.09 (^[X: $i] : refl((~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))) <=> (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(60,plain,
% 3.93/4.09 (![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))) <=> ![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[59])).
% 3.93/4.09 tff(61,plain,
% 3.93/4.09 (^[X: $i] : rewrite((~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))) <=> (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(62,plain,
% 3.93/4.09 (![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))) <=> ![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[61])).
% 3.93/4.09 tff(63,plain,
% 3.93/4.09 (![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))) <=> ![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))),
% 3.93/4.09 inference(transitivity,[status(thm)],[62, 60])).
% 3.93/4.09 tff(64,plain,
% 3.93/4.09 (^[X: $i] : trans(monotonicity(rewrite(((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) <=> ((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))), rewrite((pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))) <=> (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))), ((((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))) <=> (((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))), rewrite((((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))) <=> (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))), ((((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))) <=> (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(65,plain,
% 3.93/4.09 (![X: $i] : (((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))) <=> ![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[64])).
% 3.93/4.09 tff(66,plain,
% 3.93/4.09 (^[X: $i] : rewrite((((~pidElem(X)) | ((X = m_Down(tptp_fun_Y_0(X))) | (X = m_Halt(tptp_fun_Y_0(X))))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))) <=> (((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(67,plain,
% 3.93/4.09 (![X: $i] : (((~pidElem(X)) | ((X = m_Down(tptp_fun_Y_0(X))) | (X = m_Halt(tptp_fun_Y_0(X))))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y)))))) <=> ![X: $i] : (((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[66])).
% 3.93/4.09 tff(68,plain,
% 3.93/4.09 (![X: $i] : (pidElem(X) <=> ?[Y: $i] : ((X = m_Down(Y)) | (X = m_Halt(Y)))) <=> ![X: $i] : (pidElem(X) <=> ?[Y: $i] : ((X = m_Down(Y)) | (X = m_Halt(Y))))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(69,plain,
% 3.93/4.09 (^[X: $i] : rewrite((pidElem(X) <=> ?[Y: $i] : ((X = m_Halt(Y)) | (X = m_Down(Y)))) <=> (pidElem(X) <=> ?[Y: $i] : ((X = m_Down(Y)) | (X = m_Halt(Y)))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(70,plain,
% 3.93/4.09 (![X: $i] : (pidElem(X) <=> ?[Y: $i] : ((X = m_Halt(Y)) | (X = m_Down(Y)))) <=> ![X: $i] : (pidElem(X) <=> ?[Y: $i] : ((X = m_Down(Y)) | (X = m_Halt(Y))))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[69])).
% 3.93/4.09 tff(71,axiom,(![X: $i] : (pidElem(X) <=> ?[Y: $i] : ((X = m_Halt(Y)) | (X = m_Down(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_48')).
% 3.93/4.09 tff(72,plain,
% 3.93/4.09 (![X: $i] : (pidElem(X) <=> ?[Y: $i] : ((X = m_Down(Y)) | (X = m_Halt(Y))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[71, 70])).
% 3.93/4.09 tff(73,plain,
% 3.93/4.09 (![X: $i] : (pidElem(X) <=> ?[Y: $i] : ((X = m_Down(Y)) | (X = m_Halt(Y))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[72, 68])).
% 3.93/4.09 tff(74,plain,(
% 3.93/4.09 ![X: $i] : (((~pidElem(X)) | ((X = m_Down(tptp_fun_Y_0(X))) | (X = m_Halt(tptp_fun_Y_0(X))))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))),
% 3.93/4.09 inference(skolemize,[status(sab)],[73])).
% 3.93/4.09 tff(75,plain,
% 3.93/4.09 (![X: $i] : (((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X))) & (pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[74, 67])).
% 3.93/4.09 tff(76,plain,
% 3.93/4.09 (![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[75, 65])).
% 3.93/4.09 tff(77,plain,
% 3.93/4.09 (![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[76, 63])).
% 3.93/4.09 tff(78,plain,
% 3.93/4.09 (((~![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))) | (~((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))))))) <=> ((~![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))) | (~((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))))))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(79,plain,
% 3.93/4.09 ((~((~((m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (~pidElem(m_Down(X0!7))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))))) <=> (~((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))))))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(80,plain,
% 3.93/4.09 (((~![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))) | (~((~((m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (~pidElem(m_Down(X0!7))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))))))) <=> ((~![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))) | (~((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))))))),
% 3.93/4.09 inference(monotonicity,[status(thm)],[79])).
% 3.93/4.09 tff(81,plain,
% 3.93/4.09 (((~![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))) | (~((~((m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (~pidElem(m_Down(X0!7))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))))))) <=> ((~![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))) | (~((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))))))),
% 3.93/4.09 inference(transitivity,[status(thm)],[80, 78])).
% 3.93/4.09 tff(82,plain,
% 3.93/4.09 ((~![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))) | (~((~((m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (~pidElem(m_Down(X0!7))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))))))),
% 3.93/4.09 inference(quant_inst,[status(thm)],[])).
% 3.93/4.09 tff(83,plain,
% 3.93/4.09 ((~![X: $i] : (~((~((X = m_Halt(tptp_fun_Y_0(X))) | (X = m_Down(tptp_fun_Y_0(X))) | (~pidElem(X)))) | (~(pidElem(X) | ![Y: $i] : (~((X = m_Down(Y)) | (X = m_Halt(Y))))))))) | (~((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[82, 81])).
% 3.93/4.09 tff(84,plain,
% 3.93/4.09 (~((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[83, 77])).
% 3.93/4.09 tff(85,plain,
% 3.93/4.09 (((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))))) | (pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(86,plain,
% 3.93/4.09 (pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[85, 84])).
% 3.93/4.09 tff(87,plain,
% 3.93/4.09 ((~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y)))))) | pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(88,plain,
% 3.93/4.09 (pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[87, 86])).
% 3.93/4.09 tff(89,plain,
% 3.93/4.09 (pidElem(m_Down(X0!7))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[88, 58])).
% 3.93/4.09 tff(90,plain,
% 3.93/4.09 (((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~(pidElem(m_Down(X0!7)) | ![Y: $i] : (~((m_Down(X0!7) = m_Down(Y)) | (m_Down(X0!7) = m_Halt(Y))))))) | ((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(91,plain,
% 3.93/4.09 ((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7))))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[90, 84])).
% 3.93/4.09 tff(92,plain,
% 3.93/4.09 ((~((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7)))))) | (~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7))))),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(93,plain,
% 3.93/4.09 ((~pidElem(m_Down(X0!7))) | (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7))))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[92, 91])).
% 3.93/4.09 tff(94,plain,
% 3.93/4.09 ((m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))) | (m_Down(X0!7) = m_Halt(tptp_fun_Y_0(m_Down(X0!7))))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[93, 89])).
% 3.93/4.09 tff(95,plain,
% 3.93/4.09 (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[94, 43])).
% 3.93/4.09 tff(96,plain,
% 3.93/4.09 ((~((X0!7 = tptp_fun_Y_0(m_Down(X0!7))) <=> (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))))) | (X0!7 = tptp_fun_Y_0(m_Down(X0!7))) | (~(m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))))),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(97,plain,
% 3.93/4.09 ((~((X0!7 = tptp_fun_Y_0(m_Down(X0!7))) <=> (m_Down(X0!7) = m_Down(tptp_fun_Y_0(m_Down(X0!7)))))) | (X0!7 = tptp_fun_Y_0(m_Down(X0!7)))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[96, 95])).
% 3.93/4.09 tff(98,plain,
% 3.93/4.09 (X0!7 = tptp_fun_Y_0(m_Down(X0!7))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[97, 32])).
% 3.93/4.09 tff(99,plain,
% 3.93/4.09 (tptp_fun_Y_0(m_Down(X0!7)) = X0!7),
% 3.93/4.09 inference(symmetry,[status(thm)],[98])).
% 3.93/4.09 tff(100,plain,
% 3.93/4.09 (host(tptp_fun_Y_0(m_Down(X0!7))) = host(X0!7)),
% 3.93/4.09 inference(monotonicity,[status(thm)],[99])).
% 3.93/4.09 tff(101,plain,
% 3.93/4.09 (host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3)))),
% 3.93/4.09 inference(transitivity,[status(thm)],[100, 20, 18])).
% 3.93/4.09 tff(102,plain,
% 3.93/4.09 (s(index(pendack, host(Y0!6))) = host(X0!7)),
% 3.93/4.09 inference(symmetry,[status(thm)],[20])).
% 3.93/4.09 tff(103,plain,
% 3.93/4.09 (s(index(pendack, host(X!3))) = host(X0!7)),
% 3.93/4.09 inference(transitivity,[status(thm)],[17, 102])).
% 3.93/4.09 tff(104,plain,
% 3.93/4.09 (^[X: $i, Y: $i] : refl((~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(105,plain,
% 3.93/4.09 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> ![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[104])).
% 3.93/4.09 tff(106,plain,
% 3.93/4.09 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, X)) <=> (~((~leq(X, Y)) | (~leq(Y, X))))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))), rewrite(((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))))), rewrite((~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(107,plain,
% 3.93/4.09 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[106])).
% 3.93/4.09 tff(108,plain,
% 3.93/4.09 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(109,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_61')).
% 3.93/4.09 tff(110,plain,
% 3.93/4.09 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[109, 108])).
% 3.93/4.09 tff(111,plain,(
% 3.93/4.09 ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 3.93/4.09 inference(skolemize,[status(sab)],[110])).
% 3.93/4.09 tff(112,plain,
% 3.93/4.09 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[111, 107])).
% 3.93/4.09 tff(113,plain,
% 3.93/4.09 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[112, 105])).
% 3.93/4.09 tff(114,plain,
% 3.93/4.09 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6)))))) <=> (s(index(pendack, host(Y0!6))) = nbr_proc)))),
% 3.93/4.09 inference(quant_inst,[status(thm)],[])).
% 3.93/4.09 tff(115,plain,
% 3.93/4.09 (~(((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6)))))) <=> (s(index(pendack, host(Y0!6))) = nbr_proc))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[114, 113])).
% 3.93/4.09 tff(116,plain,
% 3.93/4.09 (leq(s(index(pendack, host(Y0!6))), nbr_proc) <=> leq(host(X0!7), nbr_proc)),
% 3.93/4.09 inference(monotonicity,[status(thm)],[102])).
% 3.93/4.09 tff(117,plain,
% 3.93/4.09 (leq(host(X0!7), nbr_proc) <=> leq(s(index(pendack, host(Y0!6))), nbr_proc)),
% 3.93/4.09 inference(symmetry,[status(thm)],[116])).
% 3.93/4.09 tff(118,plain,
% 3.93/4.09 (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(119,plain,
% 3.93/4.09 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 3.93/4.09 inference(quant_intro,[status(thm)],[118])).
% 3.93/4.09 tff(120,plain,
% 3.93/4.09 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(121,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 3.93/4.09 tff(122,plain,
% 3.93/4.09 (![P: $i] : leq(host(P), nbr_proc)),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[121, 120])).
% 3.93/4.09 tff(123,plain,(
% 3.93/4.09 ![P: $i] : leq(host(P), nbr_proc)),
% 3.93/4.09 inference(skolemize,[status(sab)],[122])).
% 3.93/4.09 tff(124,plain,
% 3.93/4.09 (![P: $i] : leq(host(P), nbr_proc)),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[123, 119])).
% 3.93/4.09 tff(125,plain,
% 3.93/4.09 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X0!7), nbr_proc)),
% 3.93/4.09 inference(quant_inst,[status(thm)],[])).
% 3.93/4.09 tff(126,plain,
% 3.93/4.09 (leq(host(X0!7), nbr_proc)),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[125, 124])).
% 3.93/4.09 tff(127,plain,
% 3.93/4.09 (leq(s(index(pendack, host(Y0!6))), nbr_proc)),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[126, 117])).
% 3.93/4.09 tff(128,plain,
% 3.93/4.09 (leq(nbr_proc, s(index(pendack, host(Y0!6))))),
% 3.93/4.09 inference(and_elim,[status(thm)],[19])).
% 3.93/4.09 tff(129,plain,
% 3.93/4.09 ((~((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6)))))),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(130,plain,
% 3.93/4.09 ((~((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[129, 128])).
% 3.93/4.09 tff(131,plain,
% 3.93/4.09 (~((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[130, 127])).
% 3.93/4.09 tff(132,plain,
% 3.93/4.09 ((((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6)))))) <=> (s(index(pendack, host(Y0!6))) = nbr_proc)) | ((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6)))))) | (s(index(pendack, host(Y0!6))) = nbr_proc)),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(133,plain,
% 3.93/4.09 (s(index(pendack, host(Y0!6))) = nbr_proc),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[132, 131, 115])).
% 3.93/4.09 tff(134,plain,
% 3.93/4.09 (nbr_proc = s(index(pendack, host(Y0!6)))),
% 3.93/4.09 inference(symmetry,[status(thm)],[133])).
% 3.93/4.09 tff(135,plain,
% 3.93/4.09 (nbr_proc = host(X0!7)),
% 3.93/4.09 inference(transitivity,[status(thm)],[134, 102])).
% 3.93/4.09 tff(136,plain,
% 3.93/4.09 (leq(nbr_proc, s(index(pendack, host(X!3)))) <=> leq(host(X0!7), host(X0!7))),
% 3.93/4.09 inference(monotonicity,[status(thm)],[135, 103])).
% 3.93/4.09 tff(137,plain,
% 3.93/4.09 (leq(host(X0!7), host(X0!7)) <=> leq(nbr_proc, s(index(pendack, host(X!3))))),
% 3.93/4.09 inference(symmetry,[status(thm)],[136])).
% 3.93/4.09 tff(138,plain,
% 3.93/4.09 (leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))) <=> leq(host(X0!7), host(X0!7))),
% 3.93/4.09 inference(monotonicity,[status(thm)],[102, 102])).
% 3.93/4.09 tff(139,plain,
% 3.93/4.09 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(140,plain,
% 3.93/4.09 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(141,plain,
% 3.93/4.09 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[140])).
% 3.93/4.09 tff(142,plain,
% 3.93/4.09 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(143,plain,
% 3.93/4.09 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(144,plain,
% 3.93/4.09 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[143])).
% 3.93/4.09 tff(145,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_62')).
% 3.93/4.09 tff(146,plain,
% 3.93/4.09 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[145, 144])).
% 3.93/4.09 tff(147,plain,
% 3.93/4.09 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[146, 142])).
% 3.93/4.09 tff(148,plain,(
% 3.93/4.09 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 3.93/4.09 inference(skolemize,[status(sab)],[147])).
% 3.93/4.09 tff(149,plain,
% 3.93/4.09 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[148, 141])).
% 3.93/4.09 tff(150,plain,
% 3.93/4.09 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[149, 139])).
% 3.93/4.09 tff(151,plain,
% 3.93/4.09 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(152,plain,
% 3.93/4.09 ((leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc))) <=> ((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(153,plain,
% 3.93/4.09 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6))))))),
% 3.93/4.09 inference(monotonicity,[status(thm)],[152])).
% 3.93/4.09 tff(154,plain,
% 3.93/4.09 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))))),
% 3.93/4.09 inference(transitivity,[status(thm)],[153, 151])).
% 3.93/4.09 tff(155,plain,
% 3.93/4.09 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc)))),
% 3.93/4.09 inference(quant_inst,[status(thm)],[])).
% 3.93/4.09 tff(156,plain,
% 3.93/4.09 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(s(index(pendack, host(Y0!6))), nbr_proc)) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[155, 154])).
% 3.93/4.09 tff(157,plain,
% 3.93/4.09 (leq(s(index(pendack, host(Y0!6))), s(index(pendack, host(Y0!6))))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[156, 150, 128, 127])).
% 3.93/4.09 tff(158,plain,
% 3.93/4.09 (leq(host(X0!7), host(X0!7))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[157, 138])).
% 3.93/4.09 tff(159,plain,
% 3.93/4.09 (leq(nbr_proc, s(index(pendack, host(X!3))))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[158, 137])).
% 3.93/4.09 tff(160,plain,
% 3.93/4.09 (index(pendack, host(Y0!6)) = index(pendack, host(X!3))),
% 3.93/4.09 inference(symmetry,[status(thm)],[16])).
% 3.93/4.09 tff(161,plain,
% 3.93/4.09 (host(Z!8) = index(pendack, host(Y0!6))),
% 3.93/4.09 inference(and_elim,[status(thm)],[19])).
% 3.93/4.09 tff(162,plain,
% 3.93/4.09 (host(Z!8) = index(pendack, host(X!3))),
% 3.93/4.09 inference(transitivity,[status(thm)],[161, 160])).
% 3.93/4.09 tff(163,plain,
% 3.93/4.09 (m_Down(tptp_fun_Y_0(m_Down(X0!7))) = m_Down(X0!7)),
% 3.93/4.09 inference(symmetry,[status(thm)],[95])).
% 3.93/4.09 tff(164,plain,
% 3.93/4.09 (elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3))) <=> elem(m_Down(X0!7), queue(host(X!3)))),
% 3.93/4.09 inference(monotonicity,[status(thm)],[163])).
% 3.93/4.09 tff(165,plain,
% 3.93/4.09 (elem(m_Down(X0!7), queue(host(X!3))) <=> elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))),
% 3.93/4.09 inference(symmetry,[status(thm)],[164])).
% 3.93/4.09 tff(166,plain,
% 3.93/4.09 (elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5) <=> elem(m_Down(X0!7), V!5)),
% 3.93/4.09 inference(monotonicity,[status(thm)],[163])).
% 3.93/4.09 tff(167,plain,
% 3.93/4.09 (elem(m_Down(X0!7), V!5) <=> elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5)),
% 3.93/4.09 inference(symmetry,[status(thm)],[166])).
% 3.93/4.09 tff(168,plain,
% 3.93/4.09 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(169,plain,
% 3.93/4.09 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[168])).
% 3.93/4.09 tff(170,plain,
% 3.93/4.09 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(171,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 3.93/4.09 tff(172,plain,
% 3.93/4.09 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[171, 170])).
% 3.93/4.09 tff(173,plain,(
% 3.93/4.09 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 3.93/4.09 inference(skolemize,[status(sab)],[172])).
% 3.93/4.09 tff(174,plain,
% 3.93/4.09 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[173, 169])).
% 3.93/4.09 tff(175,plain,
% 3.93/4.09 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) <=> ((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5)))),
% 3.93/4.09 inference(quant_inst,[status(thm)],[])).
% 3.93/4.09 tff(176,plain,
% 3.93/4.09 (elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) <=> ((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[175, 174])).
% 3.93/4.09 tff(177,plain,
% 3.93/4.09 (elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4)))),
% 3.93/4.09 inference(and_elim,[status(thm)],[19])).
% 3.93/4.09 tff(178,plain,
% 3.93/4.09 ((~(elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) <=> ((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5)))) | (~elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4)))) | ((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5))),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(179,plain,
% 3.93/4.09 ((~(elem(m_Down(X0!7), snoc(V!5, m_NotNorm(W!4))) <=> ((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5)))) | ((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[178, 177])).
% 3.93/4.09 tff(180,plain,
% 3.93/4.09 ((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5)),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[179, 176])).
% 3.93/4.09 tff(181,plain,
% 3.93/4.09 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_NotNorm(Y))) <=> (~(m_Down(X) = m_NotNorm(Y))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(182,plain,
% 3.93/4.09 (![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y)))),
% 3.93/4.09 inference(quant_intro,[status(thm)],[181])).
% 3.93/4.09 tff(183,plain,
% 3.93/4.09 (![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y)))),
% 3.93/4.09 inference(rewrite,[status(thm)],[])).
% 3.93/4.09 tff(184,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_19')).
% 3.93/4.09 tff(185,plain,
% 3.93/4.09 (![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y)))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[184, 183])).
% 3.93/4.09 tff(186,plain,(
% 3.93/4.09 ![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y)))),
% 3.93/4.09 inference(skolemize,[status(sab)],[185])).
% 3.93/4.09 tff(187,plain,
% 3.93/4.09 (![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y)))),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[186, 182])).
% 3.93/4.09 tff(188,plain,
% 3.93/4.09 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_NotNorm(Y)))) | (~(m_Down(X0!7) = m_NotNorm(W!4)))),
% 3.93/4.09 inference(quant_inst,[status(thm)],[])).
% 3.93/4.09 tff(189,plain,
% 3.93/4.09 (~(m_Down(X0!7) = m_NotNorm(W!4))),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[188, 187])).
% 3.93/4.09 tff(190,plain,
% 3.93/4.09 ((~((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5))) | (m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5)),
% 3.93/4.09 inference(tautology,[status(thm)],[])).
% 3.93/4.09 tff(191,plain,
% 3.93/4.09 ((~((m_Down(X0!7) = m_NotNorm(W!4)) | elem(m_Down(X0!7), V!5))) | elem(m_Down(X0!7), V!5)),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[190, 189])).
% 3.93/4.09 tff(192,plain,
% 3.93/4.09 (elem(m_Down(X0!7), V!5)),
% 3.93/4.09 inference(unit_resolution,[status(thm)],[191, 180])).
% 3.93/4.09 tff(193,plain,
% 3.93/4.09 (elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5)),
% 3.93/4.09 inference(modus_ponens,[status(thm)],[192, 167])).
% 3.93/4.09 tff(194,plain,
% 3.93/4.09 (^[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))))),
% 3.93/4.09 inference(bind,[status(th)],[])).
% 3.93/4.09 tff(195,plain,
% 3.93/4.09 (![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)))),
% 3.93/4.10 inference(quant_intro,[status(thm)],[194])).
% 3.93/4.10 tff(196,plain,
% 3.93/4.10 (![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)))),
% 3.93/4.10 inference(rewrite,[status(thm)],[])).
% 3.93/4.10 tff(197,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 3.93/4.10 tff(198,plain,
% 3.93/4.10 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[197, 196])).
% 3.93/4.10 tff(199,plain,(
% 3.93/4.10 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 3.93/4.10 inference(skolemize,[status(sab)],[198])).
% 3.93/4.10 tff(200,plain,
% 3.93/4.10 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[199, 195])).
% 3.93/4.10 tff(201,plain,
% 3.93/4.10 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), cons(m_NormQ(W!4), V!5)) <=> ((m_Down(tptp_fun_Y_0(m_Down(X0!7))) = m_NormQ(W!4)) | elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5)))),
% 3.93/4.10 inference(quant_inst,[status(thm)],[])).
% 3.93/4.10 tff(202,plain,
% 3.93/4.10 (elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), cons(m_NormQ(W!4), V!5)) <=> ((m_Down(tptp_fun_Y_0(m_Down(X0!7))) = m_NormQ(W!4)) | elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5))),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[201, 200])).
% 3.93/4.10 tff(203,plain,
% 3.93/4.10 (queue(host(X!3)) = cons(m_NormQ(W!4), V!5)),
% 3.93/4.10 inference(and_elim,[status(thm)],[13])).
% 3.93/4.10 tff(204,plain,
% 3.93/4.10 (cons(m_NormQ(W!4), V!5) = queue(host(X!3))),
% 3.93/4.10 inference(symmetry,[status(thm)],[203])).
% 3.93/4.10 tff(205,plain,
% 3.93/4.10 (elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), cons(m_NormQ(W!4), V!5)) <=> elem(m_Down(X0!7), queue(host(X!3)))),
% 3.93/4.10 inference(monotonicity,[status(thm)],[163, 204])).
% 3.93/4.10 tff(206,plain,
% 3.93/4.10 (elem(m_Down(X0!7), queue(host(X!3))) <=> elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), cons(m_NormQ(W!4), V!5))),
% 3.93/4.10 inference(symmetry,[status(thm)],[205])).
% 3.93/4.10 tff(207,plain,
% 3.93/4.10 ((~elem(m_Down(X0!7), queue(host(X!3)))) <=> (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), cons(m_NormQ(W!4), V!5)))),
% 3.93/4.10 inference(monotonicity,[status(thm)],[206])).
% 3.93/4.10 tff(208,assumption,(~elem(m_Down(X0!7), queue(host(X!3)))), introduced(assumption)).
% 3.93/4.10 tff(209,plain,
% 3.93/4.10 (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), cons(m_NormQ(W!4), V!5))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[208, 207])).
% 3.93/4.10 tff(210,plain,
% 3.93/4.10 ((~(elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), cons(m_NormQ(W!4), V!5)) <=> ((m_Down(tptp_fun_Y_0(m_Down(X0!7))) = m_NormQ(W!4)) | elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5)))) | elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), cons(m_NormQ(W!4), V!5)) | (~((m_Down(tptp_fun_Y_0(m_Down(X0!7))) = m_NormQ(W!4)) | elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5)))),
% 3.93/4.10 inference(tautology,[status(thm)],[])).
% 3.93/4.10 tff(211,plain,
% 3.93/4.10 (~((m_Down(tptp_fun_Y_0(m_Down(X0!7))) = m_NormQ(W!4)) | elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5))),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[210, 209, 202])).
% 3.93/4.10 tff(212,plain,
% 3.93/4.10 (((m_Down(tptp_fun_Y_0(m_Down(X0!7))) = m_NormQ(W!4)) | elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5)) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), V!5))),
% 3.93/4.10 inference(tautology,[status(thm)],[])).
% 3.93/4.10 tff(213,plain,
% 3.93/4.10 ($false),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[212, 211, 193])).
% 3.93/4.10 tff(214,plain,(elem(m_Down(X0!7), queue(host(X!3)))), inference(lemma,lemma(discharge,[]))).
% 3.93/4.10 tff(215,plain,
% 3.93/4.10 (elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[214, 165])).
% 3.93/4.10 tff(216,plain,
% 3.93/4.10 (^[Y: $i, Z: $i] : refl(((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y)) <=> ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y)))),
% 3.93/4.10 inference(bind,[status(th)],[])).
% 3.93/4.10 tff(217,plain,
% 3.93/4.10 (![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y)) <=> ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))),
% 3.93/4.10 inference(quant_intro,[status(thm)],[216])).
% 3.93/4.10 tff(218,plain,
% 3.93/4.10 (^[Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(Z = Y)) & (host(Z) = host(Y))) <=> (~((~(host(Z) = host(Y))) | (Z = Y)))), ((~((~(Z = Y)) & (host(Z) = host(Y)))) <=> (~(~((~(host(Z) = host(Y))) | (Z = Y)))))), rewrite((~(~((~(host(Z) = host(Y))) | (Z = Y)))) <=> ((~(host(Z) = host(Y))) | (Z = Y))), ((~((~(Z = Y)) & (host(Z) = host(Y)))) <=> ((~(host(Z) = host(Y))) | (Z = Y)))), (((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) <=> ((~setIn(Z, alive)) | (~setIn(Y, alive)) | ((~(host(Z) = host(Y))) | (Z = Y))))), rewrite(((~setIn(Z, alive)) | (~setIn(Y, alive)) | ((~(host(Z) = host(Y))) | (Z = Y))) <=> ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))), (((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) <=> ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))))),
% 3.93/4.10 inference(bind,[status(th)],[])).
% 3.93/4.10 tff(219,plain,
% 3.93/4.10 (![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y))))) <=> ![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))),
% 3.93/4.10 inference(quant_intro,[status(thm)],[218])).
% 3.93/4.10 tff(220,plain,
% 3.93/4.10 (![Y: $i, Z: $i] : ((~setIn(Z, alive)) | (~setIn(Y, alive)) | (~((~(Z = Y)) & (host(Z) = host(Y)))))),
% 3.93/4.10 inference(and_elim,[status(thm)],[13])).
% 3.93/4.10 tff(221,plain,
% 3.93/4.10 (![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[220, 219])).
% 3.93/4.10 tff(222,plain,
% 3.93/4.10 (![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[221, 217])).
% 3.93/4.10 tff(223,plain,
% 3.93/4.10 (setIn(Y0!6, alive)),
% 3.93/4.10 inference(and_elim,[status(thm)],[19])).
% 3.93/4.10 tff(224,plain,
% 3.93/4.10 (setIn(X!3, alive)),
% 3.93/4.10 inference(and_elim,[status(thm)],[13])).
% 3.93/4.10 tff(225,plain,
% 3.93/4.10 (((~![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))) | ((~setIn(X!3, alive)) | (~(host(X!3) = host(Y0!6))) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6))) <=> ((~![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))) | (~setIn(X!3, alive)) | (~(host(X!3) = host(Y0!6))) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6))),
% 3.93/4.10 inference(rewrite,[status(thm)],[])).
% 3.93/4.10 tff(226,plain,
% 3.93/4.10 (((~(host(X!3) = host(Y0!6))) | (~setIn(X!3, alive)) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6)) <=> ((~setIn(X!3, alive)) | (~(host(X!3) = host(Y0!6))) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6))),
% 3.93/4.10 inference(rewrite,[status(thm)],[])).
% 3.93/4.10 tff(227,plain,
% 3.93/4.10 (((~![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))) | ((~(host(X!3) = host(Y0!6))) | (~setIn(X!3, alive)) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6))) <=> ((~![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))) | ((~setIn(X!3, alive)) | (~(host(X!3) = host(Y0!6))) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6)))),
% 3.93/4.10 inference(monotonicity,[status(thm)],[226])).
% 3.93/4.10 tff(228,plain,
% 3.93/4.10 (((~![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))) | ((~(host(X!3) = host(Y0!6))) | (~setIn(X!3, alive)) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6))) <=> ((~![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))) | (~setIn(X!3, alive)) | (~(host(X!3) = host(Y0!6))) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6))),
% 3.93/4.10 inference(transitivity,[status(thm)],[227, 225])).
% 3.93/4.10 tff(229,plain,
% 3.93/4.10 ((~![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))) | ((~(host(X!3) = host(Y0!6))) | (~setIn(X!3, alive)) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6))),
% 3.93/4.10 inference(quant_inst,[status(thm)],[])).
% 3.93/4.10 tff(230,plain,
% 3.93/4.10 ((~![Y: $i, Z: $i] : ((~(host(Z) = host(Y))) | (~setIn(Z, alive)) | (~setIn(Y, alive)) | (Z = Y))) | (~setIn(X!3, alive)) | (~(host(X!3) = host(Y0!6))) | (~setIn(Y0!6, alive)) | (X!3 = Y0!6)),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[229, 228])).
% 3.93/4.10 tff(231,plain,
% 3.93/4.10 (X!3 = Y0!6),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[230, 224, 223, 15, 222])).
% 3.93/4.10 tff(232,plain,
% 3.93/4.10 (m_Ack(X!3, Z!8) = m_Ack(Y0!6, Z!8)),
% 3.93/4.10 inference(monotonicity,[status(thm)],[231])).
% 3.93/4.10 tff(233,plain,
% 3.93/4.10 (elem(m_Ack(X!3, Z!8), queue(host(X!3))) <=> elem(m_Ack(Y0!6, Z!8), queue(host(X!3)))),
% 3.93/4.10 inference(monotonicity,[status(thm)],[232])).
% 3.93/4.10 tff(234,plain,
% 3.93/4.10 (elem(m_Ack(Y0!6, Z!8), queue(host(X!3))) <=> elem(m_Ack(X!3, Z!8), queue(host(X!3)))),
% 3.93/4.10 inference(symmetry,[status(thm)],[233])).
% 3.93/4.10 tff(235,assumption,(~(elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5)) <=> ((m_Ack(Y0!6, Z!8) = m_NormQ(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)))), introduced(assumption)).
% 3.93/4.10 tff(236,plain,
% 3.93/4.10 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5)) <=> ((m_Ack(Y0!6, Z!8) = m_NormQ(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)))),
% 3.93/4.10 inference(quant_inst,[status(thm)],[])).
% 3.93/4.10 tff(237,plain,
% 3.93/4.10 ($false),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[236, 200, 235])).
% 3.93/4.10 tff(238,plain,(elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5)) <=> ((m_Ack(Y0!6, Z!8) = m_NormQ(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5))), inference(lemma,lemma(discharge,[]))).
% 3.93/4.10 tff(239,plain,
% 3.93/4.10 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) <=> ((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)))),
% 3.93/4.10 inference(quant_inst,[status(thm)],[])).
% 3.93/4.10 tff(240,plain,
% 3.93/4.10 (elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) <=> ((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5))),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[239, 174])).
% 3.93/4.10 tff(241,plain,
% 3.93/4.10 (elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4)))),
% 3.93/4.10 inference(and_elim,[status(thm)],[19])).
% 3.93/4.10 tff(242,plain,
% 3.93/4.10 ((~(elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) <=> ((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)))) | (~elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4)))) | ((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5))),
% 3.93/4.10 inference(tautology,[status(thm)],[])).
% 3.93/4.10 tff(243,plain,
% 3.93/4.10 ((~(elem(m_Ack(Y0!6, Z!8), snoc(V!5, m_NotNorm(W!4))) <=> ((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)))) | ((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5))),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[242, 241])).
% 3.93/4.10 tff(244,plain,
% 3.93/4.10 ((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[243, 240])).
% 3.93/4.10 tff(245,plain,
% 3.93/4.10 (^[X: $i, Y: $i, Z: $i] : refl((~(m_Ack(X, Y) = m_NotNorm(Z))) <=> (~(m_Ack(X, Y) = m_NotNorm(Z))))),
% 3.93/4.10 inference(bind,[status(th)],[])).
% 3.93/4.10 tff(246,plain,
% 3.93/4.10 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z)))),
% 3.93/4.10 inference(quant_intro,[status(thm)],[245])).
% 3.93/4.10 tff(247,plain,
% 3.93/4.10 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z)))),
% 3.93/4.10 inference(rewrite,[status(thm)],[])).
% 3.93/4.10 tff(248,axiom,(![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_13')).
% 3.93/4.10 tff(249,plain,
% 3.93/4.10 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z)))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[248, 247])).
% 3.93/4.10 tff(250,plain,(
% 3.93/4.10 ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z)))),
% 3.93/4.10 inference(skolemize,[status(sab)],[249])).
% 3.93/4.10 tff(251,plain,
% 3.93/4.10 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z)))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[250, 246])).
% 3.93/4.10 tff(252,plain,
% 3.93/4.10 ((~![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_NotNorm(Z)))) | (~(m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)))),
% 3.93/4.10 inference(quant_inst,[status(thm)],[])).
% 3.93/4.10 tff(253,plain,
% 3.93/4.10 (~(m_Ack(Y0!6, Z!8) = m_NotNorm(W!4))),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[252, 251])).
% 3.93/4.10 tff(254,plain,
% 3.93/4.10 ((~((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5))) | (m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)),
% 3.93/4.10 inference(tautology,[status(thm)],[])).
% 3.93/4.10 tff(255,plain,
% 3.93/4.10 ((~((m_Ack(Y0!6, Z!8) = m_NotNorm(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5))) | elem(m_Ack(Y0!6, Z!8), V!5)),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[254, 253])).
% 3.93/4.10 tff(256,plain,
% 3.93/4.10 (elem(m_Ack(Y0!6, Z!8), V!5)),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[255, 244])).
% 3.93/4.10 tff(257,plain,
% 3.93/4.10 (((m_Ack(Y0!6, Z!8) = m_NormQ(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)) | (~elem(m_Ack(Y0!6, Z!8), V!5))),
% 3.93/4.10 inference(tautology,[status(thm)],[])).
% 3.93/4.10 tff(258,plain,
% 3.93/4.10 ((m_Ack(Y0!6, Z!8) = m_NormQ(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[257, 256])).
% 3.93/4.10 tff(259,plain,
% 3.93/4.10 ((~(elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5)) <=> ((m_Ack(Y0!6, Z!8) = m_NormQ(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)))) | elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5)) | (~((m_Ack(Y0!6, Z!8) = m_NormQ(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)))),
% 3.93/4.10 inference(tautology,[status(thm)],[])).
% 3.93/4.10 tff(260,plain,
% 3.93/4.10 ((~(elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5)) <=> ((m_Ack(Y0!6, Z!8) = m_NormQ(W!4)) | elem(m_Ack(Y0!6, Z!8), V!5)))) | elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5))),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[259, 258])).
% 3.93/4.10 tff(261,plain,
% 3.93/4.10 (elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5))),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[260, 238])).
% 3.93/4.10 tff(262,plain,
% 3.93/4.10 (elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5)) <=> elem(m_Ack(Y0!6, Z!8), queue(host(X!3)))),
% 3.93/4.10 inference(monotonicity,[status(thm)],[204])).
% 3.93/4.10 tff(263,plain,
% 3.93/4.10 (elem(m_Ack(Y0!6, Z!8), queue(host(X!3))) <=> elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5))),
% 3.93/4.10 inference(symmetry,[status(thm)],[262])).
% 3.93/4.10 tff(264,plain,
% 3.93/4.10 ((~elem(m_Ack(Y0!6, Z!8), queue(host(X!3)))) <=> (~elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5)))),
% 3.93/4.10 inference(monotonicity,[status(thm)],[263])).
% 3.93/4.10 tff(265,assumption,(~elem(m_Ack(Y0!6, Z!8), queue(host(X!3)))), introduced(assumption)).
% 3.93/4.10 tff(266,plain,
% 3.93/4.10 (~elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[265, 264])).
% 3.93/4.10 tff(267,assumption,(elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5))), introduced(assumption)).
% 3.93/4.10 tff(268,plain,
% 3.93/4.10 ($false),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[267, 266])).
% 3.93/4.10 tff(269,plain,((~elem(m_Ack(Y0!6, Z!8), cons(m_NormQ(W!4), V!5))) | elem(m_Ack(Y0!6, Z!8), queue(host(X!3)))), inference(lemma,lemma(discharge,[]))).
% 3.93/4.10 tff(270,plain,
% 3.93/4.10 (elem(m_Ack(Y0!6, Z!8), queue(host(X!3)))),
% 3.93/4.10 inference(unit_resolution,[status(thm)],[269, 261])).
% 3.93/4.10 tff(271,plain,
% 3.93/4.10 (elem(m_Ack(X!3, Z!8), queue(host(X!3)))),
% 3.93/4.10 inference(modus_ponens,[status(thm)],[270, 234])).
% 3.93/4.10 tff(272,plain,
% 3.93/4.10 (index(status, host(Y0!6)) = elec_2),
% 3.93/4.10 inference(and_elim,[status(thm)],[19])).
% 3.93/4.10 tff(273,plain,
% 3.93/4.10 (index(status, host(X!3)) = index(status, host(Y0!6))),
% 3.93/4.10 inference(monotonicity,[status(thm)],[15])).
% 3.93/4.10 tff(274,plain,
% 3.93/4.10 (index(status, host(X!3)) = elec_2),
% 3.93/4.10 inference(transitivity,[status(thm)],[273, 272])).
% 3.93/4.10 tff(275,plain,
% 3.93/4.10 (^[Y: $i, Z: $i, Pid20: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))),
% 3.93/4.10 inference(bind,[status(th)],[])).
% 3.93/4.10 tff(276,plain,
% 3.93/4.10 (![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))) <=> ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))),
% 3.95/4.10 inference(quant_intro,[status(thm)],[275])).
% 3.95/4.10 tff(277,plain,
% 3.95/4.10 (^[Y: $i, Z: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)) <=> (~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))), ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) <=> (~(~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))))), rewrite((~(~((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))) <=> ((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)))), ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) <=> ((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))))), trans(monotonicity(rewrite((setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))) <=> (~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))), ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))) <=> (~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))), ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))), (((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) <=> (((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))) | ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))))), rewrite((((~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm))) | ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))), (((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))))),
% 3.95/4.10 inference(bind,[status(th)],[])).
% 3.95/4.10 tff(278,plain,
% 3.95/4.10 (![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) <=> ![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))),
% 3.95/4.10 inference(quant_intro,[status(thm)],[277])).
% 3.95/4.10 tff(279,plain,
% 3.95/4.10 (![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Y, alive) & (index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Z) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))),
% 3.95/4.10 inference(and_elim,[status(thm)],[13])).
% 3.95/4.10 tff(280,plain,
% 3.95/4.10 (![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))),
% 3.95/4.10 inference(modus_ponens,[status(thm)],[279, 278])).
% 3.95/4.10 tff(281,plain,
% 3.95/4.10 (![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))),
% 3.95/4.10 inference(modus_ponens,[status(thm)],[280, 276])).
% 3.95/4.10 tff(282,plain,
% 3.95/4.10 (setIn(Y!9, alive) & (index(ldr, host(Y!9)) = host(Y!9)) & (index(status, host(Y!9)) = norm)),
% 3.95/4.10 inference(or_elim,[status(thm)],[14])).
% 3.95/4.10 tff(283,plain,
% 3.95/4.10 (index(status, host(Y!9)) = norm),
% 3.95/4.10 inference(and_elim,[status(thm)],[282])).
% 3.95/4.10 tff(284,plain,
% 3.95/4.10 (index(ldr, host(Y!9)) = host(Y!9)),
% 3.95/4.10 inference(and_elim,[status(thm)],[282])).
% 3.95/4.10 tff(285,plain,
% 3.95/4.10 (setIn(Y!9, alive)),
% 3.95/4.10 inference(and_elim,[status(thm)],[282])).
% 3.95/4.10 tff(286,plain,
% 3.95/4.10 (((~![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(index(status, host(Y!9)) = norm)))) <=> ((~![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(index(status, host(Y!9)) = norm)))),
% 3.95/4.10 inference(rewrite,[status(thm)],[])).
% 3.95/4.10 tff(287,plain,
% 3.95/4.10 (((~setIn(X!3, alive)) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(index(status, host(Y!9)) = norm)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3)))))) <=> ((~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(index(status, host(Y!9)) = norm)))),
% 3.95/4.10 inference(rewrite,[status(thm)],[])).
% 3.95/4.10 tff(288,plain,
% 3.95/4.10 (((~![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~setIn(X!3, alive)) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(index(status, host(Y!9)) = norm)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))))) <=> ((~![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(index(status, host(Y!9)) = norm))))),
% 3.95/4.11 inference(monotonicity,[status(thm)],[287])).
% 3.95/4.11 tff(289,plain,
% 3.95/4.11 (((~![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~setIn(X!3, alive)) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(index(status, host(Y!9)) = norm)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))))) <=> ((~![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(index(status, host(Y!9)) = norm)))),
% 3.95/4.11 inference(transitivity,[status(thm)],[288, 286])).
% 3.95/4.11 tff(290,plain,
% 3.95/4.11 ((~![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~setIn(X!3, alive)) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(index(status, host(Y!9)) = norm)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))))),
% 3.95/4.11 inference(quant_inst,[status(thm)],[])).
% 3.95/4.11 tff(291,plain,
% 3.95/4.11 ((~![Y: $i, Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Y, alive)) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Z) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | (~setIn(X!3, alive)) | (~(index(status, host(X!3)) = elec_2)) | (~setIn(Y!9, alive)) | (~elem(m_Ack(X!3, Z!8), queue(host(X!3)))) | (~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~elem(m_Down(tptp_fun_Y_0(m_Down(X0!7))), queue(host(X!3)))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3))))) | (~(index(ldr, host(Y!9)) = host(Y!9))) | (~(host(Z!8) = index(pendack, host(X!3)))) | (~(index(status, host(Y!9)) = norm))),
% 3.95/4.11 inference(modus_ponens,[status(thm)],[290, 289])).
% 3.95/4.11 tff(292,plain,
% 3.95/4.11 ((~leq(nbr_proc, s(index(pendack, host(X!3))))) | (~(host(tptp_fun_Y_0(m_Down(X0!7))) = s(index(pendack, host(X!3)))))),
% 3.95/4.11 inference(unit_resolution,[status(thm)],[291, 224, 285, 284, 283, 281, 274, 271, 215, 162])).
% 3.95/4.11 tff(293,plain,
% 3.95/4.11 ($false),
% 3.95/4.11 inference(unit_resolution,[status(thm)],[292, 159, 101])).
% 3.95/4.11 % SZS output end Proof
% 3.95/4.11 % E exiting
%------------------------------------------------------------------------------