%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV464+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV464+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:51:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(elem_type, type, (
% 0.19/0.40 elem: ( $i * $i ) > $o)).
% 0.19/0.40 tff(queue_type, type, (
% 0.19/0.40 queue: $i > $i)).
% 0.19/0.40 tff(host_type, type, (
% 0.19/0.40 host: $i > $i)).
% 0.19/0.40 tff(tptp_fun_Y0_6_type, type, (
% 0.19/0.40 tptp_fun_Y0_6: $i)).
% 0.19/0.40 tff(m_Down_type, type, (
% 0.19/0.40 m_Down: $i > $i)).
% 0.19/0.40 tff(tptp_fun_X0_7_type, type, (
% 0.19/0.40 tptp_fun_X0_7: $i)).
% 0.19/0.40 tff(m_Halt_type, type, (
% 0.19/0.40 m_Halt: $i > $i)).
% 0.19/0.40 tff(tptp_fun_X_4_type, type, (
% 0.19/0.40 tptp_fun_X_4: $i)).
% 0.19/0.40 tff(snoc_type, type, (
% 0.19/0.40 snoc: ( $i * $i ) > $i)).
% 0.19/0.40 tff(s_type, type, (
% 0.19/0.40 s: $i > $i)).
% 0.19/0.40 tff(index_type, type, (
% 0.19/0.40 index: ( $i * $i ) > $i)).
% 0.19/0.40 tff(pendack_type, type, (
% 0.19/0.40 pendack: $i)).
% 0.19/0.40 tff(tptp_fun_W0_8_type, type, (
% 0.19/0.40 tptp_fun_W0_8: $i)).
% 0.19/0.40 tff(elec_2_type, type, (
% 0.19/0.40 elec_2: $i)).
% 0.19/0.40 tff(status_type, type, (
% 0.19/0.40 status: $i)).
% 0.19/0.40 tff(m_Ack_type, type, (
% 0.19/0.40 m_Ack: ( $i * $i ) > $i)).
% 0.19/0.40 tff(leq_type, type, (
% 0.19/0.40 leq: ( $i * $i ) > $o)).
% 0.19/0.40 tff(nbr_proc_type, type, (
% 0.19/0.40 nbr_proc: $i)).
% 0.19/0.40 tff(setIn_type, type, (
% 0.19/0.40 setIn: ( $i * $i ) > $o)).
% 0.19/0.40 tff(alive_type, type, (
% 0.19/0.40 alive: $i)).
% 0.19/0.40 tff(norm_type, type, (
% 0.19/0.40 norm: $i)).
% 0.19/0.40 tff(tptp_fun_Z_9_type, type, (
% 0.19/0.40 tptp_fun_Z_9: $i)).
% 0.19/0.40 tff(ldr_type, type, (
% 0.19/0.40 ldr: $i)).
% 0.19/0.40 tff(cons_type, type, (
% 0.19/0.40 cons: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_V_5_type, type, (
% 0.19/0.40 tptp_fun_V_5: $i)).
% 0.19/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.40 tptp_fun_Y_3: $i)).
% 0.19/0.40 tff(elid_type, type, (
% 0.19/0.40 elid: $i)).
% 0.19/0.40 tff(elec_1_type, type, (
% 0.19/0.40 elec_1: $i)).
% 0.19/0.40 tff(tptp_fun_V0_10_type, type, (
% 0.19/0.40 tptp_fun_V0_10: ( $i * $i ) > $i)).
% 0.19/0.40 tff(zero_type, type, (
% 0.19/0.40 zero: $i)).
% 0.19/0.40 tff(down_type, type, (
% 0.19/0.40 down: $i)).
% 0.19/0.40 tff(m_Ldr_type, type, (
% 0.19/0.40 m_Ldr: $i > $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.40 tff(6,plain,(
% 0.19/0.40 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[5])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) <=> ((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) <=> ((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 ((setIn(X!4, alive) & (~leq(nbr_proc, index(pendack, host(X!4)))) & (~((host(X!4) = host(Y0!6)) | (~(setIn(Z!9, alive) & (index(ldr, host(Z!9)) = host(Z!9)) & (index(status, host(Z!9)) = norm))) | (~(setIn(Y0!6, alive) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) & elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) & (index(status, host(Y0!6)) = elec_2) & (host(W0!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(s(index(pendack, host(X!4))) = host(Y0!6))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))) <=> (setIn(X!4, alive) & (~leq(nbr_proc, index(pendack, host(X!4)))) & (~((host(X!4) = host(Y0!6)) | (~(setIn(Z!9, alive) & (index(ldr, host(Z!9)) = host(Z!9)) & (index(status, host(Z!9)) = norm))) | (~(setIn(Y0!6, alive) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) & elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) & (index(status, host(Y0!6)) = elec_2) & (host(W0!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(s(index(pendack, host(X!4))) = host(Y0!6))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 ((~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(s(index(pendack, host(X))) = host(Y0)))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))))) | (~![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))) <=> (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(s(index(pendack, host(X))) = host(Y0)))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))))) | (~![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 ((~![V: $i, W: $i, X: $i, Y: $i] : ((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![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) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) => leq(host(Z), index(pendack, host(Pid0))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(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, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Pid20)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = nbr_proc)) & (host(Pid0) = host(Pid30))) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Pid30) = index(pendack, host(Pid0)))) & (host(Pid20) = s(index(pendack, host(Pid0))))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2)) & (host(Y) = index(pendack, host(X)))) => ((~leq(nbr_proc, index(pendack, host(X)))) => ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((s(index(pendack, host(X))) = host(Y0)) => ((~(host(X) = host(Y0))) => (((((((setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0))))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X)))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X)))) & (index(status, host(Y0)) = elec_2)) & (host(W0) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))))))))) <=> (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(s(index(pendack, host(X))) = host(Y0)))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))))) | (~![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(13,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : ((((((((((((((((![Z: $i, Pid0: $i] : (elem(m_Ldr(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![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) & elem(m_Ack(Pid0, Z), queue(host(Pid0)))) => leq(host(Z), index(pendack, host(Pid0))))) & ![Z: $i, Pid0: $i] : ((setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Pid0, Z), queue(host(Pid0)))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid20) = host(Z))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(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, Pid0: $i] : ((((((~leq(host(Z), host(Pid0))) & setIn(Z, alive)) & setIn(Pid0, alive)) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_2)) => (~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive)) & elem(m_Halt(Pid0), queue(host(Pid20)))) & (index(status, host(Pid0)) = elec_2)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid0) = nbr_proc)) & (host(Pid0) = host(Pid30))) & (index(status, host(Pid0)) = elec_1)) => (~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) & leq(nbr_proc, s(index(pendack, host(Pid0))))) & (index(status, host(Pid0)) = elec_2)) & (host(Pid30) = index(pendack, host(Pid0)))) & (host(Pid20) = s(index(pendack, host(Pid0))))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2)) & (host(Y) = index(pendack, host(X)))) => ((~leq(nbr_proc, index(pendack, host(X)))) => ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((s(index(pendack, host(X))) = host(Y0)) => ((~(host(X) = host(Y0))) => (((((((setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0))))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X)))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X)))) & (index(status, host(Y0)) = elec_2)) & (host(W0) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(s(index(pendack, host(X))) = host(Y0)))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))))) | (~![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(s(index(pendack, host(X))) = host(Y0)))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))))) | (~![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(s(index(pendack, host(X))) = host(Y0)))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))))) | (~![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | leq(nbr_proc, index(pendack, host(X))) | ![Z: $i, W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Halt(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Halt(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(s(index(pendack, host(X))) = host(Y0)))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))))) | (~![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid0) = nbr_proc) & (host(Pid0) = host(Pid30)) & (index(status, host(Pid0)) = elec_1))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (setIn(X!4, alive) & (~leq(nbr_proc, index(pendack, host(X!4)))) & (~((host(X!4) = host(Y0!6)) | (~(setIn(Z!9, alive) & (index(ldr, host(Z!9)) = host(Z!9)) & (index(status, host(Z!9)) = norm))) | (~(setIn(Y0!6, alive) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) & elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) & (index(status, host(Y0!6)) = elec_2) & (host(W0!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(s(index(pendack, host(X!4))) = host(Y0!6))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ldr(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~(host(Pid0) = host(Z))) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(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] : ((~(setIn(Pid0, alive) & elem(m_Ack(Pid0, Z), queue(host(Pid0))))) | leq(host(Z), index(pendack, host(Pid0)))) & ![Z: $i, Pid0: $i] : ((~elem(m_Ack(Pid0, Z), queue(host(Pid0)))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = elec_1)))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z)))) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)))) & ![Z: $i, Pid0: $i] : ((~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(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, Pid0: $i] : ((~leq(index(pendack, host(Z)), index(pendack, host(Pid0)))) | (~((~leq(host(Z), host(Pid0))) & setIn(Z, alive) & setIn(Pid0, alive) & (index(status, host(Z)) = elec_2) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(index(pendack, host(Pid0)), host(Z))) & setIn(Pid0, alive) & elem(m_Halt(Pid0), queue(host(Pid20))) & (index(status, host(Pid0)) = elec_2)))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_10(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_10(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_10(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_10(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (~((host(X!4) = host(Y0!6)) | (~(setIn(Z!9, alive) & (index(ldr, host(Z!9)) = host(Z!9)) & (index(status, host(Z!9)) = norm))) | (~(setIn(Y0!6, alive) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) & elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) & (index(status, host(Y0!6)) = elec_2) & (host(W0!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6)))))) | (~(s(index(pendack, host(X!4))) = host(Y0!6))))),
% 0.19/0.44 inference(and_elim,[status(thm)],[18])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (setIn(Y0!6, alive) & leq(nbr_proc, s(index(pendack, host(Y0!6)))) & elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) & elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) & (index(status, host(Y0!6)) = elec_2) & (host(W0!8) = index(pendack, host(Y0!6))) & (host(X0!7) = s(index(pendack, host(Y0!6))))),
% 0.19/0.44 inference(or_elim,[status(thm)],[19])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4)))),
% 0.19/0.44 inference(and_elim,[status(thm)],[20])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 ((~(elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) <=> ((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6)))))) | (~elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4)))) | ((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 ((~(elem(m_Down(X0!7), snoc(queue(host(Y0!6)), m_Halt(X!4))) <=> ((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6)))))) | ((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 ((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Halt(Y))) <=> (~(m_Down(X) = m_Halt(Y))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(28,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_17')).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.44 tff(30,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[29])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))) | (~(m_Down(X0!7) = m_Halt(X!4)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (~(m_Down(X0!7) = m_Halt(X!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 ((~((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6))))) | (m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 ((~((m_Down(X0!7) = m_Halt(X!4)) | elem(m_Down(X0!7), queue(host(Y0!6))))) | elem(m_Down(X0!7), queue(host(Y0!6)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (elem(m_Down(X0!7), queue(host(Y0!6)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[35, 24])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) <=> ((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) <=> ((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[37, 7])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4)))),
% 0.19/0.44 inference(and_elim,[status(thm)],[20])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 ((~(elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) <=> ((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))))) | (~elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4)))) | ((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 ((~(elem(m_Ack(Y0!6, W0!8), snoc(queue(host(Y0!6)), m_Halt(X!4))) <=> ((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))))) | ((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 ((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (^[X: $i, Y: $i, Z: $i] : refl((~(m_Ack(X, Y) = m_Halt(Z))) <=> (~(m_Ack(X, Y) = m_Halt(Z))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(46,axiom,(![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_11')).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.45 tff(48,plain,(
% 0.19/0.45 ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[47])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 ((~![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Halt(Z)))) | (~(m_Ack(Y0!6, W0!8) = m_Halt(X!4)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (~(m_Ack(Y0!6, W0!8) = m_Halt(X!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 ((~((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6))))) | (m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~((m_Ack(Y0!6, W0!8) = m_Halt(X!4)) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6))))) | elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[53, 42])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm)) <=> (~((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))))), ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) <=> (~(~((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))))))), rewrite((~(~((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))))) <=> ((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)))), ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) <=> ((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))))), trans(monotonicity(rewrite((setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))) <=> (~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))), ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))) <=> (~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))), ((~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0)))))))), (((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) <=> (((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))) | ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))))), rewrite((((~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm))) | ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))), (((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) <=> ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0))))))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~(setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Ack(Pid0, Pid30), queue(host(Pid0))) & leq(nbr_proc, s(index(pendack, host(Pid0)))) & (index(status, host(Pid0)) = elec_2) & (host(Pid30) = index(pendack, host(Pid0))) & (host(Pid20) = s(index(pendack, host(Pid0)))))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[18])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (host(X0!7) = s(index(pendack, host(Y0!6)))),
% 0.19/0.45 inference(and_elim,[status(thm)],[20])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (host(W0!8) = index(pendack, host(Y0!6))),
% 0.19/0.45 inference(and_elim,[status(thm)],[20])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (index(status, host(Y0!6)) = elec_2),
% 0.19/0.45 inference(and_elim,[status(thm)],[20])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (leq(nbr_proc, s(index(pendack, host(Y0!6))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[20])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (setIn(Y0!6, alive)),
% 0.19/0.45 inference(and_elim,[status(thm)],[20])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (setIn(Z!9, alive) & (index(ldr, host(Z!9)) = host(Z!9)) & (index(status, host(Z!9)) = norm)),
% 0.19/0.45 inference(or_elim,[status(thm)],[19])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (index(status, host(Z!9)) = norm),
% 0.19/0.45 inference(and_elim,[status(thm)],[67])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 (index(ldr, host(Z!9)) = host(Z!9)),
% 0.19/0.45 inference(and_elim,[status(thm)],[67])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (setIn(Z!9, alive)),
% 0.19/0.45 inference(and_elim,[status(thm)],[67])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~setIn(Y0!6, alive)) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | (~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~setIn(Y0!6, alive)) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (((~setIn(Y0!6, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6)))))) <=> ((~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~setIn(Y0!6, alive)) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~setIn(Y0!6, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~setIn(Y0!6, alive)) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~setIn(Y0!6, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6))))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | (~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~setIn(Y0!6, alive)) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | ((~setIn(Y0!6, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | (~elem(m_Ack(Y0!6, W0!8), queue(host(Y0!6)))) | (~setIn(Y0!6, alive)) | (~(index(status, host(Y0!6)) = elec_2)) | (~setIn(Z!9, alive)) | (~elem(m_Down(X0!7), queue(host(Y0!6)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!6))))) | (~(index(ldr, host(Z!9)) = host(Z!9))) | (~(index(status, host(Z!9)) = norm)) | (~(host(W0!8) = index(pendack, host(Y0!6)))) | (~(host(X0!7) = s(index(pendack, host(Y0!6)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[76, 70, 69, 68, 66, 65, 64, 63, 62, 61, 54, 36])).
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------