%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV460+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 180.36s 180.72s
% Output : Proof 180.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV460+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 09:52:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 180.36/180.72 % SZS status Theorem
% 180.36/180.72 % SZS output start Proof
% 180.36/180.72 tff(elem_type, type, (
% 180.36/180.72 elem: ( $i * $i ) > $o)).
% 180.36/180.72 tff(queue_type, type, (
% 180.36/180.72 queue: $i > $i)).
% 180.36/180.72 tff(host_type, type, (
% 180.36/180.72 host: $i > $i)).
% 180.36/180.72 tff(tptp_fun_X_4_type, type, (
% 180.36/180.72 tptp_fun_X_4: $i)).
% 180.36/180.72 tff(m_Down_type, type, (
% 180.36/180.72 m_Down: $i > $i)).
% 180.36/180.72 tff(tptp_fun_Y_3_type, type, (
% 180.36/180.72 tptp_fun_Y_3: $i)).
% 180.36/180.72 tff(cons_type, type, (
% 180.36/180.72 cons: ( $i * $i ) > $i)).
% 180.36/180.72 tff(tptp_fun_V_5_type, type, (
% 180.36/180.72 tptp_fun_V_5: $i)).
% 180.36/180.72 tff(elec_2_type, type, (
% 180.36/180.72 elec_2: $i)).
% 180.36/180.72 tff(index_type, type, (
% 180.36/180.72 index: ( $i * $i ) > $i)).
% 180.36/180.72 tff(status_type, type, (
% 180.36/180.72 status: $i)).
% 180.36/180.72 tff(setIn_type, type, (
% 180.36/180.72 setIn: ( $i * $i ) > $o)).
% 180.36/180.72 tff(alive_type, type, (
% 180.36/180.72 alive: $i)).
% 180.36/180.72 tff(leq_type, type, (
% 180.36/180.72 leq: ( $i * $i ) > $o)).
% 180.36/180.72 tff(pendack_type, type, (
% 180.36/180.72 pendack: $i)).
% 180.36/180.72 tff(m_Ack_type, type, (
% 180.36/180.72 m_Ack: ( $i * $i ) > $i)).
% 180.36/180.72 tff(down_type, type, (
% 180.36/180.72 down: $i)).
% 180.36/180.72 tff(elid_type, type, (
% 180.36/180.72 elid: $i)).
% 180.36/180.72 tff(elec_1_type, type, (
% 180.36/180.72 elec_1: $i)).
% 180.36/180.72 tff(m_Halt_type, type, (
% 180.36/180.72 m_Halt: $i > $i)).
% 180.36/180.72 tff(s_type, type, (
% 180.36/180.72 s: $i > $i)).
% 180.36/180.72 tff(zero_type, type, (
% 180.36/180.72 zero: $i)).
% 180.36/180.72 tff(tptp_fun_W0_7_type, type, (
% 180.36/180.72 tptp_fun_W0_7: $i)).
% 180.36/180.72 tff(tptp_fun_Z_6_type, type, (
% 180.36/180.72 tptp_fun_Z_6: $i)).
% 180.36/180.72 tff(norm_type, type, (
% 180.36/180.72 norm: $i)).
% 180.36/180.72 tff(ldr_type, type, (
% 180.36/180.72 ldr: $i)).
% 180.36/180.72 tff(wait_type, type, (
% 180.36/180.72 wait: $i)).
% 180.36/180.72 tff(nbr_proc_type, type, (
% 180.36/180.72 nbr_proc: $i)).
% 180.36/180.72 tff(1,plain,
% 180.36/180.72 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2)))))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2))))) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 180.36/180.72 inference(rewrite,[status(thm)],[])).
% 180.36/180.72 tff(2,plain,
% 180.36/180.72 ((![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) <=> (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 180.36/180.72 inference(rewrite,[status(thm)],[])).
% 180.36/180.72 tff(3,plain,
% 180.36/180.72 ((![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) <=> (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1))),
% 180.36/180.72 inference(rewrite,[status(thm)],[])).
% 180.36/180.72 tff(4,plain,
% 180.36/180.72 ((~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2))))) <=> (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2)))))),
% 180.36/180.72 inference(rewrite,[status(thm)],[])).
% 180.36/180.72 tff(5,plain,
% 180.36/180.72 (((host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2)))))) <=> ((host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2))))))),
% 180.36/180.72 inference(monotonicity,[status(thm)],[4])).
% 180.36/180.72 tff(6,plain,
% 180.36/180.72 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2)))))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2)))))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))))),
% 180.36/180.72 inference(monotonicity,[status(thm)],[5, 3, 2])).
% 180.36/180.72 tff(7,plain,
% 180.36/180.72 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ((host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2)))))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2))))) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 180.36/180.73 inference(transitivity,[status(thm)],[6, 1])).
% 180.36/180.73 tff(8,plain,
% 180.36/180.73 ((~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![W0: $i] : ((host(X) = host(W0)) | (~leq(s(host(X)), index(pendack, host(W0)))) | (~((~leq(host(Z), host(W0))) & setIn(Z, alive) & setIn(W0, alive) & (index(status, host(W0)) = elec_2))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X)) = cons(m_Down(Y), V)))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![W0: $i] : ((host(X) = host(W0)) | (~leq(s(host(X)), index(pendack, host(W0)))) | (~((~leq(host(Z), host(W0))) & setIn(Z, alive) & setIn(W0, alive) & (index(status, host(W0)) = elec_2))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 180.36/180.73 inference(rewrite,[status(thm)],[])).
% 180.36/180.73 tff(9,plain,
% 180.36/180.73 ((~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((((![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i] : ((index(status, host(Z)) = elec_2) => (~leq(index(pendack, host(Z)), host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid0), queue(host(Z)))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~leq(host(Pid0), host(Z))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Down(Pid20), queue(host(Z)))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid20), queue(host(Z)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))))) => ((![Z: $i] : (((~leq(host(X), Z)) & leq(s(zero), Z)) => (setIn(Z, index(down, host(X))) | (Z = host(Y)))) & (index(status, host(X)) = elec_1)) => ((~leq(nbr_proc, host(X))) => ![Z: $i] : ((host(X) = host(Z)) => ![W0: $i] : ((~(host(X) = host(W0))) => (((((~leq(host(Z), host(W0))) & setIn(Z, alive)) & setIn(W0, alive)) & (index(status, host(W0)) = elec_2)) => (~leq(s(host(X)), index(pendack, host(W0)))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![W0: $i] : ((host(X) = host(W0)) | (~leq(s(host(X)), index(pendack, host(W0)))) | (~((~leq(host(Z), host(W0))) & setIn(Z, alive) & setIn(W0, alive) & (index(status, host(W0)) = elec_2))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 180.36/180.73 inference(rewrite,[status(thm)],[])).
% 180.36/180.73 tff(10,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : (((((((((((((![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i] : ((index(status, host(Z)) = elec_2) => (~leq(index(pendack, host(Z)), host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid0), queue(host(Z)))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((((~leq(host(Pid0), host(Z))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Down(Pid20), queue(host(Z)))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & (host(Pid0) = host(Pid20))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~elem(m_Ack(Z, Pid20), queue(host(Z)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))))) => ((![Z: $i] : (((~leq(host(X), Z)) & leq(s(zero), Z)) => (setIn(Z, index(down, host(X))) | (Z = host(Y)))) & (index(status, host(X)) = elec_1)) => ((~leq(nbr_proc, host(X))) => ![Z: $i] : ((host(X) = host(Z)) => ![W0: $i] : ((~(host(X) = host(W0))) => (((((~leq(host(Z), host(W0))) & setIn(Z, alive)) & setIn(W0, alive)) & (index(status, host(W0)) = elec_2)) => (~leq(s(host(X)), index(pendack, host(W0)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 180.36/180.73 tff(11,plain,
% 180.36/180.73 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![W0: $i] : ((host(X) = host(W0)) | (~leq(s(host(X)), index(pendack, host(W0)))) | (~((~leq(host(Z), host(W0))) & setIn(Z, alive) & setIn(W0, alive) & (index(status, host(W0)) = elec_2))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 180.36/180.73 inference(modus_ponens,[status(thm)],[10, 9])).
% 180.36/180.73 tff(12,plain,
% 180.36/180.73 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![W0: $i] : ((host(X) = host(W0)) | (~leq(s(host(X)), index(pendack, host(W0)))) | (~((~leq(host(Z), host(W0))) & setIn(Z, alive) & setIn(W0, alive) & (index(status, host(W0)) = elec_2))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 180.36/180.73 inference(modus_ponens,[status(thm)],[11, 8])).
% 180.36/180.73 tff(13,plain,
% 180.36/180.73 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![W0: $i] : ((host(X) = host(W0)) | (~leq(s(host(X)), index(pendack, host(W0)))) | (~((~leq(host(Z), host(W0))) & setIn(Z, alive) & setIn(W0, alive) & (index(status, host(W0)) = elec_2))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 180.36/180.73 inference(modus_ponens,[status(thm)],[12, 8])).
% 180.36/180.73 tff(14,plain,
% 180.36/180.73 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![W0: $i] : ((host(X) = host(W0)) | (~leq(s(host(X)), index(pendack, host(W0)))) | (~((~leq(host(Z), host(W0))) & setIn(Z, alive) & setIn(W0, alive) & (index(status, host(W0)) = elec_2))))) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[13, 8])).
% 180.36/180.74 tff(15,plain,
% 180.36/180.74 ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (host(X!4) = host(Z!6)) & (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2))))) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i] : ((~(index(status, host(Z)) = elec_2)) | (~leq(index(pendack, host(Z)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid0), queue(host(Z)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Down(Pid20), queue(host(Z)))) | (~((~leq(host(Pid0), host(Z))) & setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid20), queue(host(Z)))) | (~(setIn(Z, alive) & setIn(Pid0, alive) & (host(Pid0) = host(Pid20)) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[14, 7])).
% 180.36/180.74 tff(16,plain,
% 180.36/180.74 (queue(host(X!4)) = cons(m_Down(Y!3), V!5)),
% 180.36/180.74 inference(and_elim,[status(thm)],[15])).
% 180.36/180.74 tff(17,plain,
% 180.36/180.74 (elem(m_Down(Y!3), queue(host(X!4))) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[16])).
% 180.36/180.74 tff(18,plain,
% 180.36/180.74 (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> elem(m_Down(Y!3), queue(host(X!4)))),
% 180.36/180.74 inference(symmetry,[status(thm)],[17])).
% 180.36/180.74 tff(19,assumption,(~elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))), introduced(assumption)).
% 180.36/180.74 tff(20,plain,
% 180.36/180.74 (^[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))))),
% 180.36/180.74 inference(bind,[status(th)],[])).
% 180.36/180.74 tff(21,plain,
% 180.36/180.74 (![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)))),
% 180.36/180.74 inference(quant_intro,[status(thm)],[20])).
% 180.36/180.74 tff(22,plain,
% 180.36/180.74 (![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)))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(23,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')).
% 180.36/180.74 tff(24,plain,
% 180.36/180.74 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[23, 22])).
% 180.36/180.74 tff(25,plain,(
% 180.36/180.74 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 180.36/180.74 inference(skolemize,[status(sab)],[24])).
% 180.36/180.74 tff(26,plain,
% 180.36/180.74 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[25, 21])).
% 180.36/180.74 tff(27,plain,
% 180.36/180.74 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(28,plain,
% 180.36/180.74 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> $true) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(29,plain,
% 180.36/180.74 (($true | elem(m_Down(Y!3), V!5)) <=> $true),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(30,plain,
% 180.36/180.74 ((m_Down(Y!3) = m_Down(Y!3)) <=> $true),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(31,plain,
% 180.36/180.74 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> ($true | elem(m_Down(Y!3), V!5))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[30])).
% 180.36/180.74 tff(32,plain,
% 180.36/180.74 (((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)) <=> $true),
% 180.36/180.74 inference(transitivity,[status(thm)],[31, 29])).
% 180.36/180.74 tff(33,plain,
% 180.36/180.74 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5))) <=> (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> $true)),
% 180.36/180.74 inference(monotonicity,[status(thm)],[32])).
% 180.36/180.74 tff(34,plain,
% 180.36/180.74 ((elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5))) <=> elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 180.36/180.74 inference(transitivity,[status(thm)],[33, 28])).
% 180.36/180.74 tff(35,plain,
% 180.36/180.74 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[34])).
% 180.36/180.74 tff(36,plain,
% 180.36/180.74 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)))),
% 180.36/180.74 inference(transitivity,[status(thm)],[35, 27])).
% 180.36/180.74 tff(37,plain,
% 180.36/180.74 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y!3), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y!3) = m_Down(Y!3)) | elem(m_Down(Y!3), V!5)))),
% 180.36/180.74 inference(quant_inst,[status(thm)],[])).
% 180.36/180.74 tff(38,plain,
% 180.36/180.74 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[37, 36])).
% 180.36/180.74 tff(39,plain,
% 180.36/180.74 ($false),
% 180.36/180.74 inference(unit_resolution,[status(thm)],[38, 26, 19])).
% 180.36/180.74 tff(40,plain,(elem(m_Down(Y!3), cons(m_Down(Y!3), V!5))), inference(lemma,lemma(discharge,[]))).
% 180.36/180.74 tff(41,plain,
% 180.36/180.74 (elem(m_Down(Y!3), queue(host(X!4)))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[40, 18])).
% 180.36/180.74 tff(42,plain,
% 180.36/180.74 (host(X!4) = host(Z!6)),
% 180.36/180.74 inference(and_elim,[status(thm)],[15])).
% 180.36/180.74 tff(43,plain,
% 180.36/180.74 (host(Z!6) = host(X!4)),
% 180.36/180.74 inference(symmetry,[status(thm)],[42])).
% 180.36/180.74 tff(44,plain,
% 180.36/180.74 (index(down, host(Z!6)) = index(down, host(X!4))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[43])).
% 180.36/180.74 tff(45,plain,
% 180.36/180.74 (setIn(host(W0!7), index(down, host(Z!6))) <=> setIn(host(W0!7), index(down, host(X!4)))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[44])).
% 180.36/180.74 tff(46,plain,
% 180.36/180.74 ((~setIn(host(W0!7), index(down, host(Z!6)))) <=> (~setIn(host(W0!7), index(down, host(X!4))))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[45])).
% 180.36/180.74 tff(47,plain,
% 180.36/180.74 (s(host(Z!6)) = s(host(X!4))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[43])).
% 180.36/180.74 tff(48,plain,
% 180.36/180.74 (s(host(X!4)) = s(host(Z!6))),
% 180.36/180.74 inference(symmetry,[status(thm)],[47])).
% 180.36/180.74 tff(49,plain,
% 180.36/180.74 (leq(s(host(X!4)), host(Z!6)) <=> leq(s(host(Z!6)), host(Z!6))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[48])).
% 180.36/180.74 tff(50,plain,
% 180.36/180.74 (leq(s(host(Z!6)), host(Z!6)) <=> leq(s(host(X!4)), host(Z!6))),
% 180.36/180.74 inference(symmetry,[status(thm)],[49])).
% 180.36/180.74 tff(51,plain,
% 180.36/180.74 ((~leq(s(host(Z!6)), host(Z!6))) <=> (~leq(s(host(X!4)), host(Z!6)))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[50])).
% 180.36/180.74 tff(52,plain,
% 180.36/180.74 (^[X: $i] : refl((~leq(s(X), X)) <=> (~leq(s(X), X)))),
% 180.36/180.74 inference(bind,[status(th)],[])).
% 180.36/180.74 tff(53,plain,
% 180.36/180.74 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 180.36/180.74 inference(quant_intro,[status(thm)],[52])).
% 180.36/180.74 tff(54,plain,
% 180.36/180.74 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(55,axiom,(![X: $i] : (~leq(s(X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_58')).
% 180.36/180.74 tff(56,plain,
% 180.36/180.74 (![X: $i] : (~leq(s(X), X))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[55, 54])).
% 180.36/180.74 tff(57,plain,(
% 180.36/180.74 ![X: $i] : (~leq(s(X), X))),
% 180.36/180.74 inference(skolemize,[status(sab)],[56])).
% 180.36/180.74 tff(58,plain,
% 180.36/180.74 (![X: $i] : (~leq(s(X), X))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[57, 53])).
% 180.36/180.74 tff(59,plain,
% 180.36/180.74 ((~![X: $i] : (~leq(s(X), X))) | (~leq(s(host(Z!6)), host(Z!6)))),
% 180.36/180.74 inference(quant_inst,[status(thm)],[])).
% 180.36/180.74 tff(60,plain,
% 180.36/180.74 (~leq(s(host(Z!6)), host(Z!6))),
% 180.36/180.74 inference(unit_resolution,[status(thm)],[59, 58])).
% 180.36/180.74 tff(61,plain,
% 180.36/180.74 (~leq(s(host(X!4)), host(Z!6))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[60, 51])).
% 180.36/180.74 tff(62,assumption,(leq(index(pendack, host(W0!7)), host(Z!6))), introduced(assumption)).
% 180.36/180.74 tff(63,plain,
% 180.36/180.74 (~((host(X!4) = host(W0!7)) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | (~((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2))))),
% 180.36/180.74 inference(and_elim,[status(thm)],[15])).
% 180.36/180.74 tff(64,plain,
% 180.36/180.74 (leq(s(host(X!4)), index(pendack, host(W0!7)))),
% 180.36/180.74 inference(or_elim,[status(thm)],[63])).
% 180.36/180.74 tff(65,plain,
% 180.36/180.74 (![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)))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(66,plain,
% 180.36/180.74 (^[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)))))),
% 180.36/180.74 inference(bind,[status(th)],[])).
% 180.36/180.74 tff(67,plain,
% 180.36/180.74 (![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)))),
% 180.36/180.74 inference(quant_intro,[status(thm)],[66])).
% 180.36/180.74 tff(68,plain,
% 180.36/180.74 (![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))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(69,plain,
% 180.36/180.74 (^[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)))),
% 180.36/180.74 inference(bind,[status(th)],[])).
% 180.36/180.74 tff(70,plain,
% 180.36/180.74 (![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))),
% 180.36/180.74 inference(quant_intro,[status(thm)],[69])).
% 180.36/180.74 tff(71,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')).
% 180.36/180.74 tff(72,plain,
% 180.36/180.74 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[71, 70])).
% 180.36/180.74 tff(73,plain,
% 180.36/180.74 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[72, 68])).
% 180.36/180.74 tff(74,plain,(
% 180.36/180.74 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 180.36/180.74 inference(skolemize,[status(sab)],[73])).
% 180.36/180.74 tff(75,plain,
% 180.36/180.74 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[74, 67])).
% 180.36/180.74 tff(76,plain,
% 180.36/180.74 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[75, 65])).
% 180.36/180.74 tff(77,plain,
% 180.36/180.74 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(s(host(X!4)), index(pendack, host(W0!7)))) | leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6))))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(78,plain,
% 180.36/180.74 ((leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6))) | (~leq(s(host(X!4)), index(pendack, host(W0!7))))) <=> ((~leq(s(host(X!4)), index(pendack, host(W0!7)))) | leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6))))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(79,plain,
% 180.36/180.74 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6))) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(s(host(X!4)), index(pendack, host(W0!7)))) | leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6)))))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[78])).
% 180.36/180.74 tff(80,plain,
% 180.36/180.74 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6))) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6))))),
% 180.36/180.74 inference(transitivity,[status(thm)],[79, 77])).
% 180.36/180.74 tff(81,plain,
% 180.36/180.74 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6))) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))))),
% 180.36/180.74 inference(quant_inst,[status(thm)],[])).
% 180.36/180.74 tff(82,plain,
% 180.36/180.74 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(s(host(X!4)), index(pendack, host(W0!7)))) | leq(s(host(X!4)), host(Z!6)) | (~leq(index(pendack, host(W0!7)), host(Z!6)))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[81, 80])).
% 180.36/180.74 tff(83,plain,
% 180.36/180.74 ($false),
% 180.36/180.74 inference(unit_resolution,[status(thm)],[82, 76, 64, 62, 61])).
% 180.36/180.74 tff(84,plain,(~leq(index(pendack, host(W0!7)), host(Z!6))), inference(lemma,lemma(discharge,[]))).
% 180.36/180.74 tff(85,plain,
% 180.36/180.74 (^[Z: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))),
% 180.36/180.74 inference(bind,[status(th)],[])).
% 180.36/180.74 tff(86,plain,
% 180.36/180.74 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))),
% 180.36/180.74 inference(quant_intro,[status(thm)],[85])).
% 180.36/180.74 tff(87,plain,
% 180.36/180.74 (^[Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2)) <=> (~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite((((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z))))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))))),
% 180.36/180.74 inference(bind,[status(th)],[])).
% 180.36/180.74 tff(88,plain,
% 180.36/180.74 (![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))),
% 180.36/180.74 inference(quant_intro,[status(thm)],[87])).
% 180.36/180.74 tff(89,plain,
% 180.36/180.74 (![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 180.36/180.74 inference(and_elim,[status(thm)],[15])).
% 180.36/180.74 tff(90,plain,
% 180.36/180.74 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[89, 88])).
% 180.36/180.74 tff(91,plain,
% 180.36/180.74 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[90, 86])).
% 180.36/180.74 tff(92,plain,
% 180.36/180.74 ((~leq(host(Z!6), host(W0!7))) & setIn(Z!6, alive) & setIn(W0!7, alive) & (index(status, host(W0!7)) = elec_2)),
% 180.36/180.74 inference(or_elim,[status(thm)],[63])).
% 180.36/180.74 tff(93,plain,
% 180.36/180.74 (index(status, host(W0!7)) = elec_2),
% 180.36/180.74 inference(and_elim,[status(thm)],[92])).
% 180.36/180.74 tff(94,plain,
% 180.36/180.74 (setIn(W0!7, alive)),
% 180.36/180.74 inference(and_elim,[status(thm)],[92])).
% 180.36/180.74 tff(95,plain,
% 180.36/180.74 (setIn(Z!6, alive)),
% 180.36/180.74 inference(and_elim,[status(thm)],[92])).
% 180.36/180.74 tff(96,plain,
% 180.36/180.74 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | ((~setIn(W0!7, alive)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~setIn(host(W0!7), index(down, host(Z!6)))))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | (~setIn(W0!7, alive)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~setIn(host(W0!7), index(down, host(Z!6)))))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(97,plain,
% 180.36/180.74 (((~setIn(W0!7, alive)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(host(W0!7), index(down, host(Z!6))))) <=> ((~setIn(W0!7, alive)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~setIn(host(W0!7), index(down, host(Z!6)))))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(98,plain,
% 180.36/180.74 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | ((~setIn(W0!7, alive)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(host(W0!7), index(down, host(Z!6)))))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | ((~setIn(W0!7, alive)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~setIn(host(W0!7), index(down, host(Z!6))))))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[97])).
% 180.36/180.74 tff(99,plain,
% 180.36/180.74 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | ((~setIn(W0!7, alive)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(host(W0!7), index(down, host(Z!6)))))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | (~setIn(W0!7, alive)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~setIn(host(W0!7), index(down, host(Z!6)))))),
% 180.36/180.74 inference(transitivity,[status(thm)],[98, 96])).
% 180.36/180.74 tff(100,plain,
% 180.36/180.74 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | ((~setIn(W0!7, alive)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(host(W0!7), index(down, host(Z!6)))))),
% 180.36/180.74 inference(quant_inst,[status(thm)],[])).
% 180.36/180.74 tff(101,plain,
% 180.36/180.74 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(host(Pid0), index(down, host(Z)))))) | (~setIn(W0!7, alive)) | (~(index(status, host(W0!7)) = elec_2)) | (~setIn(Z!6, alive)) | leq(index(pendack, host(W0!7)), host(Z!6)) | (~setIn(host(W0!7), index(down, host(Z!6))))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[100, 99])).
% 180.36/180.74 tff(102,plain,
% 180.36/180.74 (leq(index(pendack, host(W0!7)), host(Z!6)) | (~setIn(host(W0!7), index(down, host(Z!6))))),
% 180.36/180.74 inference(unit_resolution,[status(thm)],[101, 95, 94, 93, 91])).
% 180.36/180.74 tff(103,plain,
% 180.36/180.74 (~setIn(host(W0!7), index(down, host(Z!6)))),
% 180.36/180.74 inference(unit_resolution,[status(thm)],[102, 84])).
% 180.36/180.74 tff(104,plain,
% 180.36/180.74 (~setIn(host(W0!7), index(down, host(X!4)))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[103, 46])).
% 180.36/180.74 tff(105,plain,
% 180.36/180.74 (leq(host(X!4), host(W0!7)) <=> leq(host(Z!6), host(W0!7))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[42])).
% 180.36/180.74 tff(106,plain,
% 180.36/180.74 (leq(host(Z!6), host(W0!7)) <=> leq(host(X!4), host(W0!7))),
% 180.36/180.74 inference(symmetry,[status(thm)],[105])).
% 180.36/180.74 tff(107,plain,
% 180.36/180.74 ((~leq(host(Z!6), host(W0!7))) <=> (~leq(host(X!4), host(W0!7)))),
% 180.36/180.74 inference(monotonicity,[status(thm)],[106])).
% 180.36/180.74 tff(108,plain,
% 180.36/180.74 (~leq(host(Z!6), host(W0!7))),
% 180.36/180.74 inference(and_elim,[status(thm)],[92])).
% 180.36/180.74 tff(109,plain,
% 180.36/180.74 (~leq(host(X!4), host(W0!7))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[108, 107])).
% 180.36/180.74 tff(110,plain,
% 180.36/180.74 (^[P: $i] : refl(leq(s(zero), host(P)) <=> leq(s(zero), host(P)))),
% 180.36/180.74 inference(bind,[status(th)],[])).
% 180.36/180.74 tff(111,plain,
% 180.36/180.74 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 180.36/180.74 inference(quant_intro,[status(thm)],[110])).
% 180.36/180.74 tff(112,plain,
% 180.36/180.74 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 180.36/180.74 inference(rewrite,[status(thm)],[])).
% 180.36/180.74 tff(113,axiom,(![P: $i] : leq(s(zero), host(P))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_02')).
% 180.36/180.74 tff(114,plain,
% 180.36/180.74 (![P: $i] : leq(s(zero), host(P))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[113, 112])).
% 180.36/180.74 tff(115,plain,(
% 180.36/180.74 ![P: $i] : leq(s(zero), host(P))),
% 180.36/180.74 inference(skolemize,[status(sab)],[114])).
% 180.36/180.74 tff(116,plain,
% 180.36/180.74 (![P: $i] : leq(s(zero), host(P))),
% 180.36/180.74 inference(modus_ponens,[status(thm)],[115, 111])).
% 180.36/180.74 tff(117,plain,
% 180.36/180.74 ((~![P: $i] : leq(s(zero), host(P))) | leq(s(zero), host(W0!7))),
% 180.36/180.74 inference(quant_inst,[status(thm)],[])).
% 180.36/180.74 tff(118,plain,
% 180.36/180.74 (leq(s(zero), host(W0!7))),
% 180.36/180.74 inference(unit_resolution,[status(thm)],[117, 116])).
% 180.36/180.74 tff(119,plain,
% 180.36/180.74 (^[Z: $i] : refl(((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))))),
% 180.36/180.75 inference(bind,[status(th)],[])).
% 180.36/180.75 tff(120,plain,
% 180.36/180.75 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z))) <=> ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 180.36/180.75 inference(quant_intro,[status(thm)],[119])).
% 180.36/180.75 tff(121,plain,
% 180.36/180.75 (^[Z: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(X!4), Z)) & leq(s(zero), Z)) <=> (~(leq(host(X!4), Z) | (~leq(s(zero), Z))))), ((~((~leq(host(X!4), Z)) & leq(s(zero), Z))) <=> (~(~(leq(host(X!4), Z) | (~leq(s(zero), Z))))))), rewrite((~(~(leq(host(X!4), Z) | (~leq(s(zero), Z))))) <=> (leq(host(X!4), Z) | (~leq(s(zero), Z)))), ((~((~leq(host(X!4), Z)) & leq(s(zero), Z))) <=> (leq(host(X!4), Z) | (~leq(s(zero), Z))))), (((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (leq(host(X!4), Z) | (~leq(s(zero), Z)))))), rewrite(((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (leq(host(X!4), Z) | (~leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))), (((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))))),
% 180.36/180.75 inference(bind,[status(th)],[])).
% 180.36/180.75 tff(122,plain,
% 180.36/180.75 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) <=> ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 180.36/180.75 inference(quant_intro,[status(thm)],[121])).
% 180.36/180.75 tff(123,plain,
% 180.36/180.75 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z))))),
% 180.36/180.75 inference(and_elim,[status(thm)],[15])).
% 180.36/180.75 tff(124,plain,
% 180.36/180.75 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 180.36/180.75 inference(modus_ponens,[status(thm)],[123, 122])).
% 180.36/180.75 tff(125,plain,
% 180.36/180.75 (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))),
% 180.36/180.75 inference(modus_ponens,[status(thm)],[124, 120])).
% 180.36/180.75 tff(126,plain,
% 180.36/180.75 (((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | (setIn(host(W0!7), index(down, host(X!4))) | (host(W0!7) = host(Y!3)) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7))))) <=> ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | setIn(host(W0!7), index(down, host(X!4))) | (host(W0!7) = host(Y!3)) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7))))),
% 180.36/180.75 inference(rewrite,[status(thm)],[])).
% 180.36/180.75 tff(127,plain,
% 180.36/180.75 (((host(W0!7) = host(Y!3)) | setIn(host(W0!7), index(down, host(X!4))) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7)))) <=> (setIn(host(W0!7), index(down, host(X!4))) | (host(W0!7) = host(Y!3)) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7))))),
% 180.36/180.75 inference(rewrite,[status(thm)],[])).
% 180.36/180.75 tff(128,plain,
% 180.36/180.75 (((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | ((host(W0!7) = host(Y!3)) | setIn(host(W0!7), index(down, host(X!4))) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7))))) <=> ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | (setIn(host(W0!7), index(down, host(X!4))) | (host(W0!7) = host(Y!3)) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7)))))),
% 180.36/180.75 inference(monotonicity,[status(thm)],[127])).
% 180.36/180.75 tff(129,plain,
% 180.36/180.75 (((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | ((host(W0!7) = host(Y!3)) | setIn(host(W0!7), index(down, host(X!4))) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7))))) <=> ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | setIn(host(W0!7), index(down, host(X!4))) | (host(W0!7) = host(Y!3)) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7))))),
% 180.36/180.75 inference(transitivity,[status(thm)],[128, 126])).
% 180.36/180.75 tff(130,plain,
% 180.36/180.75 ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | ((host(W0!7) = host(Y!3)) | setIn(host(W0!7), index(down, host(X!4))) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7))))),
% 180.36/180.75 inference(quant_inst,[status(thm)],[])).
% 180.36/180.75 tff(131,plain,
% 180.36/180.75 ((~![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | leq(host(X!4), Z) | (~leq(s(zero), Z)))) | setIn(host(W0!7), index(down, host(X!4))) | (host(W0!7) = host(Y!3)) | leq(host(X!4), host(W0!7)) | (~leq(s(zero), host(W0!7)))),
% 180.36/180.75 inference(modus_ponens,[status(thm)],[130, 129])).
% 180.36/180.75 tff(132,plain,
% 180.36/180.75 (setIn(host(W0!7), index(down, host(X!4))) | (host(W0!7) = host(Y!3)) | leq(host(X!4), host(W0!7))),
% 180.36/180.75 inference(unit_resolution,[status(thm)],[131, 125, 118])).
% 180.36/180.75 tff(133,plain,
% 180.36/180.75 (setIn(host(W0!7), index(down, host(X!4))) | (host(W0!7) = host(Y!3))),
% 180.36/180.75 inference(unit_resolution,[status(thm)],[132, 109])).
% 180.36/180.75 tff(134,plain,
% 180.36/180.75 (host(W0!7) = host(Y!3)),
% 180.36/180.75 inference(unit_resolution,[status(thm)],[133, 104])).
% 180.36/180.75 tff(135,plain,
% 180.36/180.75 (leq(index(pendack, host(W0!7)), host(Z!6)) <=> leq(index(pendack, host(W0!7)), host(X!4))),
% 180.36/180.75 inference(monotonicity,[status(thm)],[43])).
% 180.36/180.75 tff(136,plain,
% 180.36/180.75 ((~leq(index(pendack, host(W0!7)), host(Z!6))) <=> (~leq(index(pendack, host(W0!7)), host(X!4)))),
% 180.36/180.75 inference(monotonicity,[status(thm)],[135])).
% 180.36/180.75 tff(137,plain,
% 180.36/180.75 (~leq(index(pendack, host(W0!7)), host(X!4))),
% 180.36/180.75 inference(modus_ponens,[status(thm)],[84, 136])).
% 180.36/180.75 tff(138,plain,
% 180.36/180.75 (^[Z: $i, Pid20: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))))),
% 180.36/180.75 inference(bind,[status(th)],[])).
% 180.36/180.75 tff(139,plain,
% 180.36/180.75 (![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))),
% 180.36/180.75 inference(quant_intro,[status(thm)],[138])).
% 180.36/180.75 tff(140,plain,
% 180.36/180.75 (^[Z: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)) <=> (~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite((((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))))),
% 180.36/180.75 inference(bind,[status(th)],[])).
% 180.36/180.75 tff(141,plain,
% 180.36/180.75 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))),
% 180.36/180.75 inference(quant_intro,[status(thm)],[140])).
% 180.36/180.75 tff(142,plain,
% 180.36/180.75 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 180.36/180.75 inference(and_elim,[status(thm)],[15])).
% 180.36/180.75 tff(143,plain,
% 180.36/180.75 (![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))),
% 180.36/180.75 inference(modus_ponens,[status(thm)],[142, 141])).
% 180.36/180.75 tff(144,plain,
% 180.36/180.75 (![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))),
% 180.36/180.75 inference(modus_ponens,[status(thm)],[143, 139])).
% 180.36/180.75 tff(145,plain,
% 180.36/180.75 (setIn(X!4, alive)),
% 180.36/180.75 inference(and_elim,[status(thm)],[15])).
% 180.36/180.75 tff(146,plain,
% 180.36/180.75 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))) | ((~setIn(X!4, alive)) | (~setIn(W0!7, alive)) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(X!4)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))) | (~setIn(X!4, alive)) | (~setIn(W0!7, alive)) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(X!4)))))),
% 180.36/180.75 inference(rewrite,[status(thm)],[])).
% 180.36/180.75 tff(147,plain,
% 180.36/180.75 (((~setIn(W0!7, alive)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~setIn(X!4, alive))) <=> ((~setIn(X!4, alive)) | (~setIn(W0!7, alive)) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(X!4)))))),
% 180.36/180.76 inference(rewrite,[status(thm)],[])).
% 180.36/180.76 tff(148,plain,
% 180.36/180.76 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))) | ((~setIn(W0!7, alive)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~setIn(X!4, alive)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))) | ((~setIn(X!4, alive)) | (~setIn(W0!7, alive)) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(X!4))))))),
% 180.36/180.76 inference(monotonicity,[status(thm)],[147])).
% 180.36/180.76 tff(149,plain,
% 180.36/180.76 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))) | ((~setIn(W0!7, alive)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~setIn(X!4, alive)))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))) | (~setIn(X!4, alive)) | (~setIn(W0!7, alive)) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(X!4)))))),
% 180.36/180.76 inference(transitivity,[status(thm)],[148, 146])).
% 180.36/180.76 tff(150,plain,
% 180.36/180.76 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))) | ((~setIn(W0!7, alive)) | (~elem(m_Down(Y!3), queue(host(X!4)))) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~setIn(X!4, alive)))),
% 180.36/180.76 inference(quant_inst,[status(thm)],[])).
% 180.36/180.76 tff(151,plain,
% 180.36/180.76 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~(host(Pid0) = host(Pid20))) | (~setIn(Z, alive)))) | (~setIn(X!4, alive)) | (~setIn(W0!7, alive)) | leq(index(pendack, host(W0!7)), host(X!4)) | (~(index(status, host(W0!7)) = elec_2)) | (~(host(W0!7) = host(Y!3))) | (~elem(m_Down(Y!3), queue(host(X!4))))),
% 180.36/180.76 inference(modus_ponens,[status(thm)],[150, 149])).
% 180.36/180.76 tff(152,plain,
% 180.36/180.76 (~elem(m_Down(Y!3), queue(host(X!4)))),
% 180.36/180.76 inference(unit_resolution,[status(thm)],[151, 145, 94, 93, 144, 137, 134])).
% 180.36/180.76 tff(153,plain,
% 180.36/180.76 ($false),
% 180.36/180.76 inference(unit_resolution,[status(thm)],[152, 41])).
% 180.36/180.76 % SZS output end Proof
% 180.36/180.76 % E exiting
%------------------------------------------------------------------------------