%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV463+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV463+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:51:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(elem_type, type, (
% 0.19/0.41 elem: ( $i * $i ) > $o)).
% 0.19/0.41 tff(queue_type, type, (
% 0.19/0.41 queue: $i > $i)).
% 0.19/0.41 tff(host_type, type, (
% 0.19/0.41 host: $i > $i)).
% 0.19/0.41 tff(tptp_fun_Y0_8_type, type, (
% 0.19/0.41 tptp_fun_Y0_8: $i)).
% 0.19/0.41 tff(m_Down_type, type, (
% 0.19/0.41 m_Down: $i > $i)).
% 0.19/0.41 tff(tptp_fun_X0_9_type, type, (
% 0.19/0.41 tptp_fun_X0_9: $i)).
% 0.19/0.41 tff(m_Ldr_type, type, (
% 0.19/0.41 m_Ldr: $i > $i)).
% 0.19/0.41 tff(tptp_fun_X_4_type, type, (
% 0.19/0.41 tptp_fun_X_4: $i)).
% 0.19/0.41 tff(snoc_type, type, (
% 0.19/0.41 snoc: ( $i * $i ) > $i)).
% 0.19/0.41 tff(s_type, type, (
% 0.19/0.41 s: $i > $i)).
% 0.19/0.41 tff(index_type, type, (
% 0.19/0.41 index: ( $i * $i ) > $i)).
% 0.19/0.41 tff(pendack_type, type, (
% 0.19/0.41 pendack: $i)).
% 0.19/0.41 tff(tptp_fun_W0_10_type, type, (
% 0.19/0.41 tptp_fun_W0_10: $i)).
% 0.19/0.41 tff(elec_2_type, type, (
% 0.19/0.41 elec_2: $i)).
% 0.19/0.41 tff(status_type, type, (
% 0.19/0.41 status: $i)).
% 0.19/0.41 tff(m_Ack_type, type, (
% 0.19/0.41 m_Ack: ( $i * $i ) > $i)).
% 0.19/0.41 tff(leq_type, type, (
% 0.19/0.41 leq: ( $i * $i ) > $o)).
% 0.19/0.41 tff(nbr_proc_type, type, (
% 0.19/0.41 nbr_proc: $i)).
% 0.19/0.41 tff(setIn_type, type, (
% 0.19/0.41 setIn: ( $i * $i ) > $o)).
% 0.19/0.41 tff(alive_type, type, (
% 0.19/0.41 alive: $i)).
% 0.19/0.41 tff(tptp_fun_Z_6_type, type, (
% 0.19/0.41 tptp_fun_Z_6: $i)).
% 0.19/0.41 tff(norm_type, type, (
% 0.19/0.41 norm: $i)).
% 0.19/0.41 tff(tptp_fun_V0_7_type, type, (
% 0.19/0.41 tptp_fun_V0_7: $i)).
% 0.19/0.41 tff(ldr_type, type, (
% 0.19/0.41 ldr: $i)).
% 0.19/0.41 tff(cons_type, type, (
% 0.19/0.41 cons: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_V_5_type, type, (
% 0.19/0.41 tptp_fun_V_5: $i)).
% 0.19/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.41 tptp_fun_Y_3: $i)).
% 0.19/0.41 tff(elid_type, type, (
% 0.19/0.41 elid: $i)).
% 0.19/0.41 tff(elec_1_type, type, (
% 0.19/0.41 elec_1: $i)).
% 0.19/0.41 tff(tptp_fun_V0_11_type, type, (
% 0.19/0.41 tptp_fun_V0_11: ( $i * $i ) > $i)).
% 0.19/0.41 tff(zero_type, type, (
% 0.19/0.41 zero: $i)).
% 0.19/0.41 tff(down_type, type, (
% 0.19/0.41 down: $i)).
% 0.19/0.41 tff(m_Halt_type, type, (
% 0.19/0.41 m_Halt: $i > $i)).
% 0.19/0.41 tff(acks_type, type, (
% 0.19/0.41 acks: $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 ((setIn(X!4, alive) & (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))) & leq(nbr_proc, index(pendack, host(X!4))) & ![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_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![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) & ((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))) & leq(nbr_proc, index(pendack, host(X!4))) & ![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_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) <=> (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20))))))), (((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))))), rewrite(((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))), (((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) <=> ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))))), (((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) <=> ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))))), rewrite(((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) <=> ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))), (((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) <=> ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid30), queue(host(Z))))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ((((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) <=> (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (((~(host(X!4) = host(V0!7))) & (~((host(X!4) = host(Y0!8)) | (~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))) <=> ((~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 ((((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((~(host(X!4) = host(V0!7))) & (~((host(X!4) = host(Y0!8)) | (~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) <=> (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 ((((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((~(host(X!4) = host(V0!7))) & (~((host(X!4) = host(Y0!8)) | (~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) <=> (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 ((setIn(X!4, alive) & (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((~(host(X!4) = host(V0!7))) & (~((host(X!4) = host(Y0!8)) | (~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) & leq(nbr_proc, index(pendack, host(X!4))) & ![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_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![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) & (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8)))))) & leq(nbr_proc, index(pendack, host(X!4))) & ![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_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![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(monotonicity,[status(thm)],[16, 12])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 ((setIn(X!4, alive) & (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((~(host(X!4) = host(V0!7))) & (~((host(X!4) = host(Y0!8)) | (~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))))) & leq(nbr_proc, index(pendack, host(X!4))) & ![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_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1)))) & ![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) & ((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))) & leq(nbr_proc, index(pendack, host(X!4))) & ![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_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![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)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[17, 10])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 ((~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((host(X) = host(V0)) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (index(ldr, host(V0)) = host(V0)) & (index(status, host(V0)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![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)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((host(X) = host(V0)) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (index(ldr, host(V0)) = host(V0)) & (index(status, host(V0)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![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)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 ((~![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] : ((setIn(host(Z), index(acks, host(X))) | (host(Z) = host(Y))) => ![V0: $i] : ((~(host(X) = host(V0))) => ![W0: $i, X0: $i, Y0: $i] : ((host(Z) = 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_Ldr(X)))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X)))) & (index(status, host(Y0)) = elec_2)) & (host(W0) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~((setIn(V0, alive) & (index(ldr, host(V0)) = host(V0))) & (index(status, host(V0)) = norm))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((host(X) = host(V0)) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (index(ldr, host(V0)) = host(V0)) & (index(status, host(V0)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![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)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(21,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] : ((setIn(host(Z), index(acks, host(X))) | (host(Z) = host(Y))) => ![V0: $i] : ((~(host(X) = host(V0))) => ![W0: $i, X0: $i, Y0: $i] : ((host(Z) = 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_Ldr(X)))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X)))) & (index(status, host(Y0)) = elec_2)) & (host(W0) = index(pendack, host(Y0)))) & (host(X0) = s(index(pendack, host(Y0))))) => (~((setIn(V0, alive) & (index(ldr, host(V0)) = host(V0))) & (index(status, host(V0)) = norm))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((host(X) = host(V0)) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (index(ldr, host(V0)) = host(V0)) & (index(status, host(V0)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((host(X) = host(V0)) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (index(ldr, host(V0)) = host(V0)) & (index(status, host(V0)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((host(X) = host(V0)) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (index(ldr, host(V0)) = host(V0)) & (index(status, host(V0)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((host(X) = host(V0)) | ![W0: $i, X0: $i, Y0: $i] : ((host(X) = host(Y0)) | (~(setIn(V0, alive) & (index(ldr, host(V0)) = host(V0)) & (index(status, host(V0)) = norm))) | (~(setIn(Y0, alive) & leq(nbr_proc, s(index(pendack, host(Y0)))) & elem(m_Down(X0), snoc(queue(host(Y0)), m_Ldr(X))) & elem(m_Ack(Y0, W0), snoc(queue(host(Y0)), m_Ldr(X))) & (index(status, host(Y0)) = elec_2) & (host(W0) = index(pendack, host(Y0))) & (host(X0) = s(index(pendack, host(Y0)))))) | (~(host(Z) = host(Y0)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (setIn(X!4, alive) & ((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (~(host(X!4) = host(V0!7))) & (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))) & leq(nbr_proc, index(pendack, host(X!4))) & ![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_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid0) = nbr_proc)) | (~(host(Pid0) = host(Pid30))) | (~(index(status, host(Pid0)) = elec_1))) & ![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))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.47 tff(27,plain,
% 0.19/0.47 (~((~(setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm))) | (host(X!4) = host(Y0!8)) | (~(setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8)))))) | (~(host(Z!6) = host(Y0!8))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[26])).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 (setIn(Y0!8, alive) & leq(nbr_proc, s(index(pendack, host(Y0!8)))) & elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) & (index(status, host(Y0!8)) = elec_2) & (host(W0!10) = index(pendack, host(Y0!8))) & (host(X0!9) = s(index(pendack, host(Y0!8))))),
% 0.19/0.47 inference(or_elim,[status(thm)],[27])).
% 0.19/0.47 tff(29,plain,
% 0.19/0.47 (elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[28])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 ((~(elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))))) | (~elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4)))) | ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 ((~(elem(m_Down(X0!9), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))))) | ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 ((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[31, 9])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Ldr(Y))) <=> (~(m_Down(X) = m_Ldr(Y))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(36,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_18')).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.47 tff(38,plain,(
% 0.19/0.47 ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[37])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))) | (~(m_Down(X0!9) = m_Ldr(X!4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (~(m_Down(X0!9) = m_Ldr(X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 ((~((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))) | (m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 ((~((m_Down(X0!9) = m_Ldr(X!4)) | elem(m_Down(X0!9), queue(host(Y0!8))))) | elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[43, 32])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 (elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[45, 7])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[28])).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 ((~(elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))))) | (~elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4)))) | ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 ((~(elem(m_Ack(Y0!8, W0!10), snoc(queue(host(Y0!8)), m_Ldr(X!4))) <=> ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))))) | ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 ((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (^[X: $i, Y: $i, Z: $i] : refl((~(m_Ack(X, Y) = m_Ldr(Z))) <=> (~(m_Ack(X, Y) = m_Ldr(Z))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(54,axiom,(![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_14')).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.47 tff(56,plain,(
% 0.19/0.47 ![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[55])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (~(m_Ack(X, Y) = m_Ldr(Z)))) | (~(m_Ack(Y0!8, W0!10) = m_Ldr(X!4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (~(m_Ack(Y0!8, W0!10) = m_Ldr(X!4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 ((~((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))) | (m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 ((~((m_Ack(Y0!8, W0!10) = m_Ldr(X!4)) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8))))) | elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[61, 50])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (^[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)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (![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))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (^[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))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 (![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)))))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[26])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 (host(X0!9) = s(index(pendack, host(Y0!8)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[28])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 (host(W0!10) = index(pendack, host(Y0!8))),
% 0.19/0.48 inference(and_elim,[status(thm)],[28])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 (index(status, host(Y0!8)) = elec_2),
% 0.19/0.48 inference(and_elim,[status(thm)],[28])).
% 0.19/0.48 tff(73,plain,
% 0.19/0.48 (leq(nbr_proc, s(index(pendack, host(Y0!8))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[28])).
% 0.19/0.48 tff(74,plain,
% 0.19/0.48 (setIn(Y0!8, alive)),
% 0.19/0.48 inference(and_elim,[status(thm)],[28])).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 (setIn(V0!7, alive) & (index(ldr, host(V0!7)) = host(V0!7)) & (index(status, host(V0!7)) = norm)),
% 0.19/0.48 inference(or_elim,[status(thm)],[27])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 (index(status, host(V0!7)) = norm),
% 0.19/0.48 inference(and_elim,[status(thm)],[75])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 (index(ldr, host(V0!7)) = host(V0!7)),
% 0.19/0.48 inference(and_elim,[status(thm)],[75])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 (setIn(V0!7, alive)),
% 0.19/0.48 inference(and_elim,[status(thm)],[75])).
% 0.19/0.48 tff(79,plain,
% 0.19/0.48 (((~![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!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm)))) <=> ((~![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!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 (((~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm)) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8)))))) <=> ((~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 (((~![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!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm)) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))))) <=> ((~![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!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (((~![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!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm)) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))))) <=> ((~![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!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 ((~![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!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm)) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~(index(ldr, host(Z)) = host(Z))) | (~(index(status, host(Z)) = norm)) | (~elem(m_Ack(Pid0, Pid30), queue(host(Pid0)))) | (~leq(nbr_proc, s(index(pendack, host(Pid0))))) | (~(host(Pid30) = index(pendack, host(Pid0)))) | (~(host(Pid20) = s(index(pendack, host(Pid0))))))) | (~elem(m_Ack(Y0!8, W0!10), queue(host(Y0!8)))) | (~setIn(Y0!8, alive)) | (~(index(status, host(Y0!8)) = elec_2)) | (~setIn(V0!7, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~leq(nbr_proc, s(index(pendack, host(Y0!8))))) | (~(host(W0!10) = index(pendack, host(Y0!8)))) | (~(host(X0!9) = s(index(pendack, host(Y0!8))))) | (~(index(ldr, host(V0!7)) = host(V0!7))) | (~(index(status, host(V0!7)) = norm))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[84, 78, 77, 76, 74, 73, 72, 71, 70, 69, 62, 44])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------